ALBERT

Description: In this paper we analyze the double vector meson production in photon–hadron ( \(\gamma h\) ) interactions at pp  /  pA  /  AA collisions and present predictions for the \(\rho \rho \) , \(J/\Psi J/\Psi \) , and \(\rho J/\Psi \) production considering the double scattering mechanism. We estimate the total cross sections and rapidity distributions at LHC energies and compare our results with the predictions for the double vector meson production in \(\gamma \gamma \) interactions at hadronic colliders. We present predictions for the different rapidity ranges probed by the ALICE, ATLAS, CMS, and LHCb Collaborations. Our results demonstrate that the \(\rho \rho \) and \(J/\Psi J/\Psi \) production in PbPb collisions is dominated by the double-scattering mechanism, while the two-photon mechanism dominates in pp collisions. Moreover, our results indicate that the analysis of the \(\rho J/\Psi \) production at LHC can be useful to constrain the double-scattering mechanism.

Description: We consider special supersymmetry (SUSY) transformations with m generators \(\overleftarrow{s}_\alpha ,\) for some class of models and study the physical consequences when making the Grassmann-odd transformations to form an Abelian supergroup with finite parameters and a set of group-like elements with finite parameters being functionals of the field variables. The SUSY-invariant path integral measure within conventional quantization scheme leads to the appearance of the Jacobian under a change of variables generated by such SUSY transformations, which is explicitly calculated. The Jacobian implies, first of all, the appearance of trivial interactions in the transformed action, and, second, the presence of a modified Ward identity which reduces to the standard Ward identities in the case of constant parameters. We examine the case of the \({N}=1\) and \(N=2\) supersymmetric harmonic oscillators to illustrate the general concept by a simple free model with (1, 1) physical degrees of freedom. It is shown that the interaction terms \(U_{\mathrm{tr}}\) have a corresponding SUSY-exact form: \(U_{\mathrm{tr}}= \big (V_{(1)}\overleftarrow{s}; V_{(2)}\overleftarrow{\bar{s}} \overleftarrow{s}\big )\) generated naturally under such generalized formulation. We argue that the case of a non-trivial interaction cannot be obtained in such a way.

Description: A search for squarks and gluinos in final states containing hadronic jets, missing transverse momentum but no electrons or muons is presented. The data were recorded in 2015 by the ATLAS experiment in \(\sqrt{s}=13~{\mathrm{TeV}}\) proton–proton collisions at the Large Hadron Collider. No excess above the Standard Model background expectation was observed in 3.2  \(\mathrm{fb}^{-1}\) of analyzed data. Results are interpreted within simplified models that assume R -parity is conserved and the neutralino is the lightest supersymmetric particle. An exclusion limit at the 95 % confidence level on the mass of the gluino is set at 1.51  \({\mathrm{TeV}}\) for a simplified model incorporating only a gluino octet and the lightest neutralino, assuming the lightest neutralino is massless. For a simplified model involving the strong production of mass-degenerate first- and second-generation squarks, squark masses below 1.03  \({\mathrm{TeV}}\) are excluded for a massless lightest neutralino. These limits substantially extend the region of supersymmetric parameter space excluded by previous measurements with the ATLAS detector.

Description: The low-energy and high-energy behavior of the pion–photon transition form factor \(F_{\pi \gamma }(Q^2)\) are sensitive to the transverse and longitudinal distributions of the pion wave function, respectively. A careful study of \(F_{\pi \gamma }(Q^2)\) shall thus provide helpful constraints on the properties of the pion wave function. In this paper, we present a combined analysis of the data on \(F_{\pi \gamma }(Q^2)\) reported by the CELLO, the CLEO, the BABAR, and the BELLE Collaborations. It is performed by using the method of least squares. By using the combined measurements of the BELLE and CLEO Collaborations, the pion wave function longitudinal and transverse behavior can be fixed to a certain degree, i.e. we obtain \(\beta \in [0.691,0.757]\)  GeV and \(B \in [0.00,0.235]\) for \(P_{\chi ^2} \ge 90\,\%\) , where \(\beta \) and B are two parameters of a convenient pion wave function model. It is noted that the distribution amplitude of such a pion wave function can mimic various longitudinal behaviors, as suggested in the literature under a proper choice of parameters. We observe that the CELLO, CLEO, and BELLE data are consistent with each other, all of which prefer the asymptotic-like distribution amplitude; while the BABAR data prefers a more broad distribution amplitude, such as the CZ-like one.

Description: The Einstein–Hilbert action in the context of higher derivative theories is considered for finding their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et al. the diffeomorphism symmetry is extracted. From the general form of the gauge transformations of the field, the analogous BRST transformations are calculated. The effective Lagrangian is constructed by considering two gauge-fixing conditions. Further, the BRST (conserved) charge is computed, which plays an important role in defining the physical states from the total Hilbert space of states. The finite field-dependent BRST formulation is also studied in this context where the Jacobian for the functional measure is illustrated specifically.

Description: Recently the ANTARES collaboration presented a time dependent analysis of a selected number of flaring blazars to look for upward going muon events produced from the charge current interaction of the muon neutrinos. We use the same list of flaring blazars to look for a possible positional correlation with the IceCube neutrino events. In the context of the photohadronic model we propose that the neutrinos are produced within the nuclear region of the blazar where Fermi accelerated high energy protons interact with the background synchrotron/SSC photons. Although we found that some objects from the ANTARES list are within the error circles of a few IceCube events, the statistical analysis shows that none of these sources have a significant correlation.

Description: A measurement of the W boson pair production cross section in proton-proton collisions at \(\sqrt{s} = 8\)  TeV is presented. The data collected with the CMS detector at the LHC correspond to an integrated luminosity of 19.4 \(\,\text {fb}^\text {-1}\) . The \({{\mathrm{W} }^{+} }\mathrm{W}^{-} \) candidates are selected from events with two charged leptons, electrons or muons, and large missing transverse energy. The measured \({{\mathrm{W} }^{+} }\mathrm{W}^{-} \) cross section is \(60.1\pm 0.9\,\text {(stat)} \pm 3.2\,\text {(exp)} \pm 3.1\,\text {(theo)} \pm 1.6\,\text {(lumi)} \text {\,pb} = 60.1\pm 4.8\text {\,pb} \) , consistent with the standard model prediction. The \({{\mathrm{W} }^{+} }\mathrm{W}^{-} \) cross sections are also measured in two different fiducial phase space regions. The normalized differential cross section is measured as a function of kinematic variables of the final-state charged leptons and compared with several perturbative QCD predictions. Limits on anomalous gauge couplings associated with dimension-six operators are also given in the framework of an effective field theory. The corresponding 95 % confidence level intervals are \(-5.7〈 c_{\mathrm {WWW}}/\Lambda ^2 〈 5.9\,\mathrm{TeV}^{-2}\) , \(-11.4〈 c_{\mathrm {W}}/\Lambda ^2 〈 5.4\,\mathrm{TeV}^{-2}\) , \(-29.2〈 c_{\mathrm {B}}/\Lambda ^2 〈 23.9\,\mathrm{TeV}^{-2}\) , in the HISZ basis.

Description: The thermodynamic entropy of an isolated system is given by its von Neumann entropy. Over the last few years, there has been an intense activity to understand the thermodynamic entropy from the principles of quantum mechanics. More specifically, is there a relation between the (von Neumann) entropy of entanglement between a system and some (separate) environment and the thermodynamic entropy? It is difficult to obtain the relation for many body systems, hence, most of the work in the literature has focused on small number systems. In this work, we consider black holes—which are simple yet macroscopic systems—and show that a direct connection could not be made between the entropy of entanglement and the Hawking temperature. In this work, within the adiabatic approximation, we explicitly show that the Hawking temperature is indeed given by the rate of change of the entropy of entanglement across a black hole’s horizon with regard to the system energy. This is yet other numerical evidence leading to understanding the key features of black-hole thermodynamics from the viewpoint of quantum information theory.

Description: This paper explores the dynamics of particles in higher dimensions. For this purpose, we discuss some interesting features related to the motion of particles near a Myers–Perry black hole with arbitrary extra dimensions as well as a single non-zero spin parameter. Assuming it as a supermassive black hole at the center of the galaxy, we calculate red–blue shifts in the equatorial plane for the far away observer as well as the corresponding black hole parameters of the photons. Next, we study the Penrose process and find that the energy gain of the particle depends on the variation of the black hole dimensions. Finally, we discuss the center of mass energy for 11 dimensions, which indicates a similar behavior to that of four dimensions but it is higher in four dimensions than five or more dimensions. We conclude that higher dimensions have a great impact on the particle dynamics.

