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Adnan Adnan Bashir Bashir Michoacán Michoacán University, University, Mexico Mexico Form Quarks & Gluons to Form Quarks & Gluons to Hadron Hadron Form Factors Form Factors For For Increasing Photon Increasing Photon Virtualities Virtualities Light Cone Light Cone 2013 2013 The Satellite Meeting The Satellite Meeting May 25, 2013, May 25, 2013, Skiathos Skiathos, Greece , Greece Collaborators: Collaborators: F. F. Akram Akram, L. Chang, J.R. Quintero, , L. Chang, J.R. Quintero, C.D. C.D. Roberts, Roberts, P.C. Tandy, P.C. Tandy, R. R. Bermúdez Bermúdez, L.X. , L.X. Gutiérrez,K Gutiérrez,K. Raya . Raya

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Page 1: Form Quarks & Gluons to Hadron Form Factors For Increasing ...lc2013/downloads/talks/... · Adnan Bashir Michoacán University, Mexico Form Quarks & Gluons to Hadron Form Factors

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

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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

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•• 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..

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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

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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

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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)

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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)

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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: One of the 12 One of the 12 form factorsform factors

The QuarkThe Quark--GluonGluon Vertex:Vertex: One of the 12 One of the 12 form factorsform factors

The QuarkThe Quark--Gluon VertexGluon Vertex The QuarkThe Quark--Gluon VertexGluon Vertex

Page 9: Form Quarks & Gluons to Hadron Form Factors For Increasing ...lc2013/downloads/talks/... · Adnan Bashir Michoacán University, Mexico Form Quarks & Gluons to Hadron Form Factors

•• ThusThus DCSBDCSB manifestsmanifests itselfitself notnot onlyonly inin thethe quarkquark propagatorpropagator butbut alsoalso thethe quarkquark--gluongluon vertexvertex.. •• ThusThus DCSBDCSB manifestsmanifests itselfitself notnot onlyonly inin thethe quarkquark propagatorpropagator butbut alsoalso thethe quarkquark--gluongluon vertexvertex..

The QuarkThe Quark--Gluon VGluon Vertexertex

•• QuarkQuark gluongluon vertexvertex consistsconsists ofof 1212 linearlylinearly independentindependent DiracDirac structuresstructures.. •• QuarkQuark gluongluon vertexvertex consistsconsists ofof 1212 linearlylinearly independentindependent DiracDirac structuresstructures..

•• 55 ofof thesethese 1212 structuresstructures areare generatedgenerated dynamicallydynamically inin thethe chiralchiral limitlimit.. •• 55 ofof thesethese 1212 structuresstructures areare generatedgenerated dynamicallydynamically inin thethe chiralchiral limitlimit..

•• TheThe nonnon perturbativeperturbative quarkquark--gluongluon vertexvertex isis aa complicatedcomplicated objectobject asas comparedcompared toto itsits perturbativeperturbative counterpartcounterpart.. •• TheThe nonnon perturbativeperturbative quarkquark--gluongluon vertexvertex isis aa complicatedcomplicated objectobject asas comparedcompared toto itsits perturbativeperturbative counterpartcounterpart..

Page 10: Form Quarks & Gluons to Hadron Form Factors For Increasing ...lc2013/downloads/talks/... · Adnan Bashir Michoacán University, Mexico Form Quarks & Gluons to Hadron Form Factors

•• TheThe rainbowrainbow ladderladder truncationtruncation andand thethe BallBall--ChiuChiu verticesvertices describedescribe ππ andand thethe ρρ mesonsmesons wellwell butbut failfail toto dodo soso forfor theirtheir parityparity partnerspartners σσ andand aa11..

•• TheThe rainbowrainbow ladderladder truncationtruncation andand thethe BallBall--ChiuChiu verticesvertices describedescribe ππ andand thethe ρρ mesonsmesons wellwell butbut failfail toto dodo soso forfor theirtheir parityparity partnerspartners σσ andand aa11..

•• NonNon perturbativeperturbative detailsdetails ofof thethe vertexvertex explainexplain thethe massmass splittingsplitting ofof thethe parityparity partnerspartners throughthrough thethe generationgeneration ofof anan anomalousanomalous magneticmagnetic momentmoment distributiondistribution ofof quarksquarks..

