Physics Letters B 747 (2015) 305–309
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Forward Compton scattering with weak neutral current: Constraints
from sum rules
Mikhail Gorchtein
a,∗
, Xilin Zhang
b,c,d
a
PRISMA Cluster of Excellence, Institut für Kernphysik, Johannes Gutenberg-Universität, Mainz, Germany
b
Department of Physics, University of Washington, Seattle, WA, USA
c
Institute of Nuclear and Particle Physics and Department of Physics and Astronomy, Ohio University, Athens, OH, USA
d
Fermi National Accelerator Laboratory, