论文标题
三体B衰变的有限宽度效果
Finite-Width Effects in Three-Body B Decays
论文作者
论文摘要
习惯应用所谓的狭窄宽度近似$γ（b \ to rp_3 \ to p_1p_2p_3）=γ（b \ to rp_3）br（r \ to p_1p_2）$提取Quasi-two-two-two-body decay $ b \ $ rp $ $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp $ rp_3和伪级介子。但是，上述分解仅在零宽度限制中有效。我们考虑有限宽度效果的校正参数$η_r$。我们的主要结果是：（i）我们提出了计算$η_r$的一般框架，并表明它可以根据归一化的差异率表示，并根据其在共振时的值确定。 （ii）我们为$ r（m_ {12}）\涉及的强耦合介绍了一个formation $ f（s_ {12}，m_r）$，当$ r（m_ {12}）\与p_1p_2 $衰减时，当$ m_ {12} $远离$ m_r $时。我们发现，媒介媒介作品中的外壳效果很小，但在$ k_2^*（1430）$，$σ/f_0（500）$和$ k_0^*（1430）$ resonances中突出。 （iii）我们在QCD分解（QCDF）的理论框架和实验参数化（EXPP）中评估了$η_r$的三体衰减振幅。通常，$η_r^{\ rm qcdf} $和$η_r^{\ rm expp} $对于矢量中的介子是相似的，但对于张量和标量共振而不同。对差异率的研究使我们能够了解其差异的起源。 （iv）以$ br（b^ - \至rp）的有限宽度校正_ {\ rm nwa} $在狭窄的宽度近似中获得通常很小，小于10 \％，但它们在$ b^ - \ ttoσ/f_0（500）（500）π^ - $ b^ - $ b^ - $ b^ - $ b^ - $ \ tline^tline^tline^tline^tline^ - $ y;腐烂。归一化差异速率的EXPP应与QCDF计算的理论预测形成对比，因为后者正确考虑了弱衰减幅度的能量依赖性。
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.
