Probing a Probing a Pion Pion with Photons with Photons Adnan - - PowerPoint PPT Presentation

Probing a Probing a Pion Pion with Photons with Photons

Adnan Adnan Bashir Bashir

XV Mexican Workshop on Particles and Fields XV Mexican Workshop on Particles and Fields Mazatlan, Mazatlan, México México 2-6 November 2015 6 November 2015

Collaborators: Collaborators: F.

• F. Akram

Akram, University of Punjab, Pakistan , University of Punjab, Pakistan J.

• J. Aslam

Aslam, , Quaid Quaid-i-Azam Azam University, Pakistan University, Pakistan

• A. Ayala, UNAM, Mexico

. Ayala, UNAM, Mexico

• B. El
• B. El-Bennish

Bennish, , Cruzeiro do sul Cruzeiro do sul, Brazil , Brazil Y.X. Liu, Peking University, China Y.X. Liu, Peking University, China M.R. Pennington, M.R. Pennington, JLab JLab, USA , USA J.R. Quintero, Huelva University, Spain J.R. Quintero, Huelva University, Spain A.

• A. Raya, Michoacán University, Mexico

Raya, Michoacán University, Mexico M.E. M.E. Tejeda Tejeda, USON, Mexico , USON, Mexico C.D. Roberts, Argonne National Laboratory, USA C.D. Roberts, Argonne National Laboratory, USA P.C. Tandy, Kent State University, P.C. Tandy, Kent State University, USA USA Collaborators: Collaborators:

• L. Albino, University of Michoacán, Mexico
• L. Albino, University of Michoacán, Mexico
• A. Ahmad, University of Michoacán, Mexico
• A. Ahmad, University of Michoacán, Mexico

M.A. M.A. Bedolla Bedolla, University of Michoacán, Mexico , University of Michoacán, Mexico

• R. Bermudez, University of Sonora, Mexico
• R. Bermudez, University of Sonora, Mexico

J.

• J. Cobos

Cobos, University of Michoacán, Mexico , University of Michoacán, Mexico

• L. Chang, University of Adelaide, Australia
• L. Chang, University of Adelaide, Australia

L.X. L.X. Gutiérrez Gutiérrez, University of Michoacán, Mexico , University of Michoacán, Mexico E.

• E. Gutiérrez

Gutiérrez, University of Michoacán, Mexico , University of Michoacán, Mexico

• K. Raya, University of Michoacán, Mexico
• K. Raya, University of Michoacán, Mexico
• D. Wilson,
• D. Wilson, Jlab

Jlab, USA , USA

Contents Contents

• Facts and Challenges

Facts and Challenges

• Facts and Challenges

Facts and Challenges

• Pions

Pions and and Chiral Chiral Symmetry Symmetry

• Pions

Pions and and Chiral Chiral Symmetry Symmetry

• Schwinger

Schwinger-Dyson Equations Dyson Equations

• Schwinger

Schwinger-Dyson Equations Dyson Equations

• The Quark Propagator

The Quark Propagator

• The Quark Propagator

The Quark Propagator

• The Gluon Propagator

The Gluon Propagator

• The Gluon Propagator

The Gluon Propagator

• Pion

Pion Electromagnetic Form Factor Electromagnetic Form Factor

• Pion

Pion Electromagnetic Form Factor Electromagnetic Form Factor

• Pion

Pion Transition Form Factor Transition Form Factor

• Pion

Pion Transition Form Factor Transition Form Factor

• Bethe

Bethe Salpeter Salpeter Amplitude Amplitude

• Bethe

Bethe Salpeter Salpeter Amplitude Amplitude

• Further Challenges

Further Challenges

• Further Challenges

Further Challenges

• Other Mesons and Baryons

Other Mesons and Baryons

• Other Mesons and Baryons

Other Mesons and Baryons

Facts and Challenges Facts and Challenges

• Dynamical

Dynamical mass mass generation generation for for massless massless quarks quarks; (dynamical (dynamical chiral chiral symmetry symmetry breaking) breaking).