Description: In high-energy collisions of heavy ions, experimental findings of collective flow are customarily associated with the presence of a thermalized medium expanding according to the laws of hydrodynamics. Recently, the ATLAS, CMS, and ALICE experiments found signals of the same type and magnitude in ultrarelativistic proton–proton collisions. In this study, the state-of-the-art hydrodynamic model SONIC is used to simulate the systems created in p+p collisions. By varying the size of the second-order transport coefficients, the range of applicability of hydrodynamics itself to the systems created in p+p collisions is quantified. It is found that hydrodynamics can give quantitatively reliable results for the particle spectra and the elliptic momentum anisotropy coefficient \(v_2\) . Using a simple geometric model of the proton based on the elastic form factor leads to results of similar type and magnitude to those found in experiment when allowing for a small bulk viscosity coefficient.

Description: The Wigner distributions for the u and the d quarks in a proton are calculated using the light-front wave functions of the scalar quark–diquark model for a nucleon constructed from the soft-wall AdS/QCD correspondence. We present a detailed study of the quark orbital angular momentum and its correlation with the quark spin and the proton spin. The quark density distributions, considering the different polarizations of quarks and proton, in transverse momentum plane as well as in transverse impact parameter plane are presented for both u and d quarks.

Description: The oscillation frequency, \(\Delta m_d\) , of \(B^0\) mesons is measured using semileptonic decays with a \(D^-\) or \(D^{*-}\) meson in the final state. The data sample corresponds to 3.0 \(fb^{-1}\) of pp collisions, collected by the LHCb experiment at centre-of-mass energies \(\sqrt{s}\) = 7 and 8 \(\mathrm \,TeV\) . A combination of the two decay modes gives \(\Delta m_d = (505.0 \pm 2.1 \pm 1.0) \mathrm \,ns^{-1}\) , where the first uncertainty is statistical and the second is systematic. This is the most precise single measurement of this parameter. It is consistent with the current world average and has similar precision.

Description: We compute the next-to-leading order virtual QCD corrections to Higgs-pair production via gluon fusion. We present analytic results for the two-loop contributions to the spin-0 and spin-2 form factors in the amplitude. The reducible contributions, given by the double-triangle diagrams, are evaluated exactly while the two-loop irreducible diagrams are evaluated by an asymptotic expansion in heavy top-quark mass up to and including terms of \(\mathcal {O}(1/m_t^8)\) . Assuming that the finite top-quark mass effects are of similar size in the entire range of partonic energies, we estimate that mass effects can reduce the hadronic cross section by at most \(10~\%\) .

Description: In this paper we study cosmological dynamics of the phantom as well as non-phantom fields with a linear potential in the presence of a Galileon correction \( (\partial _\mu \phi \partial ^\mu \phi ) \Box \phi \) . We show that the Big Crunch singularity is delayed compared to the standard case; the delay crucially depends upon the strength of a Galileon correction. As for the phantom Galileon, \(\rho _{\phi }\) is shown to grow more slowly compared to the standard phantom delaying the approach of the singularity. In the case, \(V\sim \phi ^n, n〉4\) , Big Rip is also delayed, similar phenomenon is shown to take place for potentials steeper than the exponential.

Description: In this work we investigate the transition from kinks to compactons at high temperatures. We deal with a family of models, described by a real scalar field with standard kinematics, controlled by a single parameter, real and positive. The family of models supports kink-like solutions, and the solutions tend to become compact when the parameter increases to larger and larger values. We study the one-loop corrections at finite temperature, to see how the thermal effects add to the effective potential. The results suggest that the symmetry is restored at very high temperatures.

Description: Two major problems, still associated with the SN1987A, are: (a) the signals observed with the gravitational waves detectors, (b) the duration of the collapse. Indeed, (a) the sensitivity of the gravitational wave detectors seems to be small for detecting gravitational waves and, (b) while some experimental data indicate a duration of order of hours, most theories assume that the collapse develops in a few seconds. Since recent data of the X-ray NuSTAR satellite show a clear evidence of an asymmetric collapse, we have revisited the experimental data recorded by the underground and gravitational wave detectors running during the SN1987A. New evidence is shown that confirms previous results, namely that the data recorded by the gravitational wave detectors running in Rome and in Maryland are strongly correlated with the data of both the Mont Blanc and the Kamiokande detectors, and that the correlation extends over a long period of time (1 or 2 h) centered at the Mont Blanc time. This result indicates that also Kamiokande detected neutrinos at the Mont Blanc time, and these interactions were not identified because not grouped in a burst.

Description: In this article, we assume that the nonet scalar mesons below \(1\,\mathrm { GeV}\) are the two-quark–tetraquark mixed states and study their masses and pole residues using the QCD sum rules. In the calculation, we take into account the vacuum condensates up to dimension 10 and the \(\mathcal {O}(\alpha _s)\) corrections to the perturbative terms in the operator product expansion. We determine the mixing angles, which indicate the two-quark components are much larger than \(50~\%\) , then we obtain the masses and pole residues of the nonet scalar mesons.

Description: We calculate the cross sections of electromagnetic productions of muon- and tauon-pair productions from the ultra-relativistic heavy ion collisions. Since the Compton wavelengths of muon and tauon are comparable to the radius of the colliding ions, nuclear form factors play important roles for calculating the cross sections. Recent measurement (Abrahamyan et al., Phys Rev Lett 108:112502, 2012 ) indicates that the neutrons are differently distributed from the protons; therefore this affects the cross section of the heavy-lepton pair production. In order to see the effects of the neutron distributions in the nucleus, we used analytical expression of the Fourier transforms of the Wood–Saxon distribution. Cross section calculations show that the Wood–Saxon distribution function is more sensitive to the parameter R compared to the parameter a .

Description: A \((n+1)\) -dimensional gravitational model with Gauss–Bonnet term and a cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with an exponential dependence of the scale factors, \(a_i \sim \exp { ( v^i t) }\) , \(i =1, \dots , n \) , are analyzed for \(n 〉 3\) . We study the stability of the solutions with non-static volume factor, i.e. if \(K(v) = \sum _{k = 1}^{n} v^k \ne 0\) . We prove that under a certain restriction R imposed solutions with \(K(v) 〉 0\) are stable, while solutions with \(K(v) 〈 0\) are unstable. Certain examples of stable solutions are presented. We show that the solutions with \(v^1 = v^2 =v^3 = H 〉 0\) and zero variation of the effective gravitational constant are stable if the restriction R is obeyed.

Description: In this paper we argue that minimal supergravity with a flat Kähler metric and a power-law superpotential can relate the Super-Higgs mechanism for the local spontaneous supersymmetry breaking and the cosmological tracking solution, leading in turn to a late-time accelerated expansion of the universe and alleviating the coincidence problem.

Description: A large effort has been carried out to characterize the background of sodium iodide crystals within the Annual modulation with NaI Scintillators (ANAIS) project. In this paper, the background models developed for three 12.5 kg NaI(Tl) scintillators produced by Alpha Spectra Inc. and operated at the Canfranc Underground Laboratory are presented together with an evaluation of the background prospects for the full experiment. Measured spectra from threshold to high energy in different conditions are well described by the models based on quantified activities. At the region of interest, crystal bulk contamination is the dominant background source. Contributions from \(^{210}\) Pb, \(^{40}\) K, \(^{22}\) Na and \(^{3}\) H are the most relevant. Those from \(^{40}\) K and \(^{22}\) Na could be efficiently suppressed thanks to anticoincidence operation in a crystals matrix or inside a liquid scintillator veto (LSV), while that from \(^{210}\) Pb has been reduced by improving crystal production methods and \(^{3}\) H production could be reduced by shielding against cosmic rays during production. Assuming the activities of the last characterized detector, for nine crystals with a total mass of 112.5 kg the expected background rate is 2.5 counts/(keV kg day) in the region from 1 to 4 keV, which could be reduced at 1.4 counts/(keV kg day) by using a LSV.

Description: We study the conditions of restoring supersymmetry (SUSY) after inflation in the supergravity-based cosmological models with a single chiral superfield and a quartic stabilization term in the Kähler potential. Some new, explicit, and viable inflationary models satisfying those conditions are found. The inflaton’s scalar superpartner is dynamically stabilized during and after inflation. We also demonstrate a possibility of having small and adjustable SUSY breaking with a tiny cosmological constant.

Description: We develop a Bloch vector representation of the Unruh channel for a Dirac field mode. This is used to provide a unified, analytical treatment of quantum Fisher and skew information for a qubit subjected to the Unruh channel, both in its pure form as well as in the presence of experimentally relevant external noise channels. The time evolution of Fisher and skew information is studied along with the impact of external environment parameters such as temperature and squeezing. The external noises are modelled by both purely dephasing phase damping and the squeezed generalised amplitude damping channels. An interesting interplay between the external reservoir temperature and squeezing on the Fisher and skew information is observed, in particular, for the action of the squeezed generalised amplitude damping channel. It is seen that for some regimes, squeezing can enhance the quantum information against the deteriorating influence of the ambient environment. Similar features are also observed for the analogous study of skew information, highlighting a similar origin of the Fisher and skew information.

