Transversity in inclusive DIS and novel TMD sum rules

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.

On the connection between quark propagation and hadronization

“…3. Finally, when inserting in a DIS diagram [65,71], which can be justified at large values of Bjorken x where 4-momentum conservation limits the amount of transverse momentum available to final state hadrons [69,75,78], the jet in question can be identified with the current jet.…”

“…The subscripts differ from the conventions discussed in Refs. [65,75], but have been chosen such that they match the customary decomposition of the fragmentation correlator to be discussed in Sect. 3.1.…”

“…Thus, we will be able to prove sum rules for unpolarized fragmentation functions only. Preliminary results on these FF sum rules have been presented at various conferences [75], and the unpolarized case has been discussed in Ref. [72].…”

“…For example, as discussed in Refs. [65,75], the correlation mass m corr also contributes coupled to the collinear transversity PDFs to the inclusive DIS g 2 structure function at large Bjorken x B . Likewise, the correlation mass couples to the collinear transversity FF H 1 in single hadron production of, say, the self-polarizing particle in semi-inclusive e + e − collisions.…”

“…We would like to stress already here that, while the fully inclusive jet correlator also finds an application in the QCD factorization of, e.g., inclusive DIS scattering at large values of the Bjorken x variable [65,[69][70][71][73][74][75][76][77][78][79][80], in this paper we consider this correlator as a theoretical object of intrinsic interest, and as a tool to derive the aforementioned sum rules, independently of any scattering process in which it may find application. In fact, as we will see, the inclusive jet correlator can be rewritten as the gauge invariant propagator of a coloraveraged quark, and the generation of intermediate hadronic states analyzed in terms of the quark's Källen-Lehmann spectral functions.…”