Schwinger-Dyson Equations - Applications Adnan Bashir, Universidad Michoacana, Mexico Researchers: Ayala, UNAM Y. Concha, UMSNH J. Cobos, UMSNH E. Gutiérrez, ITM L.X. Gutiérrez, UMSNH A. Raya, UMSNH E. Rojas, (UNAM), Antioquia, Colombia M.E. Tejeda, USON A. Weber, UMSNH Students: L. Albino, UMSNH A. Ahmad, (Gomal, Pakistan) UMSNH M. Anguiano, UMSNH M.A. Bedolla, UMSNH R. Bermudez, (UMSNH) USON P. Dall’olio, UMSNH K. Raya, UMSNH S. Sánchez, UNAM-UMSNH

Schwinger-Dyson Equations - Applications Collaborators: F. Akram, University of Punjab, Pakistan J. Aslam, Quaid-i-Azam University, Pakistan B. El-Bennish, Cruzeiro do sul, Brazil B. Masud, University of Punjab, Pakistan Y.X. Liu, Peking University, China J.R. Quintero, Huelva University, Spain C.D. Roberts, Argonne National Laboratory, USA P.C. Tandy, Kent State University, USA L. Chang, University of Adelaide, Australia A. Sultan, University of Punjab, Pakistan D. Wilson, Cambridge University, England

Chiral Symmetry Breaking Schwinger-Dyson Equations Introduction QCD Phase Diagram Magnetic Catalysis Hadron Physics Chiral Symmetry Breaking Condensed Matter Dynamical Masses Schwinger-Dyson Equations

Introduction

Introduction The QCD Lagrangian:

Schwinger-Dyson Equations QCD Schwinger-Dyson equations in covariant gauges The inverse quark propagator: The quark-gluon vertex:

Schwinger-Dyson Equations The inverse gluon propagator:

1000 MeV 5 MeV QCD We can trace the origin of 98% of the luminous matter to QCD interactions. Introduction

Introduction Asymptotic Freedom Infrared Increase 0.2 fm 0.02 fm

Introduction Through SDEs, we can study the structure of hadrons through first principles in the continuum. SDE for QCD have been extensively applied to the study of quark and gluon propagators, their interactions, meson spectra and interactions below the masses ~ 1 GeV. They have been employed to study: The gluon propagator The quark propagator A.C. Aguilar, A.A. Natale, JHEP 08, 057 (2004). A. Ayala, AB, D. Binosi, M, Crisoforetti, J. Rodríguez, Phys. Rev. D86 074512 (2012). The quark/gluon-photon interactions: P. Maris, C.D. Roberts, P. Tandy, Phys. Lett. B420 267 (1998). The masses, charge radii, decays of light/heavy mesons A. Kizilersu and M.R. Pennington Phys. Rev. D79 125020 (2009) P. Maris, P. Tandy, Phys. Rev. C60 055214 (1999). Pion and kaon valence quark-distribution functions P. Maris, C.D. Roberts, Phys. Rev. C56 3369 (1997). P. Maris, P.C. Tandy, Phys. Rev. C62 055204 (2000). M.A. Bedolla, J.J. Cobos Martínez, AB, Phys. Rev. D92 054031 (2015). L. Chang, C.D. Roberts, Phys. Rev. Lett. 103 081601 (2009) Elastic and transition pion form factors T. Nguyen, AB, C.D. Roberts, P.C. Tandy, Phys. Rev. C83062201 (2011). AB, R. Bermudez, L. Chang, C.D. Roberts, Phys. Rev. C85, 045205 (2012). R. Bermudez, L. Albino-Fernández, L.X. Gutiérrez, M.E. Tejeda, AB (in progress). L. Albino-Fernández, AB, L.X. Gutiérrez, Y. Concha, Phys. Rev. D93 065022 (2016) Nucleon elastic and transition form factors L. Gutiérrez, AB, I.C. Cloet, C.D. Roberts, Phys. Rev. C81 065202 (2010). L. Chang et. al., Phys. Rev. Lett. 111, 14 141802 (2013). K. Raya et. al., Phys. Rev. D93, 14 074071 (2016). L.X. Gutiérrez, K. Raya, AB, C. Roberts, D. Wilson (in progress) “Collective Perspective on advances in DSE QCD”, AB , L. Chang, I.C. Cloet, B. El Bennich, Y. Liu, C.D. Roberts, P.C. Tandy, Commun. Theor. Phys. 58 79 (2012)

Introduction Parity Partners & Chiral Symmetry Breaking

The Quark Propagator Quark propagator:

The Quark Propagator The quark propagator: Quark mass is a function of momentum, falling as 1/p2 in the ultraviolet.

The Line of Action Javier, Khépani, Luis, Marco, Rocío, Xiomara Faddeev Equation Masses, Decays Form Factors Bethe Salpeter Equation Schwinger- Dyson Equations Quark Propagator Theory Vs. Experiment Javier, Khépani, Luis, Marco, Rocío, Xiomara