Transversity in inclusive DIS and novel TMD sum rules

TL;DR

This paper introduces a new non-perturbative spin-flip term in inclusive DIS that impacts the $g_2$ structure function and breaks the Burkhardt-Cottingham sum rule, along with deriving novel TMD sum rules.

Contribution

It presents a novel non-perturbative spin-flip term linked to the hadronic invariant mass and derives new TMD sum rules relating fragmentation functions to the quark propagator.

Findings

The new term can explain discrepancies in $g_2$ calculations.

It breaks the Burkhardt-Cottingham sum rule.

A complete set of momentum sum rules for TMD fragmentation functions is established.

Abstract

A reanalysis of collinear factorization for inclusive Deep Inelastic Scattering shows that a novel, non perturbative spin-flip term associated with the invariant mass of the produced hadrons couples, at large enough Bjorken $x_B$, to the target's transversity distribution function. The resulting new contribution to the $g_2$ structure function can potentially explain the discrepancy between recent calculations and fits of this quantity. The new term also breaks the Burkhardt-Cottingham sum rule, now featuring an interplay between the $g_2$ and $h_1$ functions that calls for a re-examination of their small-$x$ behavior. As part of the calculation leading to these results, a new set of TMD sum rules is derived by relating the single-hadron quark fragmentation correlator to the fully dressed quark propagator by means of integration over the hadronic momenta and spins. A complete set of momentum sum rules is obtained for transverse-momentum-dependent quark fragmentation functions up to next-to-leading twist.