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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
Introduction
QCD Phase
Diagram
Hadron
Physics
Running
Quark
Masses
Magnetic
Catalysis
Chiral
Symmetry
Breaking
Schwinger-Dyson
Equations
Condensed
Matter
Systems
Introduction
Hadrons From Quark-Gluon Pieces
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
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.
Introduction
Parity
Partners &
Chiral
Symmetry
Breaking
The Quark Propagator
The quark
propagator:
Maris-Roberts-Tandy Model
Quark mass
is a function
of momentum,
falling off in
the ultraviolet.
The Gluon Propagator
Gluon Propagator:
Several SDE and lattice
results support decoupling
solution for the gluon
AB, C. Lei, I. Cloet, B. El Bennich, Y. Liu, C. Roberts,
propagator.
P. Tandy, Comm. Theor. Phys. 58 79-134 (2012)
Momentum dependent gluon mass is reminiscent of the
I.L. Bogolubsky,
et. al. Phys. Lett. B676 69 (2009).
momentum dependent quark
mass function.
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).
The Quark-Photon Vertex
D.C. Curtis and M.R. Pennington Phys. Rev. D42 4165 (1990)
AB, M.R. Pennington Phys. Rev. Phenomenology
D50 7679 (1994)
A. Kizilersu and
M.R. Pennington Phys. Rev. D79 125020 (2009)
Gauge
Lattice
Covariance
L. Chang, C.D.
Roberts, Phys. Rev. Lett. 103 081601 (2009)
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).
Significantly, this last ansatz contains nontrivial factors
Quark-photon/
Perturbation
Multiplicative
associated with those tensors
whose appearance
is solely
quark-gluon
Renormalization
drivenTheory
by dynamical chiral symmetry
breaking.
vertex
It yields gauge independent critical coupling in QED.
A careful choice of parameters can also produce large
Vertexin the infrared.
anomalous magneticQuark-photon
moment for quarks
L. Albino, R. Bermúdez, L.X. Gutiérrez:
Quark-Gluon Vertex.
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).
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.
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:
Hereuse
mG=0.8
GeV
is regularization
a gluon mass scale
is generated
We
proper
time
whichwhich
guarantees
dynamically in
QCD.
confinement
and
is backed by phenomenology.
Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pene, J. RodriguezQuintero, J. High Energy Phys. 06, 099 (2008); A.C. Aguilar, D. Binosi, J.
C. Chen,, L. Chang,
S. Wan,
D. Wilson, Few Body Syst. 52 293 (2012).
Papavassiliou,
Phys. C.D.
Rev. Roberts,
D78 025010
(2009).
AB, M. Bedolla, J. Cobos, in progress.
with
Pion Electromagnetic Form Factor
Within
The pattern
the rainbow
of chiral
ladder
symmetry
truncation,
breaking
the dictates
elastic the
electromagnetic
momentum dependence
pion form
of the
factor:
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]
Pion Electromagnetic Form Factor
When do we expect the turn over to start?
Perturbative
Momentum transfer
Q is
primarily shared equally (Q/2)
2
2
Jlab
12GeV:
<6 GeV
electromagnetic
pion form
factor.
among
quarks2<Q
as BSA
is peaked
at zero relative
momentum.
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.
CELLO H.J. Behrend et.al., Z. Phys C49 401 (1991).
0.7 – 2.2 GeV2
CLEO J. Gronberg et. al., Phys. Rev. D57 33 (1998).
1.7 – 8.0 GeV2
The leading twist asymptotic QCD calculation:
BaBar R. 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).
Belle S. Uehara et. al., arXiv:1205.3249 [hep-ex] (2012). 4.0 – 40.0 GeV2
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.
Pion to * Transition Form Factor
Transfer of momentum dependence in QCD.
F. Akram, AB, K. Raya, work in progress.
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.
Pion to * Transition Form Factor
• Double tagging?
Vladimir Savinov
• Probing the (p2)-α dependence can be neater.
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%.
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:
From Mesons to Baryons
From Mesons to Baryons
L.X. Gutiérrez, AB, C.D. Roberts,D.J. Wilson (In progress).
From Mesons to Baryons
L.X. Gutiérrez, AB, C.D. Roberts,D.J. Wilson (In progress).
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.