Eur. Phys. J. C (2016) 76: 253
https://doi.org/10.1140/epjc/s10052-016-4101-1

Regular Article - Theoretical Physics

Pion generalized parton distributions within a fully covariant constituent quark model

¹ Laboratory for Nuclear Science, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA, 02139, USA
² Physics Department “Tor Vergata” University and INFN Sezione di Tor Vergata, Via della Ricerca Scientifica 1, 00133, Rome, Italy
³ Rutherford-Appleton Lab., STFC, Harwell Campus, Didcot, OX11 0QX, UK
⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Roma, P.le A. Moro 2, 00185, Rome, Italy
⁵ Physìcs Department, “La Sapienza” University, P.le A. Moro 2, 00185, Rome, Italy
⁶ I.I.S. G. De Sanctis, Via Cassia 931, 00189, Rome, Italy

^* e-mail: salmeg@roma1.infn.it

Received: 15 March 2016
Accepted: 18 April 2016
Published online: 3 May 2016

Abstract

We extend the investigation of the generalized parton distribution for a charged pion within a fully covariant constituent quark model, in two respects: (1) calculating the tensor distribution and (2) adding the treatment of the evolution, needed for achieving a meaningful comparison with both the experimental parton distribution and the lattice evaluation of the so-called generalized form factors. Distinct features of our phenomenological covariant quark model are: (1) a 4D Ansatz for the pion Bethe–Salpeter amplitude, to be used in the Mandelstam formula for matrix elements of the relevant current operators, and (2) only two parameters, namely a quark mass assumed to be MeV and a free parameter fixed through the value of the pion decay constant. The possibility of increasing the dynamical content of our covariant constituent quark model is briefly discussed in the context of the Nakanishi integral representation of the Bethe–Salpeter amplitude.