A Bridge from Euclidean Nonperturbative approach to Minkowskian Distribution Functions

TL;DR

This paper proposes a novel method connecting Euclidean nonperturbative QCD approaches with Minkowskian distribution functions, enabling better understanding of parton distributions and nucleon structure.

Contribution

It introduces a new bridge method combining the MIT bag model with Dyson-Schwinger equations to compute parton distribution functions in Minkowski space.

Findings

Calculated longitudinal, transverse, and scalar distribution functions at 2 GeV

Provided insights into dressed effects on nucleon charges

Established a connection between Euclidean and Minkowskian QCD approaches

Abstract

We give out a simple way to connect the parton distribution functions defined in Minkowskian space and the nonperturbative QCD methods grounded in Euclidean space (e.g., lattice QCD(LQCD), Dyson-Schwinger (DS) equations, functional renormalization group (FRG) approach) in this work. We combine the MIT bag model with the DS equation approach to calculate the longitudinal distribution function, transverse distribution function and scalar distribution function in a proton at renormalization point $\mu = 2\,\text{GeV}$. We look then insight into the dressed effects on the axial, tensor and scalar charges in a nucleon to some extent. This method can be regard as a new bridge between the Euclidean non-perturbative approaches and the Minkowskian space physics.