重夸克强子共振态的在壳递推与全纯重夸克有效理论
On-shell recursion and holomorphic HQET for heavy quark hadronic resonances
AI总结：
提出基于在壳递推和全纯HQET的新框架，处理重夸克共振态，以复数动量展开，兼容B和D双重态数据，并生成大尾巴线形。
摘要：
我们为重夸克有效理论（HQET）框架内处理重夸克（HQ）共振态开发了一个新的理论框架。该框架利用在壳递推技术将共振振幅表示为在壳子振幅的乘积，从而能够采用形状因子表示强子矩阵元，并获得重夸克展开，但代价是引入复数动量。我们构建了一个广义的“全纯重夸克有效理论”（holomorphic HQET），使得此类复数动量矩阵元可以与之匹配，并证明$PT$对称性确保了Isgur-Wise函数（以及微扰修正）成为具有实系数的复数反冲参数的解析函数。因此，它们是标准HQET描述的解析延拓。该框架允许重夸克强子（强衰变）宽度展开。在二阶，我们证明它与$B_{1(2)}^{(*)}$和$D_{1(2)}^{(*)}$重夸克双重态的数据兼容。以$\bar{B} \to (D_1^*(1^-) \to Dπ)lν$系统为例，我们计算了全纯HQET展开至一阶，以及复数动量在壳子振幅。对所得微分率的玩具数值研究表明，该框架生成具有大尾巴的重夸克共振线形，与数据中观察到的相似。
英文摘要：
We develop a new theoretical framework for the treatment of heavy quark (HQ) resonances within heavy quark effective theory (HQET). This framework uses on-shell recursion techniques to express the resonant amplitude as a product of on-shell subamplitudes, which allows one to employ a form-factor representation of the hadronic matrix elements and to obtain an HQ expansion, but at the price of introducing complex momenta. We construct a generalized ``holomorphic HQET'' onto which such complex-momentum matrix elements can be matched, and we show that $PT$ symmetry ensures the Isgur-Wise functions (and the perturbative corrections) become holomorphic functions of the complex recoil parameter with real coefficients. They are thus an analytic continuation of the standard HQET description. This framework admits a HQ hadron (strong decay) width expansion. At second order, we show it is compatible with data for the $B_{1(2)}^{(*)}$ and $D_{1(2)}^{(*)}$ HQ doublets. Taking the $\bar{B} \to (D_1^*(1^-) \to Dπ)lν$ system as an example, we compute the holomorphic HQET expansion to first order, as well as the complex-momentum on-shell subamplitudes. A toy numerical study of the resulting differential rates demonstrates that this framework generates HQ resonance lineshapes with large tails, resembling those seen in data.
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