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arXiv 2011.07468hep-phhep-ex
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三体B衰变中的极宽效应

Finite-Width Effects in Three-Body B Decays

Hai-Yang Cheng, Cheng-Wei Chiang, Chun-Khiang Chua

备注：
44 pages, 8 figures, typos corrected, references updated and added, accepted by PRD
发表信息：
Phys. Rev. D 103, 036017 (2021)
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摘要：

通常应用所谓的窄宽度近似$Γ(B\to RP_3\to P_1P_2P_3)=Γ(B\to RP_3)Br(R\to P_1P_2)$来提取准二体衰变$B\to RP_3$的分支分数，其中$R$和$P_3$分别是中间共振态和赝标介子。然而，上面的因式分解仅在零宽度限制下有效。我们考虑一个修正参数$η_R$从有限宽度效应。我们的主要结果是：（i）我们提出了一个计算$η_R$的一般框架，并表明它可以用归一化微分速率表示，并由其在共振时的值确定。(ii)当$m_{12}$远离$m_R$时，我们引入了一个形状因子$F(s_{12},m_R)$用于$R(m_{12})\to P_1P_2$衰减中涉及的强耦合。我们发现离壳层效应在矢量介子产生中很小，但在$K_2^*(1430)$，$σ/f_0(500)$和$K_0^*(1430)$共振中很突出. (iii)我们评估$η_R$的QCD因子分解（QCDF）的理论框架和三体衰变振幅的实验参数化（EXPP）。一般来说，矢量介子的$η_R^{\rm QCDF}$和$η_R^{\rm EXPP}$是相似的，但张量和标量共振的不同。对差别税率的研究使我们能够理解它们之间差别的根源。(iv)在窄宽度近似下得到的$Br(B^-\to RP)_{\rm NWA}$的窄宽度修正通常很小，小于10%，但在$B^-\toσ/f_0(500)π^-$和$B^-\to \overline K_0^{*0}(1430)π^-$衰变中它们是突出的。归一化微分速率的EXPP应该与QCDF计算的理论预测进行对比，因为后者适当地考虑了弱衰变振幅的能量依赖性。

英文摘要：

It is customary to apply the so-called narrow width approximation $Γ(B\to RP_3\to P_1P_2P_3)=Γ(B\to RP_3)Br(R\to P_1P_2)$ to extract the branching fraction of the quasi-two-body decay $B\to RP_3$, with $R$ and $P_3$ being an intermediate resonant state and a pseudoscalar meson, respectively. However, the above factorization is valid only in the zero width limit. We consider a correction parameter $η_R$ from finite width effects. Our main results are: (i) We present a general framework for computing $η_R$ and show that it can be expressed in terms of the normalized differential rate and determined by its value at the resonance. (ii) We introduce a form factor $F(s_{12},m_R)$ for the strong coupling involved in the $R(m_{12})\to P_1P_2$ decay when $m_{12}$ is away from $m_R$. We find that off-shell effects are small in vector meson productions, but prominent in the $K_2^*(1430)$, $σ/f_0(500)$ and $K_0^*(1430)$ resonances. (iii) We evaluate $η_R$ in the theoretical framework of QCD factorization (QCDF) and in the experimental parameterization (EXPP) for three-body decay amplitudes. In general, $η_R^{\rm QCDF}$ and $η_R^{\rm EXPP}$ are similar for vector mesons, but different for tensor and scalar resonances. A study of the differential rates enables us to understand the origin of their differences. (iv) Finite-width corrections to $Br(B^-\to RP)_{\rm NWA}$ obtained in the narrow width approximation are generally small, less than 10\%, but they are prominent in $B^-\toσ/f_0(500)π^-$ and $B^-\to \overline K_0^{*0}(1430)π^-$ decays. The EXPP of the normalized differential rates should be contrasted with the theoretical predictions from QCDF calculation as the latter properly takes into account the energy dependence in weak decay amplitudes.

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