Nucleon quasi-Parton Distributions in the large N$_c$ limit

TL;DR

This paper explores nucleon quasi-parton distribution functions within the chiral quark soliton model, revealing how high nucleon velocities affect distribution positivity and the convergence to standard parton distributions.

Contribution

It introduces sum-rules for quasi-parton distributions depending on nucleon velocity and Dirac matrices, and provides numerical analysis within the chiral quark soliton model.

Findings

Anti-quark distribution breaks positivity at high velocities.

Large nucleon momentum needed for quasi-distributions to approximate standard PDFs.

Sum-rules depend on nucleon velocity and Dirac matrix.

Abstract

In this letter, we investigate the nucleon quasi-parton distribution functions in the chiral quark soliton model. We derive a set of sum-rules depending on the velocity of the nucleon and on the Dirac matrix defining the distribution functions. We present numerical results for the isosinglet unpolarized distribution, in which we find that the anti-quark distribution breaks the positivity condition at nucleon velocities $v\approx 0.99\;(P_N\approx 7.0 M_N)$ and smaller. We found that, for the isosinglet unpolarized case, a large nucleon momentum is required for the quasi-parton distribution to get close enough to the usual parton distribution function.