将动能质量扩展到更高阶的1/m_Q
Extending the Kinetic Mass to Higher Orders in $1/m_Q$
AI总结：
本文提出基于完整QCD的动能质量定义，通过能量动量张量推导出通用质量与极质量的关系，并计算了更高阶的动能质量，为重子展开中的更高阶应用奠定基础。
摘要：
目前，动能质量是通过极质量及阶1/m_Q²的算符定义的，这些在α_s精度下已知到N³LO。同时，包含半轻子衰变的重子展开（HQE）已知到阶1/m_Q⁵。因此，有必要将动能质量的定义扩展到更高阶的1/m_Q。原始动能质量基于重子有效理论（HQET）中的Hadron-质量公式。然而，HQE是通过在完整QCD中定义的矩阵元来表述的，以避免非局部矩阵元的出现。为了避免这一点，我们开发了一种基于完整QCD的动能质量定义。从完整QCD的能量动量张量推导出的Hadron-质量公式出发，我们定义了一个通用质量与极质量之间的关系。利用简单的截断方案，我们计算了阶1/m_Q的所有幂次的广义动能质量，其结果与已知的动能质量结果在阶1/m_Q²下一致。我们的方法为在重子展开中一致使用动能质量的更高阶提供了道路。
英文摘要：
Currently, the kinetic mass is defined in terms of the pole mass and operators at order $1/m_Q^2$, which are known to N$^3$LO accuracy in $α_s$. At the same time, the Heavy Quark Expansion (HQE) for inclusive semileptonic decays is known up to and including terms of order $1/m_Q^5$. Therefore, it is desirable to extend the definition of the kinetic mass to higher orders in $1/m_Q$. The original kinetic mass is based on the hadron-mass formula in Heavy Quark Effective Theory (HQET). However, the HQE is formulated in terms of matrix elements defined in full QCD to avoid the appearance of non-local matrix elements. To avoid this, we develop a definition of the kinetic mass rooted in full QCD. Starting from the hadron-mass formula derived from the energy-momentum tensor of full QCD, we define a relation between a general mass and the pole mass. Using a simple cut-off scheme, we compute a generalized kinetic mass at one loop to all powers of $1/m_Q$, which reproduces the well-known results for the kinetic mass up to $1/m_Q^2$. Our approach opens the road to a consistent use of the kinetic mass at higher-orders in the heavy quark expansion.
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