• Dynamical

Dynamical mass mass generation generation for for massless massless quarks quarks; (dynamical (dynamical chiral chiral symmetry symmetry breaking) breaking).

• Both these

Both these phenomena phenomena are are emergent emergent and owe themselves and owe themselves to large coupling strength in the infrared. to large coupling strength in the infrared.

• Both these

Both these phenomena phenomena are are emergent emergent and owe themselves and owe themselves to large coupling strength in the infrared. to large coupling strength in the infrared.

• Color degrees of freedom (quarks and gluons) are not

Color degrees of freedom (quarks and gluons) are not

• bservable
• bservable (confinement).

(confinement).

• Color degrees of freedom (quarks and gluons) are not

Color degrees of freedom (quarks and gluons) are not

• bservable
• bservable (confinement).

(confinement).

• Studying QCD: lattice,

Studying QCD: lattice, Schwinger Schwinger-Dyson and Bethe Dyson and Bethe- Salpeter Salpeter equations equations, , chiral chiral perturbation theory, perturbation theory, effective quark models. effective quark models.

• Studying QCD: lattice,

Studying QCD: lattice, Schwinger Schwinger-Dyson and Bethe Dyson and Bethe- Salpeter Salpeter equations equations, , chiral chiral perturbation theory, perturbation theory, effective quark models. effective quark models.

• How do we study

How do we study physics beyond perturbation theory physics beyond perturbation theory? ?

• How do we study

How do we study physics beyond perturbation theory physics beyond perturbation theory? ?

Pions Pions and and Chiral Chiral Symmetry Breaking Symmetry Breaking

In In October October 1934 1934, Hideki Hideki Yukawa Yukawa predicted predicted the the existence existence of

• f

a a “heavy “heavy quantum” quantum”, meson, meson, exchanging exchanging nuclear nuclear force force between between n neutrons eutrons and and protons protons. . In In October October 1934 1934, Hideki Hideki Yukawa Yukawa predicted predicted the the existence existence of

• f

a a “heavy “heavy quantum” quantum”, meson, meson, exchanging exchanging nuclear nuclear force force between between n neutrons eutrons and and protons protons. . It It was was discovered discovered by by Cecil Cecil Powel Powel in in 1949 1949 in in cosmic cosmic ray ray tracks racks in in a photographic photographic emulsion emulsion. . It It was was discovered discovered by by Cecil Cecil Powel Powel in in 1949 1949 in in cosmic cosmic ray ray tracks racks in in a photographic photographic emulsion emulsion. . Pion Pion was was nicely nicely accommodated accommodated in in The The Eight Eight Fold Fold way way of

• f

Murray Murray Gell Gell –Mann Mann in in 1961 1961. . Pion Pion was was nicely nicely accommodated accommodated in in The The Eight Eight Fold Fold way way of

• f

Murray Murray Gell Gell –Mann Mann in in 1961 1961. . Yoichiro Yoichiro Nambu Nambu associated associated it it with with CSB CSB in in 1960 1960. Yoichiro Yoichiro Nambu Nambu associated associated it it with with CSB CSB in in 1960 1960. 1949 1949 1950 1950 1969 1969 2008 2008

Pions Pions and and Chiral Chiral Symmetry Breaking Symmetry Breaking

Pions Pions are are the the lightest lightest of

• f hadrons
• hadrons. They

They do do not not have have zero zero mass mass. . Pions Pions are are the the lightest lightest of

• f hadrons
• hadrons. They

They do do not not have have zero zero mass mass. . A typical typical meson meson like like a ρ has has a mass mass of

• f 770

770 MeV MeV while while the the nucleon nucleon has has a mass mass of

• f

940 940 MeV

• MeV. This

This is is consistent consistent with with a constituent constituent u,d u,d, mass mass of

• f

around around 300 300 MeV MeV. A typical typical meson meson like like a ρ has has a mass mass of

• f 770

770 MeV MeV while while the the nucleon nucleon has has a mass mass of

• f

940 940 MeV

• MeV. This

This is is consistent consistent with with a constituent constituent u,d u,d, mass mass of

