Physics Letters B 753 (2016) 595–599
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Electromagnetic contribution to charge symmetry violation in parton
distributions
X.G. Wang
∗
, A.W. Thomas, R.D. Young
ARC Centre of Excellence for Particle Physics at the Terascale and CSSM, Department of Physics, University of Adelaide, Adelaide SA 5005, Australia
a r t i c l e i n f o a b s t r a c t
Article history:
Received
14 December 2015
Accepted
23 December 2015
Available
online 29 December 2015
Editor:
A. Ringwald
Keywords:
Charge
symmetry
Parton
distributions
Electromagnetic
correction
We report a calculation of the combined effect of photon radiation and quark mass differences on
charge symmetry violation (CSV) in the parton distribution functions of the nucleon. Following a recent
suggestion of Martin and Ryskin, the initial photon distribution is calculated in terms of coherent
radiation from the proton as a whole, while the effect of the quark mass difference is based on a recent
lattice QCD simulation. The distributions are then evolved to a scale at which they can be compared with
experiment by including both QCD and QED radiation. Overall, at a scale of 5GeV
2
, the total CSV effect
on the phenomenologically important difference between the d and u-quark distributions is some 20%
larger than the value based on quark mass differences alone. In total these sources of CSV account for
approximately 40% of the NuTeV anomaly.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Charge symmetry (CS) refers to the invariance of the QCD
Hamiltonian under the operator e
iπ I
2
, a rotation by 180 deg about
the 2-axis in iso-space. Under this operation u-quarks rotate into
d-quarks and vice-versa, while protons and neutrons are also in-
terchanged.
As a result, if QCD were to respect this symmetry, the
up-quark distribution in the proton, u
p
, and the down quark distri-
bution
in the neutron, d
n
, would be identical. Similarly one would
have d
p
= u
n
. Precisely these relations have been almost univer-
sally
assumed for the past 40 years, as without such an assumption
it would have been impossible to separate the flavor dependence
of the parton distribution functions (PDFs).
Studies
of strongly interacting systems have established that CS
is typically respected at the level of a fraction of a percent [1],
much better than isospin symmetry, which requires the invariance
of the Hamiltonian under all rotations in iso-space. Nevertheless,
as one uses tests of symmetries to probe for physics beyond the
Standard Model, or aims for higher precision at the LHC, it is vi-
tal
to know just how well the PDFs satisfy CS. Furthermore, subtle
tests of such a symmetry can also yield information on how QCD
itself works. Thus the study of charge symmetry violation (CSV) in
PDFs may also lead to a deeper understanding of the structure of
the nucleon itself. For reviews of CSV in PDFs we refer to Londer-
gan
et al. [2,3].
*
Corresponding author.
E-mail
address: xuan-gong.wang@adelaide.edu.au (X.G. Wang).
There are two dominant sources of CSV in the nucleon, the
electromagnetic interaction and the mass differences of the u and
d quarks, δm = m
d
− m
u
. The first investigations of CSV in the
PDFs were based on the effect of δm within the MIT bag model
[4–6]. These calculations showed CSV violating effects as large as
5% at large-x, while they were at the percent level in the momen-
tum
fractions:
δU =
1
0
dx xδu(x) ; δ D =
1
0
dx xδd(x), (1)
where the CSV PDFs are δu = u
p
−d
n
and δd = d
p
−u
n
. The major
effect, which could be understood in terms of the dominant role
played by di-quark correlations [7], arose from the mass difference
between the dd and uu spectator pairs to the struck u-quark in a
neutron and d-quark in a proton. It was found that δu and δd had
a similar magnitude and opposite sign.
In
the context of the NuTeV experiment [8], where these pub-
lished
effects were sufficiently large to reduce the anomaly to 2σ
or less [9,10] considerable work was carried out to establish the
extent to which these results were model independent. Recently,
lattice QCD studies of these moments [11,12] (although necessar-
ily
the charge conjugation positive combination, rather than the
valence combination calculated in the bag model) confirmed the
sign and magnitude of the pioneering calculations.
The
importance of QED radiation on DIS processes was recog-
nised
more than 40 years ago in the context of photon radiation
from quarks in charged current neutrino interactions [13]. In the
http://dx.doi.org/10.1016/j.physletb.2015.12.062
0370-2693/
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.