Transcript From Free Quarks to Nucleon Form Factors Adnan Bashir Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA August 15, 2012 University of South.

From Free Quarks to Nucleon Form Factors
Adnan Bashir
Michoacán University, Mexico
Argonne National Laboratory, USA
Kent State University, USA
August 15, 2012
University of South Carolina
Contents
• Schwinger-Dyson Equations – The Ingredients
• Pion Electromagnetic & Transition Form Factors
•
Rho and Diquark Form Factors
•
Nucleon Electromagnetic & Transition Form Factors
• Conclusions
Schwinger-Dyson Equations – The Ingredients
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.
Schwinger-Dyson Equations – The Ingredients
Schwinger-Dyson Equation for the
The Quark Propagator
• The gluon propagator and the quark-gluon vertex are
directly responsible for the quarks to acquire their
constituent masses.
Schwinger-Dyson Equations – The Ingredients
The Gluon Propagator
Modern 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
A. Ayala,mass
AB, D.function.
Binosi, M. Cristoforetti, J. Rodríguez
momentum dependent quark
hep-ph: arXiv:1208.0795 (2012).
It is in accord with the improved GZ-picture.
Schwinger-Dyson Equations – The Ingredients
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).
Schwinger-Dyson Equations – The Ingredients
The Quark-Photon Vertex:
In studying the elastic or transition form factors of
hadrons, it is the photon which probes its constituents,
highlighting the importance of the quark-photon vertex.
Fortunately, both the quark-photon & the quark-gluon
vertices require the same number of basis tensors (12)
for their description. So a unified approach is possible.
Schwinger-Dyson Equations – The Ingredients
Quark-Photon Vertex: (Ward-Takahashi identity)
The Ward identity is then invoked:
Schwinger-Dyson Equations – The Ingredients
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
Covariance
Lattice
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
quark-gluon
associated
is solely
Theorywith those tensors whose appearance
Renormalization
vertex
driven by dynamical chiral symmetry
breaking.
It yields gauge independent critical coupling in QED.
The Quark-Photon Vertex
It also reproduces large anomalous magnetic moment for
electrons in the infrared.
Schwinger-Dyson Equations – The Ingredients
Bethe Salpeter Amplitude:
Goldberger-Triemann
relations:
Schwinger-Dyson Equations – The Ingredients
The quark propagator, electron-photon vertex and the
Bethe Salpeter Amplitude provide the ingredients for the
pion form factor calculations.
Schwinger-Dyson Equations – The Ingredients
Contact interaction:
Pion Elastic and Transition Form Factors
Transition region for the electromagnetic pion form factor
may be accessible with the high energy electron beam
proposed for the 12 GeV upgrade at JLab.
G.P. Lepage,
Brodsky,
Phys. Rev.
D22,
L. Gutiérrez,
AB, and
I.C.S.J.
Cloet,
C.D. Roberts,
Phys.
Rev.2157
C81 (1980).
065202 (2010).
Pion Elastic and Transition Form Factors
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 pQDC calculation was carried out in:
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 Elastic and Transition Form Factors
The pattern of chiral symmetry breaking dictates the
momentum dependence of physical observables.
F. Akram, AB, L. Gutiérrez, B. Masud, J. Quintero, C. Calcaneo, M. Tejeda,
arXiv:0812---- (2012).
Pion Elastic and Transition Form Factors
When do we expect perturbation theory to set in?
Perturbative
2<9isGeV
2 electromagnetic
Momentum
transfer
primarily
shared equally
Jlab 12GeV:
2<QQ
and (Q/2)
among
quarks as
BSA
is peaked
transition
pion
form
factors.at zero relative momentum.
Rho Form Factors
ργρ Elastic Form Factors:
Electromagnetic current of a vector meson is:
Bose symmetry and charge conjugation yields:
Rho Form Factors
ργρ Elastic Form Factors:
Within the impulse approximation & the contact interaction
model:
Rho Form Factors
• The quark-photon vertex can be dressed as:
• The corresponding IBS-equation thus yields:
H.L.L. Robertes, C.D. Roberts, AB, L.X. Gutiérrez and P.C. Tandy, Phys.
Rev. C82, (065202:1-11) 2010.
Rho Form Factors
ργρ Elastic
Form Factors:
Electric, magnetic
& quadrupole form
factors
ργπ transition form factor is very similar to γ*πγ
Nucleon – 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%.
Nucleon – The Diquark Picture
In a color singlet baryon, any 2 quarks are necessarily
in a 3(bar) color state.
Color algebra of the BS equation reveals the gluon exchange
is attractive in this channel, forming confined diquarks.
Each meson has a diquark partner
which is non-point like with finite
radial extent comparable to mesons.
In the diquark picture of the nucleon, the calculation of its
electromagnetic and transition form factors requires the
knowledge of the diquarks & their interaction with photons.
Nucleon – The Diquark Picture
A nucleon primarily consists of scalar and axial vector
diquarks because they have the same parity as the nucleon.
Pseudo-scalar and vector diquarks are heavy.
Moreover, they have parity opposite to that of the nucleon.
To get the parity correct, non-zero quark angular
momentum of the quark has to be invoked. So they can be
ignored in the description of the nucleon (ground state).
To calculate the nucleon electromagnetic & transition form
factors, one needs to evaluate the diquark elastic and
transition form factors.
Transition
Transition current: quark-diquark picture of the nucleon:
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:
Transition
First look at: V→ V1V1.
Bose symmetry of
2 particles implies:
Transition
Moreover, the vector current conservation implies:
It reduces the independent form factors to two. For the
on shell vector bosons:
Ongoing...
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 is simple to implement and can help us provide
useful results which can be compared and contrasted with
full QCD calculation and experiment.
A program to provide electromagnetic as well transition
form factors for mesons, diquarks and nucleons is in
progress within the simple contact interaction model. The
momentum dependent interaction will then be implemented.