Description: Newton–Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton–Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry.

Description: The proton charge radius inferred from muonic hydrogen spectroscopy is not compatible with the previous value given by CODATA-2010, which, on its turn, essentially relies on measurements of the electron–proton interaction. The proton’s new size was extracted from the 2S–2P Lamb shift in the muonic hydrogen, which showed an energy excess of 0.3 meV in comparison to the theoretical prediction, evaluated with the CODATA radius. Higher-dimensional gravity is a candidate to explain this discrepancy, since the muon–proton gravitational interaction is stronger than the electron–proton interaction and, in the context of braneworld models, the gravitational potential can be hugely amplified in short distances when compared to the Newtonian potential. Motivated by these ideas, we study a muonic hydrogen confined in a thick brane. We show that the muon–proton gravitational interaction modified by extra dimensions can provide the additional separation of 0.3 meV between the 2S and 2P states. In this scenario, the gravitational energy depends on the higher-dimensional Planck mass and indirectly on the brane thickness. Studying the behavior of the gravitational energy with respect to the brane thickness in a realistic range, we find constraints for the fundamental Planck mass that solve the proton radius puzzle and are consistent with previous experimental bounds.

Description: The present work suggests that the isocurvature tension between axion and high energy inflationary scenarios may be avoided by considering a double field inflationary model involving the hidden Peccei–Quinn Higgs and the Standard Model one. Some terms in the lagrangian we propose explicitly violate the Peccei–Quinn symmetry but, at the present era, their effect is completely negligible. The resulting mechanism allows for a large value for the axion constant, of the order \(f_a\sim M_p\) , thus the axion isocurvature fluctuations are suppressed even when the scale of inflation \(H_{\mathrm{inf}}\) is very high, of the order of \(H_{\mathrm{inf}}\sim M_{\mathrm{gut}}\) . This numerical value is typical in Higgs inflationary models. An analysis about topological defect formation in this scenario is also performed, and it is suggested that, under certain assumptions, their effect is not catastrophic from the cosmological point of view.

Description: We study the charmless two-body \(\Lambda _b\rightarrow \Lambda (\phi ,\eta ^{(\prime )})\) and three-body \(\Lambda _b\rightarrow \Lambda K^+K^- \) decays. We obtain \(\mathcal{B}(\Lambda _b\rightarrow \Lambda \phi )=(3.53\pm 0.24)\times 10^{-6}\) to agree with the recent LHCb measurement. However, we find that \(\mathcal{B}(\Lambda _b\rightarrow \Lambda (\phi \rightarrow )K^+ K^-)=(1.71\pm 0.12)\times 10^{-6}\) is unable to explain the LHCb observation of \(\mathcal{B}(\Lambda _b\rightarrow \Lambda K^+ K^-)=(15.9\pm 1.2\pm 1.2\pm 2.0)\times 10^{-6}\) , which implies the possibility for other contributions, such as that from the resonant \(\Lambda _b\rightarrow K^- N^*,\,N^*\rightarrow \Lambda K^+\) decay with \(N^*\) as a higher-wave baryon state. For \(\Lambda _b\rightarrow \Lambda \eta ^{(\prime )}\) , we show that \(\mathcal{B}(\Lambda _b\rightarrow \Lambda \eta ,\,\Lambda \eta ^\prime )= (1.47\pm 0.35,1.83\pm 0.58)\times 10^{-6}\) , which are consistent with the current data of \((9.3^{+7.3}_{-5.3},〈3.1)\times 10^{-6}\) , respectively. Our results also support the relation of \(\mathcal{B}(\Lambda _b\rightarrow \Lambda \eta ) \simeq \mathcal{B}(\Lambda _b\rightarrow \Lambda \eta ^\prime )\) , given by the previous study.

Description: We provide a novel action principle for nonrelativistic ideal magnetohydrodynamics in the Eulerian scheme exploiting a Clebsch-type parametrisation. Both Lagrangian and Hamiltonian formulations have been considered. Within the Hamiltonian framework, two complementary approaches have been discussed using Dirac’s constraint analysis. In one case the Hamiltonian is canonical involving only physical variables but the brackets have a noncanonical structure, while the other retains the canonical structure of brackets by enlarging the phase space. The special case of incompressible magnetohydrodynamics is also considered where, again, both the approaches are discussed in the Hamiltonian framework. The conservation of the stress tensor reveals interesting aspects of the theory.

Description: The effects of several dark energy models on gravitational time delay of particles with non-zero mass are investigated and analytical expressions for the same are obtained at the first order accuracy. Also the expression for gravitational time delay under the influence of conformal gravity potential that well describes the flat rotation curve of spiral galaxies is derived. The findings suggest that (i) the conformal gravity description of dark matter reduces the net time delay in contrast to the effect of normal dark matter, and therefore in principle the models can be discriminated using gravitational time delay observations, and (ii) the effect of dark energy/flat rotation curve may be revealed from high-precision measurements of gravitational time delay of particles involving the megaparsec and beyond distance scale.

Description: In this short paper we investigate quantum gravitational effects on Einstein’s equations using Effective Field Theory techniques. We consider the leading order quantum gravitational correction to the wave equation. Besides the usual massless mode, we find a pair of modes with complex masses. These massive particles have a width and could thus lead to a damping of gravitational waves if excited in violent astrophysical processes producing gravitational waves such as e.g. black hole mergers. We discuss the consequences for gravitational wave events such as GW 150914 recently observed by the Advanced LIGO collaboration.

Description: Dark energy is investigated from the perspective of quantum cosmology. It is found that, together with an appropriate normal ordering factor q , only when there is dark energy can the cosmological wave function be normalized. This interesting observation may require further attention.

Description: We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors.

Description: The final results of the search for the lepton flavour violating decay \(\mathrm {\mu }^+ \rightarrow \mathrm {e}^+ \mathrm {\gamma }\) based on the full dataset collected by the MEG experiment at the Paul Scherrer Institut in the period 2009–2013 and totalling \(7.5\times 10^{14}\) stopped muons on target are presented. No significant excess of events is observed in the dataset with respect to the expected background and a new upper limit on the branching ratio of this decay of \( \mathcal{B} (\mu ^+ \rightarrow \mathrm{e}^+ \gamma ) 〈 4.2 \times 10^{-13}\) (90 % confidence level) is established, which represents the most stringent limit on the existence of this decay to date.

Description: Over the past years, the interpretation of measurements in the context of effective field theories has attracted much attention in the field of particle physics. We present a tool for interpreting sets of measurements in such models using a Bayesian ansatz by calculating the posterior probabilities of the corresponding free parameters numerically. An example is given, in which top-quark measurements are used to constrain anomalous couplings at the Wtb -vertex.

Description: Integrable N -particle systems have an important property that the associated Seiberg–Witten prepotentials satisfy the WDVV equations. However, this does not apply to the most interesting class of elliptic and double-elliptic systems. Studying the commutativity conjecture for theta functions on the families of associated spectral curves, we derive some other non-linear equations for the perturbative Seiberg–Witten prepotential, which turn out to have exactly the double-elliptic system as their generic solution. In contrast with the WDVV equations, the new equations acquire non-perturbative corrections which are straightforwardly deducible from the commutativity conditions. We obtain such corrections in the first non-trivial case of \(N=3\) and describe the structure of non-perturbative solutions as expansions in powers of the flat moduli with coefficients that are (quasi)modular forms of the elliptic parameter.

Description: A search for new physics is performed using events with two isolated same-sign leptons, two or more jets, and missing transverse momentum. The results are based on a sample of proton–proton collisions at a center-of-mass energy of 13 \(\,\text {TeV}\) recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 2.3  \(\mathrm{fb}^{1}\) . Multiple search regions are defined by classifying events in terms of missing transverse momentum, the scalar sum of jet transverse momenta, the transverse mass associated with a \(\mathrm {W}\) boson candidate, the number of jets, the number of \(\mathrm{b} \) quark jets, and the transverse momenta of the leptons in the event. The analysis is sensitive to a wide variety of possible signals beyond the standard model. No excess above the standard model background expectation is observed. Constraints are set on various supersymmetric models, with gluinos and bottom squarks excluded for masses up to 1300 and 680 \(\,\text {GeV}\) , respectively, at the 95 % confidence level. Upper limits on the cross sections for the production of two top quark-antiquark pairs (119 \(\,\text {fb}\) ) and two same-sign top quarks (1.7 \(\,\text {pb}\) ) are also obtained. Selection efficiencies and model independent limits are provided to allow further interpretations of the results.

