OPE analysis of the nucleon scattering tensor including weak interaction and finite mass effects

TL;DR

This work provides a comprehensive OPE-based analysis of the nucleon scattering tensor Wμν, incorporating electromagnetic and weak interactions with finite quark masses and higher-twist corrections up to twist-4. By organizing terms through twist and flavor structure, it derives the lowest moments of all 14 structure functions and links them to nucleon matrix elements of local operators, yielding new mass-corrected sum rules and parity-violating relations. The results extend known Callan-Gross–type and Bjorken-type sum rules to include γ–Z0 interference and W± exchange, offering new insights into flavor decomposition and spin-momentum correlations. The framework supports nonperturbative determinations (e.g., lattice QCD) and provides testable predictions for polarization and parity-violating DIS, while noting that higher-order cat-ear effects would require extending the analysis beyond the current order.

Abstract

We perform a systematic operator product expansion of the most general form of the nucleon scattering tensor $W_{μν}$ including electro-magnetic and weak interaction processes. Finite quark masses are taken into account and a number of higher-twist corrections are included. In this way we derive relations between the lowest moments of all 14 structure functions and matrix elements of local operators. Besides reproducing well-known results, new sum rules for parity-violating polarized structure functions and new mass correction terms are obtained.