Abstract
A measurement of the number of J/ψ events collected with the BESIII detector in 2009 and 2012 is performed using inclusive decays of the J/ψ. The number of J/ψ events taken in 2009 is recalculated to be (223.7 ± 1.4) × 106, which is in good agreement with the previous measurement, but with significantly improved precision due to improvements in the BESIII software. The number of J/ψ events taken in 2012 is determined to be (1086.9 ± 6.0) × 106. In total, the number of J/ψ events collected with the BESIII detector is measured to be (1310.6 ± 7.0) × 106, where the uncertainty is dominated by systematic effects and the statistical uncertainty is negligible.
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1. Introduction
Studies of J/ψ decays have provided a wealth of information since the discovery of the J/ψ in 1974 [1, 2]. Decays of the J/ψ offer a clean laboratory for light hadron spectroscopy, provide an insight into decay mechanisms and help in distinguishing between conventional hadronic states and exotic states.
A lot of important progress in light hadron spectroscopy has been achieved based on a sample of (225.3±2.8) × 106 J/ψ events collected by the BESIII experiment [3] in 2009. To further comprehensively study the J/ψ decay mechanism, investigate the light hadron spectrum, and search for exotic states, e.g. glueballs, hybrids and multi-quark states, an additional, larger J/ψ sample was collected in 2012. A precise determination of the number of J/ψ events is essential for analyses based on these data samples. With improvements in the BESIII software, particularly in Monte Carlo (MC) simulations and the reconstruction of tracks in the main drift chamber (MDC), it is possible to perform a more precise measurement of the number of J/ψ events taken in 2009 and 2012. The relevant data samples used in this analysis are listed in Table 1.
Table 1. Data samples used in the determination of the number of J/ψ events collected in 2009 and 2012.
| data set |  |
 |
date(duration) (MM/DD/YYYY) |
|---|---|---|---|
| J/ψ | 3.097 GeV | 323pb−1 | 4/10/2012–5/22/2012 |
| QED1 | 3.08 GeV | 13pb−1 | 4/8/2012 |
| QED2 | 3.08 GeV | 17pb−1 | 5/23/2012–5/24/2012 |
| ψ(3686) | 3.686 GeV | 7.5pb−1 | 5/26/2012 |
| J/ψ | 3.097 GeV | 82pb−1 | 6/12/2009–7/28/2009 |
| QED | 3.08 GeV | 0.3pb−1 | 6/19/2009 |
| ψ(3686) | 3.686 GeV | 150pb−1 | 3/7/2009–4/14/2009 |
We implement the same method as that used in the previous study [4] to determine the number of J/ψ events. The advantage of this approach is that the detection efficiency of inclusive J/ψ decays can be extracted directly from the data sample taken at the peak of the ψ(3686). This is useful because the correction factor of the detection efficiency is less dependent on the MC model for the inclusive J/ψ decay and therefore the systematic uncertainty can be reduced significantly. The number of J/ψ events, NJ/ψ, is calculated as
where Nsel is the number of inclusive J/ψ events selected from the J/ψ data; Nbg is the number of background events estimated with continuum data taken at 
trig is the trigger efficiency; 
is the inclusive J/ψ detection efficiency determined experimentally using the J/ψ sample from the reaction ψ(3686) → π+π− J/ψ. fcor is a correction factor that accounts for the difference in the detection efficiency between the J/ψ events produced at rest and those produced in ψ(3686) → π+π− J/ψ. fcor is expected to be approximately unity, and is determined by the MC simulation sample with
where 
is the detection efficiency of inclusive J/ψ events determined from the MC sample of J/ψ events produced directly in electron-positron collisions, and 
is that from the MC sample of ψ(3686) → π+π− J/ψ (J/ψ → inclusive) events. In MC simulation, the J/ψ and ψ(3686) resonances are simulated with KKMC [5]. The known decay modes of the J/ψ and ψ(3686) are generated by EVTGEN [6, 7] with branching fractions taken from the Review of Particle Physics [8], while the remaining decays are generated according to the LUNDCHARM model [9, 10]. All of the MC events are fed into a GEANT4-based [11] simulation package, which takes into account the detector geometry and response.
2. Inclusive J/ψ selection criteria
To distinguish the inclusive J/ψ decays from Quantum Electrodynamics (QED) processes (i.e. Bhabha and dimuon events) and background events from cosmic rays and beam-gas interactions, a series of selection criteria are applied to the candidate events. The charged tracks are required to be detected in the MDC within a polar angle range of |cosθ| < 0.93, and to have a momentum of p < 2.0 GeV/c. Each track is required to originate from the interaction region by restricting the distance of closest approach to the run-dependent interaction point in the radial direction, Vr < 1 cm, and in the beam direction, |Vz| < 15 cm. For photon clusters in the electromagnetic calorimeter (EMC), the deposited energy is required to be greater than 25 (50) MeV for the barrel (endcap) region of |cosθ| < 0.83 (0.86 < |cosθ| < 0.93). In addition, the EMC cluster timing T must satisfy 0 < T ⩽ 700 ns, which is used to suppress electronics noise and energy deposits unrelated to the event.
The candidate event must contain at least two charged tracks. The visible energy Evis, defined as the sum of charged particle energies computed from the track momenta by assuming a pion mass and from the neutral shower energies deposited in the EMC, is required to be greater than 1.0 GeV. A comparison of the Evis distribution between the J/ψ data, the data taken at 
, and the inclusive J/ψ MC sample is illustrated in Fig. 1. The requirement Evis > 1.0 GeV removes one third of the background events while retaining 99.4% of the signal events.
Fig. 1. Distributions of the visible energy Evis for J/ψ data (dots with error bars), continuum data at 
(open circles with error bars) and MC simulation of inclusive J/ψ events (histogram). The arrow indicates the minimum Evis required to select inclusive events.
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Standard image High-resolution imageSince Bhabha (e+e− → e+e−) and dimuon (e+e− → μ+μ−) events are two-body decays, each charged track carries the same energy, close to half of the center-of-mass energy. Therefore, for events with only two charged tracks, we require that the momentum of each charged track is less than 1.5 GeV/c in order to remove Bhabha and dimuon events. This requirement is depicted by the solid lines in the scatter plot of the momenta of the two charged tracks (Fig. 2). The Bhabha events are characterized by a significant peak around 1.5 GeV in the distribution of energy deposited in the EMC, shown in Fig. 3. Hence an additional requirement that the energy deposited in the EMC for each charged track is less than 1 GeV is applied to further reject the Bhabha events.
Fig. 2. Scatter plot of the momenta of the charged tracks for 2-prong events in data. The cluster around 1.55 GeV/c corresponds to the contribution from lepton pairs and the cluster at 1.23 GeV/c comes from J/ψ → p
. Most of lepton pairs are removed with the requirements on the two charged tracks, p1 < 1.5 GeV/c and p2 < 1.5 GeV/c, as indicated by the solid lines.
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Fig. 3. Distributions of deposited energy in the EMC for the charged tracks of 2-prong events for J/ψ data (dots with error bars) and for the combined, normalized MC simulations of e+e− → e+e−(γ) and J/ψ → e+e−(γ) (histogram).
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Standard image High-resolution imageAfter the above requirements, Nsel = (854.60±0.03) × 106 candidate events are selected from the J/ψ data taken in 2012. The distributions of the track parameters of closest approach in the beam line and radial directions (Vz and Vr), the polar angle (cosθ), and the total energy deposited in the EMC (EEMC) after subtracting background events estimated with the continuum data taken at 
(see Sec. 3 for details) are shown in Fig. 4. Reasonable agreement between the data and MC samples is observed. The multiplicity of charged tracks (Ngood) is shown in Fig. 5, where the MC sample generated according to the LUNDCHARM model agrees very well with the data while the MC sample generated without the LUNDCHARM model deviates from the data. The effect of this discrepancy on the determination of the number of J/ψ events is small, as described in Sec. 6.
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Fig. 4. Comparison of distributions between J/ψ data (dots with error bars) and MC simulation of inclusive J/ψ (histogram): (a) Vz, (b) Vr, (c) cosθ of charged tracks, (d) total energy deposited in the EMC.
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Fig. 5. Distributions of the reconstructed charged track multiplicity of inclusive J/ψ events for J/ψ data (dots with error bars) and ψ(3686) data (squares with error bars) and MC simulation generated with and without the LUNDCHARM model (solid and dashed histograms, respectively).
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Standard image High-resolution image3. Background analysis
In this analysis, the data samples taken at 
and in close chronological order to the J/ψ sample are used to estimate the background due to QED processes, beam-gas interactions and cosmic rays. To normalize the selected background events to the J/ψ data, the integrated luminosity for the data samples taken at the J/ψ peak and at 
is determined using the precess e+e− → γ γ, respectively.
To determine the integrated luminosity, the candidate events e+e− → γγ are selected by requiring at least two showers in the EMC. It is further required that the energy of the second most energetic shower is between 1.2 and 1.6 GeV and that the polar angles of the two showers are in the range |cosθ | < 0.8. The number of signal events is determined from the number of events in the signal region |Δϕ| < 2.5° and the background is estimated from those in the sideband region 2.5° < |Δϕ| < 5°, where Δϕ = |ϕγ1 − ϕγ2| − 180° and ϕγ1/2 is the azimuthal angle of the photon. Taking into account the detector efficiency obtained from the MC simulation and the cross section of the QED process e+e− → γγ, the integrated luminosities of the J/ψ data sample and the sample taken at 
taken in 2012 are determined to be (315.02±0.14) pb−1 and (30.84±0.04) pb−1, respectively, where the errors are statistical only.
After applying the same selection criteria as for the J/ψ data, N3.08=1,440,376±1,200 events are selected from the continuum data taken at 
. Assuming the same detection efficiency at 
as for the J/ψ peak and taking into account the energy-dependent cross section of the QED processes, the number of background events for the J/ψ sample, Nbg, is estimated to be
where 
and 
are the integrated luminosities for the J/ψ data sample and the data sample taken at 
, respectively, and sJ/ψ and s3.08 are the corresponding squares of the center-of-mass energies. The background is calculated to be 1.7% of the number of selected inclusive J/ψ events taken in 2012.
According to the studies of the MC sample and the Vz distribution, the QED background fraction is found to be about 1.5% of the total data. J/ψ → μ+μ− events are selected and those MDC hits away from μ+μ− tracks come from beam related background, electronic noise etc. The result indicates the beam conditions for the data taken in 2009 were worse, the corresponding noise level was higher and the background was much higher than for the 2012 sample. With the same method, the total background (including the QED contribution) for the 2009 sample is estimated to be 3.7%.
4. Determination of the detection efficiency and correction factor
In the previous study, the detection efficiency was determined using a MC simulation of the reaction J/ψ → inclusive, assuming that both the physics process of the inclusive J/ψ decay and the detector response were simulated well. In this analysis, to reduce the uncertainty related to the discrepancy between the MC simulation and the data, the detection efficiency is determined experimentally using a sample of J/ψ events from the reaction ψ(3686) → π+π− J/ψ. To ensure that the beam conditions and detector status are similar to those of the sample collected at the J/ψ peak, a dedicated ψ(3686) sample taken on May 26, 2012 is used for this study.
To select ψ(3686) → π+π− J/ψ events, there must be at least two soft pions with opposite charge in the MDC within the polar angle range |cosθ| < 0.93, having Vr < 1 cm and |Vz| < 15 cm, and momenta less than 0.4 GeV/c. No further selection criteria on the remaining charged tracks or showers are required. The distribution of the invariant mass recoiling against all possible soft π+π− pairs is shown in Fig. 6 (a). A prominent peak around 3.1 GeV/c2, corresponding to the decay of ψ(3686) → π+π− J/ψ, J/ψ → inclusive, is observed over a smooth background. The total number of inclusive J/ψ events, Ninc = (1147.8±1.9) × 103, is obtained by fitting a double-Gaussian function for the J/ψ signal plus a second-order Chebychev polynomial for the background to the π+π− recoil mass spectrum.
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Fig. 6. Invariant mass recoiling against selected π+π− pairs for the ψ(3686) data sample. The curves are the results of the fit described in the text: (a) for the sample with soft pion selection criteria applied, and (b) for the sample with the addition of the inclusive J/ψ event selection criteria applied.
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To measure the detection efficiency of inclusive J/ψ events, the same selection criteria as described in Sec. 2 are applied to the remaining charged tracks and showers at the event level. The distribution of the invariant mass recoiling against π+π− for the remaining events is shown in Fig. 6 (b); it is fitted with the same function as described above. The number of selected inclusive J/ψ events, 
, is determined to be (877.6±1.7) × 103. The detection efficiency of inclusive J/ψ events, 
, is calculated from the ratio of the number of inclusive J/ψ events with and without the inclusive J/ψ event selection criteria applied.
Since the J/ψ particle in the decay ψ(3686) → π+π− J/ψ is not at rest, a correction factor, defined in Eq. (2), is used to take into account the kinematical effect on the detection efficiency of the inclusive J/ψ event selection. Two large statistics, inclusive ψ(3686) and J/ψ MC samples are produced and are subjected to the same selection criteria as the data samples. The detection efficiencies of inclusive J/ψ events are determined to be 
and 
for the two inclusive MC samples, respectively. The correction factor fcor for the detection efficiency is therefore taken as
5. The number of J/ψ events
Using Eq. (1), the number of J/ψ events collected in 2012 is calculated to be (1086.90±0.04) × 106. The values used in this calculation are summarized in Table 2. The trigger efficiency of the BESIII detector is 100%, based on the study of various reactions [12]. With the same procedure, the number of J/ψ events taken in 2009 is determined to be (223.72±0.01) × 106. Here, the statistical uncertainty is from the number of J/ψ events only, while the statistical fluctuation of Nbg is taken into account as part of the systematic uncertainty (see Sec. 6.4). The systematic uncertainties from different sources are discussed in detail in Sec. 6.
Table 2. Summary of the values used in the calculation and the resulting number of J/ψ events.
| item | 2012 | 2009 |
|---|---|---|
| Nsel | (854.60±0.03) × 106 | (179.63±0.01) × 106 |
| Nbg | (14.55±0.02) × 106 | (6.58±0.04) × 106 |
| trig |
1.00 | 1.00 |
 |
0.7646±0.0007 | 0.7655±0.0001 |
 |
0.7576±0.0006 | 0.7581±0.0005 |
 |
0.7658±0.0004 | 0.7660±0.0004 |
| fcor | 1.0109±0.0009 | 1.0105±0.0009 |
| NJ/ψ | (1086.90±0.04) × 106 | (223.72±0.01) × 106 |
6. Systematic uncertainty
The sources of systematic uncertainty and their corresponding contributions are summarized in Table 3, and are discussed in detail below.
Table 3. Summary of systematic sources and the corresponding contributions to the number of J/ψ events, where the superscript* means the error is common for the data samples taken in 2009 and 2012.
| sources | 2012 (%) | 2009(%) |
|---|---|---|
| *MC model uncertainty | 0.42 | 0.36 |
| track reconstruction efficiency | 0.03 | 0.30 |
| fit to J/ψ peak | 0.19 | 0.17 |
| background uncertainty | 0.06 | 0.13 |
| noise mixing | 0.09 | 0.12 |
| *π+π − uncertainty |
0.28 | 0.34 |
| total | 0.55 | 0.63 |
6.1. MC model uncertainty
In the measurement of the number of J/ψ events, only the efficiency correction factor, fcor, is dependent on the MC simulation. To evaluate the uncertainty due to the MC model, we generate a set of MC samples without the LUNDCHARM model and compare the correction factor determined using these samples to its nominal value. According to the distributions of the charged track multiplicity shown in Fig. 5, the MC simulation without the LUNDCHARM model poorly describes the data, which means this method will overestimate the systematic uncertainty. The studies show that the correction factor has a slight dependence on the MC mode of inclusive J/ψ decays. To be conservative, the change in the correction factor, 0.42% (0.36%), is taken as the systematic uncertainty due to the MC model on the number of J/ψ events taken in 2012 (2009).
6.2. Track reconstruction efficiency
According to studies of the track reconstruction efficiency, the difference in track reconstruction efficiencies between the MC and data samples of J/ψ decays is less than 1% for each charged track.
