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Adnan Bashir, Michoacán University, Mexico * Transition Form Factor Theory vs Experiment: Past, Present & Future Collaborators: F. Akram, University of Punjab, Pakistan Y.X. Liu, Peking University, China M.R. Pennington, Durham University & JLab, UK J.R. Quintero, Huelva University, Spain A. Raya, Michoacán University, Mexico C.D. Roberts, Argonne National Laboratory, USA P.C. Tandy, Kent State University, USA L. Albino, University of Michoacán, Mexico R. Bermudez, University of Sonora, Mexico L. Chang, University of Adelaide, Australia L.X. Gutiérrez, University of Michoacán, Mexico K. Raya, University of Michoacán, Mexico D. Wilson, Jlab, USA Institute of High Energy Physics Chinese Academy of Sciences November 7, 2013

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Contents Conclusions Conclusions Conclusions Conclusions Conclusions Conclusions Conclusions Conclusions Introduction Introduction Introduction Introduction Introduction Introduction Introduction Introduction Schwinger-Dyson Equations – The Ingredients Schwinger-Dyson Equations – The Ingredients Schwinger-Dyson Equations – The Ingredients Schwinger-Dyson Equations – The Ingredients Schwinger-Dyson Equations – The Ingredients Schwinger-Dyson Equations – The Ingredients Schwinger-Dyson Equations – The Ingredients Schwinger-Dyson Equations – The Ingredients 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 Vertex Quark-Photon Vertex/Quark Gluon Vertex Quark-Photon Vertex/Quark Gluon Vertex Quark-Photon Vertex/Quark Gluon Vertex Pion Electromagnetic Form Factor Pion Electromagnetic Form Factor Pion Electromagnetic Form Factor Pion Electromagnetic Form Factor Gluon Propagator Gluon Propagator Gluon Propagator Gluon Propagator The Q 2 Evolution of Form Factors: The Q 2 Evolution of Form Factors: The Q 2 Evolution of Form Factors: The Q 2 Evolution of Form Factors: The Q 2 Evolution of Form Factors: The Q 2 Evolution of Form Factors: The Q 2 Evolution of Form Factors: The Q 2 Evolution of Form Factors: Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor Mass Function and Form Factors Mass Function and Form Factors Mass Function and Form Factors Mass Function and Form Factors

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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: Introduction

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The transition form factor: The transition form factor: The transition form factor: The transition form factor: CELLO CELLO H.J. Behrend et.al., Z. Phys C49 401 (1991). 0.7 – 2.2 GeV 2 CLEO CLEO J. Gronberg et. al., Phys. Rev. D57 33 (1998). 1.7 – 8.0 GeV 2 BaBar BaBar R. Aubert et. al., Phys. Rev. D80 052002 (2009). 4.0 – 40.0 GeV 2 The leading twist pQDC calculation was carried out in: The leading twist pQDC calculation was carried out in: The leading twist pQDC calculation was carried out in: The leading twist pQDC calculation was carried out in: G.P. Lepage, and S.J. Brodsky, Phys. Rev. D22, 2157 (1980). Introduction

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

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Introduction Hadronic form factors are intimately related to their Hadronic form factors are intimately related to their internal structure. The challenge of their understanding internal structure. The challenge of their understanding occupies a central place in particle/nuclear physics. occupies a central place in particle/nuclear physics. Hadronic form factors are intimately related to their Hadronic form factors are intimately related to their internal structure. The challenge of their understanding internal structure. The challenge of their understanding occupies a central place in particle/nuclear physics. occupies a central place in particle/nuclear physics. QCD is the established theory of strong interactions QCD is the established theory of strong interactions which is responsible for binding quarks and gluons to which is responsible for binding quarks and gluons to form these hadrons (mesons and baryons). form these hadrons (mesons and baryons). QCD is the established theory of strong interactions QCD is the established theory of strong interactions which is responsible for binding quarks and gluons to which is responsible for binding quarks and gluons to form these hadrons (mesons and baryons). form these hadrons (mesons and baryons). Unraveling hadronic form factors from the basic building Unraveling hadronic form factors from the basic building blocks of QCD is an outstanding problem. blocks of QCD is an outstanding problem. Unraveling hadronic form factors from the basic building Unraveling hadronic form factors from the basic building blocks of QCD is an outstanding problem. blocks of QCD is an outstanding problem. Schwinger-Dyson equations are the fundamental equations Schwinger-Dyson equations are the fundamental equations of QCD and combine its UV and IR behavior. of QCD and combine its UV and IR behavior. Schwinger-Dyson equations are the fundamental equations Schwinger-Dyson equations are the fundamental equations of QCD and combine its UV and IR behavior. of QCD and combine its UV and IR behavior. Thus they provide a platform to study the form factors Thus they provide a platform to study the form factors from small to large photon virtualities, studied at different from small to large photon virtualities, studied at different hadron facilities. hadron facilities. Thus they provide a platform to study the form factors Thus they provide a platform to study the form factors from small to large photon virtualities, studied at different from small to large photon virtualities, studied at different hadron facilities. hadron facilities.

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SDE for QCD have been extensively applied to meson SDE for QCD have been extensively applied to meson SDE for QCD have been extensively applied to meson SDE for QCD have been extensively applied to meson spectra and interactions below the masses ~ 1 GeV. spectra and interactions below the masses ~ 1 GeV. SDE for QCD have been extensively applied to meson SDE for QCD have been extensively applied to meson SDE for QCD have been extensively applied to meson SDE for QCD have been extensively applied to meson spectra and interactions below the masses ~ 1 GeV. spectra and interactions below the masses ~ 1 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: 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 (1997). P. Maris, P.C. Tandy, Phys. Rev. C62 055204 (2000). D. Jarecke, P. Maris, P.C. Tandy, Phys. Rev. C67 035202 (2003). the masses, charge radii and decays of mesons the masses, charge radii and decays of mesons the masses, charge radii and decays of mesons the masses, charge radii and decays of mesons elastic pion and kaon form factors elastic pion and kaon form factors elastic pion and kaon form factors elastic pion and kaon form factors pion and kaon valence quark-distribution functions pion and kaon valence quark-distribution functions pion and kaon valence quark-distribution functions pion and kaon valence quark-distribution functions T. Nguyen, AB, C.D. Roberts, P.C. Tandy, T. Nguyen, AB, C.D. Roberts, P.C. Tandy, Phys. Rev. C83062201 (2011). nucleon form factors nucleon form factors nucleon form factors nucleon 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). “Collective Perspective on advances in DSE QCD”,AB, L. Chang, I.C. Cloet, B. El Bennich, Y. Liu, C.D. Roberts, P.C. Tandy, Commun. Theor. Phys. 58 79 (2012) Introduction Through SDEs, we can study the structure of hadrons Through SDEs, we can study the structure of hadrons Through SDEs, we can study the structure of hadrons Through SDEs, we can study the structure of hadrons through first principles in the continuum. through first principles in the continuum. Through SDEs, we can study the structure of hadrons Through SDEs, we can study the structure of hadrons Through SDEs, we can study the structure of hadrons Through SDEs, we can study the structure of hadrons through first principles in the continuum. through first principles in the continuum.

