Adnan Bashir, Michoacán University, Mexico * Transition Form Factor Theory vs Experiment: Past,...

Adnan Bashir , Michoacán Adnan Bashir , Michoacán University, MexicoUniversity, Mexico

* * Transition Form FactorTransition Form FactorTheory vs Experiment: Past, Present & Theory vs Experiment: Past, Present &

Future Future

Collaborators:Collaborators:F. Akram, University of Punjab, PakistanF. Akram, University of Punjab, PakistanY.X. Liu, Peking University, ChinaY.X. Liu, Peking University, ChinaM.R. Pennington, Durham University & JLab, UKM.R. Pennington, Durham University & JLab, UKJ.R. Quintero, Huelva University, SpainJ.R. Quintero, Huelva University, SpainA. Raya, Michoacán University, MexicoA. Raya, Michoacán University, MexicoC.D. Roberts, Argonne National Laboratory, USAC.D. Roberts, Argonne National Laboratory, USAP.C. Tandy, Kent State University, USAP.C. Tandy, Kent State University, USAL. Albino, University of Michoacán, MexicoL. Albino, University of Michoacán, MexicoR. Bermudez, University of Sonora, MexicoR. Bermudez, University of Sonora, MexicoL. Chang, University of Adelaide, AustraliaL. Chang, University of Adelaide, AustraliaL.X. Gutiérrez, University of Michoacán, MexicoL.X. Gutiérrez, University of Michoacán, MexicoK. Raya, University of Michoacán, MexicoK. Raya, University of Michoacán, MexicoD. Wilson, Jlab, USA D. Wilson, Jlab, USA

Institute of High Energy PhysicsInstitute of High Energy PhysicsChinese Academy of SciencesChinese Academy of Sciences

November 7, 2013 November 7, 2013

ContentsContents

• ConclusionsConclusions• ConclusionsConclusions

• IntroductionIntroduction• IntroductionIntroduction

• Schwinger-Dyson Equations – The Schwinger-Dyson Equations – The IngredientsIngredients

• Schwinger-Dyson Equations – The Schwinger-Dyson Equations – The IngredientsIngredients

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

Quark-Photon Vertex/Quark Gluon VertexQuark-Photon Vertex/Quark Gluon VertexQuark-Photon Vertex/Quark Gluon VertexQuark-Photon Vertex/Quark Gluon Vertex

Pion Electromagnetic Form Factor Pion Electromagnetic Form Factor Pion Electromagnetic Form Factor Pion Electromagnetic Form Factor

Gluon PropagatorGluon PropagatorGluon PropagatorGluon Propagator

• The QThe Q22 Evolution of Form Factors: Evolution of Form Factors: • The QThe Q22 Evolution of Form Factors: Evolution of Form Factors:

Pion to Pion to * Transition Form Factor * Transition Form Factor Pion to Pion to * Transition Form Factor * Transition Form Factor

Mass Function and Form Factors Mass Function and Form Factors Mass Function and Form Factors Mass Function and Form Factors

The transition form factor is measured The transition form factor is measured through the process: through the process: The transition form factor is measured The transition form factor is measured through the process: through the process:

IntroductionIntroductionIntroductionIntroduction

The transition form factor: The transition form factor: The transition form factor: The transition form factor:

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

The leading twist pQDC calculation was carried The leading twist pQDC calculation was carried out in: out in: The leading twist pQDC calculation was carried The leading twist pQDC calculation was carried out in: out in:

G.P. Lepage, and S.J. Brodsky, G.P. Lepage, and S.J. Brodsky, Phys. Rev. D22, 2157 Phys. Rev. D22, 2157 (1980).(1980).



