# Off-shell quark bilinear operator Green's functions at two loops

## TL;DR

This paper computes two-loop Green's functions for off-shell quark bilinear operators, including mass, vector, tensor, and Wilson operators, providing detailed theoretical results for quantum chromodynamics calculations.

## Contribution

It presents the first detailed two-loop calculations of off-shell Green's functions for various quark bilinear operators in a general off-shell configuration.

## Key findings

- Two-loop Green's functions for quark bilinear operators are explicitly constructed.
- Results include mass, vector, tensor, and Wilson operators in off-shell configurations.
- Provides foundational data for precision QCD computations.

## Abstract

We construct the two loop Green's functions for a quark bilinear operator inserted at non-zero momentum in a quark 2-point function for the most general off-shell configuration. In particular we consider the quark mass operator, vector and tensor currents as well as the second moment of the flavour non-singlet Wilson operator.