• f

around around 300 300 MeV MeV. However, However, pions pions only

• nly weigh

weigh about about 140 140 MeV MeV, , which which is is 1/5th th of

• f

the the mass mass of

• f the

the ρ. However, However, pions pions only

• nly weigh

weigh about about 140 140 MeV MeV, , which which is is 1/5th th of

• f

the the mass mass of

• f the

the ρ. This This cannot cannot be be an an accident accident. This This cannot cannot be be an an accident accident. The The connection connection of

• f pions

pions with with chiral chiral symmetry symmetry breaking breaking was was present present in in the the Gell Gell-Mann Mann-Oakes Oakes-Renner Renner relation relation. The The connection connection of

• f pions

pions with with chiral chiral symmetry symmetry breaking breaking was was present present in in the the Gell Gell-Mann Mann-Oakes Oakes-Renner Renner relation relation.

Nobel Prize 2008: Nobel Prize 2008: “for “for the the discovery discovery of

• f

the the mechanism mechanism

• f
• f

spontaneous spontaneous broken broken symmetry symmetry in in subatomic subatomic physics” physics” Nobel Prize 2008: Nobel Prize 2008: “for “for the the discovery discovery of

• f

the the mechanism mechanism

• f
• f

spontaneous spontaneous broken broken symmetry symmetry in in subatomic subatomic physics” physics”

quark-anti-quark quark-anti-quark

Pions Pions and and Chiral Chiral Symmetry Breaking Symmetry Breaking

Dynamical Dynamical chiral chiral symmery symmery breaking breaking yields yields large large effective effective quark quark masses masses and and the the existence existence of

• f

Goldstone Goldstone bosons bosons: pions pions. Dynamical Dynamical chiral chiral symmery symmery breaking breaking yields yields large large effective effective quark quark masses masses and and the the existence existence of

• f

Goldstone Goldstone bosons bosons: pions pions.

Chiral Chiral Symmetry and Its Breaking Symmetry and Its Breaking Chiral Chiral Symmetry and Its Breaking Symmetry and Its Breaking

2% % of

• f visible

visible mass mass is is due due to to Higgs Higgs. 2% % of

• f visible

visible mass mass is is due due to to Higgs Higgs. 98 98% % of

• f visible

visible mass mass is is due due to to dynamical dynamical chiral chiral symmetry symmetry breaking breaking. . 98 98% % of

• f visible

visible mass mass is is due due to to dynamical dynamical chiral chiral symmetry symmetry breaking breaking. .

Chiral Chiral Symmetry and Its Breaking Symmetry and Its Breaking Chiral Chiral Symmetry and Its Breaking Symmetry and Its Breaking

Parity Parity Partners & Partners & Chiral Chiral Symmetry Symmetry Breaking Breaking Parity Parity Partners & Partners & Chiral Chiral Symmetry Symmetry Breaking Breaking ~500 MeV ~500 MeV

Nucleon Nucleon And its And its Parity Parity Partner Partner Nucleon Nucleon And its And its Parity Parity Partner Partner

Chiral Chiral Symmetry and Its Breaking Symmetry and Its Breaking Chiral Chiral Symmetry and Its Breaking Symmetry and Its Breaking

Schwinger Schwinger-Dyson Dyson equations equations in in covariant covariant gauges gauges Schwinger Schwinger-Dyson Dyson equations equations in in covariant covariant gauges gauges

Schwinger Schwinger-

• Dyson Equations

Dyson Equations Schwinger Schwinger-

• Dyson Equations

Dyson Equations

The The inverse inverse quark quark propagator propagator: The The inverse inverse quark quark propagator propagator: The The quark quark-gluon gluon vertex vertex: : The The quark quark-gluon gluon vertex vertex: :

Schwinger Schwinger-

• Dyson Equations

Dyson Equations Schwinger Schwinger-

• Dyson Equations

Dyson Equations

The The inverse inverse gluon gluon propagator propagator: The The inverse inverse gluon gluon propagator propagator:

The Quark Propagator The Quark Propagator The Quark Propagator The Quark Propagator

The quark The quark propagator: propagator: The quark The quark propagator: propagator:

The quark The quark propagator: propagator: The quark The quark propagator: propagator:

The Quark Propagator The Quark Propagator The Quark Propagator The Quark Propagator

• K. Raya, Ph.D. Student, University of Michoacán
• K. Raya, Ph.D. Student, University of Michoacán

“Bridging Bridging a gap a gap between between continuum continuum-QCD and ab initio QCD and ab initio predictions predictions of

• f hadron

hadron

• bservables”
• bservables” ,

, Binosi Binosi,, Chang Chang, Papavassiliou Papavassiliou, Roberts, Roberts, Phys.Lett Phys.Lett. B742 . B742 183 ( 183 (2015 2015). ).

The Gluon Propagator The Gluon Propagator

Several SDE and lattice Several SDE and lattice results support decoupling results support decoupling solution for the gluon solution for the gluon propagator. propagator. Several SDE and lattice Several SDE and lattice results support decoupling results support decoupling solution for the gluon solution for the gluon propagator. propagator. Momentum dependent gluon mass is reminiscent of the Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass function. momentum dependent quark mass function. Momentum dependent gluon mass is reminiscent of the Momentum dependent gluon mass is reminiscent of the momentum dependent quark mass function. momentum dependent quark mass function. It is in accord with the improved GZ It is in accord with the improved GZ-picture. picture. It is in accord with the improved GZ It is in accord with the improved GZ-picture. picture.

• A. Ayala et. al. Phys. Rev. D86 074512 (2012).
• A. Ayala et. al. Phys. Rev. D86 074512 (2012).

AB, C. Lei, I. AB, C. Lei, I. Cloet Cloet, B. El , B. El Bennich Bennich, Y. Liu, C. Roberts, , Y. Liu, C. Roberts,

• P. Tandy, Comm.
• P. Tandy, Comm. Theor
• Theor. Phys. 58 79

. Phys. 58 79-134 (2012) 134 (2012)

Gluon Propagator: Gluon Propagator: Gluon Propagator: Gluon Propagator:

AB, A. Raya, J. AB, A. Raya, J. Rodrigues Rodrigues-Quintero, Quintero,

• Phys. Rev. D88 054003 (2013
• Phys. Rev. D88 054003 (2013).

). I.L. I.L. Bogolubsky Bogolubsky, et. al. Phys. , et. al. Phys. Lett

• Lett. B676 69 (2009).

. B676 69 (2009).

The The Quark Quark-Gluon Vertex Gluon Vertex The The Quark Quark-Gluon Vertex Gluon Vertex

Phenomenology Gauge Covariance Lattice Multiplicative Renormalization Perturbation Theory Quark-photon/ quark-gluon vertex

J

• J. Skullerud

Skullerud, P. Bowman, Bowman, A. Kizilersu Kizilersu, D. Leinweber Leinweber, A

• A. Williams,

Williams, J. High High Energy Energy Phys Phys. 04 04 047 047 (2003 2003)

• M. Bhagwat

Bhagwat, M. Pichowsky Pichowsky, C. Roberts, Roberts, P. Tandy, Tandy, Phys Phys. . Rev Rev. . C68 68 015203 015203 (2003 2003). AB, AB, L. . Gutiérrez Gutiérrez, M. Tejeda Tejeda, AIP AIP Conf

• Conf. Proc
• Proc. 1026

1026 262 262 (2008 2008).