Collinear factorization:Collinear factorization:Collinear factorization:Collinear factorization:

Transition form factor is the correlator of two Transition form factor is the correlator of two currents :currents :Transition form factor is the correlator of two Transition form factor is the correlator of two currents :currents :

T: hard scattering amplitude with quark gluon sub-T: hard scattering amplitude with quark gluon sub-processes.processes.T: hard scattering amplitude with quark gluon sub-T: hard scattering amplitude with quark gluon sub-processes.processes.

is the pion distribution is the pion distribution amplitude:amplitude:is the pion distribution is the pion distribution amplitude:amplitude:

In asymptotic QCD:In asymptotic QCD:In asymptotic QCD:In asymptotic QCD:


Hadronic form factorsHadronic form factors are intimately related to are intimately related to their their internal structure. The challenge of their internal structure. The challenge of their understandingunderstandingoccupies a central place in particle/nuclear occupies a central place in particle/nuclear physics. physics.

Hadronic form factorsHadronic form factors are intimately related to are intimately related to their their internal structure. The challenge of their internal structure. The challenge of their understandingunderstandingoccupies a central place in particle/nuclear occupies a central place in particle/nuclear physics. physics. QCDQCD is the established theory of strong is the established theory of strong interactions interactions which is responsible for binding which is responsible for binding quarks and gluonsquarks and gluons totoform these form these hadrons (mesons and baryons)hadrons (mesons and baryons). .

QCDQCD is the established theory of strong is the established theory of strong interactions interactions which is responsible for binding which is responsible for binding quarks and gluonsquarks and gluons totoform these form these hadrons (mesons and baryons)hadrons (mesons and baryons). . Unraveling Unraveling hadronic form factors hadronic form factors from thefrom the basic basic buildingbuildingblocks of QCDblocks of QCD is an outstanding problem. is an outstanding problem.

Unraveling Unraveling hadronic form factors hadronic form factors from thefrom the basic basic buildingbuildingblocks of QCDblocks of QCD is an outstanding problem. is an outstanding problem. Schwinger-Dyson equationsSchwinger-Dyson equations are the fundamental are the fundamental equationsequationsof QCD and combine its of QCD and combine its UVUV and and IRIR behavior. behavior.

Schwinger-Dyson equationsSchwinger-Dyson equations are the fundamental are the fundamental equationsequationsof QCD and combine its of QCD and combine its UVUV and and IRIR behavior. behavior. Thus they provide a platform to study the Thus they provide a platform to study the form form factorsfactorsfrom small to large photon virtualitiesfrom small to large photon virtualities, studied at , studied at differentdifferenthadron facilities. hadron facilities.

Thus they provide a platform to study the Thus they provide a platform to study the form form factorsfactorsfrom small to large photon virtualitiesfrom small to large photon virtualities, studied at , studied at differentdifferenthadron facilities. hadron facilities.

• SDE for QCD have been extensively applied to SDE for QCD have been extensively applied to mesonmeson spectra and interactions below the masses ~ 1 spectra and interactions below the masses ~ 1 GeV. GeV.

• SDE for QCD have been extensively applied to SDE for QCD have been extensively applied to mesonmeson spectra and interactions below the masses ~ 1 spectra and interactions below the masses ~ 1 GeV. GeV. • They have been employed to calculate:They have been employed to calculate:• They have been employed to calculate:They have been employed to calculate:

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

P. Maris, P.C. Tandy, Phys. Rev. C62 055204 P. Maris, P.C. Tandy, Phys. Rev. C62 055204 (2000).(2000).D. Jarecke, P. Maris, P.C. Tandy, Phys. Rev. C67 035202 (2003).D. Jarecke, P. Maris, P.C. Tandy, Phys. Rev. C67 035202 (2003).

the masses, charge radii and decays of mesonsthe masses, charge radii and decays of mesons the masses, charge radii and decays of mesonsthe masses, charge radii and decays of mesons

elastic pion and kaon form factorselastic pion and kaon form factors elastic pion and kaon form factorselastic pion and kaon form factors

pion and kaon valence quark-distribution pion and kaon valence quark-distribution functionsfunctions pion and kaon valence quark-distribution pion and kaon valence quark-distribution functionsfunctions

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

G. Eichmann, et. al., G. Eichmann, et. al., Phys. Rev. C79 012202 (2009).D. Wilson, L. Chang and C.D. Roberts, Phys. Rev. C85 025205 (2012).D. Wilson, L. Chang and C.D. Roberts, Phys. Rev. C85 025205 (2012).““Collective Perspective on advances in DSE QCD”,AB , Collective Perspective on advances in DSE QCD”,AB , L. ChangL. Chang, I.C. , I.C. Cloet, B. El Bennich, Cloet, B. El Bennich, Y. LiuY. Liu, C.D. Roberts, P.C. Tandy, Commun. Theor. , C.D. Roberts, P.C. Tandy, Commun. Theor. Phys. 58 79 (2012) Phys. 58 79 (2012)


• Through Through SDEsSDEs, we can study the structure of , we can study the structure of hadronshadrons through through first principles in the continuumfirst principles in the continuum. .