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Introduction Parity Partners & Parity Partners & Chiral Symmetry Breaking Chiral Symmetry Breaking Parity Partners & Parity Partners & Chiral Symmetry Breaking Chiral Symmetry Breaking

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

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0.2 fm0.02 fm0.002 fm 1000 MeV 5 MeV QCD 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.Introduction Asymptotic Freedom Asymptotic Freedom Asymptotic Freedom Asymptotic Freedom Infrared Slavery Infrared Slavery

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Introduction

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Simplest SDE - Simplest SDE - quark propagator: quark propagator: Simplest SDE - Simplest SDE - quark propagator: quark propagator: The Quark Propagator The Quark Propagator The Quark Propagator The Quark Propagator

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The quark The quark propagator: The quark The quark propagator: Quark mass is a Quark mass is a function of momentum, function of momentum, dropping as 1/p 2 in the dropping as 1/p 2 in the ultraviolet. Quark mass is a Quark mass is a function of momentum, function of momentum, dropping as 1/p 2 in the dropping as 1/p 2 in the ultraviolet. Higgs mechanism is Higgs mechanism is almost irrelevant to the almost irrelevant to the infrared enhancement of infrared enhancement of quark mass. quark mass. Higgs mechanism is Higgs mechanism is almost irrelevant to the almost irrelevant to the infrared enhancement of infrared enhancement of quark mass. quark mass. The Quark Propagator The Quark Propagator The Quark Propagator The Quark Propagator

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The Gluon Propagator Modern SDE and lattice results support decoupling solution for the gluon propagator. Modern SDE and lattice results support decoupling solution for the gluon propagator. Modern SDE and lattice results support decoupling solution for the gluon propagator. Modern SDE and lattice results support decoupling solution for the gluon propagator. Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass function. Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass function. Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass function. Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass 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. Roberts, AB, C. Lei, I. Cloet, B. El Bennich, Y. Liu, C. Roberts, 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). I.L. Bogolubsky, et. al. Phys. Lett. B676 69 (2009). I.L. Bogolubsky, et. al. Phys. Lett. B676 69 (2009).

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J. Skullerud, P. Bowman, A. Kizilersu, D. Leinweber, A. Williams, J. High Energy Phys. 04 047 (2003) M. Bhagwat, M. Pichowsky, C. Roberts, P. Tandy, Phys. Rev. C68 015203 (2003). AB, L. Gutiérrez, M. Tejeda, AIP Conf. Proc. 1026 262 (2008). The Quark-Gluon The Quark-Gluon Vertex: One of the 12 form factors One of the 12 form factors The Quark-Gluon The Quark-Gluon Vertex: One of the 12 form factors One of the 12 form factors The Quark-Gluon Vertex The Quark-Gluon Vertex The Quark-Gluon Vertex The Quark-Gluon Vertex

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Fortunately, both the quark-photon & the quark-gluon vertices require the same number of basis tensors for their description. So a unified approach is possible. The Quark-Photon Vertex In studying the elastic or transition form factors of hadrons, it is the photon which probes its constituents, highlighting the importance of the quark-photon vertex.

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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. Kizilersu and M.R. Pennington Phys. Rev. D79 125020 (2009) A. Kizilersu and M.R. Pennington Phys. Rev. D79 125020 (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, Phys. Rev. C85, 045205 (2012). AB, R. Bermudez, L. Chang, C.D. Roberts, Phys. Rev. C85, 045205 (2012). Phenomenology Gauge Covariance Lattice Multiplicative Renormalization Perturbation Theory Quark-photon/ quark-gluon vertex Significantly, this last ansatz contains nontrivial factors associated with those tensors whose appearance is solely driven by dynamical chiral symmetry breaking. It yields gauge independent critical coupling in QED. Quark-photon Vertex Quark-photon Vertex Quark-photon Vertex Quark-photon Vertex The Quark-Photon Vertex The Quark-Photon Vertex The Quark-Photon Vertex The Quark-Photon Vertex It also reproduces large anomalous magnetic moment for quarks in infrared. Rocío Bermúdez, Luis Albino : Quark-Gluon Vertex.