•• NonNon perturbativeperturbative detailsdetails ofof thethe vertexvertex explainexplain thethe massmass splittingsplitting ofof thethe parityparity partnerspartners throughthrough thethe generationgeneration ofof anan anomalousanomalous magneticmagnetic momentmoment distributiondistribution ofof quarksquarks..

•• TheThe associatedassociated correctionscorrections cancelcancel inin thethe pseudoscalarpseudoscalar andand vectorvector channelschannels butbut addadd inin thethe scalarscalar andand axialaxial vectorvector channelschannels..

•• TheThe associatedassociated correctionscorrections cancelcancel inin thethe pseudoscalarpseudoscalar andand vectorvector channelschannels butbut addadd inin thethe scalarscalar andand axialaxial vectorvector channelschannels..

L. Chang, C.D. Roberts, Phys. Rev. L. Chang, C.D. Roberts, Phys. Rev. LettLett. 103 081601 (2009) . 103 081601 (2009)

The QuarkThe Quark--Gluon VertexGluon Vertex The QuarkThe Quark--Gluon VertexGluon Vertex

Page 11: Form Quarks & Gluons to Hadron Form Factors For Increasing ...lc2013/downloads/talks/... · Adnan Bashir Michoacán University, Mexico Form Quarks & Gluons to Hadron Form Factors

The vertex which successfully explains the mass splittingThe vertex which successfully explains the mass splitting between between ρ and aρ and a11 mesons produces the following mesons produces the following magnetic magnetic moment distributionmoment distribution..

The QuarkThe Quark--Gluon VertexGluon Vertex The QuarkThe Quark--Gluon VertexGluon Vertex

Page 12: Form Quarks & Gluons to Hadron Form Factors For Increasing ...lc2013/downloads/talks/... · Adnan Bashir Michoacán University, Mexico Form Quarks & Gluons to Hadron Form Factors

BallBall andand ChiuChiu constructionconstruction:: (Ward(Ward--TakahashiTakahashi identity)identity)

The QuarkThe Quark--Photon VPhoton Vertexertex

TheThe WardWard identityidentity isis thenthen invokedinvoked::

Page 13: Form Quarks & Gluons to Hadron Form Factors For Increasing ...lc2013/downloads/talks/... · Adnan Bashir Michoacán University, Mexico Form Quarks & Gluons to Hadron Form Factors

The transverse basis:The transverse basis:

The QuarkThe Quark--Photon VPhoton Vertexertex

Page 14: Form Quarks & Gluons to Hadron Form Factors For Increasing ...lc2013/downloads/talks/... · Adnan Bashir Michoacán University, Mexico Form Quarks & Gluons to Hadron Form Factors

Phenomenology

Gauge

Covariance Lattice

Multiplicative

Renormalization

Perturbation

Theory

Quark-photon/

quark-gluon

vertex

QuarkQuark--photonphoton VertexVertex QuarkQuark--photonphoton VertexVertex

The QuarkThe Quark--Photon VertexPhoton Vertex The QuarkThe Quark--Photon VertexPhoton Vertex

Page 15: Form Quarks & Gluons to Hadron Form Factors For Increasing ...lc2013/downloads/talks/... · Adnan Bashir Michoacán University, Mexico Form Quarks & Gluons to Hadron Form Factors

AB, M.R. Pennington Phys. Rev. D50 7679 (1994) AB, M.R. Pennington Phys. Rev. D50 7679 (1994)

D.C. Curtis and M.R. Pennington Phys. Rev. D42 4165 (1990)D.C. Curtis and M.R. Pennington Phys. Rev. D42 4165 (1990)

A. A. KizilersuKizilersu and M.R. Pennington Phys. Rev. D79 125020 (2009)and M.R. Pennington Phys. Rev. D79 125020 (2009)

L. Chang, C.D. Roberts, Phys. Rev. L. Chang, C.D. Roberts, Phys. Rev. LettLett. 103 081601 (2009) . 103 081601 (2009)

AB, C. AB, C. CalcaneoCalcaneo, L. , L. GutiérrezGutiérrez, M. , M. TejedaTejeda, Phys. Rev. D83 033003 (2011), Phys. Rev. D83 033003 (2011)

AB, R. Bermudez, L. Chang, C.D. Roberts,AB, R. Bermudez, L. Chang, C.D. Roberts, PhysPhys. Rev. C85, 045205 (2012). Rev. C85, 045205 (2012)..

