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Adnan Bashir , Michoacán University, Mexico

 * Transition Form Factor Theory vs Experiment: Past, Present & Future. Adnan Bashir , Michoacán University, Mexico. Collaborators: F. Akram , University of Punjab, Pakistan Y.X. Liu, Peking University, China M.R. Pennington, Durham University & JLab , UK

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Adnan Bashir , Michoacán University, Mexico

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  1.  * Transition Form Factor • Theory vs Experiment: Past, Present & Future AdnanBashir , Michoacán University, Mexico 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

  2. Contents • Introduction • Schwinger-Dyson Equations – The Ingredients Quark Propagator: Quark Mass Function Gluon Propagator Quark-Photon Vertex/Quark Gluon Vertex • The Q2 Evolution of Form Factors: Mass Function and Form Factors Pion Electromagnetic Form Factor Pion to * Transition Form Factor • Conclusions

  3. Introduction The transition form factor is measured through the process:

  4. Introduction The transition form factor: CELLOH.J. Behrend et.al., Z. Phys C49 401 (1991). 0.7 – 2.2 GeV2 The leading twist pQDC calculation was carried out in: CLEOJ. Gronberg et. al., Phys. Rev. D57 33 (1998).1.7 – 8.0 GeV2 G.P. Lepage, and S.J. Brodsky,Phys. Rev. D22, 2157 (1980). BaBarR. Aubert et. al., Phys. Rev. D80 052002 (2009). 4.0 – 40.0 GeV2

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

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

  7. Introduction • Through SDEs, we can study the structure of hadrons • through first principles in the continuum. • SDE for QCD have been extensively applied to meson • spectra and interactions below the masses ~ 1 GeV. • They have been employed to calculate: the masses, charge radii and decays of mesons elastic pion and kaon form factors P. Maris, C.D. Roberts, Phys. Rev. C56 3369 (1997). pion and kaon valence quark-distribution functions P. Maris, P.C. Tandy, Phys. Rev. C62 055204 (2000). nucleon form factors D. Jarecke, P. Maris, P.C. Tandy, Phys. Rev. C67 035202 (2003). T. Nguyen, AB, C.D. Roberts, P.C. Tandy, Phys. Rev. C83062201 (2011). 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)

  8. Introduction Parity Partners & Chiral Symmetry Breaking

  9. Introduction The QCD Lagrangian:

  10. 0.2 fm 0.02 fm 0.002 fm Introduction 1000 MeV 5 MeV We can trace the origin of 98% of the luminous matter to QCD interactions. Asymptotic Freedom Infrared Slavery QCD

  11. Introduction

  12. The Quark Propagator • Simplest SDE - • quark propagator:

  13. The Quark Propagator • The quark • propagator: • Quark mass is a • function of momentum, • dropping as 1/p2 in the • ultraviolet. • Higgs mechanism is • almost irrelevant to the • infrared enhancement of • quark mass.

  14. The Gluon Propagator • Gluon Propagator: Modern SDE and lattice results support decoupling solution for the gluon propagator. AB, C. Lei, I. Cloet, B. El Bennich, Y. Liu, C. Roberts, P. Tandy, Comm. Theor. Phys. 58 79-134 (2012) Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass function. I.L. Bogolubsky, et. al. Phys. Lett. B676 69 (2009). A. Ayala et. al. Phys. Rev. D86 074512 (2012). It is in accord with the improved GZ-picture. A. Bashir, A. Raya, J. Rodrigues-Quintero, Phys. Rev. D88 054003 (2013).

  15. The Quark-Gluon Vertex The Quark-Gluon Vertex: One of the 12 form factors 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).

  16. 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. 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.

  17. The Quark-Photon Vertex Phenomenology Gauge Covariance Lattice Significantly, this last ansatz contains nontrivial factors associated with those tensors whose appearance is solely driven by dynamical chiral symmetry breaking. D.C. Curtis and M.R. Pennington Phys. Rev. D42 4165 (1990) Quark-photon/ quark-gluon vertex Perturbation Theory Multiplicative Renormalization AB, M.R. Pennington Phys. Rev. D50 7679 (1994) A. Kizilersu and M.R. Pennington Phys. Rev. D79 125020 (2009) It yields gauge independent critical coupling in QED. L. Chang, C.D. Roberts, Phys. Rev. Lett. 103 081601 (2009) It also reproduces large anomalous magnetic moment for quarks in infrared. Quark-photon Vertex 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). RocíoBermúdez,LuisAlbino: Quark-Gluon Vertex.

