# Theory Center Research Highlights

### Hadron Form Factors and Quark-Gluon Distributions

Form Factors

Structure Functions

Generalized Parton Distributions

## Form Factors

**
"Review of two-photon exchange in electron scattering"
**

J. Arrington, P. G. Blunden, W. Melnitchouk

*Prog. Part. Nucl. Phys.* **66**, 782 (2011)

The role of two-photon exchange (TPE) in electron-hadron scattering is
reviewed, with particular focus on hadronic frameworks suitable for
describing the low and moderate *Q*^{2} region relevant to
most experimental studies. The effects of TPE on the extraction of nucleon
form factors is discussed, together with their role in the resolution
of the proton electric to magnetic form factor ratio puzzle. The
implications of TPE on various other observables, including neutron form
factors, electroproduction of resonances and pions, and nuclear form
factors, are summarized.
Measurements seeking to directly identify TPE effects, such as through the
angular dependence of polarization measurements, nonlinear epsilon
contributions to the cross sections, and via *e ^{+}p*
to

*e*cross section ratios, are also outlined.

^{-}p**
"Global analysis of proton elastic form factors data with two-photon
exchange corrections"
**

J. Arrington, W. Melnitchouk and J.A. Tjon

*Phys. Rev. C* **76**, 035205 (2007)

Using the world's data on elastic electron-proton scattering and
calculations of two-photon exchange effects, corrected values of
the proton's electric and magnetic form factors are extracted over the
full *Q*^{2} range of the existing data. The analysis
combines the corrected Rosenbluth cross section and polarization transfer
data, and is the first extraction of *G _{Ep}* and

*G*including explicit two-photon exchange corrections and their associated uncertainties. In addition, the angular dependence of the corrected cross sections is examined, and the possible nonlinearities of the cross section discussed as a function of ε.

_{Mp}
The extrapolated proton and neutron magnetic form factors at the
physical pion mass versus the momentum transfer, *Q*^{2}.
The open and filled square points denote fits with and without
inclusion of the form factor of the pion, respectively.
The solid curves represent the empirical nucleon form factors.

**
"Chiral extrapolation of nucleon magnetic form factors"
**

P. Wang, D. B. Leinweber, A. W. Thomas, R. D. Young

*Phys. Rev. D* **75**, 073012 (2007)

The extrapolation of nucleon magnetic form factors calculated in
lattice QCD is investigated within a framework based on heavy baryon
chiral effective field theory. All one-loop graphs are considered at
arbitrary momentum transfer and all octet and decuplet baryons are
included in the intermediate states. Finite range regularization is
applied to improve the convergence in the quark-mass expansion.
At each value of the momentum transfer *Q*^{2}, a separate
extrapolation to the physical pion mass is carried out as a function of
*m*_{π} alone. Because of the large values of
*Q*^{2} involved, the role of the pion form factor in the
standard pion-loop integrals is also investigated. The resulting values
of the form factors at the physical pion mass are compared with
experimental data as a function of *Q*^{2} and demonstrate
the utility and accuracy of the chiral extrapolation methods.

## Structure Functions

Results of the CTEQ6X fit for the *u*- and *d*-quark
distributions with expanded kinematics and inclusion of TMC, HT and
nuclear corrections, normalized to the earlier global CTEQ6.1 PDFs.
The vertical lines show the approximate values of x above which PDFs
are not directly constrained by data. The error bands correspond to
Δχ=1.

**
"New parton distributions from large- x and low-Q^{2}
data"**

A. Accardi, M. E. Christy, C. E. Keppel, W. Melnitchouk, J. Morfin, P. Monahan, J. Owens

*Phys. Rev. D*

**81**, 034016 (2010)

A new global next-to-leading order fit of parton distribution functions
is performed in which cuts on *W* and *Q* are relaxed, thereby
including more data at high values of *x*. Effects of target mass
corrections (TMCs), higher twist contributions, and nuclear corrections
for deuterium data are significant in the large-*x* region. The
leading twist parton distributions are found to be stable to TMC model
variations as long as higher twist contributions are also included. The
behavior of the *d* quark as *x* → 1 is particularly
sensitive to the deuterium corrections, and using realistic nuclear
smearing models the *d*-quark distribution at large *x* is
found to be softer than in previous fits performed with more restrictive
cuts.
Application of the results of the CTEQ6X analysis will help constrain the
uncertainty in computing QCD backgrounds in searches for new physics
beyond the Standard Model in collider experiments, and the analysis of
neutrino oscillation experiments.

Extracted neutron *F*_{2}^{n} structure function
at *Q*^{2} = 1.7 and 5 GeV^{2}, together with proton
and deuteron data, and the reconstructed deuteron. The proton and neutron
data are compared with the global QCD fit from Alekhin *et al.*
The dependence of the iteration on the initial value is illustrated in
the insert.