• Through Through SDEsSDEs, we can study the structure of , we can study the structure of hadronshadrons through through first principles in the continuumfirst principles in the continuum. .


Parity Parity Partners Partners &&

Chiral Chiral Symmetry Symmetry BreakingBreaking

Parity Parity Partners Partners &&

Chiral Chiral Symmetry Symmetry BreakingBreaking

IntroductionIntroduction

The QCD Lagrangian:The QCD Lagrangian:The QCD Lagrangian:The QCD Lagrangian:

0.2 fm 0.02 fm 0.002 fm

1000 MeV1000 MeV

5 MeV5 MeV

QCDQCD

We can trace the origin of 98% of the luminous matter to QCD

interactions.

We can trace the origin of 98% of the luminous matter to QCD

interactions.

IntroductionIntroduction

AsymptotiAsymptotic Freedomc FreedomAsymptotiAsymptotic Freedomc Freedom

InfraredInfraredSlaverySlaveryInfraredInfraredSlaverySlavery

Simplest SDE -Simplest SDE -quark propagator:quark propagator:Simplest SDE -Simplest SDE -quark propagator:quark propagator:

The Quark PropagatorThe Quark PropagatorThe Quark PropagatorThe Quark Propagator

The quark The quark propagatorpropagator

::

The quark The quark propagatorpropagator

::

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

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

Higgs mechanism isHiggs mechanism is almost almost irrelevantirrelevant to the to theinfrared enhancement infrared enhancement

ofofquark mass.quark mass.

Higgs mechanism isHiggs mechanism is almost almost irrelevantirrelevant to the to theinfrared enhancement infrared enhancement

ofofquark mass.quark mass.

The Quark PropagatorThe Quark PropagatorThe Quark PropagatorThe Quark Propagator

The Gluon PropagatorThe Gluon Propagator

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

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

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

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

A. Ayala et. al. Phys. Rev. D86 074512 (2012).A. Ayala et. al. Phys. Rev. D86 074512 (2012).

AB, C. Lei, I. Cloet, B. El Bennich, Y. Liu, C. AB, C. Lei, I. Cloet, B. El Bennich, Y. Liu, C. Roberts, Roberts,

P. Tandy, Comm. Theor. Phys. 58 79-134 (2012) P. Tandy, Comm. Theor. Phys. 58 79-134 (2012)

Gluon Propagator:Gluon Propagator: Gluon Propagator:Gluon Propagator:

A. Bashir, A. Raya, J. Rodrigues-Quintero, A. Bashir, A. Raya, J. Rodrigues-Quintero, Phys. Rev. D88 054003 (2013).Phys. Rev. D88 054003 (2013).

I.L. Bogolubsky, et. al. Phys. Lett. B676 69 I.L. Bogolubsky, et. al. Phys. Lett. B676 69 (2009). (2009).

J. Skullerud, P. Bowman, A. Kizilersu, D. Leinweber, A. Williams, J. High J. Skullerud, P. Bowman, A. Kizilersu, D. Leinweber, A. Williams, J. High Energy Phys. 04 047 (2003) Energy Phys. 04 047 (2003)

M. Bhagwat, M. Pichowsky, C. Roberts, P. Tandy, Phys. Rev. C68 015203 M. Bhagwat, M. Pichowsky, C. Roberts, P. Tandy, Phys. Rev. C68 015203 (2003).(2003).AB, L. Gutiérrez, M. Tejeda, AIP Conf. Proc. 1026 262 (2008).AB, L. Gutiérrez, M. Tejeda, AIP Conf. Proc. 1026 262 (2008).

