Pion transverse momentum dependent parton distributions in the Nambu and Jona-Lasinio model

Santiago Noguera,Sergio Scopetta

doi:10.1007/jhep11(2015)102

Abstract

An explicit evaluation of the two pion transverse momentum dependent parton distributions at leading twist is presented, in the framework of the Nambu-Jona Lasinio model with Pauli-Villars regularization. The transverse momentum dependence of the obtained distributions is generated solely by the dynamics of the model. Using these results, the so called generalized Boer-Mulders shift is studied and compared with recent lattice data. The obtained agreement is very encouraging, in particular because no additional parameter has been introduced. A more conclusive comparison would require a precise knowledge of the QCD evolution of the transverse momentum dependent parton distributions under scrutiny.

Highlights

The Nambu and Jona-Lasinio (NJL) model is the most realistic model for the pseudoscalar mesons based on a local quantum field theory built with quarks
The NJL model has a long tradition of successful predictions of different observables related to the parton structure of pseudoscalar mesons, such as the parton distribution [18, 19], generalized parton distributions [20], distribution amplitudes [21], transition distribution amplitudes [22, 23], transition form factors [24,25,26]
We have considered the well-established NJL model, without any additional parameter, for the study of the two leading twist pion TMDs, the unpolarized, f1,π(x, kT2 ), and the BoerMulders one, h⊥1,π(x, kT2 )

Summary

TMDs in the NJL model

For a spinless particle, such as the pion, only two leading twist TMDs arise, in contrast to the eight found for spin-. 1 2 particles [3]. TMD f1,π is the unpolarized quark distribution, whereas the Boer-Mulders (BM) function [6], h⊥1,π, describes the distribution of transversely polarized quarks in the pion. The BM function is odd under time reversal (T-odd). A non-zero value for this function is originated by the final and initial state interactions, in the SIDIS and DY processes, respectively, which break the symmetry of the events under time reversal. The calculation of f1,π and h⊥1,π in the NJL model will be described in the following two subsections, respectively

Unpolarized TMD

Boer-Mulders function

Conclusions

A The NJL model and regularization scheme