Highlights of pion and kaon structure from continuum analyses


  • Khépani Raya Universidad de Granada
  • José Rodríguez-Quintero University of Huelva




Nambu-Goldstone bosons, generalized parton distributions, continuum Schwinger methods


One of the biggest challenges in contemporary physics is understanding the origin and dynamics of the internal structure of hadrons which, at a fundamental level, is described by quantum chromodynamics (QCD). Taking great prominence amongst hadrons are pions and kaons which, despite being the lightest hadrons in nature, their very existence is intimately connected to those mechanisms responsible for almost all of the mass of the visible matter. In this manuscript we discuss many aspects of the pion and kaon structure via light front wave functions and generalized parton distributions, and a collection of other distributions and structural properties that are inferred therefrom.


G. P. Lepage and S. J. Brodsky, Exclusive Processes in Perturbative Quantum Chromodynamics. Phys. Rev. D, 22 (1980) 2157.

G. Peter Lepage and S. J. Brodsky, Exclusive Processes in Quantum Chromodynamics Evolution Equations for Hadronic Wave Functions and the Form-Factors of Mesons. Phys. Lett. B, 87 (1979) 359

E. L. Berger and S. J. Brodsky, Quark Structure Functions of Mesons and the Drell-Yan Process. Phys. Rev. Lett., 42 (1979) 940

G. R. Farrar and D. R. Jackson, Pion and Nucleon Structure Functions Near x = 1. Phys. Rev. Lett., 35 (1975) 1416

C. D Roberts, Empirical Consequences of Emergent Mass. Symmetry, 12 (2020) 1468

J. Rodríguez-Quintero, L. Chang, K. Raya, and C. D. Roberts, Process-independent effective coupling and the pion structure function. J. Phys. Conf. Ser., 1643 (2020) 012177

Z.-F. Cui et al., Effective charge from lattice QCD. Chin. Phys. C, 44 (2020) 083102

José Rodríguez-Quintero, Daniele Binosi, Cedric Mezrag, Joannis Papavassiliou, and Craig D. Roberts. Process in dependent effective coupling. From QCD Green’s functions to phenomenology. Few Body Syst., 59 (2018) 121

D, Binosi, C. Mezrag, J. Papavassiliou, C. D. Roberts, and J. Rodríguez-Quintero. Processindependent strong running coupling. Phys. Rev. D, 96 (2017) 054026

R. Hofstadter, Electron scattering and nuclear structure. Rev. Mod. Phys., 28 (1956) 214

M. Breidenbach et al., Observed behavior of highly inelastic electron-proton scattering. Phys. Rev. Lett., 23 (1969) 935

R. Keith Ellis, W. James Stirling, and B. R. Webber, QCD and collider physics, volume 8. (Cambridge University Press, 2 2011)

I. G. Aznauryan et al., Studies of Nucleon Resonance Structure in Exclusive Meson Electroproduction. Int. J. Mod. Phys. E, 22 (2013) 1330015

C. D. Roberts, D. G. Richards, T. Horn, and L. Chang, Insights into the emergence of mass from studies of pion and kaon structure. Prog. Part. Nucl. Phys., 120 (2021) 103883

J. Arrington et al., Revealing the structure of light pseudoscalar mesons at the electron-ion collider. J. Phys. G, 48 (2021) 075106

A. C. Aguilar et al., Pion and Kaon Structure at the ElectronIon Collider. Eur. Phys. J. A, 55 (2019) 190

D. P. Anderle et al., Electron-ion collider in China. Front. Phys. (Beijing), 16 (2021) 64701

B. Adams et al., Letter of Intent A New QCD facility at the M2 beam line of the CERN SPS (COMPASS++/AMBER). 8 (2018)

K. Raya, Z.-F. Cui, L. Chang, J.-M. Morgado, C. D. Roberts, and J. Rodríguez-Quintero, Revealing pion and kaon structure via generalised parton distributions. 9 (2021)

A. V. Efremov and A. V. Radyushkin, Factorization and Asymptotical Behavior of Pion Form-Factor in QCD. Phys. Lett. B, 94 (1980) 245

Y. L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e +e − Annihilation by Perturbation Theory in Quantum Chromodynamics. Sov. Phys. JETP, 46 (1977) 641,

V. N. Gribov and L. N. Lipatov, Deep inelastic e p scattering in perturbation theory. Sov. J. Nucl. Phys., 15 (1972) 438

L. N. Lipatov, The parton model and perturbation theory. Yad. Fiz., 20 (1974) 181

G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B, 126 (1977) 298

C. D. Roberts and A. G. Williams. D.-Schwinger, equations and their application to hadronic physics. Prog. Part. Nucl. Phys., 33 (1994) 477

G. Eichmann, H. Sanchis-Alepuz, R. Williams, R. Alkofer, and C. S. Fischer, Baryons as relativistic three-quark bound states. Prog. Part. Nucl. Phys., 91 (2016) 1.

L. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt, and P. C. Tandy, Pion electromagnetic form factor at spacelike momenta. Phys. Rev. Lett., 111 (2013) 141802

K. Raya et al., Structure of the neutral pion and its electromagnetic transition form factor. Phys. Rev. D, 93 (2016) 074017

F. Gao, L. Chang, Y.-X. Liu, C. D. Roberts, and P. C. Tandy, Exposing strangeness projections for kaon electromagnetic form factors. Phys. Rev. D, 96 (2017) 034024

Gernot Eichmann, Christian S. Fischer, and Richard Williams. Kaon-box contribution to the anomalous magnetic moment of the muon. Phys. Rev. D, 101 (2020) 054015

A. Miramontes, A. Bashir, K. Raya, and P. Roig. Pion and Kaon box contribution to aHLbL µ. 12 (2021).

Lei Chang, I. C. Cloet, J. J. Cobos-Martinez, C. D. Roberts, S. M. Schmidt, and P. C. Tandy, Imaging dynamical chiral symmetry breaking pion wave function on the light front. Phys. Rev. Lett., 110 (2013) 132001

Chao Shi, Lei Chang, Craig D. Roberts, Sebastian M. Schmidt, Peter C. Tandy, and Hong-Shi Zong, Flavour symmetry breaking in the kaon parton distribution amplitude. Phys. Lett. B, 738 (2014) 512

Chao Shi, Chen Chen, Lei Chang, Craig D. Roberts, Sebastian M. Schmidt, and Hong-Shi Zong, Kaon and pion parton distribution amplitudes to twist-three. Phys. Rev. D, 92 (2015) 014035

M. Ding, K. Raya, D. Binosi, L. Chang, C. D Roberts, and S. M. Schmidt, Symmetry, breaking, and pion parton distributions. Phys. Rev. D, 101 (2020) 054014

M. Ding, K. Raya, D. Binosi, L. Chang, C.D Roberts, and S. M Schmidt, Drawing insights from pion parton distributions. Chin. Phys. C, 44 (2020) 031002

Z.-F. Cui et al., Higgs modulation of emergent mass as revealed in kaon and pion parton distributions. Eur. Phys. J. A, 57 (2021) 5

Z.-F. Cui et al., Kaon and pion parton distributions. Eur. Phys. J. C, 80 (2020) 1064

G. Eichmann, E. Ferreira, and A. Stadler, Going to the light front with contour deformations. 12 (2021)

C. Shi, M. Li, X. Chen, and W. Jia, Ground state pseudoscalar mesons on the light front From the light to heavy sector. Phys. Rev. D, 104 (2021) 094016

J.-L. Zhang et al., Measures of pion and kaon structure from generalised parton distributions. Phys. Lett. B, 815 (2021) 136158

S.-Sheng Xu, L. Chang, C. D. Roberts, and H.-S. Zong, Pion and kaon valence-quark parton quasidistributions. Phys. Rev. D, 97 (2018) 094014

C. Mezrag, H. Moutarde, and J. Rodriguez-Quintero. From Bethe-SalpeterWave functions to Generalised Parton Distributions. Few Body Syst., 57 (2016) 729

N. Chouika, C. Mezrag, H. Moutarde, and J. Rodríguez- Quintero, A Nakanishi-based model illustrating the covariant extension of the pion GPD overlap representation and its ambiguities. Phys. Lett. B, 780 (2018) 287

N. Chouika, C. Mezrag, H. Moutarde, and J. Rodríguez- Quintero, Covariant Extension of the GPD overlap representation at low Fock states. Eur. Phys. J. C, 77 (2017) 906

M. Atif Sultan, K. Raya, F. Akram, A. Bashir, and B. Masud, Effect of the quark-gluon vertex on dynamical chiral symmetry breaking. Phys. Rev. D, 103 (2021) 054036

D. Binosi, L. Chang, J. Papavassiliou, S.-X. Qin, and C. D. Roberts. Natural constraints on the gluon-quark vertex. Phys. Rev. D, 95 (2017) 031501

M. Diehl, Generalized parton distributions. Phys. Rept., 388 (2003) 41

J. M. Morgado Chavezet al., and Jorge Segovia. Pion GPDs A path toward phenomenology. 10 (2021)

J. M. Morgado Chávez et al., Accessing the pion 3D structure at US and China Electron-Ion Colliders. 10 (2021)

P. A. Zyla et al., Review of Particle Physics. PTEP, 2020 (2020) 083C01

M. V. Polyakov and P. Schweitzer, Forces inside hadrons pressure, surface tension, mechanical radius, and all that. Int. J. Mod. Phys. A, 33 (2018) 1830025

J.-L. Zhang, Z.-F. Cui, J. Ping, and C. D Roberts, Contact interaction analysis of pion GTMDs. Eur. Phys. J. C, 81 (2021) 6

H. P. Blok et al., Charged pion form factor between Q2=0.60 and 2.45 GeV2. I. Measurements of the cross section for the 1H(e, e0π +)n reaction. Phys. Rev. C, 78 (2008) 045202

S. R. Amendolia et al., A Measurement of the Space - Like Pion Electromagnetic Form-Factor. Nucl. Phys. B, 277 (1986) 168

M. Burkardt, Impact parameter space interpretation for generalized parton distributions. Int. J. Mod. Phys. A, 18 (2003) 173

L. Albino, I. M. Higuera, A. Bashir, and K. Raya. Work under development and I. M. Higuera’s contribution to this volume.




How to Cite

Raya K, Rodríguez-Quintero J. Highlights of pion and kaon structure from continuum analyses. Supl. Rev. Mex. Fis. [Internet]. 2022 Jun. 8 [cited 2022 Dec. 7];3(3):0308008 1-8. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/6281