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

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

The Quark-Gluon VertexThe Quark-Gluon VertexThe Quark-Gluon VertexThe Quark-Gluon Vertex

Fortunately, both the quark-photon & the quark-Fortunately, both the quark-photon & the quark-gluongluonvertices require the same number of basis tensors vertices require the same number of basis tensors forfortheir description. So a unified approach is their description. So a unified approach is possible.possible.

The Quark-Photon Vertex The Quark-Photon Vertex In studying the elastic or transition form factors In studying the elastic or transition form factors ofofhadrons, it is the photon which probes its hadrons, it is the photon which probes its constituents,constituents,highlighting the importance of the quark-photon highlighting the importance of the quark-photon vertex. vertex.

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

A. Kizilersu and M.R. Pennington Phys. Rev. D79 125020 A. Kizilersu and M.R. Pennington Phys. Rev. D79 125020 (2009)(2009) L. Chang, C.D. Roberts, Phys. Rev. Lett. 103 081601 (2009) L. Chang, C.D. Roberts, Phys. Rev. Lett. 103 081601 (2009)

AB, C. Calcaneo, L. Gutiérrez, M. Tejeda, Phys. Rev. D83 033003 (2011)AB, C. Calcaneo, L. Gutiérrez, M. Tejeda, Phys. Rev. D83 033003 (2011)

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

Phenomenology

GaugeCovariance

Lattice

MultiplicativeRenormalization

PerturbationTheory

Quark-photon/ quark-gluon

vertex

Significantly, this last ansatz contains nontrivial Significantly, this last ansatz contains nontrivial factors associated with those tensors whose factors associated with those tensors whose appearance is solely driven by dynamical chiral appearance is solely driven by dynamical chiral symmetry breaking.symmetry breaking.It yields gauge independent critical coupling in It yields gauge independent critical coupling in QED.QED.

Quark-photon Quark-photon VertexVertexQuark-photon Quark-photon VertexVertex

The Quark-Photon VertexThe Quark-Photon VertexThe Quark-Photon VertexThe Quark-Photon Vertex

It also reproduces large anomalous It also reproduces large anomalous magnetic moment for quarks in infrared.magnetic moment for quarks in infrared.RocíoRocío Bermúdez,Bermúdez, LuisLuis AlbinoAlbino: Quark-Gluon Vertex.: Quark-Gluon Vertex.

The QThe Q22 Evolution of Form Evolution of Form FactorsFactors


Observing the transition of the hadron from a sea Observing the transition of the hadron from a sea ofofquarks and gluons to the one with valence quarks quarks and gluons to the one with valence quarks alone is an experimental and theoretical alone is an experimental and theoretical challenge. challenge.

Observing the transition of the hadron from a sea Observing the transition of the hadron from a sea ofofquarks and gluons to the one with valence quarks quarks and gluons to the one with valence quarks alone is an experimental and theoretical alone is an experimental and theoretical challenge. challenge.

Schwinger-Dyson equations are the fundamental Schwinger-Dyson equations are the fundamental equationsequationsof QCD and combine its of QCD and combine its UV and IR behaviourUV and IR behaviour. .

Schwinger-Dyson equations are the fundamental Schwinger-Dyson equations are the fundamental equationsequationsof QCD and combine its of QCD and combine its UV and IR behaviourUV and IR behaviour. .

The QThe Q22 Evolution of Form Factors Evolution of Form Factors

Nobel Prize 2008:Nobel Prize 2008:

““for the discovery of the mechanism of for the discovery of the mechanism of spontaneousspontaneous broken symmetry in subatomic physics”broken symmetry in subatomic physics”

Nobel Prize 2008:Nobel Prize 2008:

““for the discovery of the mechanism of for the discovery of the mechanism of spontaneousspontaneous broken symmetry in subatomic physics”broken symmetry in subatomic physics”

quark-anti-quarkquark-anti-quark

We assume that quarks interact not via massless We assume that quarks interact not via massless vector vector boson but instead through a boson but instead through a contact interactioncontact interaction of of veryverymassive gauge boson by assuming:massive gauge boson by assuming:

We assume that quarks interact not via massless We assume that quarks interact not via massless vector vector boson but instead through a boson but instead through a contact interactioncontact interaction of of veryverymassive gauge boson by assuming:massive gauge boson by assuming:

Here Here mmGG=0.8 GeV is a =0.8 GeV is a gluon mass scalegluon mass scale which is which is generatedgenerateddynamically in QCD. dynamically in QCD.

