论文标题
从晶格QCD的非弹性$ \ ell n $散射截面的完全非扰动计算
Towards fully non-perturbative computation of inelastic $\ell N$ scattering cross sections from lattice QCD
论文作者
论文摘要
我们提出了一种完全非扰动方法，以使用晶格QCD计算非弹性Lepton-Nucleon（$ \ ell n $）散射横截面。该方法即使在低能能下也适用，例如与最近和未来中微子核子（$νn$）散射实验相关的能量区域，为此，扰动分析无效。基本的构建块是在欧几里得晶格上计算的前向康普顿散落幅度或hadronic张量。总横截面是通过繁殖相空间因子并整合最终耐药状态的能量和动量来构建的。通过将相位空间因子推广到晶格上的传输矩阵编写的运算符中，可以隐式地执行诱导所有可能最终状态的总和的能量积分。形式主义是从包容性的半蛋白质B梅森腐烂中进口的[P. Gambino，S。Hashimoto，Arxiv：2005.13730]。可以将其推广以计算$ \ ell n $散射横截面及其时刻，以及对核$β$ -Decay的虚拟校正。总结了与要在晶格上计算的康普顿振幅相对应的两个当前插入的必要夸克收缩。
We propose a fully non-perturbative method to compute inelastic lepton-nucleon ($\ell N$) scattering cross sections using lattice QCD. The method is applicable even at low energies, such as the energy region relevant for the recent and future neutrino-nucleon ($νN$) scattering experiments, for which perturbative analysis is invalidated. The basic building block is the forward Compton-scattering amplitude, or the hadronic tensor, computed on a Euclidean lattice. Total cross section is constructed from the hadronic tensor by multiplying a phase space factor and integrating over the energy and momentum of final hadronic states. The energy integral that induces a sum over all possible final states is performed implicitly by promoting the phase space factor to an operator written in terms of the transfer matrix on the lattice. The formalism is imported from that of the inclusive semileptonic B meson decay [P. Gambino, S. Hashimoto, arXiv:2005.13730]. It can be generalized to compute the $\ell N$ scattering cross sections and their moments, as well as the virtual correction to the nuclear $β$-decay. Necessary quark-line contractions for two current insertions corresponding to the Compton amplitude to be computed on the lattice are summarized.