  18. The Q2 Evolution of Form Factors Schwinger-Dyson equations are the fundamental equations of QCD and combine its UV and IR behaviour. 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.

  19. The Q2 Evolution of Form Factors Nobel Prize 2008: “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics” quark-anti-quark

  20. The Q2 Evolution of Form Factors We assume that quarks interact not via massless vector boson but instead through a contact interaction of very massive gauge boson by assuming: Here mG=0.8 GeV is a gluon mass scale which is generated dynamically in QCD. • We use proper time regularization which guarantees • confinement and is backed by phenomenology. Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pene, J. Rodriguez- Quintero, J. High Energy Phys. 06, 099 (2008). • with

  21. The Q2 Evolution of Form Factors Bethe-Salpeter amplitude for the pion: Goldberger-Triemann relations:

  22. The Q2 Evolution of Form Factors Pion Form Factor: Thus the pseudo-vector component of the BS- amplitude dictates the transition of the pion form factor to the perturbative limit. P. Maris and C.D. Roberts, Phys. Rev. C58 3659-3665 (1998).

  23. The Q2 Evolution of Form Factors For the contact interaction: Employing a proper time regularization scheme, one can ensure (i) confinement, (ii) axial vector Ward Takahashi identity is satisfied and (iii) the corresponding Goldberger-Triemann relations are obeyed:

  24. The Q2 Evolution of Form Factors 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. 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 JP = ½- state lies above the second JP = ½+ state. Lattice has not achieved this so far. 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), Form factors are harder but their ratios may be closer to exact SDE predictions.

  25. Pion Electromagnetic Form Factor Within the rainbow ladder truncation, the elastic electromagnetic pion form factor: The pattern of chiral symmetry breaking dictates the momentum dependence of the elastic pion form factor. 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]

  26. Pion Electromagnetic Form Factor 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. Jlab 12GeV: 2<Q2<9 GeV2 electromagnetic and transition pion form factors.

  27. Pion to * Transition Form Factor The transition form factor: H.L.L. Robertes, C.D. Roberts, AB, L.X. Gutiérrez and P.C. Tandy, Phys. Rev. C82, (065202:1-11) 2010. CELLOH.J. Behrend et.al., Z. Phys C49 401 (1991). 0.7 – 2.2 GeV2 CLEOJ. Gronberg et. al., Phys. Rev. D57 33 (1998).1.7 – 8.0 GeV2 The leading twist asymptotic QCD calculation: BaBarR. Aubert et. al., Phys. Rev. D80 052002 (2009). 4.0 – 40.0 GeV2 G.P. Lepage, and S.J. Brodsky,Phys. Rev. D22, 2157 (1980). BelleS. Uehara et. al., arXiv:1205.3249 [hep-ex] (2012). 4.0 – 40.0 GeV2

  28. Pion to * Transition Form Factor The transition form factor: • Belle II will have 40 times more luminosity. • Vladimir Savinov: • 5th Workshop of the APS • Topical Group on Hadronic • Physics, April 2013. Precise measurements at large Q2 will provide a stringent constraint on the pattern of chiral symmetry breaking.

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

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

  31. Charting out the Q2 Evolution Bethe Salpeter Amplitudes: How this dependence feeds into the study of the pion electromagnetic and transition form factors form factors calculation is under study. F. Akram, AB, K. Raya, work in progress.

  32. Pion to * Transition Form FactorC Precise calculations with different interactions (p2)-α at increasing Q2 will provide a stringent constraint on the pattern of chiral symmetry breaking.

  33. Pion to * Transition Form FactorC • Double tagging? • Vladimir Savinov • Probing the (p2)-α dependence can be neater.

  34. Conclusions The large Q2 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 degrees of freedom, namely quarks and gluons. A systematic framework based upon the QCD equations of motion (SDE) and its symmetries is required to chart out and comprehend the Q2 evolution of these form factors and make predictions. Predictions based upon the contact interaction, QCD SDE as well as the intermediate power laws (p2)- can provide experimentalist with a platform to compare and contrast future experimental results. Mesons, diquarks, baryons!!!

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

  36. Pattern of DCSB & Experimental Signatures There are attempts to explain the BaBar data which employ pion DAs in disaccord with asymptotic QCD. However, high Q2BaBar data requires a pion DA with a sizeable number of higher Gegenbauer coefficients. 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). There are suggestions of higher resonance contributions altering the high Q2 monopole behavior of the π0TFF. 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 assumptions seeking theoretical justifications. The rapid growth of TFF for π0is also not compatible with light-front holographic models which yield results in good agreement with the TFFs of η and η*. 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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