Description: We construct a theory in which the gravitational interaction is described only by torsion, but that generalizes the teleparallel theory still keeping the invariance of local Lorentz transformations in one particular case. We show that our theory falls, in a certain limit of a real parameter, under \(f(\bar{R})\) gravity or, in another limit of the same real parameter, under modified f ( T ) gravity; on interpolating between these two theories it still can fall under several other theories. We explicitly show the equivalence with \(f(\bar{R})\) gravity for the cases of a Friedmann–Lemaître–Robertson–Walker flat metric for diagonal tetrads, and a metric with spherical symmetry for diagonal and non-diagonal tetrads. We study four applications, one in the reconstruction of the de Sitter universe cosmological model, for obtaining a static spherically symmetric solution of de Sitter type for a perfect fluid, for evolution of the state parameter \(\omega _{\mathrm{DE}}\) , and for the thermodynamics of the apparent horizon.

Description: We study the effects of a class of features of the potential of slow-roll inflationary models corresponding to a step symmetrically dumped by an even power negative exponential factor, which we call local features. Local-type features differ from other branch-type features considered previously, because the potential is only affected in a limited range of the scalar field value, and they are symmetric with respect to the location of the feature. This type of feature only affects the spectrum and bispectrum in a narrow range of scales which leave the horizon during the time interval corresponding to the modification of the potential. On the contrary branch-type features have effects on all the perturbation modes leaving the horizon when the field value is within the interval defining the branch, introducing for example differences in the power spectrum between large and small scale which are absent in the case of local-type features. The spectrum and bispectrum of primordial curvature perturbations are affected by oscillations around the scale \(k_0\) exiting the horizon at the time \(\tau _0\) corresponding to the feature. We also compute the effects of the features on the CMB temperature and polarization spectra, showing the effects of different choices of parameters.

Description: In this article, we construct the axialvector-diquark–axialvector-antidiquark type tensor current to interpolate both the vector- and the axialvector-tetraquark states, then calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and we obtain the QCD sum rules for both the vector- and the axialvector-tetraquark states. The numerical results support assigning the \(Z_c(4020/4025)\) to be the \(J^{PC}=1^{+-}\) diquark–antidiquark type tetraquark state, and assigning the Y (4660) to be the \(J^{PC}=1^{--}\) diquark–antidiquark type tetraquark state. Furthermore, we take the Y (4260) and Y (4360) as the mixed charmonium–tetraquark states, and we construct the two-quark–tetraquark type tensor currents to study the masses and pole residues. The numerical results support assigning the Y (4260) and Y (4360) to be the mixed charmonium–tetraquark states.

Description: We investigate black hole production in \(p\,p\) collisions at the Large Hadron Collider by employing the horizon quantum mechanics for models of gravity with extra spatial dimensions. This approach can be applied to processes around the fundamental gravitational scale and naturally yields a suppression below the fundamental gravitational scale and for increasing number of extra dimensions. The results of numerical simulations performed with the black hole event generator BLACKMAX are here reported in order to illustrate the main differences in the numbers of expected black hole events and mass distributions.

Description: The measurement of Higgs pair production will be a cornerstone of the LHC program in the coming years. Double Higgs production provides a crucial window upon the mechanism of electroweak symmetry breaking and has a unique sensitivity to the Higgs trilinear coupling. We study the feasibility of a measurement of Higgs pair production in the \(b\bar{b}b\bar{b}\) final state at the LHC. Our analysis is based on a combination of traditional cut-based methods with state-of-the-art multivariate techniques. We account for all relevant backgrounds, including the contributions from light and charm jet mis-identification, which are ultimately comparable in size to the irreducible 4 b QCD background. We demonstrate the robustness of our analysis strategy in a high pileup environment. For an integrated luminosity of \({\mathcal {L}}=3\)  ab \(^{-1}\) , a signal significance of \(S/\sqrt{B}\simeq 3\) is obtained, indicating that the \(b\bar{b}b\bar{b}\) final state alone could allow for the observation of double Higgs production at the High Luminosity LHC.

Description: In the context of track fitting problems by a Kalman filter, the appropriate functional forms of the elements of the random process noise matrix are derived for tracking through thick layers of dense materials and magnetic field. This work complements the form of the process noise matrix obtained by Mankel [ 1 ].

Description: According to the braneworld idea, ordinary matter is confined on a three-dimensional space (brane) that is embedded in a higher-dimensional space-time where gravity propagates. In this work, after reviewing the limits coming from general relativity, finiteness of pressure and causality on the brane, we derive observational constraints on the braneworld parameters from the existence of stable compact stars. The analysis is carried out by solving numerically the brane-modified Tolman–Oppenheimer–Volkoff equations, using different representative equations of state to describe matter in the star interior. The cases of normal dense matter, pure quark matter and hybrid matter are considered.

Description: Supernova neutrinos have several exceptional features which can lead to interesting physical consequences. At the production point their wave packets have an extremely small size \(\sigma _{x} \sim 10^{-11}\)  cm; hence the energy uncertainty can be as large as the energy itself, \(\sigma _{E} \sim E\) , and the coherence length is short. On the way to the Earth the wave packets of mass eigenstates spread to macroscopic sizes and separate. Inside the Earth the mass eigenstates split into eigenstates in matter and oscillate again. The coherence length in the Earth is comparable with the radius of the Earth. We explore these features and their consequences. (1) We present new estimates of the wave packet size. (2) We consider the decoherence condition for the case of wave packets with spatial spread and show that it is not modified by the spread. (3) We study the coherence of neutrinos propagating in a multi-layer medium with density jumps at the borders of layers. In this case coherence can be partially restored due to a “catch-up effect”, increasing the coherence length beyond the usual estimate. This catch-up effect can occur for supernova neutrinos as they cross the shock wave fronts in the exploding star or the core of the Earth.

Description: In D -dimensional spherically symmetric f ( R ) gravity there are three unknown functions to be determined from the fourth order differential equations. It is shown that the system remarkably may be integrated to relate two functions through the third one to provide a reduction to second order equations accompanied with a large class of potential solutions. The third function, which acts as the generator of the process, is \(F(R) =\frac{\mathrm{\mathrm{d}}f(R)}{\mathrm{d}R}\) . We recall that our generating function has been employed as a scalar field with an accompanying self-interacting potential previously, which is entirely different from our approach. Reduction of f ( R ) theory into a system of equations seems to be efficient enough to generate a solution corresponding to each generating function. As particular examples, besides the known ones, we obtain new black hole solutions in any dimension D . We further extend our analysis to cover non-zero energy-momentum tensors. Global monopole and Maxwell sources are given as examples.

Description: We consider the soft wall holographic approach for description of the high- \(T_c\) superconductivity. In comparison with the existing bottom-up holographic superconductors, the proposed approach is more phenomenological and does not describe the superconducting phase transition. On the other hand, technically it is simpler and has more freedom for fitting the conductivity properties of the real high- \(T_c\) materials in the superconducting phase. Some examples of emerging models are analyzed.

Description: We consider the minimal version of an extension of the standard electroweak model based on the \(SU(3)_c \times SU(3)_L \times U(1)_X\) gauge symmetry (the 3-3-1 model). We analyze the most general potential constructed from three scalars in the triplet representation of \(SU(3)_L\) , whose neutral components develop nonzero vacuum expectation values, giving mass for all the model’s massive particles. For different choices of parameters, we obtain the particle spectrum for the two symmetry breaking scales: one where the \(SU(3)_L \times U(1)_X\) group is broken down to \(SU(2)_L\times U(1)_Y\) and a lower scale similar to the standard model one. Within the considerations used, we show that the model encodes two first-order phase transitions, respecting the pattern of symmetry restoration. The last transition, corresponding to the standard electroweak one, is found to be very weak first-order, most likely turning second-order or a crossover in practice. However, the first transition in this model can be strongly first-order, which might happen at a temperature not too high above the second one. We determine the respective critical temperatures for symmetry restoration for the model.

Description: We introduce a nonlinear extension of Proca’s field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schrödinger, Dirac, and Klein–Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit \(q \rightarrow 1\) . We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field \(\Psi ^{\mu }(\vec {x},t)\) , involves an additional field \(\Phi ^{\mu }(\vec {x},t)\) . We obtain exact time-dependent soliton-like solutions for these fields having the form of a q -plane wave, and we show that both field equations lead to the relativistic energy-momentum relation \(E^{2} = p^{2}c^{2} + m^{2}c^{4}\) for all values of q . This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q -generalized Proca theory reduces to Maxwell electromagnetism, and the q -plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed.

Description: We consider the cosmological dynamics of a nonminimally coupled scalar field in scalar–torsion gravity in the presence of hydrodynamical matter. The potential of the scalar field have been chosen as power law with negative index, this type of potentials is usually used in quintessence scenarios. We identify several asymptotic regimes, including de Sitter, kinetic dominance, kinetic tracker, and tracker solutions and study the conditions for their existence and stability. We show that for each combination of coupling constant and potential power index one of the regimes studied in the present paper is stable to the future.

