Pion model with the Nakanishi integral representation

Authors

  • R. Moreira Moita Instituto Tecnologico de Aeronáutica, DCTA
  • Joao de Mello LFTC - Univeridade Cruzeiro do Sul / UNICID
  • T. Federico Instituto Tecnologico de Aeronáutica, DCTA
  • W. de Paula Instituto Tecnologico de Aeronáutica, DCTA

DOI:

https://doi.org/10.31349/SuplRevMexFis.3.0308089

Keywords:

QCD, Pion, Bethe-Salpeter amplitude, Nakanishi Integral Representation.

Abstract

In the present work, we describe a model for the pion based on an analytic expression for the Bethe-Salpeter (BSA) amplitude, combined with some ingredients from Lattice QCD calculations. The running quark mass function M(p2), used here, reproduces well the results of Lattice QCD calculations. The analytical form of the running quark mass function contains a single time-like pole, which implies in time-like poles of the dressed quark propagator. Such a form allows to build the weight functions, Gi(γ, z), for the Nakanishi integral representation of each scalar function, χi(k, p), appearing in the decomposition of the Bethe-Salpeter amplitude in terms of Dirac operators. Such scalar amplitudes can also be used to obtain the pion valence light-front wave function.

References

C. Itzkyson and J.-B.Zuber, ”Quantum Field Theory”, McGraw-Hill, New York, International Series In Pure and Applied Physics, (1980).

I. C. Cloët and C. D. Roberts, Explanation and Prediction of Observables using Continuum Strong QCD, Prog. Part. Nucl. Phys. 77 (2014) 1.

R. Moita, J. P. B. C. de Melo, K. Tsushima and T. Frederico, Exploring the flavor content of light and heavy-light pseudoscalars, Phys. Rev. D 104 (2021) 096020, doi: 10.1103/Phys-RevD.104.096020

M. B. Parappilly, P. O. Bowman, U. M. Heller, D. B. Leinweber, A. G. Williams and J. B. Zhang, Scaling behavior of quark

propagator in full QCD, Phys. Rev. D 73 (2006) 054504.

C. S. Mello, J. P. B. C. Melo and T. Frederico, Minkowski space pion model inspired by lattice QCD running quark mass, Phys.

Lett. B766 (2017) 86.

J. P. B. C. de Melo, R. M. Moita and T. Frederico, Pion observables with the Minkowski Space Pion Model, PoS LC2019 (2019) 037, doi=10.22323/1.374.0037.

E. Rojas, J. P. B. C. de Melo, B. El-Bennich, O. Oliveira and T. Frederico, On the Quark-Gluon Vertex and Quark-Ghost Kernel: combining Lattice Simulations with Dyson-Schwinger equations, JHEP 1310 (2013) 193.

O. Oliveira, W. de Paula, T. Frederico and J. P. B. C. de Melo, The Quark-Gluon Vertex and the QCD Infrared Dynamics, Eur.

Phys. J. C 79 (2019) 116, doi:10.1140/epjc/s10052-019-6617-7

W. de Paula, T. Frederico, G. Salmè and M. Viviani, Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space, Phys. Rev. D 94 (2016) 071901, doi:10.1103/PhysRevD.94.071901

W. de Paula, T. Frederico, G. Salmè, M. Viviani and R. Pimentel, Fermionic bound states in Minkowski-space: Light-cone singularities and structure, Eur. Phys. J. C 77 (2017) 764, doi:10.1140/epjc/s10052-017-5351-2

E. Ydrefors, W. de Paula, J. H. A. Nogueira, T. Frederico and G. Salmé, Phys. Lett. B 820 (2021), 136494

doi:10.1016/j.physletb.2021.136494 [arXiv:2106.10018 [hep-ph]].

W. de Paula, E. Ydrefors, J. H. Alvarenga Nogueira, T. Frederico and G. Salmè, Observing the Minkowskian dynamics of the pion on the null-plane, Phys. Rev. D 103 (2021) 014002, doi:10.1103/PhysRevD.103.014002

Downloads

Published

2022-06-14

How to Cite

1.
Moreira Moita R, de Mello J, Federico T, de Paula W. Pion model with the Nakanishi integral representation. Supl. Rev. Mex. Fis. [Internet]. 2022 Jun. 14 [cited 2022 Dec. 7];3(3):0308089 1-5. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/6192