Transition Form Factor: QCD & BaBar

1. γ*π0γTransition Form Fatctor: QCD & BaBar AdnanBashir Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA March 15, 2012 Jefferson Laboratory, USA

2. Contents • Introduction • Schwinger-Dyson Equations Quark Propagator: Quark Mass Function Pion Bethe-Salpeter Amplitude Quark-Photon Vertex • Pion Electromagnetic Form Factor • Pion 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. Schwinger-Dyson Equations • Schwinger-Dyson Equations (SDE) are the fundamental • equations of a field theory. • SDE for QCD have been extensively applied to meson • spectra and interactions below the masses ~ 1 GeV. • SDE 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, arXiv:1201.3366[nucl-th]

7. Schwinger-Dyson Equations Rainbow-ladder truncation • SDE: Full quark propagator:

8. Schwinger-Dyson Equations • Contact interaction:

9. Schwinger-Dyson Equations Bethe-Salpeter amplitude for the pion: Goldberger-Triemann relations:

10. Schwinger-Dyson Equations 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).

11. Schwinger-Dyson Equations 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:

12. Schwinger-Dyson Equations 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) Quark-photon Vertex AB, C. Calcaneo, L. Gutiérrez, M. Tejeda, Phys. Rev. D83 033003 (2011) It also reproduces large anomalous magnetic moment for electrons in the infrared. AB, R. Bermudez, L. Chang, C.D. Roberts, arXiv:1112.4847 [nucl-th].

13. 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).

14. 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.

15. Pion Electromagnetic Form Factor • We can dress quark-photon vertex: • The corresponding IBS-equation thus yields: H.L.L. Robertes, C.D. Roberts, A. Bashir, L.X. Gutiérrez and P.C. Tandy, Phys. Rev. C82, (065202:1-11) 2010.

16. Pion Electromagnetic Form factor • Dressed quark-photon vertex with ρ-pole on the time- • like axis does not alter the asymptotic behaviour of the • form factor for large space-like momenta. H.L.L. Robertes, C.D. Roberts, A. Bashir, L.X. Gutiérrez and P.C. Tandy, Phys. Rev. C82, (065202:1-11) 2010.

17. Pattern of DCSB & Experimental Signatures

18. Pattern of DCSB & Experimental Signatures Quark propagator: quark mass function Pion Bethe-Salpeter amplitude Dressed quark-photon vertex QCD based prediction through SDE Contact interaction PQCD prediction H.L.L. Robertes, C.D. Roberts, AB, L.X. Gutiérrez and P.C. Tandy, Phys. Rev. C82, (065202:1-11) 2010.

19. Pattern of DCSB & Experimental Signatures

20. Pattern of DCSB & Experimental Signatures • Other transition form factors are in accordance with • asymptotic QCD:

21. Pattern of DCSB & Experimental Signatures Could anything conceivably go astray in the experiment? A possible erroneous way to extract the pion transition form factor from the data could be the problem of π0-π0 subtraction. There is another channel which is the crossed channel of virtual Compton scattering on a pion. The misinterpretation of some events (where the second π0 is not seen) may be different at different Q2. Diehl et. al. Phys. Rev. D62 073014 (2000).

22. Conclusions Dynamical chiral symmetry breaking and the momentum dependence of the quark mass function in QCD have experimental signals which enable us to differentiate its predictions from others. A fully consistent treatment of the contact interaction model produces results for pion elastic and transition form factors that are in striking disagreement with experiment. In a fully consistent treatment of pion in SDE QCD (static properties, elastic and transition form factors), the asymptotic limit of the product Q2G(Q2), is not exceeded at any finite value of spacelike momentum transfer and is in disagreement with BaBar data for large momenta.