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

The Quark The Quark-

• Gluon Vertex

Gluon Vertex The Quark The Quark-

• Gluon Vertex

Gluon Vertex

Studying Studying the the transition transition

• f
• f

hadrons hadrons from from them them being being made made

• f
• f a sea

sea of

• f quarks

quarks and and gluons gluons to to valence valence quarks quarks alone alone can can be be studied studied naturally naturally through through SDE SDE. . Studying Studying the the transition transition

• f
• f

hadrons hadrons from from them them being being made made

• f
• f a sea

sea of

• f quarks

quarks and and gluons gluons to to valence valence quarks quarks alone alone can can be be studied studied naturally naturally through through SDE SDE. . Schwinger Schwinger-Dyson Dyson equations equations are are the the fundamental fundamental equations equations

• f
• f QCD

QCD and and combine combine its its UV UV and and IR IR behaviour behaviour. Schwinger Schwinger-Dyson Dyson equations equations are are the the fundamental fundamental equations equations

• f
• f QCD

QCD and and combine combine its its UV UV and and IR IR behaviour behaviour.

The Quark The Quark-

• Gluon Vertex

Gluon Vertex

Bethe Bethe-Salpeter Salpeter amplitude amplitude for for the the pion pion: Bethe Bethe-Salpeter Salpeter amplitude amplitude for for the the pion pion: Goldberger Goldberger-Triemann Triemann relations: relations: Goldberger Goldberger-Triemann Triemann relations: relations:

The Bethe The Bethe-Salpeter Salpeter Amplitudes Amplitudes The Bethe The Bethe-Salpeter Salpeter Amplitudes Amplitudes

Pion Pion Electromagnetic Form Factor Electromagnetic Form Factor

Pion Pion Electromagnetic Form Factor Electromagnetic Form Factor

1980’s 2001 2006 2017?

Within Within the the rainbow rainbow ladder ladder truncation, truncation, the the elastic elastic electromagnetic electromagnetic pion pion form form factor factor: Within Within the the rainbow rainbow ladder ladder truncation, truncation, the the elastic elastic electromagnetic electromagnetic pion pion form form factor factor: The The pattern pattern of

• f chiral

chiral symmetry symmetry breaking breaking dictates dictates the the momentum momentum dependence dependence of

• f the

the elastic elastic pion pion form form factor factor. The The pattern pattern of

• f chiral

chiral symmetry symmetry breaking breaking dictates dictates the the momentum momentum dependence dependence of

• f the

the elastic elastic pion pion form form factor factor.

L.

• L. Gutiérrez

Gutiérrez, AB, I.C. , AB, I.C. Cloet Cloet, C.D. Roberts, Phys. Rev. C81 065202 (2010). , C.D. Roberts, Phys. Rev. C81 065202 (2010).

Pion Pion Electromagnetic Form Factor Electromagnetic Form Factor

Experiments Experiments on

• n pions

pions indicate indicate a contact contact like like interaction? interaction? Experiments Experiments on

• n pions

pions indicate indicate a contact contact like like interaction? interaction?

Pion Pion Electromagnetic Form Factor Electromagnetic Form Factor

Pion Pion Electromagnetic Form Factor Electromagnetic Form Factor

The The most most important important achievements achievements

• f
• f last

last 7 years years Page Page 22 22: Pion Pion electromagnetic electromagnetic form form factor factor through through SDES SDES

Pion Pion Electromagnetic Form Factor Electromagnetic Form Factor

• L. Chang,
• L. Chang, I.C.

I.C. Cloët Cloët, C.D. Roberts, C.D. Roberts, S.M. Schmidt, S.M. Schmidt, P.C. P.C. Tanday Tanday, , Phys

• Phys. Rev.

. Rev. Lett Lett. . 111, 14 141802 (2013) 111, 14 141802 (2013)

Pion Pion to to  * Transition Form Factor Transition Form Factor Pion Pion to to  * Transition Form Factor Transition Form Factor

The The transition transition form form factor factor: The The transition transition form form factor factor:

CELLO CELLO H.J. Behrend et.al., Z. Phys C49 401 (1991). 0.7 – 2.2 GeV2 CLEO CLEO J. Gronberg et. al., Phys. Rev. D57 33 (1998). 1.7 – 8.0 GeV2 BaBar BaBar R. Aubert et. al., Phys. Rev. D80 052002 (2009). 4.0 – 40.0 GeV2

Lowest Lowest order

• rder in

in perturbation perturbation theory theory and and the the leading leading twist twist asymptotic asymptotic QCD QCD calculation calculation: Lowest Lowest order

• rder in

in perturbation perturbation theory theory and and the the leading leading twist twist asymptotic asymptotic QCD QCD calculation calculation:

G.P. G.P. Lepage Lepage, and S.J. Brodsky, , and S.J. Brodsky, Phys

• Phys. Rev. D22, 2157 (1980).

