Assembling Hadrons From Quark-Gluon Pieces

1. Assembling Hadrons From Quark-Gluon Pieces AdnanBashir, Michoacán University, Mexico • Collaborators: • J. Aslam, Quaid-i-Azam University, Pakistan • F. Akram, University of Punjab, Pakistan • Ayala, UNAM, Mexico • B. El Bennich, Cruzeiro do Sul, Brazil • I. Cloet, Argonne National Labotory • S. Ishaq, NCP, Pakistan • Y.X. Liu, Peking University, China • J.R. Quintero, Huelva University, Spain • Raya, Michoacán University, Mexico • Riazuddin, NCP, Pakistan • M.E. Tejeda, USON, Mexico • C.D. Roberts, Argonne National Laboratory, USA • P.C. Tandy, Kent State University, USA Collaborators: L. Albino, University of Michoacán, Mexico A. Ahmad, University of Michoacán, Mexico M.A. Bedolla, University of Michoacán, Mexico R. Bermudez, University of Sonora, Mexico J. Cobos, University of Michoacán, Mexico L. Chang, University of Adelaide, Australia L.X. Gutiérrez, University of Michoacán, Mexico E. Gutiérrez, University of Michoacán, Mexico K. Raya, University of Michoacán, Mexico E. Rojas, Cruzeiro do Sul, Brazil D. Wilson, Jlab, USA

2. Introduction QCD Phase Diagram Hadron Physics Magnetic Catalysis Chiral Symmetry Breaking Running Quark Masses Condensed Matter Systems Schwinger-Dyson Equations

3. Introduction Hadrons From Quark-Gluon Pieces

4. Contents • Introduction to Hadron Form Factors • Schwinger-Dyson Equations – The Ingredients Quark Propagator: Quark Mass Function The Gluon Propagator/Quark Gluon Vertex Quark-Photon Vertex Bethe-Salpeter Amplitude • The Q2 Evolution of Form Factors Momentum Dependent Mass and Form Factors Contact Interaction From Mesons to Baryons • Conclusions

5. Introduction Hadronic form factors are related to their internal structure, the distribution of charge and magnetization. The challenge of their understanding & hence their internal dynamics occupies a central place in hadron 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 an ideal platform to study the form factors from small to large probing photon virtualities, measured at different hadron facilities.

6. Introduction Parity Partners & Chiral Symmetry Breaking

7. The Quark Propagator • The quark • propagator: • Maris-Roberts-Tandy Model • Quark mass • is a function • of momentum, • falling off in • the ultraviolet.

8. The Gluon Propagator • Gluon Propagator: Several 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).

9. 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) A careful choice of parameters can also produce large anomalous magnetic moment for quarks in the 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). L.Albino, R.Bermúdez, L.X. Gutiérrez: Quark-Gluon Vertex.

10. 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).

11. 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.

12. 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); A.C. Aguilar, D. Binosi, J. Papavassiliou, Phys. Rev. D78 025010 (2009). C. Chen,, L. Chang, C.D. Roberts, S. Wan, D. Wilson, Few Body Syst. 52 293 (2012). AB, M. Bedolla, J. Cobos, in progress. • with

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

14. Pion Electromagnetic Form Factor When do we expect the turn over to start? Perturbative Momentum transfer Q is primarily shared equally (Q/2) among quarks as BSA is peaked at zero relative momentum. Jlab 12GeV: 2<Q2<6 GeV2 electromagnetic pion form factor.

15. 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

16. 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, 2013. Precise measurements at large Q2 will provide a stringent constraint on the pattern of chiral symmetry breaking.

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

18. 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.

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

20. From Mesons to Baryons The Diquark Picture: Faddeev equation for a baryon. G. Eichmann, Phys. Rev. D84, 014014 (2011). Faddeev equation in the quark diquark picture reproduces nucleon masses to within 5%.

21. Transition The nucleon primarily consists of scalar and axial vector diquarks and N(1535) of its parity partners. In the contact interaction model, the calculation of the transition form factors involves the diagram:

22. From Mesons to Baryons

23. From Mesons to Baryons L.X. Gutiérrez, AB, C.D. Roberts,D.J. Wilson (In progress).

24. From Mesons to Baryons L.X. Gutiérrez, AB, C.D. Roberts,D.J. Wilson (In progress).

25. Conclusions The large Q2 evolution of the hadronic 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 can provide experimentalist with a platform to compare and contrast the future experimental results.