In the analysis, the ψ(3686) data sample used to determine the detection efficiency is taken in close chronological order to the J/ψ sample. The consistency of track reconstruction efficiency between the MC and data samples in ψ(3686) decays is assumed to be exactly the same as that in J/ψ decays. Therefore the track reconstruction efficiencies in both J/ψ and ψ(3686) MC samples are varied by −1% to evaluate the uncertainty due to the MDC tracking. As expected, the change in the correction factor is very small, 0.03%, and this value is taken as a systematic uncertainty.
In the determination of the number of J/ψ events taken in 2009, the J/ψ and ψ(3686) data samples were collected at different times, which may lead to slight differences in the tracking efficiency between the two data sets due to the imperfect description of detector performance and response in the MC simulation. To estimate the corresponding systematic uncertainty, we adjust the track reconstruction efficiency by −0.5% in the J/ψ MC sample, keeping it unchanged for the ψ(3686) MC sample. The resulting change in the correction factor, 0.30%, is taken as a systematic uncertainty on the number of J/ψ events in 2009.
6.3. Fit to the J/ψ peak
In this measurement, the selection efficiency of inclusive J/ψ events is estimated experimentally with the ψ(3686) data sample (ψ(3686) → π+π− J/ψ), and the yield of J/ψ events used in the efficiency calculation is determined by a fit to the invariant mass spectra recoiling against π+π−. The following systematic uncertainties of the fit are considered: (a) the fit: we propagate the statistical uncertainties of the J/ψ signal yield from the fit to the selection efficiency, and the resulting uncertainties, 0.09% and 0.08% for 
and 
, respectively, are considered to be the uncertainty from the fit itself. (b) the fit range: we change the fit range on the π+π− recoiling mass from [3.07, 3.13] GeV/c2 to [3.08, 3.12] GeV/c2, and the resulting difference, 0.08% is taken as a systematic uncertainty. (c) the signal shape: we perform an alternative fit by describing the J/ψ signal with a histogram obtained from the recoil mass spectrum of π+π− in ψ(3686) → π+π− J/ψ, J/ψ → μ+μ−, and the resulting change, 0.12%, is considered to be the associated systematic uncertainty. (d) the background shape: the uncertainty due to the background shape, 0.02%, is estimated by replacing the second-order Chebychev polynomial with a first-order Chebychev polynomial. By assuming that all of the sources of systematic uncertainty are independent, the fit uncertainty for the 2012 J/ψ sample, 0.19%, is obtained by adding all of the above effects in quadrature.
The same sources of systematic uncertainty are considered for the J/ψ sample taken in 2009. The fit has an uncertainty of 0.02% for 
and 0.07% for 
. The uncertainties from the fit range, signal function and background shape are 0.02%, 0.15% and 0.02%, respectively. The total uncertainty from the fit for the 2009 data is 0.17%.
6.4. Background uncertainty
In the measurement of the number of J/ψ events, the number of background events from QED processes, cosmic rays, and beam-gas interactions is estimated by normalizing the number of events in the continuum data sample taken at 
according to Eq. (3). Therefore the background uncertainty mainly comes from the normalization method, the statistics of the sample taken at 
, the statistical uncertainty of the integrated luminosity and the uncertainty due to beam associated backgrounds.
In practice, Eq. (3) is improper for the normalization of the background of cosmic rays and beam-gas. The number of cosmic rays is proportional to the time of data taking, while beam-gas interaction backgrounds are related to the vacuum status and beam current during data taking in addition to the time of data taking. Assuming a stable beam and vacuum status, the backgrounds of cosmic rays and beam-gas interactions are proportional to the integrated luminosity. Therefore, the difference in the estimated number of backgrounds between that with and without the energy-dependent factor in Eq. (3) is considered to be the associated systematic uncertainty.
In 2012, two data samples with 
were taken at the beginning and end of the J/ψ data taking. To estimate the uncertainty of the background related with the stability of the beam and vacuum status, we estimated the background with Eq. (3) for the two continuum data samples, individually. The maximum change in the nominal results, 0.05%, is taken as the associated systematic uncertainty. In the background estimation for data taken in 2009, only one continuum data sample was taken. The corresponding uncertainty is estimated by comparing the selected background events from the continuum sample to those from the J/ψ data, which is described in detail in Ref. [4].
