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arXiv 1111.1849hep-ph
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大反冲时重到轻子形状因子

Heavy-to-light baryonic form factors at large recoil

Thomas Mannel, Yu-Ming Wang

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19 pages
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摘要：

我们分析了大反冲下的重子到轻子的形状因子，导出了这些形状因子在重夸克极限下的标度行为。结果表明，在轻重子的大反冲极限下，只需要一个普适的形状因子就可以将Lambda_b参数化为p和Lambda_b参数化为Lambda矩阵元，而在σ重子的大能量极限下，由于时空宇称对称性，Lambda_b到σ跃迁的强子矩阵元消失了.利用前导共形自旋下的核子分布振幅，导出了引起Lambda_b到p跃迁的软形状因子eta（P^{ \prime } \cdot v）的标度律，P^{ \prime }和v分别为核子动量和Lambda_b重子速度.特别地，我们验证了这种标度行为与在重夸克极限下的光锥求和规则方法完全一致。利用这些形状因子，我们进一步研究了Lambda_b到Lambda_gamma中的Lambda重子极化不对称性α和Lambda_b到Lambda_l^{+} l^{-}中的前后不对称性A_{FB}.这两个观测量（α和A_{FB}）都与强子形状因子无关，其主导幂为1/m_b，主导阶为α_s。我们还扩展了对Omega_b到Omega跃迁到罕见的Omega_b到Omega_gamma和Omega_b到Omega_l^{+} l^{-}衰变的强子矩阵元的分析，发现辐射Omega_b到Omega_gamma衰变可能是最有希望的FCNC b到s辐射重子衰变通道。此外，有趣的是注意到，如果形状因子\bar夸克模型在数值上与所指示的一样小，则Omega_b到Omega l^{+} l ^{-}的前后不对称的零点与Lambda_b到Lambda l^{+} l^{-}到首阶精度的零点相同。

英文摘要：

We analyze heavy-to-light baryonic form factors at large recoil and derive the scaling behavior of these form factors in the heavy quark limit. It is shown that only one universal form factor is needed to parameterize Lambda_b to p and Lambda_b to Lambda matrix elements in the large recoil limit of light baryons, while hadronic matrix elements of Lambda_b to Sigma transition vanish in the large energy limit of Sigma baryon due to the space-time parity symmetry. The scaling law of the soft form factor eta(P^{\prime} \cdot v), P^{\prime} and v being the momentum of nucleon and the velocity of Lambda_b baryon, responsible for Lambda_b to p transitions is also derived using the nucleon distribution amplitudes in leading conformal spin. In particular, we verify that this scaling behavior is in full agreement with that from light-cone sum rule approach in the heavy-quark limit. With these form factors, we further investigate the Lambda baryon polarization asymmetry alpha in Lambda_b to Lambda gamma and the forward-backward asymmetry A_{FB} in Lambda_b to Lambda l^{+} l^{-}. Both two observables (alpha and A_{FB}) are independent of hadronic form factors in leading power of 1/m_b and in leading order of alpha_s. We also extend the analysis of hadronic matrix elements for Omega_b to Omega transitions to rare Omega_b to Omega gamma and Omega_b to Omega l^{+} l^{-} decays and find that radiative Omega_b to Omega gamma decay is probably the most promising FCNC b to s radiative baryonic decay channel. In addition, it is interesting to notice that the zero-point of forward-backward asymmetry of Omega_b to Omega l^{+} l^{-} is the same as the one for Lambda_b to Lambda l^{+} l^{-} to leading order accuracy provided that the form factors \barζ_i (i=3, 4, 5) are numerically as small as indicated from the quark model.

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