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arXiv 1409.2995hep-ph
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QCDF中$B_{u,d,s}$ $\to$ $PP$衰变湮没修正的组合拟合

A Combined Fit on the Annihilation Corrections in $B_{u,d,s}$ $\to$ $PP$ Decays Within QCDF

Qin Chang, Junfeng Sun, Yueling Yang, Xiaonan Li

备注：
12 pages, version accepted by PLB
发表信息：
Phys Lett B 740, 56 (2015)
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摘要：

基于最近对非轻子湮灭B介子衰变的CDF和LHCb测量所暗示的可能的大湮灭贡献，以及对强子B介子衰变的精细实验测量，本文研究了QCD因子分解（QCDF）中湮灭贡献的强度.利用两体B_{u,d,s} -> pi pi，pi K，K K衰变的现有测量数据，用统计卡方^[2]方法对用于参数化湮灭振幅端点奇异性的唯象参数X_A^{i，f}（或rho_A^{i，f}和phi_A^{i，f}）进行了全面拟合。结果表明：（1）由于实验误差和理论不确定性，很难区分X_{A,s} ^i和X_{A,d} ^i的味对称性破缺效应，其中X_{A,s} ^i和X_{A,d} ^i分别与B_s和B_{u,d}衰变的非因子化湮灭贡献有关.所以X_{A,s} ^i = X_{A,d} ^i是一个很好的近似值。(2)原则上，与因子分解湮没贡献相关且与初始状态无关的参数X_{A} ^f可以被视为B_{u,d,s}衰变的同一变量。(3)从数值上讲，有两个解，一个是（rho_A^i，phi_A^i）=（2.98^+1.12_-0.86，-105^+34_-24）和（rho_A^f，phi_A^f）=（1.18^+0.20_-0.23，-40^+11_-8），另一个是（rho_A^i，phi_A^i）=（2.97^+1.19_-0.90，-105^+32_-24）和（rho_A^f，phi_A^f）=（2.80^+0.25_-0.21，165 ^+4_-3）。显然，非因式分解湮灭参数X_A^i与因式分解湮灭参数X_A^f一般不相等，这与传统的处理方法不同。用拟合的参数，对B_{u,d,s} ->pi pi，pi K，KK衰变的观测量的计算结果与实验数据符合得很好.

英文摘要：

Motivated by the possible large annihilation contributions implied by recent CDF and LHCb measurements on nonleptonic annihilation B meson decays, and the refined experimental measurements on hadronic B meson decays, we study the strength of annihilation contributions within QCD factorization (QCDF) in this paper. With the available measurements of two-body B_{u,d,s} -> pi pi, pi K, K K decays, a comprehensive fit on the phenomenological parameters X_A^{i,f} (or rho_A^{i,f} and phi_A^{i,f}) which are used to parameterize the endpoint singularity in annihilation amplitudes is performed with the statistical chi^2 approach. It is found that (1) flavor symmetry breaking effects are hardly to be distinguished between X_{A,s}^i and X_{A,d}^i due to the large experimental errors and theoretical uncertainties, where X_{A,s}^i and X_{A,d}^i are related to the nonfactorization annihilation contributions in B_s and B_{u,d} decays, respectively. So X_{A,s}^i = X_{A,d}^i is a good approximation by now. (2) In principle, parameter X_{A}^f which is related to the factorization annihilation contributions and independent of the initial state can be regarded as the same variable for B_{u,d,s} decays. (3) Numerically, two solutions are found, one is (rho_A^i, phi_A^i) = (2.98^+1.12_-0.86,-105^+34_-24) and (rho_A^f, phi_A^f) = (1.18^+0.20_-0.23,-40^+11_-8), the other is (rho_A^i, phi_A^i) = (2.97^+1.19_-0.90,-105^+32_-24) and (rho_A^f, phi_A^f) = (2.80^+0.25_-0.21,165^+4_-3). Obviously, nonfactorization annihilation parameter X_A^i is generally unequal to factorization annihilation parameter X_A^f, which differ from the traditional treatment. With the fitted parameters, all results for observables of B_{u,d,s} ->pi pi, pi K, K K decays are in good agreement with experimental data.

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