**
"Confirmation of quark-hadron duality in the neutron F_{2}
structure function"**

S. P. Malace, Y. Kahn, W. Melnitchouk, C. E. Keppel

*Phys. Rev. Lett.*

**104**, 102001 (2010)

A recently developed extraction technique is applied to obtain for
the first time the neutron *F*_{2}^{n} structure
function from inclusive proton and deuteron data in the nucleon
resonance region, and test the validity of quark-hadron duality in
the deutron.
The accuracy of duality in the low-lying neutron resonance regions is
established over a range of *Q*^{2}, and results compared
with the corresponding results on the proton and with theoretical
expectations.
The confirmation of duality in both the neutron and proton opens the
possibility of using resonance region data to constrain parton
distributions at large *x*.

**
"Quark-hadron duality and truncated moments of nucleon structure
functions"**

A. Psaker, W. Melnitchouk, M. E. Christy, C. Keppel

*Phys. Rev. C* **78**, 025206 (2008)

A novel new approach is employed to study local quark-hadron duality
using "truncated" moments, or integrals of structure functions over
restricted regions of *x*, to determine the degree to which
individual resonance regions are dominated by leading twist.
Because truncated moments obey the same *Q*^{2} evolution
equations as the leading twist parton distributions, this approach
makes possible for the first time a description of resonance region
data and the phenomenon of quark-hadron duality directly from QCD.

**
"Next-to-leading order evolution of color dipoles"
**

I. Balitsky, G.A. Chirilli

*Phys. Rev. D* **74**, 014001 (2007) &
*Phys. Rev. D* **77**, 014019 (2008)

Deep inelastic scattering in the saturation region (for small *x*
and/or large nucleus) is described by the evolution of color dipoles.
In the leading order this evolution is governed by the non-linear
Balitsky-Kovchegov (BK) equation. To see if this equation is relevant for
existing or future accelerators (like the Electron Ion Collider) one needs
to know how large are the next-to-leading order (NLO) corrections.
In addition, the NLO corrections define the scale of the running coupling
constant in the BK equation and therefore determine the magnitude of the
leading-order cross sections.

**
"Quark-hadron duality in neutrino scattering"
**

O. Lalakulich, W. Melnitchouk, E.A. Paschos

*Phys. Rev. C* **75**, 015202 (2007)

A phenomenological model of the quark-hadron transition in
neutrino-nucleon scattering is presented. Using recently extracted weak
nucleon transition form factors, the extent to which local and global
quark-hadron duality is applicable in the neutrino
*F _{1}*,

*F*and

_{2}*F*structure functions is investigated, and contrasted with duality in electron scattering. The findings suggest that duality works relatively well for neutrino-nucleon scattering for the

_{3}*F*and

_{2}*F*structure functions, but not as well for

_{3}*F*. The quasi-elastic, resonance and deep inelastic contributions to the Adler sum rule are also calculated, and found to be satisfied to within 10% for 0.5 <

_{1}*Q*< 2 GeV

^{2}^{2}.

**
"Target mass corrections revisited"
**

F.M. Steffens, W. Melnitchouk

*Phys. Rev. C* **73**, 055202 (2006)

A new implementation of target mass corrections (TMCs) to
nucleon structure functions is proposed, which, unlike existing
treatments, has the correct kinematic threshold behavior at finite
Q^{2} in the *x* -> 1 limit. The differences between the
new approach and existing prescriptions are illustrated by considering
specific examples for the *F _{2}* and

*F*structure functions, and the broader implications of the results are discussed, which call into question the notion of universal parton distribution at finite

_{L}*Q*.

^{2}Ratios of the spin-independent and spin-dependent nuclear to nucleon
structure functions at nuclear matter density. The upper curve is the
ratio of unpolarized isoscalar *F _{2}* structure functions
in medium and in free space, compared with data which have been
extrapolated from finite nuclei to nuclear matter. The lower curve is the
ratio of the polarized proton

*g*structure function in medium and in free space.

_{1}**
"Spin-dependent structure functions in nuclear matter and the polarized
EMC effect"
**

I.C. Cloet, W. Bentz, A.W. Thomas

*Phys. Rev. Lett.* **95**, 052302 (2005)

An excellent description of both spin-independent and spin-dependent
quark distributions and structure functions has been obtained with a
modified Nambu-Jona-Lasinio model, which is free of unphysical thresholds
for nucleon decay into quarks - hence incorporating an important aspect
of confinement. This model is utilized to investigate nuclear medium
modifications to structure functions, and found to reproduce both nuclear
matter saturation and the experimental
*F _{2}^{N/A}/F_{2}^{N}* ratio
(the

*EMC effect*). Applying this framework to determine

*g*, the ratio

_{1}^{p/A}*g*is found to differ significantly from 1, with the quenching caused by the nuclear medium being about twice that of the spin-independent case. This represents an exciting result, which if confirmed experimentally, will reveal much about the quark structure of nuclear matter.