Significantly, this last Significantly, this last ansatzansatz contains nontrivial factors contains nontrivial factors associated with those tensors whose appearance is solely associated with those tensors whose appearance is solely driven by dynamical driven by dynamical chiralchiral symmetry breaking.symmetry breaking.

It yields gauge independent critical coupling in QED.It yields gauge independent critical coupling in QED.

It also reproduces large anomalous magnetic It also reproduces large anomalous magnetic moment moment distribution for distribution for quarks in the infrared.quarks in the infrared.

The QuarkThe Quark--Photon VertexPhoton Vertex The QuarkThe Quark--Photon VertexPhoton Vertex

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AB, R. Bermudez, L. Chang, C.D. Roberts,AB, R. Bermudez, L. Chang, C.D. Roberts, PhysPhys. Rev. C85, 045205 (2012). Rev. C85, 045205 (2012)..

The QuarkThe Quark--Photon VertexPhoton Vertex The QuarkThe Quark--Photon VertexPhoton Vertex

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Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

ObservingObserving thethe transitiontransition ofof thethe hadronhadron fromfrom aa seasea ofof quarksquarks andand gluonsgluons toto thethe oneone withwith valencevalence quarksquarks alonealone isis anan experimentalexperimental andand theoreticaltheoretical challengechallenge..

ObservingObserving thethe transitiontransition ofof thethe hadronhadron fromfrom aa seasea ofof quarksquarks andand gluonsgluons toto thethe oneone withwith valencevalence quarksquarks alonealone isis anan experimentalexperimental andand theoreticaltheoretical challengechallenge..

SchwingerSchwinger--DysonDyson equationsequations areare thethe fundamentalfundamental equationsequations ofof QCDQCD andand combinecombine itsits UVUV andand IRIR behaviourbehaviour.. SchwingerSchwinger--DysonDyson equationsequations areare thethe fundamentalfundamental equationsequations ofof QCDQCD andand combinecombine itsits UVUV andand IRIR behaviourbehaviour..

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Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

1980’s 2001 2006 2015?

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

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TheThe experimentsexperiments wouldwould bebe ableable toto distinguishdistinguish betweenbetween differentdifferent patternspatterns ofof chiralchiral symmetrysymmetry breakingbreaking withwith increasingincreasing photonphoton virtualitiesvirtualities::

TheThe experimentsexperiments wouldwould bebe ableable toto distinguishdistinguish betweenbetween differentdifferent patternspatterns ofof chiralchiral symmetrysymmetry breakingbreaking withwith increasingincreasing photonphoton virtualitiesvirtualities::

L. L. GutiérrezGutiérrez, AB, I.C. , AB, I.C. CloetCloet, C.D. Roberts, Phys. Rev. C81 065202 (2010)., C.D. Roberts, Phys. Rev. C81 065202 (2010).

Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

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

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Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

Future form factor measurements can lift the degeneracy Future form factor measurements can lift the degeneracy between minute variations of the mass function.between minute variations of the mass function. Future form factor measurements can lift the degeneracy Future form factor measurements can lift the degeneracy between minute variations of the mass function.between minute variations of the mass function.

F. F. AkramAkram, AB, K. Raya, work in progress. , AB, K. Raya, work in progress.

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TheThe transitiontransition formform factorfactor:: TheThe transitiontransition formform factorfactor::

CELLOCELLO H.J. Behrend et.al., Z. Phys C49 401 (1991). 0.7 – 2.2 GeV2

CLEOCLEO J. Gronberg et. al., Phys. Rev. D57 33 (1998). 1.7 – 8.0 GeV2

BaBarBaBar R. Aubert et. al., Phys. Rev. D80 052002 (2009). 4.0 – 40.0 GeV2

G.P. G.P. LepageLepage, and S.J. Brodsky,, and S.J. Brodsky, PhysPhys. Rev. D22, 2157 (1980).. Rev. D22, 2157 (1980). BelleBelle S. Uehara et. al., arXiv:1205.3249 [hep-ex] (2012). 4.0 – 40.0 GeV2

H.L.L. H.L.L. RobertesRobertes, C.D. Roberts, AB, L.X. , C.D. Roberts, AB, L.X. GutiérrezGutiérrez and P.C. Tandy, and P.C. Tandy, PhysPhys. Rev. C82, . Rev. C82, (065202:1(065202:1--11) 2010.11) 2010.

Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

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TheThe transitiontransition formform factorfactor:: TheThe transitiontransition formform factorfactor::

TheThe leadingleading twisttwist pQDCpQDC calculationcalculation:: TheThe leadingleading twisttwist pQDCpQDC calculationcalculation::

G.P. G.P. LepageLepage, and S.J. Brodsky,, and S.J. Brodsky, PhysPhys. Rev. D22, 2157 (1980).. Rev. D22, 2157 (1980).

Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

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Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

TheThe transitiontransition formform factorfactor:: TheThe transitiontransition formform factorfactor::

•• BelleBelle IIII willwill havehave 4040 timestimes moremore luminosityluminosity.. •• BelleBelle IIII willwill havehave 4040 timestimes moremore luminosityluminosity..

PrecisePrecise measurementsmeasurements atat largelarge QQ22 willwill provideprovide aa stringentstringent constraintconstraint onon thethe patternpattern ofof chiralchiral symmetrysymmetry breakingbreaking.. PrecisePrecise measurementsmeasurements atat largelarge QQ22 willwill provideprovide aa stringentstringent constraintconstraint onon thethe patternpattern ofof chiralchiral symmetrysymmetry breakingbreaking..

Vladimir Vladimir SavinovSavinov:: 55thth Workshop of the APSWorkshop of the APS Topical Group on Topical Group on HadronicHadronic PhysicsPhysics

Vladimir Vladimir SavinovSavinov:: 55thth Workshop of the APSWorkshop of the APS Topical Group on Topical Group on HadronicHadronic PhysicsPhysics

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•• DoubleDouble taggingtagging?? •• DoubleDouble taggingtagging??

Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

•• AsAs thisthis processprocess isis independentindependent ofof thethe PDA,PDA, probingprobing thethe patternpattern ofof chiralchiral symmetrysymmetry breakingbreaking cancan bebe neaterneater.. •• AsAs thisthis processprocess isis independentindependent ofof thethe PDA,PDA, probingprobing thethe patternpattern ofof chiralchiral symmetrysymmetry breakingbreaking cancan bebe neaterneater..

Vladimir Vladimir SavinovSavinov Vladimir Vladimir SavinovSavinov

•• AtAt largelarge QQ22,, thethe formform factorfactor calculationscalculations requirerequire knowingknowing massmass functionfunction inin complexcomplex spacespace wherewhere singularitiessingularities areare present,present, makingmaking numericalnumerical integrationintegration impossibleimpossible..

•• AtAt largelarge QQ22,, thethe formform factorfactor calculationscalculations requirerequire knowingknowing massmass functionfunction inin complexcomplex spacespace wherewhere singularitiessingularities areare present,present, makingmaking numericalnumerical integrationintegration impossibleimpossible..

•• HowHow mustmust oneone proceedproceed?? •• HowHow mustmust oneone proceedproceed??

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Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

•• QuarkQuark PropagatorPropagator:: •• QuarkQuark PropagatorPropagator::

also for s and also for s and c quarksc quarks

also for s and also for s and c quarksc quarks

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Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

•• InverseInverse QuarkQuark PropagatorPropagator:: •• InverseInverse QuarkQuark PropagatorPropagator::

also for s and also for s and c quarksc quarks

also for s and also for s and c quarksc quarks

Page 27: Form Quarks & Gluons to Hadron Form Factors For Increasing ...lc2013/downloads/talks/... · Adnan Bashir Michoacán University, Mexico Form Quarks & Gluons to Hadron Form Factors

Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

•• FittingFitting thethe BSABSA ofof thethe pionpion:: •• FittingFitting thethe BSABSA ofof thethe pionpion::

•• HowHow wellwell cancan oneone reproducereproduce thethe BSABSA andand thethe associatedassociated physicalphysical observables?observables? •• HowHow wellwell cancan oneone reproducereproduce thethe BSABSA andand thethe associatedassociated physicalphysical observables?observables?

