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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
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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
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Chiral Symmetry Breaking Schwinger-Dyson Equations
Introduction QCD Phase Diagram Magnetic Catalysis Hadron Physics Chiral Symmetry Breaking Condensed Matter Dynamical Masses Schwinger-Dyson Equations
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Introduction
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Introduction The QCD Lagrangian:
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Schwinger-Dyson Equations
QCD Schwinger-Dyson equations in covariant gauges The inverse quark propagator: The quark-gluon vertex:
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Schwinger-Dyson Equations
The inverse gluon propagator:
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1000 MeV 5 MeV QCD We can trace the origin of 98% of the luminous matter to QCD interactions. Introduction
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Introduction Asymptotic Freedom Infrared Increase 0.2 fm 0.02 fm
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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. D (2012). The quark/gluon-photon interactions: P. Maris, C.D. Roberts, P. Tandy, Phys. Lett. B (1998). The masses, charge radii, decays of light/heavy mesons A. Kizilersu and M.R. Pennington Phys. Rev. D (2009) P. Maris, P. Tandy, Phys. Rev. C (1999). Pion and kaon valence quark-distribution functions P. Maris, C.D. Roberts, Phys. Rev. C (1997). P. Maris, P.C. Tandy, Phys. Rev. C (2000). M.A. Bedolla, J.J. Cobos Martínez, AB, Phys. Rev. D (2015). L. Chang, C.D. Roberts, Phys. Rev. Lett (2009) Elastic and transition pion form factors T. Nguyen, AB, C.D. Roberts, P.C. Tandy, Phys. Rev. C (2011). AB, R. Bermudez, L. Chang, C.D. Roberts, Phys. Rev. C85, (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. D (2016) Nucleon elastic and transition form factors L. Gutiérrez, AB, I.C. Cloet, C.D. Roberts, Phys. Rev. C (2010). L. Chang et. al., Phys. Rev. Lett. 111, (2013). K. Raya et. al., Phys. Rev. D93, (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 (2012)
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Introduction Parity Partners & Chiral Symmetry Breaking
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The Quark Propagator Quark propagator:
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The Quark Propagator The quark propagator:
Quark mass is a function of momentum, falling as 1/p2 in the ultraviolet.
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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
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