On the extraction of the valence transversity distributions from SIDIS data

TL;DR

This paper discusses methods to extract the valence transversity distributions of u and d quarks from SIDIS data, proposing new ratio-based measurements to improve direct access to these distributions.

Contribution

It introduces a novel approach using ratios of SIDIS cross sections to directly determine the transversity ratio without relying on the Collins function.

Findings

Proposes ratios of spin asymmetries to extract transversity.

Suggests new measurements involving cross section ratios.

Provides numerical estimates for the proposed method.

Abstract

The transversity distribution for $u$ and $d$ quarks is usually extracted from data on spin asymmetries in Semi Inclusive Deep Inelastic Scattering (SIDIS): however, due to its chiral odd nature, it has to be coupled to another chiral odd function, typically the Collins or the di-hadron fragmentation function. A recent suggestion of considering SIDIS data involving ratios of spin asymmetries and avoiding a knowledge of the Collins function, is briefly discussed. New measurements, involving ratios of cross sections, are suggested. They would allow a direct extraction of the transversity ratio, $h_1^{d_V}/h_1^{u_V}$. Numerical estimates are given.