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The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors Observing the transition of the hadron from a sea of Observing the transition of the hadron from a sea of quarks and gluons to the one with valence quarks alone is an experimental and theoretical challenge. quarks and gluons to the one with valence quarks alone is an experimental and theoretical challenge. Observing the transition of the hadron from a sea of Observing the transition of the hadron from a sea of quarks and gluons to the one with valence quarks alone is an experimental and theoretical challenge. quarks and gluons to the one with valence quarks alone is an experimental and theoretical challenge. Schwinger-Dyson equations are the fundamental equations Schwinger-Dyson equations are the fundamental equations of QCD and combine its UV and IR behaviour. of QCD and combine its UV and IR behaviour. Schwinger-Dyson equations are the fundamental equations Schwinger-Dyson equations are the fundamental equations of QCD and combine its UV and IR behaviour. of QCD and combine its UV and IR behaviour.

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The Q 2 Evolution of Form Factors Nobel Prize 2008: Nobel Prize 2008: “for the discovery of the mechanism of spontaneous “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics” broken symmetry in subatomic physics” Nobel Prize 2008: Nobel Prize 2008: “for the discovery of the mechanism of spontaneous “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics” broken symmetry in subatomic physics” quark-anti-quark

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We assume that quarks interact not via massless vector We assume that quarks interact not via massless vector boson but instead through a contact interaction of very boson but instead through a contact interaction of very massive gauge boson by assuming: massive gauge boson by assuming: We assume that quarks interact not via massless vector We assume that quarks interact not via massless vector boson but instead through a contact interaction of very boson but instead through a contact interaction of very massive gauge boson by assuming: massive gauge boson by assuming: Here m G =0.8 GeV is a gluon mass scale which is generated Here m G =0.8 GeV is a gluon mass scale which is generated dynamically in QCD. dynamically in QCD. Here m G =0.8 GeV is a gluon mass scale which is generated Here m G =0.8 GeV is a gluon mass scale which is generated dynamically in QCD. dynamically in QCD. Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pene, J. Rodriguez- Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pene, J. Rodriguez- Quintero, J. High Energy Phys. 06, 099 (2008). Quintero, J. High Energy Phys. 06, 099 (2008). Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pene, J. Rodriguez- Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pene, J. Rodriguez- Quintero, J. High Energy Phys. 06, 099 (2008). Quintero, J. High Energy Phys. 06, 099 (2008). We use proper time regularization which guarantees We use proper time regularization which guarantees confinement and is backed by phenomenology. confinement and is backed by phenomenology. We use proper time regularization which guarantees We use proper time regularization which guarantees confinement and is backed by phenomenology. confinement and is backed by phenomenology. with The Q 2 Evolution of Form Factors

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Bethe-Salpeter amplitude for the pion: Bethe-Salpeter amplitude for the pion: Bethe-Salpeter amplitude for the pion: Bethe-Salpeter amplitude for the pion: Goldberger-Triemann relations: Goldberger-Triemann relations: The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors

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P. Maris and C.D. Roberts, Phys. Rev. C58 3659-3665 (1998). Thus the pseudo-vector Thus the pseudo-vector component of the BS- component of the BS- amplitude dictates the amplitude dictates the transition of the pion transition of the pion form factor to the form factor to the perturbative limit. perturbative limit. Thus the pseudo-vector Thus the pseudo-vector component of the BS- component of the BS- amplitude dictates the amplitude dictates the transition of the pion transition of the pion form factor to the form factor to the perturbative limit. perturbative limit. Pion Form Factor: Pion Form Factor: Pion Form Factor: Pion Form Factor: The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors

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For the contact interaction: For the contact interaction: For the contact interaction: For the contact interaction: Employing a proper time regularization scheme, one can Employing a proper time regularization scheme, one can ensure (i) confinement, (ii) axial vector Ward ensure (i) confinement, (ii) axial vector Ward Takahashi identity is satisfied and (iii) the corresponding Takahashi identity is satisfied and (iii) the corresponding Goldberger-Triemann relations are obeyed: Goldberger-Triemann relations are obeyed: Employing a proper time regularization scheme, one can Employing a proper time regularization scheme, one can ensure (i) confinement, (ii) axial vector Ward ensure (i) confinement, (ii) axial vector Ward Takahashi identity is satisfied and (iii) the corresponding Takahashi identity is satisfied and (iii) the corresponding Goldberger-Triemann relations are obeyed: Goldberger-Triemann relations are obeyed: The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors

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A fully consistent treatment of the contact interaction model is simple to implement and can help us provide useful results which can be compared and contrasted with QCD calculation and experiment. A fully consistent treatment of the contact interaction model is simple to implement and can help us provide useful results which can be compared and contrasted with full QCD calculation and experiment. With the contact interaction, masses of meson and baryon ground and excited-states can and have been obtained successfully. C. Chen, L. Chang, C.D. Roberts, S. Wan, D.J. Wilson, Few Body Syst. 53, 293 (2012) H.L.L. Roberts, L. Chang, I.C. Cloet, C.D. Roberts, Few Body Syst. 51, 1 (2011), Even a simple contact interaction produces a parity-partner for each ground-state that is always more massive than its first radial excitation so that, in the nucleon channel, e.g., the first J P = ½ - state lies above the second J P = ½ + state. Lattice has not achieved this so far. Form factors are harder but their ratios may be closer to exact SDE predictions. The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors The Q 2 Evolution of Form Factors

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Within the rainbow ladder truncation, the elastic Within the rainbow ladder truncation, the elastic electromagnetic pion form factor: electromagnetic pion form factor: Within the rainbow ladder truncation, the elastic Within the rainbow ladder truncation, the elastic electromagnetic pion form factor: electromagnetic pion form factor: The pattern of chiral symmetry breaking dictates the The pattern of chiral symmetry breaking dictates the momentum dependence of the elastic pion form factor. momentum dependence of the elastic pion form factor. The pattern of chiral symmetry breaking dictates the The pattern of chiral symmetry breaking dictates the momentum dependence of the elastic pion form factor. momentum dependence of the elastic pion form 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, Phys Rev. D87 013011 (2013). [QED] Pion Electromagnetic Form Factor

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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 (Q/2) among quarks as BSA is peaked at zero relative momentum. Momentum transfer Q is primarily shared equally (Q/2) among quarks as BSA is peaked at zero relative momentum. Momentum transfer Q is primarily shared equally (Q/2) among quarks as BSA is peaked at zero relative momentum. Momentum transfer Q is primarily shared equally (Q/2) among quarks as BSA is peaked at zero relative momentum. Jlab 12GeV: 2
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The transition form factor: The transition form factor: The transition form factor: The transition form factor: CELLO CELLO H.J. Behrend et.al., Z. Phys C49 401 (1991). 0.7 – 2.2 GeV 2 CLEO CLEO J. Gronberg et. al., Phys. Rev. D57 33 (1998). 1.7 – 8.0 GeV 2 BaBar BaBar R. Aubert et. al., Phys. Rev. D80 052002 (2009). 4.0 – 40.0 GeV 2 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, Phys. Rev. D22, 2157 (1980). Belle Belle S. Uehara et. al., arXiv:1205.3249 [hep-ex] (2012). 4.0 – 40.0 GeV 2 H.L.L. Robertes, C.D. Roberts, AB, L.X. Gutiérrez and P.C. Tandy, Phys. Rev. C82, (065202:1-11) 2010. Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor

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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. 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 Q 2 will provide a stringent Precise measurements at large Q 2 will provide a stringent constraint on the pattern of chiral symmetry breaking. constraint on the pattern of chiral symmetry breaking. Precise measurements at large Q 2 will provide a stringent Precise measurements at large Q 2 will provide a stringent constraint on the pattern of chiral symmetry breaking. constraint on the pattern of chiral symmetry breaking. Vladimir Savinov: Vladimir Savinov: 5 th Workshop of the APS 5 th Workshop of the APS Topical Group on Hadronic Topical Group on Hadronic Physics, April 2013. Physics, April 2013. Vladimir Savinov: Vladimir Savinov: 5 th Workshop of the APS 5 th Workshop of the APS Topical Group on Hadronic Topical Group on Hadronic Physics, April 2013. Physics, April 2013. Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor

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Transfer of momentum dependence in QCD is different. Transfer of momentum dependence in QCD is different. Transfer of momentum dependence in QCD is different. Transfer of momentum dependence in QCD is different. F. Akram, AB, K. Raya, work in progress. Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor

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Bethe Salpeter Amplitudes: Bethe Salpeter Amplitudes: Bethe Salpeter Amplitudes: Bethe Salpeter Amplitudes: F. Akram, AB, K. Raya, work in progress. Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor

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Charting out the Q 2 Evolution Charting out the Q 2 Evolution Charting out the Q 2 Evolution Charting out the Q 2 Evolution Bethe Salpeter Amplitudes: Bethe Salpeter Amplitudes: Bethe Salpeter Amplitudes: Bethe Salpeter Amplitudes: F. Akram, AB, K. Raya, work in progress. How this dependence feeds into the study of the pion electromagnetic and transition form factors form factors calculation is under study. How this dependence feeds into the study of the pion electromagnetic and transition form factors form factors calculation is under study. How this dependence feeds into the study of the pion electromagnetic and transition form factors form factors calculation is under study. How this dependence feeds into the study of the pion electromagnetic and transition form factors form factors calculation is under study.

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Pion to * Transition Form FactorC Pion to * Transition Form FactorC Pion to * Transition Form FactorC Pion to * Transition Form FactorC Precise calculations with different interactions (p 2 ) -α at Precise calculations with different interactions (p 2 ) -α at increasing Q 2 will provide a stringent constraint on the increasing Q 2 will provide a stringent constraint on the pattern of chiral symmetry breaking. pattern of chiral symmetry breaking. Precise calculations with different interactions (p 2 ) -α at Precise calculations with different interactions (p 2 ) -α at increasing Q 2 will provide a stringent constraint on the increasing Q 2 will provide a stringent constraint on the pattern of chiral symmetry breaking. pattern of chiral symmetry breaking.

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Double tagging? Double tagging? Double tagging? Double tagging? Double tagging? Double tagging? Double tagging? Double tagging? Probing the (p 2 ) -α dependence can be neater. Probing the (p 2 ) -α dependence can be neater. Probing the (p 2 ) -α dependence can be neater. Probing the (p 2 ) -α dependence can be neater. Probing the (p 2 ) -α dependence can be neater. Probing the (p 2 ) -α dependence can be neater. Probing the (p 2 ) -α dependence can be neater. Probing the (p 2 ) -α dependence can be neater. Vladimir Savinov Vladimir Savinov Vladimir Savinov Vladimir Savinov Pion to * Transition Form FactorC Pion to * Transition Form FactorC Pion to * Transition Form FactorC Pion to * Transition Form FactorC

