PDFs and Neutrino-Nucleon Scattering from Hadronic Tensor

Jian Liang, Keh-Fei Liu
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引用次数: 3

Abstract

We review the Euclidean path-integral formulation of the nucleon hadronic tensor and classify the gauge invariant and topologically distinct insertions in terms of connected and disconnected insertions and also in terms of leading and higher-twist contributions in the DIS region. Converting the Euclidean hadronic tensor back to the Minkowski space requires solving an inverse problem of the Laplace transform. We have investigated several inverse algorithms and studied the pros and cons of each. We show a result with a relatively large momentum transfer ($Q^2 \sim 4\, {\rm GeV^2}$) to suppress the elastic scattering and reveal the contributions from the resonance and inelastic region of the neutrino-nucleon scattering. For elastic scattering, the hadronic tensor is the the product of the elastic form factors for the two corresponding currents. We checked numerically for the case of two charge vector currents ($V_4$) with the electric form factor calculated from the three-point function and found they agree within errors.
pdf和强子张量中的中微子-核子散射
我们回顾了核子强子张量的欧几里得路径积分公式,并根据连接和断开插入以及根据DIS区域的领先和高扭转贡献对规范不变和拓扑不同的插入进行了分类。将欧几里德强子张量转换回闵可夫斯基空间需要求解拉普拉斯变换的逆问题。我们研究了几种逆算法,并研究了每种算法的优缺点。我们展示了一个相对较大的动量转移($Q^2 \sim 4\, {\rm GeV^2}$)抑制弹性散射的结果,并揭示了共振区和非弹性区对中微子-核子散射的贡献。对于弹性散射,强子张量是两个对应电流的弹性形状因子的乘积。我们对两个电荷矢量电流($V_4$)的情况用三点函数计算的电形因子进行了数值检查,发现它们在误差范围内一致。
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