Here Here mmGG=0.8 GeV is a =0.8 GeV is a gluon mass scalegluon mass scale which is which is generatedgenerateddynamically in QCD. dynamically in QCD. Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pene, J. Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pene, J. Rodriguez-Rodriguez-Quintero, J. High Energy Phys. 06, 099 (2008). Quintero, J. High Energy Phys. 06, 099 (2008).

We use We use proper time regularization which proper time regularization which guaranteesguarantees

confinementconfinement and is backed by phenomenology. and is backed by phenomenology.

We use We use proper time regularization which proper time regularization which guaranteesguarantees

confinementconfinement and is backed by phenomenology. and is backed by phenomenology.

withwithwithwith

The QThe Q22 Evolution of Form Factors Evolution of Form Factors

Bethe-Salpeter amplitude for the Bethe-Salpeter amplitude for the pion:pion:Bethe-Salpeter amplitude for the Bethe-Salpeter amplitude for the pion:pion:

Goldberger-Goldberger-Triemann Triemann

relations:relations:

Goldberger-Goldberger-Triemann Triemann

relations:relations:



P. Maris and C.D. Roberts, Phys. Rev. C58 3659-3665 (1998).

Thus the pseudo-Thus the pseudo-vectorvector

component of the BS-component of the BS-amplitude dictates amplitude dictates

thethetransition of the piontransition of the pionform factor to the form factor to the perturbative limit.perturbative limit.

Thus the pseudo-Thus the pseudo-vectorvector

component of the BS-component of the BS-amplitude dictates amplitude dictates

thethetransition of the piontransition of the pionform factor to the form factor to the perturbative limit.perturbative limit.

Pion Form Pion Form Factor:Factor:Pion Form Pion Form Factor:Factor:



For the contact interaction:For the contact interaction:For the contact interaction:For the contact interaction:

Employing a proper time regularization scheme, Employing a proper time regularization scheme, one canone can

ensure ensure (i)(i) confinement, confinement, (ii)(ii) axial vector Ward axial vector WardTakahashi identity is satisfied and Takahashi identity is satisfied and (iii)(iii) the the

correspondingcorrespondingGoldberger-Triemann relations are obeyed:Goldberger-Triemann relations are obeyed:

Employing a proper time regularization scheme, Employing a proper time regularization scheme, one canone can

ensure ensure (i)(i) confinement, confinement, (ii)(ii) axial vector Ward axial vector WardTakahashi identity is satisfied and Takahashi identity is satisfied and (iii)(iii) the the

correspondingcorrespondingGoldberger-Triemann relations are obeyed:Goldberger-Triemann relations are obeyed:



A fully consistent treatment of the contact A fully consistent treatment of the contact interaction model is interaction model is simple to implementsimple to implement and and can help us provide useful results which can be can help us provide useful results which can be compared and contrasted with compared and contrasted with full QCD QCD calculation and experiment.calculation and experiment.With the contact interaction, With the contact interaction, masses of meson and masses of meson and baryon ground and excited-statesbaryon ground and excited-states can and have can and have been obtained been obtained successfully.successfully.C. Chen, L. Chang, C.D. Roberts, S. Wan, D.J. Wilson, Few Body Syst. C. Chen, L. Chang, C.D. Roberts, S. Wan, D.J. Wilson, Few Body Syst. 53, 293 (2012)53, 293 (2012)

H.L.L. Roberts, L. Chang, I.C. Cloet, C.D. Roberts, Few Body Syst. H.L.L. Roberts, L. Chang, I.C. Cloet, C.D. Roberts, Few Body Syst. 51, 1 (2011),51, 1 (2011),