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Conclusions A systematic framework based upon the QCD equations A systematic framework based upon the QCD equations of motion (SDE) and its symmetries is required to chart of motion (SDE) and its symmetries is required to chart out and comprehend the Q 2 evolution of these form out and comprehend the Q 2 evolution of these form factors and make predictions. factors and make predictions. A systematic framework based upon the QCD equations A systematic framework based upon the QCD equations of motion (SDE) and its symmetries is required to chart of motion (SDE) and its symmetries is required to chart out and comprehend the Q 2 evolution of these form out and comprehend the Q 2 evolution of these form factors and make predictions. factors and make predictions. The large Q 2 evolution of the pion form factors, their experimental evaluation and theoretical predictions are likely to provide us with deep understanding of the The large Q 2 evolution of the pion form factors, their experimental evaluation and theoretical predictions are likely to provide us with deep understanding of the pattern of DCSB and confinement of the fundamental pattern of DCSB and confinement of the fundamental degrees of freedom, namely quarks and gluons. degrees of freedom, namely quarks and gluons. The large Q 2 evolution of the pion form factors, their experimental evaluation and theoretical predictions are likely to provide us with deep understanding of the The large Q 2 evolution of the pion form factors, their experimental evaluation and theoretical predictions are likely to provide us with deep understanding of the pattern of DCSB and confinement of the fundamental pattern of DCSB and confinement of the fundamental degrees of freedom, namely quarks and gluons. degrees of freedom, namely quarks and gluons. Predictions based upon the contact interaction, QCD SDE Predictions based upon the contact interaction, QCD SDE as well as the intermediate power laws (p 2 ) - can provide experimentalist with a platform to compare and contrast future experimental results. Mesons, diquarks, baryons!!! as well as the intermediate power laws (p 2 ) - can provide experimentalist with a platform to compare and contrast future experimental results. Mesons, diquarks, baryons!!! Predictions based upon the contact interaction, QCD SDE Predictions based upon the contact interaction, QCD SDE as well as the intermediate power laws (p 2 ) - can provide experimentalist with a platform to compare and contrast future experimental results. Mesons, diquarks, baryons!!! as well as the intermediate power laws (p 2 ) - can provide experimentalist with a platform to compare and contrast future experimental results. Mesons, diquarks, baryons!!!

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V.P. Druzhinin, PoS EPS-HEP2009, 051 (2009) [arXiv:0909.3148 [hep-ex]] and preliminary results presented at ICHEP2010. BaBar transition form BaBar transition form factors: BaBar transition form BaBar transition form factors: These results are in These results are in agreement with pQCD: agreement with pQCD: These results are in These results are in agreement with pQCD: agreement with pQCD: T. Feldman, P. Kroll, Phys. Lett. B 413 410 (1997). Pattern of DCSB & Experimental Signatures

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There are attempts to explain the BaBar data which There are attempts to explain the BaBar data which employ pion DAs in disaccord with asymptotic QCD. employ pion DAs in disaccord with asymptotic QCD. There are attempts to explain the BaBar data which There are attempts to explain the BaBar data which employ pion DAs in disaccord with asymptotic QCD. employ pion DAs in disaccord with asymptotic QCD. However, high Q 2 BaBar data requires a pion DA with a However, high Q 2 BaBar data requires a pion DA with a sizeable number of higher Gegenbauer coefficients. sizeable number of higher Gegenbauer coefficients. However, high Q 2 BaBar data requires a pion DA with a However, high Q 2 BaBar data requires a pion DA with a sizeable number of higher Gegenbauer coefficients. sizeable number of higher Gegenbauer coefficients. The rapid growth of TFF for π 0 is also not compatible with The rapid growth of TFF for π 0 is also not compatible with light-front holographic models which yield results in good light-front holographic models which yield results in good agreement with the TFFs of η and η*. agreement with the TFFs of η and η*. The rapid growth of TFF for π 0 is also not compatible with The rapid growth of TFF for π 0 is also not compatible with light-front holographic models which yield results in good light-front holographic models which yield results in good agreement with the TFFs of η and η*. agreement with the TFFs of η and η*. There are suggestions of higher resonance contributions There are suggestions of higher resonance contributions altering the high Q 2 monopole behavior of the π 0 TFF. altering the high Q 2 monopole behavior of the π 0 TFF. There are suggestions of higher resonance contributions There are suggestions of higher resonance contributions altering the high Q 2 monopole behavior of the π 0 TFF. altering the high Q 2 monopole behavior of the π 0 TFF. 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 requires Axial anomaly sum rule has also been invoked. It requires assumptions seeking theoretical justifications. assumptions seeking theoretical justifications. Axial anomaly sum rule has also been invoked. It requires Axial anomaly sum rule has also been invoked. It requires assumptions 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).

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