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  • Letter
  • Open Access

Parton distribution function in a pion with Minkowskian dynamics

W. de Paula1, E. Ydrefors2, J. H. Alvarenga Nogueira1,3,4, T. Frederico1, and G. Salmè4

  • 1Instituto Tecnológico de Aeronáutica, DCTA, 12228-900 São José dos Campos, Brazil
  • 2Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
  • 3Dipartimento di Fisica, Università di Roma La Sapienza”, Piazzale A. Moro 2, 00185 Rome, Italy
  • 4INFN, Sezione di Roma, Piazzale A. Moro 2, 00185 Rome, Italy

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Phys. Rev. D 105, L071505 – Published 26 April, 2022

DOI: https://doi.org/10.1103/PhysRevD.105.L071505

Abstract

The parton distribution of the pion is obtained for the first time from the solution of a dynamical equation in Minkowski space. The adopted equation is the homogeneous Bethe-Salpeter one with a ladder kernel, described in terms of (i) constituent quarks and gluons degrees of freedom, and (ii) an extended quark-gluon vertex. The masses of quark and gluon as well as the interaction-vertex scale have been chosen in a range suggested by lattice QCD calculations, and calibrated to reproduce both pion mass and decay constant. In addition to the full parton distribution, we have also calculated the contribution from the light-front valence wave function, corresponding to the lowest Fock component in the expansion of the pion state. After applying an evolution with an effective charge and a LO splitting function, a detailed and inspiring comparison with both the extracted experimental data (with and without resummation effects) and other recent calculations obtained in different frameworks is presented. Interestingly, in a wide region of longitudinal-momentum fraction, the parton distribution function receives sizable contributions from the higher Fock-components of the pion state at the initial scale, while approaching the tail the light-front valence component dominates, as expected. Moreover, an exponent ∼3 is found suitable for describing the tail at the scale 5.2 GeV.

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Phys. Rev. D 105, L071505– Published 26 April, 2022
  • Received 4 April 2022
  • Accepted 13 April 2022
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