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Assembling Hadrons From Quark-Gluon Pieces Adnan Bashir, Michoacán University, Mexico Collaborators: J. Aslam, Quaid-i-Azam University, Pakistan F. Akram, University of Punjab, Pakistan A.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 A.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

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

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Introduction Hadrons From Quark-Gluon Pieces Hadrons From Quark-Gluon Pieces Hadrons From Quark-Gluon Pieces Hadrons From Quark-Gluon Pieces

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Contents Conclusions Conclusions Conclusions Conclusions Conclusions Conclusions Conclusions Conclusions Introduction to Hadron Form Factors Introduction to Hadron Form Factors Introduction to Hadron Form Factors Introduction to Hadron Form Factors Introduction to Hadron Form Factors Introduction to Hadron Form Factors Introduction to Hadron Form Factors Introduction to Hadron Form Factors 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-Photon Vertex Quark-Photon Vertex Quark-Photon Vertex Contact Interaction Contact Interaction Contact Interaction Contact Interaction The Gluon Propagator/Quark Gluon Vertex The Gluon Propagator/Quark Gluon Vertex The Gluon Propagator/Quark Gluon Vertex The Gluon Propagator/Quark Gluon Vertex 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 From Mesons to Baryons From Mesons to Baryons From Mesons to Baryons From Mesons to Baryons Momentum Dependent Mass and Form Factors Momentum Dependent Mass and Form Factors Momentum Dependent Mass and Form Factors Momentum Dependent Mass and Form Factors Bethe-Salpeter Amplitude Bethe-Salpeter Amplitude Bethe-Salpeter Amplitude Bethe-Salpeter Amplitude

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

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

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The Gluon Propagator Several SDE and lattice results support decoupling solution for the gluon propagator. Several SDE and lattice results support decoupling solution for the gluon propagator. Several SDE and lattice results support decoupling solution for the gluon propagator. Several 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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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. A careful choice of parameters can also produce large anomalous magnetic moment for quarks in the infrared. 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 L. Albino, R. Bermúdez, L.X. Gutiérrez: Quark-Gluon Vertex.

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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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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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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); A.C. Aguilar, D. Binosi, J. Papavassiliou, Phys. Rev. D78 025010 (2009). Quintero, J. High Energy Phys. 06, 099 (2008); A.C. Aguilar, D. Binosi, J. Papavassiliou, Phys. Rev. D78 025010 (2009). 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); A.C. Aguilar, D. Binosi, J. Papavassiliou, Phys. Rev. D78 025010 (2009). Quintero, J. High Energy Phys. 06, 099 (2008); A.C. Aguilar, D. Binosi, J. Papavassiliou, Phys. Rev. D78 025010 (2009). 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 C. Chen,, L. Chang, C.D. Roberts, S. Wan, D. Wilson, Few Body Syst. 52 293 (2012). C. Chen,, L. Chang, C.D. Roberts, S. Wan, D. Wilson, Few Body Syst. 52 293 (2012). AB, M. Bedolla, J. Cobos, in progress. AB, M. Bedolla, J. Cobos, in progress.

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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 the turn over to start? When do we expect the turn over to start? When do we expect the turn over to start? 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. 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, 2013. Physics, 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, 2013. Physics, 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. Transfer of momentum dependence in QCD. Transfer of momentum dependence in QCD. Transfer of momentum dependence in QCD. 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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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 Factor Pion to * Transition Form Factor Pion to * Transition Form Factor Pion to * Transition Form Factor

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

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

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From Mesons to Baryons

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L.X. Gutiérrez, AB, C.D. Roberts,D.J. Wilson (In progress).

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

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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 hadronic 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 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 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 hadronic 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 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 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 can provide experimentalist with a platform to compare and contrast the future experimental results. as well as the intermediate power laws can provide experimentalist with a platform to compare and contrast the future experimental results. Predictions based upon the contact interaction, QCD SDE 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. as well as the intermediate power laws can provide experimentalist with a platform to compare and contrast the future experimental results.

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