Description: I perform a combined analysis of the ATLAS and CMS diphoton data, using both Run-I and Run-II results, including those released at the 2016 Moriond conference. I find combining the ATLAS and CMS results from Run-II increases the statistical significance of the reported 750 GeV anomaly, assuming a spin-0 mediator coupling to gluons or heavy quarks with a width much smaller than the detector resolution. This significance does not decrease when the 8 TeV data is included. A spin-2 mediator is disfavored compared to the spin-0 case. The cross section required to fit the ATLAS anomaly is in tension with the aggregate data, all of which prefers a smaller value. The best fit for all models I consider is a 4.0 \(\sigma \) local significance for a 750 GeV spin-0 mediator coupling to gluons with a cross section of 4 fb at 13 TeV (assuming narrow width) or 10 fb (assuming \(\Gamma =45\)  GeV).

Description: In a recent paper in EPJC doi: 10.1140/epjc/s10052-016-4037-5 , Faria has shown that quantum massive conformal gravity is renormalizable but has ghost states. We comment this paper on the aspect of renormalizability.

Description: The production of K \(^{*}\) (892) \(^{0}\) and \(\phi \) (1020) mesons has been measured in p–Pb collisions at \(\sqrt{s_{{\text {NN}}}}\) \(=\) 5.02 TeV. K \(^{*0}\) and \(\phi \) are reconstructed via their decay into charged hadrons with the ALICE detector in the rapidity range \(-0.5 〈y 〈0\) . The transverse momentum spectra, measured as a function of the multiplicity, have a p \(_{\mathrm {T}}\) range from 0 to 15 GeV/ c for K \(^{*0}\) and from 0.3 to 21 GeV/ c for \(\phi \) . Integrated yields, mean transverse momenta and particle ratios are reported and compared with results in pp collisions at \(\sqrt{s}\) \(=\) 7 TeV and Pb–Pb collisions at \(\sqrt{s_{{\text {NN}}}}\) \(=\) 2.76 TeV. In Pb–Pb and p–Pb collisions, K \(^{*0}\) and \(\phi \) probe the hadronic phase of the system and contribute to the study of particle formation mechanisms by comparison with other identified hadrons. For this purpose, the mean transverse momenta and the differential proton-to- \(\phi \)  ratio are discussed as a function of the multiplicity of the event. The short-lived K \(^{*0}\) is measured to investigate re-scattering effects, believed to be related to the size of the system and to the lifetime of the hadronic phase.

Description: The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold \(\mathbb {S}^3\) , when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge.

Description: We present models of wormhole under the Finslerian structure of spacetime. This is a sequel of our previous work (Eur Phys J 75:564, 2015 ) where we constructed a toy model for compact stars based on the Finslerian spacetime geometry. In the present investigation, a wide variety of solutions are obtained, which explore the wormhole geometry by considering different choices for the form function and energy density. The solutions, like in the previous work, are revealed to be physically interesting and viable models for the explanation of wormholes as far as the background theory and literature are concerned.

Description: In this paper, we analyze the theoretically possible scenario beyond the standard model in order to show how the presence of the exotic scalar, tensor, \({V}+{A}\) weak interactions in addition to the standard vector-axial ( \({V}-{A}\) ) ones may help to distinguish the Dirac from Majorana neutrinos in the elastic scattering of an (anti)neutrino beam off the unpolarized electrons in the relativistic limit. We assume that the incoming (anti)neutrino beam comes from the polarized muon decay at rest and is the left–right chiral superposition with assigned direction of the transversal spin polarization with respect to the production plane. Our analysis is carried out for the flavour (current) neutrino eigenstates. It means that the transverse neutrino polarization estimates are the same both for the Dirac and Majorana cases. We display that the azimuthal asymmetry in the angular distribution of recoil electrons is generated by the interference terms between the standard and exotic couplings, which are proportional to the transversal (anti)neutrino spin polarization and independent of the neutrino mass. This asymmetry for the Majorana neutrinos is larger than for the Dirac ones. We also indicate the possibility of utilizing the azimuthal asymmetry measurements to search for the new CP-violating phases. Our study is based on the assumption that the possible detector (running for 1 year) has the shape of a flat circular ring, while the intense neutrino source is located in the centre of the ring and polarized perpendicularly to the ring. In addition, the large low-threshold, real-time detector is able to measure with a high resolution both the polar angle and the azimuthal angle of outgoing electron momentum. Our analysis is model-independent and consistent with the current upper limits on the non-standard couplings.

Description: The Gupta–Bleuler triplet for a vector-spinor gauge field is presented in the de Sitter ambient space formalism. The invariant space of field equation solutions is obtained with respect to an indecomposable representation of the de Sitter group. By using the general solution of the massless spin- \(\frac{3}{2}\) field equation, the vector-spinor quantum field operator and its corresponding Fock space is constructed. The quantum field operator can be written in terms of the vector-spinor polarization states and a quantum conformally coupled massless scalar field, which is constructed on Bunch–Davies vacuum state. The two-point function is also presented, which is de Sitter covariant and analytic.

Description: This paper is devoted to investigate cylindrical solutions in mimetic gravity. The explicit forms of the metric of this theory, namely mimetic-Kasner (say) have been obtained. In this study we have noticed that the Kasner’s family of exact solutions needs to be reconsidered under this type of modified gravity. A no-go theorem is proposed for the exact solutions in the presence of a cosmological constant.

Description: We study the experimental DK invariant mass spectra of the reactions , \(B^{0} \rightarrow D^{-} D^{0} K^{+}\) (measured by the BaBar collaboration) and \(B_s \rightarrow \pi ^{+} \bar{D}^{0} K^{-}\) (measured by the LHCb collaboration), where an enhancement right above the threshold is seen. We show that this enhancement is due to the presence of \(D^*_{s0}(2317)\) , which is a DK bound state in the \(I(J^P) = 0(0^{+})\) sector. We employ a unitarized amplitude with an interaction potential fixed by heavy meson chiral perturbation theory. We obtain a mass \(M_{D^*_{s0}} = 2315^{+12}_{-17}\ ^{+10}_{-5}\ \text {MeV}\) , and we also show, by means of the Weinberg compositeness condition, that the DK component in the wave function of this state is \(P_{DK} = 70^{+4}_{-6}\ ^{+4}_{-8} \,\%\) , where the first (second) error is statistical (systematic).

Description: The NuMI Off-Axis \(\nu _{e}\) Appearance (NO \(\nu \) A) is the currently running leading long-baseline neutrino oscillation experiment, whose main physics goal is to explore the current issues in the neutrino sector, such as determination of the neutrino mass ordering, resolution of the octant of the atmospheric mixing angle, and to constrain the Dirac-type CP violating phase \(\delta _\mathrm{CP}\) . In this paper, we would like to investigate whether it is possible to extract the best possible results from NO \(\nu \) A with a shorter time span than its scheduled run period by analyzing its capability to discriminate the degeneracy among various neutrino oscillation parameters within 4 years of run time, with 2 years in each neutrino and antineutrino modes. Further, we study the same by adding the data from the T2K experiment for a total of 5 years run with 3.5 years in neutrino mode and 1.5 years in antineutrino mode. We find that NO \(\nu \) A ( \(2+2\) ) has a better oscillation parameter degeneracy discrimination capability compared to its scheduled run period for 4 years, i.e., NO \(\nu \) A ( \(3+1\) ).

Description: In this work, we investigate the thermodynamics of black p -branes (BB) in the context of Gravity’s Rainbow. We investigate this using rainbow functions that have been motivated from loop quantum gravity and \(\kappa \) -Minkowski non-commutative spacetime. Then for the sake of comparison, we examine a couple of other rainbow functions that have also appeared in the literature. We show that, for consistency, Gravity’s Rainbow imposes a constraint on the minimum mass of the BB, a constraint that we interpret here as implying the existence of a black p -brane remnant. This interpretation is supported by the computation of the black p -brane’s heat capacity that shows that the latter vanishes when the Schwarzschild radius takes on a value that is bigger than its extremal limit. We found that the same conclusion is reached for the third version of rainbow functions treated here but not with the second one for which only standard black p -brane thermodynamics is recovered.

Description: A diphoton excess with an invariant mass of about 750 GeV has been recently reported by both ATLAS and CMS experiments at LHC. While the simplest interpretation requires the resonant production of a 750 GeV (pseudo)scalar, here we consider an alternative setup, with an additional heavy parent particle which decays into a pair of 750 GeV resonances. This configuration improves the agreement between the 8 and 13 TeV data. Moreover, we include a dark matter candidate in the form of a Majorana fermion which interacts through the 750 GeV portal. The invisible decays of the light resonance help to suppress additional decay channels into Standard Model particles in association with the diphoton signal. We realise our hierarchical framework in the context of an effective theory, and we analyse the diphoton signal as well as the consistency with other LHC searches. We finally address the interplay of the LHC results with the dark matter phenomenology, namely the compatibility with the relic density abundance and the indirect detection bounds.

Description: In connection with the discussion and the measurements fulfilled in Ref. (Eur Phys J C 75:137, 2015 ), the full identity is demonstrated between the Feynman formula for the field of a moving charge and the Liénard-Wiechert potentials.

Description: In this paper, we take into account black hole solutions of Brans–Dicke–Maxwell theory and investigate their stability and phase transition points. We apply the concept of geometry in thermodynamics to obtain phase transition points and compare its results with those, calculated in the canonical ensemble through heat capacity. We show that these black holes enjoy second order phase transitions. We also show that there is a lower bound for the horizon radius of physical charged black holes in Brans–Dicke theory, which originates from restrictions of positivity of temperature. In addition, we find that employing a specific thermodynamical metric in the context of geometrical thermodynamics yields divergencies for the thermodynamical Ricci scalar in places of the phase transitions. It will be pointed out that due to the characteristic behavior of the thermodynamical Ricci scalar around its divergence points, one is able to distinguish the physical limitation point from the phase transitions. In addition, the free energy of these black holes will be obtained and its behavior will be investigated. It will be shown that the behavior of the free energy in the place where the heat capacity diverges demonstrates second order phase transition characteristics.

Description: A summary of measurements of the fragmentation of charm quarks into a specific hadron is given. Measurements performed in photoproduction and deep inelastic scattering in \(e^{\pm }p\) , pp and \(e^+e^-\) collisions are compared, using up-to-date branching ratios. Within uncertainties, all measurements agree, supporting the hypothesis that fragmentation is independent of the specific production process. Averages of the fragmentation fractions over all measurements are presented. The average has significantly reduced uncertainties compared to individual measurements.

Description: Due to the absence of tantalising hints for new physics during the LHC’s Run 1, the extension of the Higgs sector by dimension-six operators will provide the new phenomenological standard for searches of non-resonant extensions of the Standard Model. Using all dominant and subdominant Higgs production mechanisms at the LHC, we compute the constraints on Higgs physics-relevant dimension-six operators in a global and correlated fit. We show in how far these constraints can be improved by new Higgs channels becoming accessible at higher energy and luminosity, both through inclusive cross sections as well as through highly sensitive differential distributions. This allows us to discuss the sensitivity to new effects in the Higgs sector that can be reached at the LHC if direct hints for physics beyond the SM remain elusive. We discuss the impact of these constraints on well-motivated BSM scenarios.

Description: Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogeneous cosmological model in \(n+1\) dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of \(n+1\) dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the \(n+1\) dimensional model and the \(3+1\) dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology.

Description: This paper presents measurements of distributions of charged particles which are produced in proton–proton collisions at a centre-of-mass energy of \(\sqrt{s} = 8 \mathrm {\, TeV}\) and recorded by the ATLAS detector at the LHC. A special dataset recorded in 2012 with a small number of interactions per beam crossing (below 0.004) and corresponding to an integrated luminosity of 160  \(\upmu \mathrm{b}^{-1}\) was used. A minimum-bias trigger was utilised to select a data sample of more than 9 million collision events. The multiplicity, pseudorapidity, and transverse momentum distributions of charged particles are shown in different regions of kinematics and charged-particle multiplicity, including measurements of final states at high multiplicity. The results are corrected for detector effects and are compared to the predictions of various Monte Carlo event generator models which simulate the full hadronic final state.

Description: The continuous spontaneous localization (CSL) model has been proposed as a possible solution to the quantum measurement problem by modifying the Schrödinger equation. In this work, we apply the CSL model to two cosmological models of the early Universe: the matter bounce scenario and slow roll inflation. In particular, we focus on the generation of the classical primordial inhomogeneities and anisotropies that arise from the dynamical evolution, provided by the CSL mechanism, of the quantum state associated to the quantum fields. In each case, we obtained a prediction for the shape and the parameters characterizing the primordial spectra (scalar and tensor), i.e. the amplitude, the spectral index and the tensor-to-scalar ratio. We found that there exist CSL parameter values, allowed by other non-cosmological experiments, for which our predictions for the angular power spectrum of the CMB temperature anisotropy are consistent with the best fit canonical model to the latest data released by the Planck Collaboration.

Description: We modify and generalize the known solution for the electromagnetic field when a vacuum, stationary, axisymmetric black hole is immersed in a uniform magnetic field to the case of nonvacuum black holes (of modified gravity) and determine all linear terms of the vector potential in powers of the magnetic field and the rotation parameter.

Description: The understanding of the pion structure as described in terms of transverse-momentum-dependent parton distribution functions (TMDs) is of importance for the interpretation of currently ongoing Drell–Yan experiments with pion beams. In this work we discuss the description of pion TMDs beyond leading twist in a pion model formulated in the light-front constituent framework. For comparison, we also review and derive new results for pion TMDs in the bag and spectator model.

Description: The asymptotic form of Dirac spinors in the field of the Reissner–Nordström black hole is derived for the scattering states (with \(E〉mc^2\) ) obtaining the phase shifts of the partial wave analysis of Dirac fermions scattered from charged black holes. Elastic scattering and absorption are studied giving analytic formulas for the partial amplitudes and cross sections. A graphical study is performed for analyzing the differential cross section (forward/backward scattering) and the polarization degrees as functions of the scattering angle.

Description: The complete effective chiral Lagrangian for a dynamical Higgs is presented and constrained by means of a global analysis including electroweak precision data together with Higgs and triple gauge-boson coupling data from the LHC Run I. The operators’ basis up to next-to-leading order in the expansion consists of 148 (188 considering right-handed neutrinos) flavour universal terms and it is presented here making explicit the custodial nature of the operators. This effective Lagrangian provides the most general description of the physical Higgs couplings once the electroweak symmetry is assumed, and it allows for deviations from the \(SU(2)_L\) doublet nature of the Standard Model Higgs. The comparison with the effective linear Lagrangian constructed with an exact \(SU(2)_L\) doublet Higgs and considering operators with at most canonical dimension six is presented. A promising strategy to disentangle the two descriptions consists in analysing (i) anomalous signals present only in the chiral Lagrangian and not expected in the linear one, that are potentially relevant for LHC searches, and (ii) decorrelation effects between observables that are predicted to be correlated in the linear case and not in the chiral one. The global analysis presented here, which includes several kinematic distributions, is crucial for reducing the allowed parameter space and for controlling the correlations between parameters. This improves previous studies aimed at investigating the Higgs Nature and the origin of the electroweak symmetry breaking.

Description: The propagation of neutrinos in long baselines experiments may be influenced by dissipation effects. Using the Lindblad master equation we evolve neutrinos taking into account these dissipative effects. The MSW and the dissipative effects may change the behavior of the probabilities. In this work, we show and explain how the behavior of the probabilities can change due to the decoherence and relaxation effects acting individually with the MSW effect. A new exotic peak appears in this case and we show the difference between the decoherence and relaxation effects in the appearance of this peak. We also adapt the usual approximate expression for survival and appearance probabilities with all possible decoherence effects. We suppose the baseline of DUNE and show how each of the decoherence parameters changes the probabilities analyzing the possible modification using a numeric and an analytic approach.

Description: A remarkable feature of Schur functions—the common eigenfunctions of cut-and-join operators from \(W_\infty \) —is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of \(U_q(SL_N)\) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding–Iohara–Miki algebras, which play the central role in modern studies in Seiberg-Witten–Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization—on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding.

Description: In search of the extra dimensions in the ongoing LHC experiments, the signatures of the Randall–Sundrum (RS) lightest KK graviton have been in the main focus in recent years. The recent data from the dilepton decay channel at the LHC has determined the experimental lower bound on the mass of the RS lightest Kaluza–Klein (KK) graviton for different choices of the underlying parameters of the theory. In this work we explore the effects of the back-reaction of the bulk scalar field, which is employed to stabilise the RS model, in modifying the couplings of the lightest KK graviton with the standard model matter fields located on the visible brane. In such a modified background geometry we show that the coupling of the lightest KK graviton with the SM matter fields gets a significant suppression due to the inclusion of the back-reaction of the bulk stabilising scalar field. This implies that the back-reaction parameter weakens the signals from the RS scenario in collider experiments, which in turn explains the non-visibility of KK graviton in colliders. Thus we show that the modulus stabilisation plays a crucial role in the search of warped extra dimensions in collider experiments.

Description: We calculate the squeezed back-to-back correlation (BBC) functions of \(\phi \phi \) and \(K^+K^-\) for heavy-ion collisions at RHIC and LHC energies, using ( \(2+1\) )-dimensional hydrodynamics with fluctuating initial conditions. The BBC functions averaged over event-by-event calculations for many events for the hydrodynamic sources are smoothed as a function of the particle momentum. For heavy-ion collisions of Au  \(+\)  Au at \(\sqrt{s_{NN}}=200\)  GeV, the BBC functions are larger than those for collisions of Pb  \(+\)  Pb at \(\sqrt{s_{NN}}=2.76\)  TeV. The BBC of \(\phi \phi \) may possibly be observed in peripheral collisions at the RHIC and LHC energies. It is large for the smaller sources of Cu  \(+\)  Cu collisions at \(\sqrt{s_{NN}}=200\)  GeV.

Description: The nature of dark energy affects the Hubble expansion rate (namely, the expansion history) H ( z ) by an integral over w ( z ). However, the usual observables are the luminosity distances or the angular diameter distances, which measure the distance–redshift relation. Actually, the property of dark energy affects the distances (and the growth factor) by a further integration over functions of H ( z ). Thus, the direct measurements of the Hubble parameter H ( z ) at different redshifts are of great importance for constraining the properties of dark energy. In this paper, we show how the typical dark energy models, for example, the \(\Lambda \) CDM, w CDM, CPL, and holographic dark energy models, can be constrained by the current direct measurements of H ( z ) (31 data used in total in this paper, covering the redshift range of \(z\in [0.07,2.34]\) ). In fact, the future redshift-drift observations (also referred to as the Sandage–Loeb test) can also directly measure H ( z ) at higher redshifts, covering the range of \(z\in [2,5]\) . We thus discuss what role the redshift-drift observations can play in constraining dark energy with the Hubble parameter measurements. We show that the constraints on dark energy can be improved greatly with the H ( z ) data from only a 10-year observation of redshift drift.

Description: We evaluate differential cross sections for production of four jets in multi-Regge kinematics at a hadron collider. The main focus lies on the azimuthal angle dependences. As in previous studies, the ratios of correlation functions of products of cosines of azimuthal angle differences among the tagged jets offer us the cleanest quantities to compare with the experimental data. The calculations are based on the jet production from a single BFKL ladder with a convolution of three BFKL Green functions where we always have two forward/backward jets tagged in the final state. We also demand the tagging of two further jets in more central regions of the detectors with a relative separation in rapidity from each other, plus the inclusive production of an arbitrary number of mini-jets. We show that dependences on the transverse momenta and rapidity of the two central jets can be a distinct signal of the onset of BFKL dynamics.

Description: In this paper we use the conformal teleparallel gravity to study an isotropic and homogeneous Universe which is settled by the Friedmann–Robertson–Walker metric. The conformal symmetry demands the existence of a scalar field which works as a dark field for this model. We solve numerically the field equations then we obtain the behavior of some cosmological parameters such as the scale factor, the deceleration parameter and the energy density of the perfect fluid which is the matter field of our model. The field equations, which we called modified Friedmann equations, allow us to define a dark fluid, with dark energy density and pressure, responsible for the acceleration in the Universe, once we defined an equation of state for the dark fluid.

Description: On gravity’s rainbow, the energy of test particles deforms the geometry of a black hole in such a way that the corresponding Hawking temperature is expected to be modified. It means that the fiducial and free-fall temperatures on the black hole background should also be modified according to deformation of the geometry. In this work, the probing energy of test particles is assumed as the average energy of the Hawking particle in order to study the particle back reaction of the geometry by using the advantage of gravity’s rainbow. We shall obtain the modified fiducial and free-fall temperatures, respectively. The behaviors of these two temperatures on the horizon tell us that black hole complementarity is still well defined on gravity’s rainbow.

Description: We analyze the tidal forces produced in the spacetime of Reissner–Nordström black holes. We point out that the radial component of the tidal force changes sign just outside the event horizon if the charge-to-mass ratio is close to 1, unlike in Schwarzschild spacetime of uncharged black holes, and that the angular component changes sign between the outer and inner horizons. We solve the geodesic deviation equations for radially falling bodies toward the charged black hole. We find, for example, that the radial component of the geodesic deviation vector starts decreasing inside the event horizon unlike in the Schwarzschild case.

Description: Fermionic T-duality transformation is studied for supersymmetric solutions of massive type IIA supergravity with the metric \(AdS_{10-k} \times M_k\) for \(k=3\) and 5. We derive the Killing spinors of these backgrounds and use them as input for the fermionic T-duality transformation. The resulting dual solutions form a large family of supersymmetric deformations of the original solutions by complex valued RR fluxes. We observe that the Romans mass parameter does not change under fermionic T-duaity, and prove its invariance in the \(k=3\) case.

Description: The physics impact of a staged approach for double- \(\beta \) decay experiments based on \(^{\text {76}}\) Ge is studied. The scenario considered relies on realistic time schedules envisioned by the Gerda and the Majorana collaborations, which are jointly working towards the realization of a future larger scale \(^{\text {76}}\) Ge experiment. Intermediate stages of the experiments are conceived to perform quasi background-free measurements, and different data sets can be reliably combined to maximize the physics outcome. The sensitivity for such a global analysis is presented, with focus on how neutrino flavor models can be probed already with preliminary phases of the experiments. The synergy between theory and experiment yields strong benefits for both sides: the model predictions can be used to sensibly plan the experimental stages, and results from intermediate stages can be used to constrain whole groups of theoretical scenarios. This strategy clearly generates added value to the experimental efforts, while at the same time it allows to achieve valuable physics results as early as possible.

Description: With a combined analysis of data on \(\Upsilon (5S)\rightarrow h_b(1P,2P)\pi ^+\pi ^-\) and \(\Upsilon (5S)\rightarrow B^{(*)}\bar{B}^{(*)}\pi \) in an effective field theory approach, we determine resonance parameters of \(Z_b\) states in two scenarios. In one scenario we assume that \(Z_b\) states are pure molecular states, while in the other one we assume that \(Z_b\) states contain compact components. We find that the present data favor that there should be some compact components inside \(Z_b^{(\prime )}\) associated with the molecular components. By fitting the invariant mass spectra of \(\Upsilon (5S)\rightarrow h_b(1P,2P)\pi ^+\pi ^-\) and \(\Upsilon (5S)\rightarrow B^{(*)}\bar{B}^{*}\pi \) , we determine that the probability of finding the compact components in \(Z_b\) states may be as large as about 40 %.

Description: We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q -derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

Description: In this paper, using the combined Lorenz–diffeomorphism symmetry, we find a general formula for the quasi-local conserved charge of the covariant gravity theories in a first order formalism of gravity. We simplify the general formula for the Lovelock theory of gravity. Afterwards, we apply the obtained formula on BHT gravity to obtain the energy and angular momentum of the rotating OTT black hole solution in the context of this theory.

Description: The Korea Invisible Mass Search (KIMS) collaboration has developed low-background NaI(Tl) crystals that are suitable for the direct detection of WIMP dark matter. Building on experience accumulated during the KIMS-CsI programs, the KIMS-NaI experiment will consist of a 200 kg NaI(Tl) crystal array surrounded by layers of shielding structures and will be operated at the Yangyang underground laboratory. The goal is to provide an unambiguous test of the DAMA/LIBRA annual modulation signature. Measurements of six prototype crystals show progress in the reduction of internal contamination from radioisotopes. Based on our understanding of these measurements, we expect to achieve a background level in the final detector configuration that is less than 1 count/day/keV/kg for recoil energies around 2 keV. The annual modulation sensitivity for the KIMS-NaI experiment shows that an unambiguous 7 \(\sigma \) test of the DAMA/LIBRA signature would be possible with a 600 kg year exposure with this system.

Description: We argue that the secondaries produced in high-energy hadron collisions are emitted by small-size sources distributed over a much larger area in impact parameter space occupied by the interaction amplitude. That is, Bose–Einstein correlation of two emitted identical particles should be described by a ‘two-radii’ parametrisation ansatz. We discuss the expected energy, charged multiplicity and transverse momentum of the pair (that is, \(\sqrt{s},~N_\mathrm{ch}, k_t\) ) behaviour of both the small and the large size components.

Description: In this paper we show that the excess of the \( \tau \tau \) events with respect to the Standard Model background predictions, observed by the ATLAS and CMS collaborations and interpreted as the evidence of the Higgs-boson decay into a pair of \(\tau \) -leptons, may be accounted for by properly taking into account QED radiative corrections in the modelling of the \(Z/\gamma ^* \rightarrow \tau \tau \) background.

Description: We study the charmonium \(p \bar{p} \rightarrow \psi (3770) \pi ^0\) reaction using the effective Lagrangian approach where the contributions from well-established \(N^*\) states are considered, and all parameters are fixed in the process of \(e^+e^- \rightarrow p \bar{p}\pi ^0\) at center of mass energy \(\sqrt{s} = 3.773\)  GeV. The experimental data on the line shape of the mass distribution of the \(e^+e^- \rightarrow p\bar{p}\pi ^0\) can be well reproduced. Based on the study of \(e^+e^- \rightarrow p \bar{p}\pi ^0\) , the total and differential cross sections of the \(p \bar{p} \rightarrow \psi (3770) \pi ^0\) reaction are predicted. At the same time we evaluated also the cross sections of the \(p \bar{p} \rightarrow \psi (3686) \pi ^0\) reaction. It is shown that the contribution of the nucleon pole to this reaction is largest close to the reaction threshold. However, the interference between nucleon pole and the other nucleon resonance can still change the angle distributions significantly. Those theoretical results may be tested by the future experiments at \(\overline{\text{ P }}\) ANDA.

