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Pion Transition Form Factor

Pion Transition Form Factor. Adnan Bashir University of Michoacán, Mexico. Collaborators: F. Akram , University of Punjab, Pakistan J. Aslam , Quaid-i-Azam University, Pakistan B. El- Bennish , Cruzeiro do sul , Brazil Y.X. Liu, Peking University, China

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Pion Transition Form Factor

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  1. Pion Transition Form Factor AdnanBashir University of Michoacán, Mexico • Collaborators: • F. Akram, University of Punjab, Pakistan • J. Aslam, Quaid-i-Azam University, Pakistan • B. El-Bennish, Cruzeiro do sul, Brazil • Y.X. Liu, Peking University, China • M.R. Pennington, Durham University, UK • J.R. Quintero, Huelva University, Spain • Raya, Michoacán University, Mexico • C.D. Roberts, Argonne National Laboratory, USA • P.C. Tandy, Kent State University, USA Collaborators: L. Albino, University of Michoacán, Mexico M.A. Bedolla, University of Michoacán, Mexico R. Bermudez, University of Sonora, Mexico J. Cobos, University of Michoacán, Mexico L. Chang, University of Adelaide, Australia L.X. Gutiérrez, University of Michoacán, Mexico K. Raya, University of Michoacán, Mexico

  2. MRP

  3. MRP

  4. Contents • Facts and Challenges • Pions and Chiral Symmetry Breaking • Schwinger-Dyson Equations (SDE) • The Quark Propagator • The Quark-Photon Vertex • Bethe Salpeter Amplitude • Pion Electromagnetic Form Factor • Pion Transition Form Factor • SDE - Scope

  5. Facts and Challenges • Color degrees of freedom (quarks and gluons) are not • observable (confinement). • Dynamical mass generation for massless quarks; • (dynamical chiral symmetry breaking). • Both these phenomena are emergent and owe themselves • to large coupling strength in the infrared. • How do we study physics beyond perturbation theory? • Studying QCD: lattice, Schwinger-Dyson and Bethe- • Salpeter equations, chiral perturbation theory, • effective quark models.

  6. Schwinger-Dyson Equations • 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. CobosMartínez, AB, Phys. Rev. D92 054031 (2015). M.A. Bedolla, K. Raya, J.J. CobosMartínez, AB, Phys. Rev. D93 094025 (2016). L. Chang, C.D. Roberts, Phys. Rev. Lett. 103 081601 (2009) 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). • Elastic and transition pion form factors T. Nguyen, AB, C.D. Roberts, P.C. Tandy, Phys. Rev. C83062201 (2011). • 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). “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) L.X. Gutiérrez, K. Raya, AB, C. Roberts, D. Wilson (in progress)

  7. Pions & Chiral Symmetry Breaking

  8. Pions and Chiral Symmetry Breaking In October 1934, Hideki Yukawa predicted the existence of a “heavy quantum”, meson, exchanging nuclear force between neutrons and protons. 1949 1950 1969 2008 It was discovered by Cecil Powel in 1949 in cosmic ray tracks in a photographic emulsion. Pion was nicely accommodated in The Eight Fold way of Murray Gell –Mann in 1961. YoichiroNambu associated it with CSB in 1960.

  9. Chiral Symmetry and Its Breaking The connection of the smallness of pions with chiral symmetry breaking is reflected in the long known following relations: GellMann-Oakes- Renner relation Gell-Mann-Okubo mass formulae ~500 MeV Parity Partners & Chiral Symmetry Breaking ~500 MeV

  10. Chiral Symmetry and Its Breaking Nucleon And its Parity Partner

  11. Schwinger-Dyson Equations: From Infrared to Ultraviolet

  12. Schwinger-Dyson Equtions Schwinger-Dyson equations are the fundamental equations of QCD and combine its UV and IR behaviour. Observing the transition of the pion (form factors, such as ) from quarks and gluons to one with valence quarks alone can be studied naturally through SDE.

  13. The Quark Propagator • The quark propagator:

  14. The Quark Propagator This solution violates the axiom of reflection positivity and the corresponding excitation is confined. Thus chiral symmetry breaking and confinement are intimately connected to each other.

  15. The Quark-Photon Vertex For current conservation and Ward identities, a proper quark-photon vertex is essential. “Truncating the Schwinger-Dyson equations: How multiplicative renormalizability and the Ward identity restrict the three point vertex in QED” D.C. Curtis and M.R. Pennington, Phys. Rev. D42 4165 (1990) “Nonperturbative study of the fermion propagator in quenched QED in covariant gauges using a renormalizable truncation of the Schwinger- Dyson equation” D.C. Curtis and M.R. Pennington, Phys. Rev. D48 4933 (1993) “Gauge independent chiral symmetry breaking in quenched QED” AB, M.R. Pennington Phys. Rev. D50 7679 (1994) “The Nonperturbative three point vertex in massless quenched QED and perturbation theory constraints” AB, A. Kizilersu, M.R. Pennington Phys. Rev. D57 1242 (1998)

  16. The Quark-Photon Vertex

  17. The Quark-Photon/Gluon Vertex For current conservation and Ward identities, a proper quark-photon vertex is essential. D.C. Curtis and M.R. Pennington Phys. Rev. D42 4165 (1990) AB, M.R. Pennington Phys. Rev. D50 7679 (1994) A. Kizilersu and M.R. Pennington Phys. Rev. D79 125020 (2009) L. Chang, C.D. Roberts, Phys. Rev. Lett. 103 081601 (2009) AB, R. Bermudez, L. Chang, C.D. Roberts, Phys. Rev. C85 045205 (2012). R. Delbourgo, A. Salam, Phys. Rev. 135 1398 (1964). LA Fernández, AB, L.X. Gutiérrez, Y. Concha, Phys. Rev. C85 065022 (2016). It respects the separation of scales involved. It ensures chiral anomaly at zero momentum transfer. It reproduces one-loop vertex for asymptotic momenta. It satisfies multiplicative renormalizability condition. AB, A. Raya, S. Sanchez-Madrigal, C.D. Roberts Few Body Syst. 46 229(2009). M. J. Aslam, AB, L.X. Gutiérrez, Phys. Rev. 93 076001 (2016).

  18. The Bethe-Salpeter Amplitudes Bethe-Salpeter Amplitude for the pion: Goldberger-Triemann relations: Nakanishi-like representation

  19. Pion Transition Form Factor

  20. Pion to * Transition Form Factor The transition is studied through process:

  21. Pion to * Transition Form Factor The transition form factor: CELLOH.J. Behrend et.al., Z. Phys C49 401 (1991). 0.7 – 2.2 GeV2 The leading twist pQDC calculation was carried out in: CLEOJ. Gronberg et. al., Phys. Rev. D57 33 (1998).1.7 – 8.0 GeV2 G.P. Lepage, and S.J. Brodsky,Phys. Rev. D22, 2157 (1980). BaBarR. Aubert et. al., Phys. Rev. D80 052002 (2009). 4.0 – 40.0 GeV2

  22. Pion to * Transition Form Factor Transition form factor is the correlator of two currents : Collinear factorization: T: hard scattering amplitude with quark gluon sub-processes. is the pion distribution amplitude: In asymptotic QCD:

  23. Valence Quark Parton Distribution Amplitude for Pion

  24. Valence Quark Parton Distribution Amplitude Pion’s PDA – (x,Q2): is a probability amplitude that describes the momentum distribution of a quark and anti-quark in the bound-state’s valence Fock state. x is the light-cone momentum fraction: Among other processes, it enters the calculation of both the pion electromagnetic and transition form factors. (x, Q2): is an essentially non-perturbative quantity whose asymptotic form is known. What we can know is the evolution of this function with the momentum scale Q2. ERBL evolution equations.

  25. Valence Quark Parton Distribution Amplitude

  26. Valence Quark Parton Distribution Amplitude

  27. Valence Quark Parton Distribution Amplitude I.C. Cloet, QCD TNT4, Ilhabela, 2015

  28. Pion Electromagnetic Form Factor

  29. Pion Electromagnetic Form Factor

  30. Pion Electromagnetic Form Factor 2017? 1980’s 2001 2006

  31. Pion Electromagnetic Form Factor The pattern of chiral symmetry breaking dictates the momentum dependence of the elastic pion form factor. Within the rainbow ladder truncation, the elastic electromagnetic pion form factor: Experiments on pions indicate a contact like interaction? L. Gutiérrez, AB, I.C. Cloet, C.D. Roberts, Phys. Rev. C81 065202 (2010).

  32. Pion Electromagnetic Form Factor L. Chang, I.C. Cloët, C.D. Roberts, S.M. Schmidt, P.C. Tandy, Phys. Rev. Lett. 111, 14 141802 (2013)

  33. Pion Transition Form Factor

  34. Pion to * Transition Form Factor

  35. Pion to * Transition Form Factor The transition form factor: H.L.L. Robertes, C.D. Roberts, AB, L.X. Gutiérrez and P.C. Tandy, Phys. Rev. C82, (065202:1-11) 2010. CELLOH.J. Behrend et.al., Z. Phys C49 401 (1991). 0.7 – 2.2 GeV2 Lowest order in perturbation theory and the leading twist asymptotic QCD calculation: CLEOJ. Gronberg et. al., Phys. Rev. D57 33 (1998).1.7 – 8.0 GeV2 BaBarR. Aubert et. al., Phys. Rev. D80 052002 (2009). 4.0 – 40.0 GeV2 G.P. Lepage, and S.J. Brodsky,Phys. Rev. D22, 2157 (1980). BelleS. Uehara et. al., Phys. Rev. D86 092007 (2012). 4.0 – 40.0 GeV2

  36. Pion to * Transition Form Factor The transition form factor: K. Raya, L. Chang, AB, J.J. Cobos-Martinez, L.X. Gutiérrez-Guerrero,  C.D. Roberts, P.C. Tandy, Phys. Rev. D93 074017 (2016)

  37. Pion to * Transition Form Factor The transition form factor: • Belle II will have 40 times more luminosity. • Vladimir Savinov: • 5th Workshop of the APS • Topical Group on Hadronic • Physics, 2013. Precise measurements at large Q2 will provide a stringent constraint on the pattern of chiral symmetry breaking.

  38. Schwinger-Dyson Equations: The Scope

  39. Schwinger-Dyson Equations: The Scope Faddeev Equation Masses, Decays Form Factors Bethe Salpeter Equation Schwinger- Dyson Equations Quark Propagator Theory Vs. Experiment

  40. Schwinger-Dyson Equations: The Scope QCD Phase Diagram Magnetic Catalysis Hadron Physics Chiral Symmetry Breaking Condensed Matter Dynamical Masses Schwinger-Dyson Equations

  41. Happy Birthday Mike!

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