Even a simple contact interaction produces a Even a simple contact interaction produces a parity-parity-partner for each ground-statepartner for each ground-state that is always that is always more more massive than its first radial excitationmassive than its first radial excitation so that, in the so that, in the nucleon channel, e.g., the first nucleon channel, e.g., the first JJPP = ½ = ½-- state lies state lies above the second Jabove the second JPP = ½ = ½++ state. Lattice has not state. Lattice has not achieved this so far.achieved this so far.Form factorsForm factors are harder but their are harder but their ratiosratios may be may be closercloserto exact SDE predictions.to exact SDE predictions.



Within the rainbow ladder truncation, the elasticWithin the rainbow ladder truncation, the elasticelectromagnetic pion form factor: electromagnetic pion form factor: Within the rainbow ladder truncation, the elasticWithin the rainbow ladder truncation, the elasticelectromagnetic pion form factor: electromagnetic pion form factor: The pattern of chiral symmetry breaking The pattern of chiral symmetry breaking dictates dictates the the momentum dependence of the elastic pion form momentum dependence of the elastic pion form factor. factor.

The pattern of chiral symmetry breaking The pattern of chiral symmetry breaking dictates dictates the the momentum dependence of the elastic pion form momentum dependence of the elastic pion form factor. factor.

L. Gutiérrez, AB, I.C. Cloet, C.D. Roberts, Phys. Rev. C81 065202 (2010).L. Gutiérrez, AB, I.C. Cloet, C.D. Roberts, Phys. Rev. C81 065202 (2010).

F. Akram, AB, L. Gutiérrez, B. Masud, J. Quintero, C. Calcaneo, M. Tejeda, F. Akram, AB, L. Gutiérrez, B. Masud, J. Quintero, C. Calcaneo, M. Tejeda, Phys Rev. D87 013011 (2013). [QED]Phys Rev. D87 013011 (2013). [QED]

Pion Electromagnetic Form FactorPion Electromagnetic Form Factor

Pion Electromagnetic Form FactorPion Electromagnetic Form Factor

When do we expect perturbation theory to set in? When do we expect perturbation theory to set in? When do we expect perturbation theory to set in? When do we expect perturbation theory to set in?

Perturbative

Momentum transfer Q is primarily shared equally Momentum transfer Q is primarily shared equally (Q/2) among quarks as BSA is peaked at zero (Q/2) among quarks as BSA is peaked at zero relative momentum. relative momentum.

Momentum transfer Q is primarily shared equally Momentum transfer Q is primarily shared equally (Q/2) among quarks as BSA is peaked at zero (Q/2) among quarks as BSA is peaked at zero relative momentum. relative momentum.

Jlab 12GeV: 2<Q2<9 GeV2 electromagnetic and transition pion form factors.

The The transition form factor:transition form factor: The The transition form factor:transition form factor:

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

The leading twist asymptotic QCD calculation: The leading twist asymptotic QCD calculation: The leading twist asymptotic QCD calculation: The leading twist asymptotic QCD calculation:

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

GeV2

H.L.L. Robertes, C.D. Roberts, AB, L.X. H.L.L. Robertes, C.D. Roberts, AB, L.X. Gutiérrez and P.C. Tandy, Gutiérrez and P.C. Tandy, Phys. Rev. Phys. Rev. C82, (065202:1-11) 2010.C82, (065202:1-11) 2010.

Pion to Pion to * Transition Form * Transition Form FactorFactor


The transition form factor: The transition form factor: The transition form factor: The transition form factor:

• Belle II will have 40 times more luminosity. Belle II will have 40 times more luminosity. • Belle II will have 40 times more luminosity. Belle II will have 40 times more luminosity.

Precise measurements at large QPrecise measurements at large Q22 will provide a will provide a stringentstringentconstraint on the constraint on the pattern of chiral symmetry pattern of chiral symmetry breakingbreaking. .

Precise measurements at large QPrecise measurements at large Q22 will provide a will provide a stringentstringentconstraint on the constraint on the pattern of chiral symmetry pattern of chiral symmetry breakingbreaking. .

Vladimir Savinov:Vladimir Savinov: 55thth Workshop of the APS Workshop of the APSTopical Group on HadronicTopical Group on HadronicPhysics, April 2013.Physics, April 2013.

Vladimir Savinov:Vladimir Savinov: 55thth Workshop of the APS Workshop of the APSTopical Group on HadronicTopical Group on HadronicPhysics, April 2013.Physics, April 2013.



Transfer of momentum dependence in QCD is Transfer of momentum dependence in QCD is different.different.Transfer of momentum dependence in QCD is Transfer of momentum dependence in QCD is different.different.

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



Bethe Salpeter Amplitudes:Bethe Salpeter Amplitudes:Bethe Salpeter Amplitudes:Bethe Salpeter Amplitudes:

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



Charting out the QCharting out the Q22 Evolution EvolutionCharting out the QCharting out the Q22 Evolution Evolution

Bethe Salpeter Amplitudes:Bethe Salpeter Amplitudes:Bethe Salpeter Amplitudes:Bethe Salpeter Amplitudes:

F. Akram, AB, K. Raya, work in progress. F. Akram, AB, K. Raya, work in progress. How this dependence feeds into the study of the How this dependence feeds into the study of the pion electromagnetic and transition form factors pion electromagnetic and transition form factors form factors calculation is under study.form factors calculation is under study.

How this dependence feeds into the study of the How this dependence feeds into the study of the pion electromagnetic and transition form factors pion electromagnetic and transition form factors form factors calculation is under study.form factors calculation is under study.

Pion to Pion to * Transition Form * Transition Form FactorCFactorC


Precise calculations with different interactions (pPrecise calculations with different interactions (p22))--

α α atatincreasing Qincreasing Q22 will provide a stringent constraint on will provide a stringent constraint on thethepattern of chiral symmetry breakingpattern of chiral symmetry breaking. .

Precise calculations with different interactions (pPrecise calculations with different interactions (p22))--

α α atatincreasing Qincreasing Q22 will provide a stringent constraint on will provide a stringent constraint on thethepattern of chiral symmetry breakingpattern of chiral symmetry breaking. .

• Double tagging? Double tagging? • Double tagging? Double tagging?

• Probing the (pProbing the (p22))-α-α dependence can be neater. dependence can be neater. • Probing the (pProbing the (p22))-α-α dependence can be neater. dependence can be neater.

Vladimir SavinovVladimir SavinovVladimir SavinovVladimir Savinov



ConclusionsConclusions

A systematic framework based upon the A systematic framework based upon the QCD QCD equationsequationsof motion (SDE)of motion (SDE) and its symmetries is required to and its symmetries is required to chartchartout and comprehend the out and comprehend the QQ22 evolution evolution of these of these form form factorsfactors and make predictions. and make predictions.

A systematic framework based upon the A systematic framework based upon the QCD QCD equationsequationsof motion (SDE)of motion (SDE) and its symmetries is required to and its symmetries is required to chartchartout and comprehend the out and comprehend the QQ22 evolution evolution of these of these form form factorsfactors and make predictions. and make predictions.

The large QThe large Q22 evolution of the pion form factors, evolution of the pion form factors, their their experimental evaluationexperimental evaluation and and theoretical theoretical predictionspredictions are likely to provide us with deep are likely to provide us with deep understanding of the understanding of the pattern of pattern of DCSB DCSB and and confinementconfinement of the of the fundamentalfundamentaldegrees of freedom, namely degrees of freedom, namely quarksquarks and and gluonsgluons..

Predictions based upon the Predictions based upon the contact interactioncontact interaction, , QCD SDEQCD SDEas well as the as well as the intermediate power lawsintermediate power laws (p (p22))-- can can provide experimentalist with a platform to provide experimentalist with a platform to compare and contrast compare and contrast future future experimental resultsexperimental results. . Mesons, diquarks, baryonsMesons, diquarks, baryons!!! !!!

