A quark model analysis of the transversity distribution

TL;DR

This work investigates the transversity distribution $h_1(x,Q^2)$, a chiral-odd twist-2 parton function inaccessible in inclusive DIS, by computing it within the nonrelativistic Isgur-Karl framework and the relativistic MIT bag model. By anchoring to a hadronic scale $\mu_0^2$ and applying LO QCD evolution, the authors show that $h_1$ and the helicity distribution $g_1$ evolve differently and diverge, especially at small $x$, despite similar initial conditions. They test Soffer's inequalities, which relate $h_1$ to $f_1$ and $g_1$, and find approximate compatibility after evolution, with the level of agreement depending on the hadronic scale and presence of gluons. The study highlights the importance of the hadronic input and evolution for interpreting transversity and guides experimental expectations in polarized Drell-Yan and SIDIS experiments.

Abstract

The feasibility of measuring chiral-odd parton distribution functions in polarized Drell-Yan and semi-inclusive experiments has renewed theoretical interest in their study. Models of hadron structure have proven succesful in describing the gross features of the chiral-even structure functions. Similar expectations support our study of the transversity parton distributions in the Isgur-Karl and MIT bag models. We confirm the diverse low x behavior of the transversity and spin structure functions at the experimental scale and show that it is fundamentally a consequence of the different behavior under evolution of these functions. The inequalities of Soffer establish constraints between data and model calculations of the chiral-odd transversity function. The approximate compatibility of our model calculations with these constraints conferes credibility to our estimates.