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  • AdnanAdnan BashirBashir Michoacán Michoacán University, University,

    MexicoMexico

    Form Quarks & Gluons to Form Quarks & Gluons to HadronHadron Form FactorsForm Factors For For Increasing Photon Increasing Photon VirtualitiesVirtualities

    Light Cone Light Cone 2013 2013 –– The Satellite Meeting The Satellite Meeting May 25, 2013, May 25, 2013, SkiathosSkiathos, Greece, Greece

    Collaborators:Collaborators: F. F. AkramAkram, L. Chang, J.R. Quintero, , L. Chang, J.R. Quintero, C.D. C.D. Roberts, Roberts, P.C. Tandy, P.C. Tandy, R. R. BermúdezBermúdez, L.X. , L.X. Gutiérrez,KGutiérrez,K. Raya. Raya

  • ContentsContents

    •• ConclusionsConclusions •• ConclusionsConclusions

    •• IntroductionIntroduction •• IntroductionIntroduction

    •• SchwingerSchwinger--Dyson Equations Dyson Equations –– The IngredientsThe Ingredients •• SchwingerSchwinger--Dyson Equations Dyson Equations –– The IngredientsThe Ingredients

    Quark Propagator: Quark Mass Function Quark Propagator: Quark Mass Function Quark Propagator: Quark Mass Function Quark Propagator: Quark Mass Function

    Quark Gluon Vertex/QuarkQuark Gluon Vertex/Quark--Photon VertexPhoton Vertex Quark Gluon Vertex/QuarkQuark Gluon Vertex/Quark--Photon VertexPhoton Vertex

    PionPion Elastic Form Factor Elastic Form Factor PionPion Elastic Form Factor Elastic Form Factor

    The Gluon PropagatorThe Gluon Propagator The Gluon PropagatorThe Gluon Propagator

    •• Charting Out the Charting Out the Large QLarge Q22 EvolutionEvolution: : •• Charting Out the Charting Out the Large QLarge Q22 EvolutionEvolution: :

    PionPion Transition Form Factor Transition Form Factor PionPion Transition Form Factor Transition Form Factor

    Quark Propagator & Quark Propagator & PionPion Bethe Bethe SalpeterSalpeter Amplitudes Amplitudes Quark Propagator & Quark Propagator & PionPion Bethe Bethe SalpeterSalpeter Amplitudes Amplitudes

  • •• SDESDE forfor QCDQCD havehave beenbeen extensivelyextensively appliedapplied toto mesonmeson spectraspectra andand interactionsinteractions belowbelow thethe massesmasses ~~ 11 GeVGeV.. •• SDESDE forfor QCDQCD havehave beenbeen extensivelyextensively appliedapplied toto mesonmeson spectraspectra andand interactionsinteractions belowbelow thethe massesmasses ~~ 11 GeVGeV..

    •• TheyThey havehave beenbeen employedemployed toto calculatecalculate:: •• TheyThey havehave beenbeen employedemployed toto calculatecalculate::

    P. Maris, C.D. Roberts, Phys. Rev. C56 3369 (1997).P. Maris, C.D. Roberts, Phys. Rev. C56 3369 (1997).

    P. Maris, P.C. Tandy, Phys. Rev. C62 055204 (2000).P. Maris, P.C. Tandy, Phys. Rev. C62 055204 (2000).

    D. D. JareckeJarecke, P. Maris, P.C. Tandy, Phys. Rev. C67 035202 (2003)., P. Maris, P.C. Tandy, Phys. Rev. C67 035202 (2003).

    thethe masses,masses, chargecharge radiiradii andand decaysdecays ofof mesonsmesons thethe masses,masses, chargecharge radiiradii andand decaysdecays ofof mesonsmesons

    IntroductionIntroduction IntroductionIntroduction

    •• ThroughThrough SDEs,SDEs, wewe cancan studystudy hadronhadron formform factorsfactors fromfrom firstfirst principlesprinciples inin thethe continuumcontinuum.. •• ThroughThrough SDEs,SDEs, wewe cancan studystudy hadronhadron formform factorsfactors fromfrom firstfirst principlesprinciples inin thethe continuumcontinuum..

  • P. Maris, P.C. Tandy, Phys. Rev. C62 055204 (2000).P. Maris, P.C. Tandy, Phys. Rev. C62 055204 (2000).

    D. D. JareckeJarecke, P. Maris, P.C. Tandy, Phys. Rev. C67 035202 (2003)., P. Maris, P.C. Tandy, Phys. Rev. C67 035202 (2003).

    elasticelastic pionpion andand kaonkaon formform factorsfactors elasticelastic pionpion andand kaonkaon formform factorsfactors

    pionpion andand kaonkaon valencevalence quarkquark--distributiondistribution functionsfunctions pionpion andand kaonkaon valencevalence quarkquark--distributiondistribution functionsfunctions

    T. Nguyen, AB, C.D. Roberts, P.C. Tandy, T. Nguyen, AB, C.D. Roberts, P.C. Tandy, Phys. Rev. C83062201 (2011).

    nucleonnucleon formform factorsfactors nucleonnucleon formform factorsfactors

    G. Eichmann, et. al., G. Eichmann, et. al., Phys. Rev. C79 012202 (2009). D. Wilson, L. Chang and C.D. Roberts, D. Wilson, L. Chang and C.D. Roberts, PhysPhys. Rev. C85 025205 (2012).. Rev. C85 025205 (2012).