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Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

•• FittingFitting thethe BSABSA ofof thethe pionpion:: (F(F.. AkramAkram,, AB,AB, …… )) •• FittingFitting thethe BSABSA ofof thethe pionpion:: (F(F.. AkramAkram,, AB,AB, …… ))

•• SuchSuch formform allowsallows oneone toto fitfit nicelynicely thethe BSAsBSAs E,F,G,HE,F,G,H asas wellwell asas capturecapture theirtheir asymptoticasymptotic momentummomentum dependencedependence satisfactorilysatisfactorily..

•• SuchSuch formform allowsallows oneone toto fitfit nicelynicely thethe BSAsBSAs E,F,G,HE,F,G,H asas wellwell asas capturecapture theirtheir asymptoticasymptotic momentummomentum dependencedependence satisfactorilysatisfactorily..

•• TheThe firstfirst fewfew momentsmoments ofof ChebyshevChebyshev polynomialspolynomials areare alsoalso ratherrather wellwell reproducedreproduced.. •• TheThe firstfirst fewfew momentsmoments ofof ChebyshevChebyshev polynomialspolynomials areare alsoalso ratherrather wellwell reproducedreproduced..

•• TheseThese areare beingbeing implementedimplemented inin formform factorfactor calculationscalculations forfor arbitrarilyarbitrarily highhigh virtualitiesvirtualities.. •• TheseThese areare beingbeing implementedimplemented inin formform factorfactor calculationscalculations forfor arbitrarilyarbitrarily highhigh virtualitiesvirtualities..

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Charting out the QCharting out the Q22 EvolutionEvolution Charting out the QCharting out the Q22 EvolutionEvolution

•• LL.. ChangChang –– IVIV InternationalInternational MeetingMeeting onon NonNon PerturbativePerturbative MethodsMethods inin FieldField TheoryTheory,, MoreliaMorelia,, Mexico,Mexico, 66--1010 May,May, 20132013.. •• LL.. ChangChang –– IVIV InternationalInternational MeetingMeeting onon NonNon PerturbativePerturbative MethodsMethods inin FieldField TheoryTheory,, MoreliaMorelia,, Mexico,Mexico, 66--1010 May,May, 20132013..

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ConclusionsConclusions

Dynamical Dynamical chiralchiral symmetry breaking and the momentum symmetry breaking and the momentum dependence of the quark mass function in QCD have dependence of the quark mass function in QCD have experimental signals which enable us to differentiate experimental signals which enable us to differentiate their predictions from alternative patterns of SB.their predictions from alternative patterns of SB.

Dynamical Dynamical chiralchiral symmetry breaking and the momentum symmetry breaking and the momentum dependence of the quark mass function in QCD have dependence of the quark mass function in QCD have experimental signals which enable us to differentiate experimental signals which enable us to differentiate their predictions from alternative patterns of SB.their predictions from alternative patterns of SB.

A systematic framework based upon the QCD equationsA systematic framework based upon the QCD equations of motion of motion (Euclidean based SDE(Euclidean based SDE) and its symmetries ) and its symmetries can can help chart out help chart out and comprehend the Qand comprehend the Q22 evolution of these evolution of these form form factorsfactors. .

A systematic framework based upon the QCD equationsA systematic framework based upon the QCD equations of motion of motion (Euclidean based SDE(Euclidean based SDE) and its symmetries ) and its symmetries can can help chart out help chart out and comprehend the Qand comprehend the Q22 evolution of these evolution of these form form factorsfactors. .

The QThe Q22 evolution of the evolution of the hadronichadronic form factors, their form factors, their experimental evaluation and theoretical predictions areexperimental evaluation and theoretical predictions are likely to provide likely to provide better better understanding of how DCSBunderstanding of how DCSB and confinement work in QCD.and confinement work in QCD.

The QThe Q22 evolution of the evolution of the hadronichadronic form factors, their form factors, their experimental evaluation and theoretical predictions areexperimental evaluation and theoretical predictions are likely to provide likely to provide better better understanding of how DCSBunderstanding of how DCSB and confinement work in QCD.and confinement work in QCD.