After considering the above effects, the uncertainties on the number of J/ψ events related to the background are 0.06% and 0.13% for the data taken in 2012 and 2009, respectively. The uncertainties are determined from the quadratic sum of the above individual uncertainties, assuming all of them to be independent.
6.5. Noise mixing
In the BESIII simulation software, the detector noise and machine background are included in the MC simulation by mixing the simulated events with events recorded by a random trigger. To determine the systematic uncertainty associated with the noise realization in the MC simulation, the ψ(3686) MC sample is reconstructed by mixing the noise sample accompanying the J/ψ data taking. The change of the correction factor for the detection efficiency, 0.09%, is taken as the systematic uncertainty due to noise mixing for the number of J/ψ events taken in 2012.
In the determination of the number of J/ψ events collected in 2009, 106 million of ψ(3686) events taken in 2009 are used to determine the detection efficiency, and the corresponding uncertainty related to the noise realization is estimated to be 0.10% with the same method. However, the noise level was not entirely stable during the time of the ψ(3686) data taking. To check the effect on the detection efficiency related to the different noise levels, the ψ(3686) data and the MC samples are divided into three sub-samples, and the detection efficiency and the correction factor are determined for the three sub-samples individually. The resulting maximum change in the number of J/ψ events, 0.06%, is taken as an additional systematic uncertainty associated with the noise realization. The total systematic uncertainty due to the noise is estimated to be 0.12% for the J/ψ events taken in 2009.
6.6. Uncertainty of selection efficiency of two soft pions
According to the MC study, the selection efficiency of soft pions, π+π−, recoiling against the J/ψ in ψ(3686) → π+π−J/ψ is found to depend on the multiplicity of the J/ψ decays. Differences between the data and MC samples may lead to a change in the number of J/ψ events. We compare the multiplicity distribution of J/ψ decays in the ψ(3686) → π+π− J/ψ data sample to that of the J/ψ data at rest to obtain the dependence of π+π− in the data. The efficiency determined from the ψ(3686) → π+π− J/ψ(J/ψ → inclusive) MC sample, 
in Eq. (2), is reweighted with the dependence of π+π− from the data sample. The resulting change in the number of J/ψ events, 0.28% (0.34%) is taken as the uncertainty for the data taken in 2012 (2009).
The systematic uncertainties from the different sources studied above are summarized in Table 3. The total systematic uncertainty for the number of J/ψ in 2012 (2009), 0.55% (0.63%), is the quadratic sum of the individual uncertainties.
7. Summary
Using inclusive J/ψ events, the number of J/ψ events collected with the BESIII detector in 2012 is determined to be NJ/ψ2012 = (1086.9±6.0) × 106, where the uncertainty is systematic only and the statistical uncertainty is negligible. The number of J/ψ events taken in 2009 is recalculated to be NJ/ψ2009= (223.7±1.4) × 106, which is consistent with the previous measurement [4], but with improved precision.
In summary, the total number of J/ψ events taken with BESIII detector is determined to be NJ/ψ= (1310.6±7.0) × 106. Here, the total uncertainty is determined by adding the common uncertainties directly and the independent ones in quadrature.
Acknowledgments
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their hard efforts.
Footnotes
- *
Supported by National Key Basic Research Program of China (2015CB856700), National Natural Science Foundation of China (NSFC) (10805053, 11125525, 11175188, 11235011, 11322544, 11335008, 11425524), Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program, the CAS Center for Excellence in Particle Physics (CCEPP), Collaborative Innovation Center for Particles and Interactions (CICPI), Joint Large-Scale Scientific Facility Funds of NSFC and CAS (11179007, U1232201, U1232107, U1332201), CAS (KJCX2-YW-N29, KJCX2-YW-N45), 100 Talents Program of CAS, INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology, German Research Foundation DFG (Collaborative Research Center CRC-1044), Istituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey (DPT2006K-120470), Russian Foundation for Basic Research (14-07-91152), U. S. Department of Energy (DE-FG02-04ER41291, DE-FG02-05ER41374, DE-FG02-94ER40823, DESC0010118), U.S. National Science Foundation, University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research Foundation of Korea (R32-2008-000-10155-0)