    “Collective Perspective on advances in DSE QCD”,AB , L. Chang, I.C. “Collective Perspective on advances in DSE QCD”,AB , L. Chang, I.C. CloetCloet, B. El , B. El BennichBennich, Y. Liu, C.D. Roberts, P.C. Tandy, , Y. Liu, C.D. Roberts, P.C. Tandy, CommunCommun. . TheorTheor. Phys. 58 79 (2012) . Phys. 58 79 (2012)

    IntroductionIntroduction IntroductionIntroduction

    reviewreview articlearticle reviewreview articlearticle

  • The quark The quark propagator:propagator: The quark The quark propagator:propagator:

    Quark mass is a Quark mass is a function of momentum,function of momentum, dropping as 1/pdropping as 1/p22 in thein the ultraviolet.ultraviolet.

    Quark mass is a Quark mass is a function of momentum,function of momentum, dropping as 1/pdropping as 1/p22 in thein the ultraviolet.ultraviolet.

    Higgs mechanism isHiggs mechanism is almost almost irrelevantirrelevant to theto the infrared enhancement ofinfrared enhancement of quark mass.quark mass.

    Higgs mechanism isHiggs mechanism is almost almost irrelevantirrelevant to theto the infrared enhancement ofinfrared enhancement of quark mass.quark mass.

    The Quark PropagatorThe Quark Propagator The Quark PropagatorThe Quark Propagator

    SchwingerSchwinger--Dyson Equation for theDyson Equation for the quark propagatorquark propagator

    SchwingerSchwinger--Dyson Equation for theDyson Equation for the quark propagatorquark propagator

  • The Gluon propagatorThe Gluon propagator The Gluon propagatorThe Gluon propagator

    The Gluon Propagator:The Gluon Propagator: The Gluon Propagator:The Gluon Propagator:

    Modern SDE and lattice Modern SDE and lattice results support decoupling results support decoupling solution for the gluon solution for the gluon propagator.propagator.

    Modern SDE and lattice Modern SDE and lattice results support decoupling results support decoupling solution for the gluon solution for the gluon propagator.propagator.

    Momentum dependent gluon mass is reminiscent of the Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass function.momentum dependent quark mass function. Momentum dependent gluon mass is reminiscent of the Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass function.momentum dependent quark mass function. It is in accord with the refined GZIt is in accord with the refined GZ--picture.picture. It is in accord with the refined GZIt is in accord with the refined GZ--picture.picture.

    A. Ayala, AB, D. A. Ayala, AB, D. BinosiBinosi, M. , M. CristoforettiCristoforetti, J. , J. RodríguezRodríguez, , Phys. Rev. D86 074512 (2012).Phys. Rev. D86 074512 (2012).

    AB, A. Raya, J. AB, A. Raya, J. RodríguezRodríguez, arXiv:1302.5829 , arXiv:1302.5829 (light (light flavorflavor dependence of the quark mass)dependence of the quark mass)

  • The Gluon propagatorThe Gluon propagator The Gluon propagatorThe Gluon propagator

    The Gluon Propagator:The Gluon Propagator: The Gluon Propagator:The Gluon Propagator:

    Modern SDE and lattice Modern SDE and lattice results support decoupling results support decoupling solution for the gluon solution for the gluon propagator.propagator.

    Modern SDE and lattice Modern SDE and lattice results support decoupling results support decoupling solution for the gluon solution for the gluon propagator.propagator.

    Momentum dependent gluon mass is reminiscent of the Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass function.momentum dependent quark mass function. Momentum dependent gluon mass is reminiscent of the Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass function.momentum dependent quark mass function.

    It is in accord with the refined GZIt is in accord with the refined GZ--picture.picture. It is in accord with the refined GZIt is in accord with the refined GZ--picture.picture.

    AB, C. Lei, I. AB, C. Lei, I. CloetCloet, B. El , B. El BennichBennich, Y. Liu, C. Roberts, , Y. Liu, C. Roberts, P. Tandy, Comm. P. Tandy, Comm. TheorTheor. Phys. 58 79. Phys. 58 79--134 (2012) 134 (2012)

  • JJ.. SkullerudSkullerud,, PP.. Bowman,Bowman, AA.. KizilersuKizilersu,, DD.. LeinweberLeinweber,, AA.. Williams,Williams, JJ.. HighHigh EnergyEnergy PhysPhys.. 0404 047047 ((20032003))

    MM.. BhagwatBhagwat,, MM.. PichowskyPichowsky,, CC.. Roberts,Roberts, PP.. Tandy,Tandy, PhysPhys.. RevRev.. CC6868 015203015203 ((20032003))..

    AB,AB, LL.. GutiérrezGutiérrez,, MM.. TejedaTejeda,, AIPAIP ConfConf.. ProcProc.. 10261026 262262 ((20082008))..

    The QuarkThe Quark--GluonGluon Vertex:Vertex: