Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National...

22
Adnan Bashir Adnan Bashir Michoacán Michoacán University, Mexico University, Mexico Argonne National Laboratory, USA Argonne National Laboratory, USA Kent State University, USA Kent State University, USA γ γ * * π π 0 γ γ Transition Form Fatctor Transition Form Fatctor : QCD & : QCD & BaBar BaBar March 15, 2012 March 15, 2012 Jefferson Laboratory, Jefferson Laboratory, USA USA

Transcript of Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National...

Page 1: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

Adnan Bashir Adnan Bashir Michoacán Michoacán University, MexicoUniversity, Mexico

Argonne National Laboratory, USAArgonne National Laboratory, USAKent State University, USA Kent State University, USA

γγ**ππ00γγ Transition Form FatctorTransition Form Fatctor: QCD & : QCD & BaBarBaBar

March 15, 2012March 15, 2012Jefferson Laboratory, Jefferson Laboratory,

USAUSA

Page 2: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

ContentsContents

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

• ConclusionsConclusions• ConclusionsConclusions

• IntroductionIntroduction• IntroductionIntroduction

• Schwinger-Dyson EquationsSchwinger-Dyson Equations• Schwinger-Dyson EquationsSchwinger-Dyson Equations

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

Quark-Photon VertexQuark-Photon VertexQuark-Photon VertexQuark-Photon Vertex

Pion Bethe-Salpeter Amplitude Pion Bethe-Salpeter Amplitude Pion Bethe-Salpeter Amplitude Pion Bethe-Salpeter Amplitude

• Pion Transition Form Factor Pion Transition Form Factor • Pion Transition Form Factor Pion Transition Form Factor

Page 3: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

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

Page 4: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

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).

IntroductionIntroductionIntroductionIntroduction

Page 5: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

IntroductionIntroductionIntroductionIntroduction

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:

Page 6: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

Schwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson Equations

• Schwinger-Dyson Equations (SDE) are the Schwinger-Dyson Equations (SDE) are the fundamentalfundamental equations of a field theory. equations of a field theory.

• Schwinger-Dyson Equations (SDE) are the Schwinger-Dyson Equations (SDE) are the fundamentalfundamental equations of a field theory. equations of a field theory. • 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. • SDE have been employed to calculate:SDE have been employed to calculate:• SDE have been employed to calculate:SDE 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 , L. Chang, I.C. Collective Perspective on advances in DSE QCD”,AB , L. Chang, I.C. Cloet, B. El Bennich, Y. Liu, C.D. Roberts, P.C. Tandy, Cloet, B. El Bennich, Y. Liu, C.D. Roberts, P.C. Tandy, arXiv:1201.3366[nucl-th]arXiv:1201.3366[nucl-th]

Page 7: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

Schwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson Equations

Rainbow-ladder Rainbow-ladder truncationtruncationRainbow-ladder Rainbow-ladder truncationtruncation

SDE: SDE: Full quark Full quark propagator:propagator:

SDE: SDE: Full quark Full quark propagator:propagator:

Page 8: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

Schwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson Equations

Contact Contact interaction:interaction:

Contact Contact interaction:interaction:

Page 9: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

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:

Schwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson Equations

Page 10: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

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:

Schwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson Equations

Page 11: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

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

Schwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson Equations

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:

Page 12: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

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, arXiv:1112.4847 [nucl-th]..

Phenomenology

GaugeCovariance

Lattice

MultiplicativeRenormalization

PerturbationTheory

Quark-photon/ quark-gluon

vertex

Schwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson EquationsSchwinger-Dyson Equations

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

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

Page 13: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

Pion Electromagnetic Form FactorPion Electromagnetic Form Factor

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).

Page 14: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

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.

Page 15: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

• We can dress We can dress quark-photon vertexquark-photon vertex: : • We can dress We can dress quark-photon vertexquark-photon vertex: :

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

• The corresponding IBS-equation thus yields: The corresponding IBS-equation thus yields: • The corresponding IBS-equation thus yields: The corresponding IBS-equation thus yields:

Pion Electromagnetic Form FactorPion Electromagnetic Form Factor

Page 16: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

• Dressed quark-photon vertexDressed quark-photon vertex with ρ-pole on the with ρ-pole on the time-time- like axis does not alter the asymptotic behaviour like axis does not alter the asymptotic behaviour of theof the form factor for large space-like momenta. form factor for large space-like momenta.

• Dressed quark-photon vertexDressed quark-photon vertex with ρ-pole on the with ρ-pole on the time-time- like axis does not alter the asymptotic behaviour like axis does not alter the asymptotic behaviour of theof the form factor for large space-like momenta. form factor for large space-like momenta.

