标题： 从格点QCD走向核子的hadronic张量 显示英文标题

标题： Towards the nucleon hadronic tensor from lattice QCD

摘要： 我们首次在晶格上计算了核子的hadronic张量。该张量可以用于提取深非弹性散射中的结构函数，同时也为中微子-核子散射提供了信息，这对低能中微子-原子核散射实验至关重要。计算中最具挑战的部分是解决一个反问题。我们使用模拟数据实现了并测试了三种算法，结果显示贝叶斯重建方法在提取峰值结构方面具有最佳分辨率，而Backus-Gilbert和最大熵方法对于平滑谱函数稍微更稳定。数值结果展示了弹性情况（域墙构型上的clover费米子，参数为$m_\pi\sim$ 370 MeV 和$a\sim$ 0.06 fm）以及大动量转移情况（各向异性clover晶格，参数为$m_\pi\sim$ 380 MeV 和$a_t\sim$ 0.035 fm）下的结果。对于前者，重建出的闵可夫斯基hadronic张量精确地给出了矢量电荷，证明了该方法的可行性。而对于后者，核共振及可能的浅层非弹性散射贡献在大约$\nu=1$ GeV 处被清晰观测到，但对于更高激发态（$\nu>2$ GeV），未获得相关信息。通过不同晶格设置下$\rho$ 介子的有效质量检查表明，为了达到更高的能量转移，使用较小晶格间距的晶格是至关重要的。 显示英文摘要

摘要： We present the first calculation of the hadronic tensor on the lattice for the nucleon. The hadronic tensor can be used to extract the structure functions in deep inelastic scatterings and also provide information for the neutrino-nucleon scattering which is crucial to the neutrino-nucleus scattering experiments at low energies. The most challenging part in the calculation is to solve an inverse problem. We have implemented and tested three algorithms using mock data, showing that the Bayesian Reconstruction method has the best resolution in extracting peak structures while the Backus-Gilbert and Maximum Entropy methods are somewhat more stable for the flat spectral function. Numerical results are presented for both the elastic case (clover fermions on domain wall configuration with $m_\pi\sim$ 370 MeV and $a\sim$ 0.06 fm) and a case (anisotropic clover lattice with $m_\pi\sim$ 380 MeV and $a_t\sim$ 0.035 fm) with large momentum transfer. For the former case, the reconstructed Minkowski hadronic tensor gives precisely the vector charge which proves the feasibility of the approach. While for the latter case, the nucleon resonances and possibly shallow inelastic scattering contributions around $\nu=1$ GeV are clearly observed but no information is obtained for higher excited states with $\nu>2$ GeV. A check of the effective masses of $\rho$ meson with different lattice setups indicates that, in order to reach higher energy transfers, using lattices with smaller lattice spacings is essential.