Measurement of branching fraction and first evidence of $CP$ violation in ${B}^{0}\ensuremath{\rightarrow}{a}_{1}^{\mathbf{\ifmmode\pm\else\textpm\fi{}}}\mathbf{(}1260\mathbf{)}{\ensuremath{\pi}}^{\mathbf{\ensuremath{\mp}}}$ decays

Measurement of branching fraction and first evidence of $C P$ violation in $B^{0} \to a_{1}^{\pm} (1260) π^{\mp}$ decays

J. Dalseno et al. (Belle Collaboration)

Phys. Rev. D 86, 092012 – Published 26 November 2012

Abstract

We present a measurement of the branching fraction and time-dependent $C P$ violation parameters in $B^{0} \to a_{1}^{\pm} (1260) π^{\mp}$ decays. The results are obtained from the final data sample containing $772 \times 10^{6}$ $B \bar{B}$ pairs collected at the $Υ (4 S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+} e^{-}$ collider. We obtain the product branching fraction $B (B^{0} \to a_{1}^{\pm} (1260) π^{\mp}) \times B (a_{1}^{\pm} (1260) \to π^{\pm} π^{\mp} π^{\pm}) = (11.1 \pm 1.0 (stat) \pm 1.4 (syst)) \times 10^{- 6}$ and an upper limit on the product branching fraction for a possible decay with the same final state $B (B^{0} \to a_{2}^{\pm} (1320) π^{\mp}) \times B (a_{2}^{\pm} (1320) \to π^{\pm} π^{\mp} π^{\pm}) < 2.2 \times 10^{- 6} at 90 % CL$ . In a time-dependent measurement to extract $C P$ asymmetries, we obtain the $C P$ violation parameters $A_{C P} = - 0.06 \pm 0.05 (stat) \pm 0.07 (syst)$ , $C_{C P} = - 0.01 \pm 0.11 (stat) \pm 0.09 (syst)$ , $S_{C P} = - 0.51 \pm 0.14 (stat) \pm 0.08 (syst)$ , representing time- and flavor-integrated direct, flavor-dependent direct and mixing-induced $C P$ violation, respectively. Simultaneously, we also extract the $C P$ -conserving parameters $Δ C = + 0.54 \pm 0.11 (stat) \pm 0.07 (syst)$ , $Δ S = - 0.09 \pm 0.14 (stat) \pm 0.06 (syst)$ , which, respectively, describe a rate difference and strong phase difference between the decay channels where the $a_{1}^{\pm}$ does not contain the spectator quark and those where it does. We find first evidence of mixing-induced $C P$ violation in $B^{0} \to a_{1}^{\pm} (1260) π^{\mp}$ decays with $3.1 σ$ significance. The rate where the $a_{1}^{\pm}$ does not contain the spectator quark from the $B$ meson is found to dominate the rate where it does at the $4.1 σ$ level. However, there is no evidence for either time- and flavor-integrated direct $C P$ violation or flavor-dependent direct $C P$ violation.

Received 31 May 2012

DOI:https://doi.org/10.1103/PhysRevD.86.092012

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Vol. 86, Iss. 9 — 1 November 2012

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Figure 1
Leading-order tree (left) and penguin (right) diagrams for the decay $B^{0} \to a_{1}^{\pm} π^{\mp}$ , where the parentheses in the figure indicate the two possible decays of the $B^{0}$ . The $d$ quark may become part of the $π^{-}$ or $a_{1}^{-}$ . In the penguin diagram, the $x$ in $V_{x b}$ refers to the flavor of the intermediate-state quark ( $x = u$ , $c$ , $t$ ).
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Figure 2
Simulated (MC) and off-resonance data distributions for the quantities used to construct the Fisher discriminant $F_{b \bar{b} / q \bar{q}}$ , normalized to have the same area. The solid blue histograms show signal MC events, while the dashed red histograms show continuum events from data taken below the $Υ (4 S)$ resonance.
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Figure 3
Projections of the fit to the $B^{0} \to a_{1}^{\pm} π^{\mp}$ data. The points with error bars represent the data and the solid black histogram represents the fit result. (a) shows the $Δ E$ projection for $F_{b \bar{b} / q \bar{q}} > 0.5$ and $r > 0.5$ . The blue hatched histogram shows the peaking background, the dashed red histogram shows the continuum contribution and the dash-dotted green histogram shows the total background. (b) shows the $F_{b \bar{b} / q \bar{q}}$ projection for $| Δ E | < 0.01 GeV$ and $r > 0.5$ . The dashed red histogram shows the continuum background contribution. (c) and (d) show the $m_{3 π}$ and $H_{3 π}$ projections, respectively, for $F_{b \bar{b} / q \bar{q}} > 0.5$ , $| Δ E | < 0.01 GeV$ and $r > 0.5$ . The dashed blue histogram shows the $a_{1}^{\pm}$ contribution, the red hatched histogram shows the $a_{2}^{\pm}$ contribution and the dash-dotted green histogram shows the total background.
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Figure 4
Background subtracted time-dependent fit results for $B^{0} \to a_{1}^{\pm} π^{\mp}$ . (a) and (b) show the $Δ t$ distributions for the $B_{Tag}^{0}$ flavor $q$ and the product of the $B_{Tag}^{0}$ flavor and $a_{1}$ charge $q c$ , respectively. The left plots are useful for visualizing the effect of flavor-dependent $C P$ violation, while the plots on the right show the effects of the $C P$ -conserving parameters. The solid blue and dashed red curves represent the $Δ t$ distributions for positive and negative quantity, respectively. (c) and (d) show the asymmetry of the plots immediately above them, $(N_{+}^{Fit} - N_{-}^{Fit}) / (N_{+}^{Fit} + N_{-}^{Fit})$ , where $N_{+}^{Fit}$ ( $N_{-}^{Fit}$ ) is the measured signal yield of positive (negative) quantities in bins of $Δ t$ .
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Figure 5
Difference 1-CL plotted for a range of $ϕ_{2}^{eff}$ values as shown by the solid curve. The $p$ value is taken as the maximum $p$ value that can be calculated from all four solutions. The dashed line indicates $CL = 90 %$ .
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Figure 6
Likelihood scan of $S_{C P}$ (a) and $Δ C$ (b). The dotted blue curve shows the statistical likelihood, while the solid black curve includes the systematic uncertainty.
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Physical Review D

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Measurement of branching fraction and first evidence of $C P$ violation in $B^{0} \to a_{1}^{\pm} (1260) π^{\mp}$ decays

J. Dalseno et al. (Belle Collaboration)

Phys. Rev. D 86, 092012 – Published 26 November 2012

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Physical Review D

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Measurement of branching fraction and first evidence of CP violation in B0→a1±(1260)π∓ decays

J. Dalseno et al. (Belle Collaboration)

Phys. Rev. D 86, 092012 – Published 26 November 2012

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Measurement of branching fraction and first evidence of $C P$ violation in $B^{0} \to a_{1}^{\pm} (1260) π^{\mp}$ decays