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

Pion Electromagnetic Form factorPion Electromagnetic Form factor

Page 17: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

Pattern of DCSB & Experimental Pattern of DCSB & Experimental SignaturesSignatures

Page 18: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

QCD based prediction QCD based prediction through SDEthrough SDEQCD based prediction QCD based prediction through SDEthrough SDE

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

Pattern of DCSB & Experimental Pattern of DCSB & Experimental SignaturesSignatures

Quark propagator: quark mass function Quark propagator: quark mass function Quark propagator: quark mass function Quark propagator: quark mass function

Dressed quark-photon vertexDressed quark-photon vertexDressed quark-photon vertexDressed quark-photon vertexPion Bethe-Salpeter amplitude Pion Bethe-Salpeter amplitude Pion Bethe-Salpeter amplitude Pion Bethe-Salpeter amplitude

PQCD predictionPQCD predictionPQCD predictionPQCD prediction

Contact Contact interactioninteractionContact Contact interactioninteraction

Page 19: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

Pattern of DCSB & Experimental Pattern of DCSB & Experimental SignaturesSignatures

Page 20: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

Pattern of DCSB & Experimental Pattern of DCSB & Experimental SignaturesSignatures

• Other transition form factors are in accordance Other transition form factors are in accordance withwith asymptotic QCD: asymptotic QCD:

• Other transition form factors are in accordance Other transition form factors are in accordance withwith asymptotic QCD: asymptotic QCD:

Page 21: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

Could anything conceivably go astray in the Could anything conceivably go astray in the experiment? experiment? Could anything conceivably go astray in the Could anything conceivably go astray in the experiment? experiment? A possible erroneous way to extract the pion A possible erroneous way to extract the pion transitiontransitionform factor from the data could be the problem form factor from the data could be the problem of of ππ00-π-π0 0 subtraction.subtraction.

A possible erroneous way to extract the pion A possible erroneous way to extract the pion transitiontransitionform factor from the data could be the problem form factor from the data could be the problem of of ππ00-π-π0 0 subtraction.subtraction. There is another channel which is the There is another channel which is the crossedcrossedchannel of virtual Compton scattering on a pion.channel of virtual Compton scattering on a pion.

Diehl et. al. Phys. Rev. D62 073014 Diehl et. al. Phys. Rev. D62 073014 (2000). (2000).

The misinterpretation of some events (where the The misinterpretation of some events (where the secondsecondππ0 0 is not seen) may be different at different Qis not seen) may be different at different Q22..

Pattern of DCSB & Experimental Pattern of DCSB & Experimental SignaturesSignatures

Page 22: Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA γ * π 0 γ Transition.

ConclusionsConclusions

Dynamical chiral symmetry breaking and the Dynamical chiral symmetry breaking and the momentum dependence of the quark mass momentum dependence of the quark mass function in QCD have experimental signals which function in QCD have experimental signals which enable us to differentiate its predictions from enable us to differentiate its predictions from others.others.

Dynamical chiral symmetry breaking and the Dynamical chiral symmetry breaking and the momentum dependence of the quark mass momentum dependence of the quark mass function in QCD have experimental signals which function in QCD have experimental signals which enable us to differentiate its predictions from enable us to differentiate its predictions from others.others.

In a fully consistent treatment of pion in SDE QCD In a fully consistent treatment of pion in SDE QCD (static properties, elastic and transition form (static properties, elastic and transition form factors), the asymptotic limit of the product factors), the asymptotic limit of the product QQ22G(QG(Q22), is not exceeded at any finite value of ), is not exceeded at any finite value of spacelike momentum transfer and is in spacelike momentum transfer and is in disagreement with BaBar data for large momentadisagreement with BaBar data for large momenta..

In a fully consistent treatment of pion in SDE QCD In a fully consistent treatment of pion in SDE QCD (static properties, elastic and transition form (static properties, elastic and transition form factors), the asymptotic limit of the product factors), the asymptotic limit of the product QQ22G(QG(Q22), is not exceeded at any finite value of ), is not exceeded at any finite value of spacelike momentum transfer and is in spacelike momentum transfer and is in disagreement with BaBar data for large momentadisagreement with BaBar data for large momenta..

A fully consistent treatment of the contact A fully consistent treatment of the contact interaction model produces results for pion elastic interaction model produces results for pion elastic and transition form factors that are in striking and transition form factors that are in striking disagreement with experiment.disagreement with experiment.

A fully consistent treatment of the contact A fully consistent treatment of the contact interaction model produces results for pion elastic interaction model produces results for pion elastic and transition form factors that are in striking and transition form factors that are in striking disagreement with experiment.disagreement with experiment.