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arXiv 1202.4100hep-ph
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重夸克有效理论中重子衰变Lambda_b -> Lambda_c cell nu的新结果

New results on the baryon decay Lambda_b -> Lambda_c ell nu in Heavy Quark Effective Theory

F. Jugeau, Yu Jia, L. Oliver

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摘要：

在LHCb上将详细测量重子衰变$Λ_b \to Λ_c \ell \barν_\ell$的重子微分谱。我们在重夸克有效理论的重夸克展开式中得到了一些新的形状因子，这些结果对解释实验数据是有用的。我们制定了一个求和规则的弹性subleading形状因子$A(w)$在顺序$1/m_Q$，起源于拉格朗日微扰$\mathcal{L}_{kin}$。在求和规则中，仅出现中间状态$(j^P, J^P) = (0^+, {1 \over 2}^+)$，其也进入对轴向形状因子$G_1(w)$的$1/{m_Q^2}$校正中，其有助于零反冲$w = 1$处的微分速率。这个结果，与另一个总和规则在前进方向上的$|G_1(1)|^2$，允许我们获得一个下限的修正在零反冲$- δ_{1/{m_Q^2}}^{(G_1)}$的衍生物$A'_1(1)$和斜率$ρ^2_Λ$和曲率$σ^2_Λ$的弹性Isgur-Wise功能$ξ_Λ(w)$。另一个理论含义是，对于$ρ^2_Λ$和$σ^2_Λ$之间的某种关系，以及对于$ρ^2_Λ\to 0$，$A'(1)$必须为零，从而在前导IW函数$ξ_Λ(w)$和子前导IW函数$A(w)$之间建立非平凡的相关性。这两个函数的现象学估计允许获得$- δ_{1/{m_Q^2}}^{(G_1)}$的下限。

英文摘要：

The baryon differential spectrum of the baryon decay $Λ_b \to Λ_c \ell \barν_\ell$ will be measured in detail at LHCb. We obtain new results on the form factors in the heavy quark expansion of Heavy Quark Effective Theory that can be useful in the interpretation of the data. We formulate a sum rule for the elastic subleading form factor $A(w)$ at order $1/m_Q$, that originates from the Lagrangian perturbation $\mathcal{L}_{kin}$. In the sum rule appear only the intermediate states $(j^P, J^P) = (0^+, {1 \over 2}^+)$, entering also in the $1/{m_Q^2}$ correction to the axial form factor $G_1(w)$, that contributes to the differential rate at zero recoil $w = 1$. This result, together with another sum rule in the forward direction for $|G_1(1)|^2$, allows us to obtain a lower bound for the correction at zero recoil $- δ_{1/{m_Q^2}}^{(G_1)}$ in terms of the derivative $A'_1(1)$ and the slope $ρ^2_Λ$ and curvature $σ^2_Λ$ of the elastic Isgur-Wise function $ξ_Λ(w)$. Another theoretical implication is that $A'(1)$ must vanish for some relation between $ρ^2_Λ$ and $σ^2_Λ$, as well as for $ρ^2_Λ\to 0$, establishing a non-trivial correlation between the leading IW function $ξ_Λ(w)$ and the subleading one $A(w)$. A phenomenological estimation of these two functions allows to obtain a lower bound on $- δ_{1/{m_Q^2}}^{(G_1)}$.

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