Transverse Momentum and Transverse Momentum Distributions in the MIT Bag Model

TL;DR

This paper calculates transverse momentum dependent distribution functions in the MIT Bag Model, finding larger widths than previous models and good agreement with experimental data after evolution to higher scales.

Contribution

It introduces a generalized relativistic formalism to compute TMDs in the MIT Bag Model, resulting in larger transverse momentum widths and improved experimental agreement.

Findings

Transverse momentum widths are significantly larger than previous calculations.

The model's TMDs agree well with experimental data after evolution.

The formalism enables detailed examination of $k_T$ dependence.

Abstract

The typical transverse momentum of a quark in the proton is a basic property of any QCD based model of nucleon structure. However, calculations in phenomenological models typically give rather small values of transverse momenta, which are difficult to reconcile with the larger values observed in high energy experiments such as Drell-Yan reactions and Semi-inclusive deep inelastic scattering. In this letter we calculate the leading twist transverse momentum dependent distribution functions (TMDs) using a generalization of the Adelaide group's relativistic formalism that has previously given good fits to the parton distributions. This enables us to examine the $k_{T}$ dependence of the TMDs in detail, and determine typical widths of these distributions. These are found to be significantly larger than those of previous calculations. We then use TMD factorization in order to evolve these distributions up to experimental scales where we can compare with data on $\langle k_{T} \rangle$ and $\langle k^{2}_{T} \rangle$. Our distributions agree well with this data.