_{1}^{p/A}/ g_{1}^{p}## Generalized Parton Distributions

**
"DVCS off nucleons and nuclei in the generalized vector meson dominance
model"
**

K. Goeke, V. Guzey, M. Siddikov

*Eur. Phys. J. A* **36**, 49 (2008)

Deeply Virtual Compton Scattering (DVCS) off nucleons and nuclei is
considered in the framework of generalized vector meson dominance (GVMD)
model. The GVMD model is demonstraed to provide a good description of
the HERA data for the dependence of the proton DVCS cross section on
*Q*^{2}, *W* (at *Q*^{2} = 4 GeV^{2})
and *t*. At *Q*^{2} = 8 GeV^{2}, the soft
*W*-behavior of the GVMD model somewhat underestimates the *W*
dependence of the DVCS cross section due to the hard contribution not
present in the GVMD model. The 1/*Q*^{2} power-suppressed
corrections to the DVCS amplitude and the DVCS cross section are also
computed and found to be large. Predictions are also made for the
nuclear DVCS amplitude and cross section in the kinematics of a future
Electron-Ion Collider. Significant nuclear shadowing is predicted,
which matches well with predictions of the leading-twist nuclear
shadowing in DIS on nuclei.

The ratio of the coherent ^{4}He to free proton beam-spin
DVCS asymmetries,
*A _{LU}^{A}(φ)
/ A_{LU}^{p}(φ)*,
as a function of the momentum transfer

*t*. The calculation corresponds to JLab kinematics,

*E*=6 GeV,

*x*=0.15,

_{Bj}*Q*=1.5 GeV

^{2}^{2}, with

*φ*=90

^{o}.

**
"Neutron contribution to nuclear DVCS asymmetries"
**

V. Guzey

*Phys. Rev. C* **78**, 025211 (2008)

Using a simple model for nuclear GPDs, the role of the neutron
contribution to nuclear DVCS observables is studied. As an example,
the beam-spin asymmetry *A _{LU}^{A}* measured in
coherent and incoherent DVCS on a wide range of nuclear targets in
HERMES and JLab kinematics is considered. At small values of
the momentum transfer

*t*,

*A*is found to be dominated by the coherent-enriched contribution, which enhances

_{LU}^{A}*A*compared to the free proton asymmetry

_{LU}^{A}*A*, with

_{LU}^{p}*A*= 1.8 - 2.2. At large values of

_{LU}^{A}(φ) / A_{LU}^{p}(φ)*t*, the nuclear asymmetry is dominated by the incoherent contribution and

*A*= 0.66 - 0.74. The deviation of this ratio from unity at large

_{LU}^{A}(φ) / A_{LU}^{p}(φ)*t*is a result of the neutron contribution, which gives a possibility to constain neutron GPDs in incoherent nuclear DVCS. These predictions will be tested in the new Jefferson Lab experiment PR-08-024 (2008), which will measure coherent (see figure) and incoherent DVCS on

^{4}He.

**
"The physics of ultraperipheral collisions at the LHC"
**

K. Hencken *et al.*

*Phys. Rep.* **458**, 1 (2008)

Ultraperipheral ion-ion collisions (UPC) at the LHC are reactions in
which two ions interact via their cloud of quasi-real photons (see
figure). The UPC allow one to study various photon-nucleus processes
at very high photon energy, up to 10^{6} GeV in the rest frame
of the target nucleus. Among predictions for various observables,
the cross sections of coherent photoproduction of *J/Ψ* and
Υ vector mesons on heavy nuclear targets,
*γ A → J/Ψ (Υ) A* are calculated.
These measurements will probe the nuclear gluon GPD at small values of
*x _{Bj}*.

**
"Weak deeply virtual Compton scattering"
**

A. Psaker, W. Melnitchouk, A. Radyushkin

*Phys. Rev. D* **75**, 054001 (2007)

The analysis of the deeply virtual Compton scattering process is extended to the weak interaction sector in the generalized Bjorken limit. The virtual Compton scattering amplitudes for the weak neutral and charged currents are calculated at the leading twist within the framework of the nonlocal light-cone expansion via coordinate space QCD string operators. Using a simple model, cross sections are calculated for neutrino scattering off the nucleon, relevant for future high-intensity neutrino beam facilities.