. Rev. D22, 2157 (1980). Belle Belle S. Uehara et. al., Phys. Rev. D86 092007 (2012). 4.0 – 40.0 GeV2 H.L.L. H.L.L. Robertes Robertes, C.D. Roberts, AB, L.X. , C.D. Roberts, AB, L.X. Gutiérrez Gutiérrez and P.C. Tandy, and P.C. Tandy, Phys

• Phys. Rev. C82,

. Rev. C82, (065202:1 (065202:1-11) 2010. 11) 2010. 78 78 citations citations

Pion Pion to to  * Transition Form Factor Transition Form Factor Pion Pion to to  * Transition Form Factor Transition Form Factor

H.L.L. H.L.L. Robertes Robertes, C.D. Roberts, AB, L.X. , C.D. Roberts, AB, L.X. Gutiérrez Gutiérrez and P.C. Tandy, and P.C. Tandy, Phys

• Phys. Rev.

. Rev. C82, (065202:1 C82, (065202:1-11) 2010. 11) 2010.

Pion Pion to to  * Transition Form Factor Transition Form Factor Pion Pion to to  * Transition Form Factor Transition Form Factor

The The transition transition form form factor factor: The The transition transition form form factor factor:

• K. Raya, L. Chang, AB, J.J. Cobos-Martinez, L.X. Gutiérrez-Guerrero,

C.D. Roberts, P.C. Tandy, e-Print: arXiv:1510.02799. (2015)

The The transition transition form form factor factor: The The transition transition form form factor factor:

• Belle

Belle II II will will have have 40 40 times times more more luminosity luminosity.

• Belle

Belle II II will will have have 40 40 times times more more luminosity luminosity. Precise Precise measurements measurements at at large large Q Q2 will will provide provide a stringent stringent constraint constraint on

• n the

the pattern pattern

• f
• f chiral

chiral symmetry symmetry breaking breaking. Precise Precise measurements measurements at at large large Q Q2 will will provide provide a stringent stringent constraint constraint on

• n the

the pattern pattern

• f
• f chiral

chiral symmetry symmetry breaking breaking.

Vladimir Vladimir Savinov Savinov: 5 5th

th Workshop of the APS

Workshop of the APS Topical Group on Topical Group on Hadronic Hadronic Physics, 2013. Physics, 2013. Vladimir Vladimir Savinov Savinov: 5 5th

th Workshop of the APS

Workshop of the APS Topical Group on Topical Group on Hadronic Hadronic Physics, 2013. Physics, 2013.

Pion Pion to to  * Transition Form Factor Transition Form Factor Pion Pion to to  * Transition Form Factor Transition Form Factor

Challenges within Standard Model Challenges within Standard Model

Gluon mass in the infrared. Last 10 years. Gluon mass in the infrared. Last 10 years. Gluon mass in the infrared. Last 10 years. Gluon mass in the infrared. Last 10 years. Pion Pion after after 80 80 years. years. Pion Pion after after 80 80 years. years. First excited states of nucleon after 50 years. Inverted First excited states of nucleon after 50 years. Inverted hierarchy in lattice. hierarchy in lattice. First excited states of nucleon after 50 years. Inverted First excited states of nucleon after 50 years. Inverted hierarchy in lattice. hierarchy in lattice. BRST BRST symmetry breaking? symmetry breaking? BRST BRST symmetry breaking? symmetry breaking? Dynamical Dynamical diquarks diquarks within baryons. within baryons. Dynamical Dynamical diquarks diquarks within baryons. within baryons. Elastic and transition form factors at large Elastic and transition form factors at large virtualities virtualities. . Elastic and transition form factors at large Elastic and transition form factors at large virtualities virtualities. .