Description: In this paper we consider a model for gravity in four-dimensional space-time originally proposed by Chamseddine, which may be derived by dimensional reduction and truncation from a five-dimensional Chern–Simons theory. Its topological origin makes it an interesting candidate for an easier quantization, e.g., in the loop quantization framework. The present paper is dedicated to a classical analysis of the model’s properties. Cosmological solutions as well as wave solutions are found and compared with the corresponding solutions of Einstein’s general relativity with cosmological constant.

Description: We present a range of physics results for central exclusive production processes at the LHC, using the new SuperChic 2 Monte Carlo event generator. This includes significant theoretical improvements and updates, most importantly a fully differential treatment of the soft survival factor, as well as a greater number of generated processes. We provide an overview of the latest theoretical framework, and consider in detail a selection of final states, namely exclusive 2 and 3 jets, photoproduced vector mesons, two-photon initiated muon and W boson pairs and heavy \(\chi _{c,b}\) quarkonia.

Description: Fiducial cross-sections for \(t\bar{t} \) production with one or two additional b -jets are reported, using an integrated luminosity of 20.3 fb \(^{-1}\) of proton–proton collisions at a centre-of-mass energy of 8 TeV at the Large Hadron Collider, collected with the ATLAS detector. The cross-section times branching ratio for \(t\bar{t} \) events with at least one additional b -jet is measured to be 950 \(\pm \) 70 (stat.) \(^{+240}_{-190}\)  (syst.) fb in the lepton-plus-jets channel and 50 \(\pm \) 10 (stat.) \(^{+15}_{-10}\)  (syst.) fb in the \(e \mu \) channel. The cross-section times branching ratio for events with at least two additional b -jets is measured to be 19.3 \(\pm \) 3.5 (stat.) \(\pm \) 5.7 (syst.) fb in the dilepton channel ( \(e \mu \) ,  \(\mu \mu \) , and   ee ) using a method based on tight selection criteria, and 13.5 \(\pm \) 3.3 (stat.)  \(\pm \) 3.6 (syst.) fb using a looser selection that allows the background normalisation to be extracted from data. The latter method also measures a value of 1.30 \(\pm \) 0.33 (stat.) \(\pm \) 0.28 (syst.)% for the ratio of \(t\bar{t}\) production with two additional b -jets to \(t\bar{t}\) production with any two additional jets. All measurements are in good agreement with recent theory predictions.

Description: A search for the flavour-changing neutral-current decay \(t\rightarrow qZ\) is presented. Data collected by the ATLAS detector during 2012 from proton–proton collisions at the Large Hadron Collider at a centre-of-mass energy of \(\sqrt{s}=8\)  TeV, corresponding to an integrated luminosity of 20.3 fb \(^{-1}\) , are analysed. Top-quark pair-production events with one top quark decaying through the \(t\rightarrow qZ\) ( \(q=u,c\) ) channel and the other through the dominant Standard Model mode \(t\rightarrow bW\) are considered as signal. Only the decays of the Z boson to charged leptons and leptonic W boson decays are used. No evidence for a signal is found and an observed (expected) upper limit on the \(t\rightarrow qZ\) branching ratio of \(7\times 10^{-4}\) ( \(8\times 10^{-4}\) ) is set at the 95 % confidence level

Description: A measurement is presented of differential cross sections for Higgs boson (H) production in pp collisions at \(\sqrt{s}=8\) \(\,\text {TeV}\) . The analysis exploits the \({H} \rightarrow {\gamma }{\gamma }\) decay in data corresponding to an integrated luminosity of 19.7 \(\,\text {fb}^\text {-1}\) collected by the CMS experiment at the LHC. The cross section is measured as a function of the kinematic properties of the diphoton system and of the associated jets. Results corrected for detector effects are compared with predictions at next-to-leading order and next-to-next-to-leading order in perturbative quantum chromodynamics, as well as with predictions beyond the standard model. For isolated photons with pseudorapidities \(|\eta |〈2.5\) , and with the photon of largest and next-to-largest transverse momentum ( \(p_{\mathrm {T}} ^{\gamma }\) ) divided by the diphoton mass \(m_{\gamma \gamma }\) satisfying the respective conditions of \(p_{\mathrm {T}} ^{\gamma }/m_{\gamma \gamma }〉 1/3\) and \({〉}1/4\) , the total fiducial cross section is \(32 \pm 10\) \(\text {\,fb}\) .

Description: We apply the Symanzik improvement programme to the \(4+1\) -dimensional local re-formulation of the gradient flow in pure SU ( N ) lattice gauge theories. We show that the classical nature of the flow equation allows one to eliminate all cutoff effects at \(\mathcal O(a^2)\) , which originate either from the discretised gradient flow equation or from the gradient flow observable. All the remaining \(\mathcal O(a^2)\) effects can be understood in terms of local counterterms at the zero flow-time boundary. We classify these counterterms and provide a complete set as required for on-shell improvement. Compared to the 4-dimensional pure gauge theory only a single additional counterterm is required, which corresponds to a modified initial condition for the flow equation. A consistency test in perturbation theory is passed and allows one to determine all counterterm coefficients to lowest non-trivial order in the coupling.

Description: We present an exact spherical black hole solution in de Rham, Gabadadze, and Tolley (dRGT) massive gravity for a generic choice of the parameters in the theory, and also discuss the thermodynamical and phase structure of the black hole in both the grand canonical and the canonical ensembles (for the charged case). It turns out that the dRGT black hole solution includes other known solutions to the Einstein field equations, such as the monopole-de Sitter–Schwarzschild solution with the coefficients of the third and fourth terms in the potential and the graviton mass in massive gravity naturally generates the cosmological constant and the global monopole term. Furthermore, we compute the mass, temperature and entropy of the dRGT black hole, and also perform thermodynamical stability analysis. It turns out that the presence of the graviton mass completely changes the black hole thermodynamics, and it can provide the Hawking–Page phase transition which also occurs for the charged black holes. Interestingly, the entropy of a black hole is barely affected and still obeys the standard area law. In particular, our results, in the limit \(m_g \rightarrow 0\) , reduced exactly to the results of general relativity.

Description: We speculate about the origin of the recent excess at \(\sim \) 750 GeV in diphoton resonance searches observed by the ATLAS and CMS experiments using the first 13 TeV data. Its interpretation as a new scalar resonance produced in gluon fusion and decaying to photons is consistent with all relevant exclusion bounds from the 8 TeV LHC run. We provide a simple phenomenological framework to parametrize the properties of the new resonance and show in a model-independent way that, if the scalar is produced in gluon fusion, additional new colored and charged particles are required. Finally, we discuss some interpretations in various concrete setups, such as a singlet (pseudo-) scalar, composite Higgs, and the MSSM.

Description: We discuss the production of a heavy neutral Higgs boson of a \(\mathcal {CP}\) -conserving two-Higgs-doublet model in gluon fusion and its decay into a four-fermion final state, \(gg (\rightarrow VV) \rightarrow e^+e^-\mu ^+\mu ^-/e^+e^-\nu _l\bar{\nu }_l\) . We investigate the interference contributions to invariant mass distributions of the four-fermion final state and other relevant kinematical observables. The relative importance of the different contributions is quantified for the process in the on-shell approximation, \(gg\rightarrow ZZ\) . We show that interferences of the heavy Higgs with the light Higgs boson and background contributions are essential for a correct description of the differential cross section. Even though they contribute below \({\mathcal {O}}(10~\%)\) to those heavy Higgs signal cross sections, to which the experiments at the Large Hadron Collider were sensitive in its first run, we find that they are sizable in certain regions of the parameter space that are relevant for future heavy Higgs boson searches. In fact, the interference contributions can significantly enhance the experimental sensitivity to the heavy Higgs boson.

Description: The radiative neutrino mass model can relate neutrino masses and dark matter at a TeV scale. If we apply this model to thermal leptogenesis, we need to consider resonant leptogenesis at that scale. It requires both finely degenerate masses for the right-handed neutrinos and a tiny neutrino Yukawa coupling. We propose an extension of the model with a U (1) gauge symmetry, in which these conditions are shown to be simultaneously realized through a TeV scale symmetry breaking. Moreover, this extension can bring about a small quartic scalar coupling between the Higgs doublet scalar and an inert doublet scalar which characterizes the radiative neutrino mass generation. It also is the origin of the \(Z_2\) symmetry which guarantees the stability of dark matter. Several assumptions which are independently supposed in the original model are closely connected through this extension.