Predictions based upon the Predictions based upon the contact interactioncontact interaction, , QCD SDEQCD SDEas well as the as well as the intermediate power lawsintermediate power laws (p (p22))-- can can provide experimentalist with a platform to provide experimentalist with a platform to compare and contrast compare and contrast future future experimental resultsexperimental results. . Mesons, diquarks, baryonsMesons, diquarks, baryons!!! !!!

V.P.V.P. Druzhinin, PoS EPS-HEP2009, 051 (2009) [arXiv:0909.3148 [hep-Druzhinin, PoS EPS-HEP2009, 051 (2009) [arXiv:0909.3148 [hep-ex]] and preliminary results presented at ICHEP2010.ex]] and preliminary results presented at ICHEP2010.

BaBar transition BaBar transition form form factors: factors:

BaBar transition BaBar transition form form factors: factors:

These results are inThese results are inagreement with pQCD: agreement with pQCD: These results are inThese results are inagreement with pQCD: agreement with pQCD:

T. Feldman, P. Kroll, Phys. Lett. B T. Feldman, P. Kroll, Phys. Lett. B 413413410 (1997).410 (1997).

Pattern of DCSB & Experimental Pattern of DCSB & Experimental SignaturesSignatures

Pattern of DCSB & Experimental Pattern of DCSB & Experimental SignaturesSignatures

There are attempts to explain the BaBar data There are attempts to explain the BaBar data whichwhichemploy pion DAs in disaccord with asymptotic employ pion DAs in disaccord with asymptotic QCD. QCD.

There are attempts to explain the BaBar data There are attempts to explain the BaBar data whichwhichemploy pion DAs in disaccord with asymptotic employ pion DAs in disaccord with asymptotic QCD. QCD. However, high QHowever, high Q22 BaBar data requires a pion DA BaBar data requires a pion DA with awith asizeable number of higher Gegenbauer sizeable number of higher Gegenbauer coefficients. coefficients.

However, high QHowever, high Q22 BaBar data requires a pion DA BaBar data requires a pion DA with awith asizeable number of higher Gegenbauer sizeable number of higher Gegenbauer coefficients. coefficients.

The rapid growth of TFF for The rapid growth of TFF for ππ00 is also not is also not compatible withcompatible withlight-front holographic models which yield results light-front holographic models which yield results in goodin goodagreement with the TFFs of agreement with the TFFs of ηη and and ηη**. .

The rapid growth of TFF for The rapid growth of TFF for ππ00 is also not is also not compatible withcompatible withlight-front holographic models which yield results light-front holographic models which yield results in goodin goodagreement with the TFFs of agreement with the TFFs of ηη and and ηη**. .

There are suggestions of higher resonance There are suggestions of higher resonance contributionscontributionsaltering the high Qaltering the high Q22 monopole behavior of the monopole behavior of the ππ00 TFFTFF..

There are suggestions of higher resonance There are suggestions of higher resonance contributionscontributionsaltering the high Qaltering the high Q22 monopole behavior of the monopole behavior of the ππ00 TFFTFF..

P. Kroll, Eur. Phys. J. C71, 1623 (2011).A.V. Radyushkin, Phys. Rev. D80, 094009 (2009).A. Dorokhov, JETP Lett. 92, 707 (2010).T. N. Pham and X. Y. Pham, Int. J. Mod. Phys. A26 4125 (2011).

A.P. Bakulev et. Al. Nucl. Phys. B219 133 (2011).S. Brodsky et. al. Phys. Rev. D84 033001 (2011)

Axial anomaly sum rule has also been invoked. It Axial anomaly sum rule has also been invoked. It requiresrequiresassumptions seeking theoretical justifications. assumptions seeking theoretical justifications.

Axial anomaly sum rule has also been invoked. It Axial anomaly sum rule has also been invoked. It requiresrequiresassumptions seeking theoretical justifications. assumptions seeking theoretical justifications.

D. Melikhov and B. Stech, arXiv:1202.4471 [hep-ph].

S.J. Brodsky, F-G. Cao, G.F. Teramond, Phys. Rev. D84 075012 (2011).

Adnan Bashir, Michoacán University, Mexico * Transition Form Factor Theory vs Experiment: Past,...

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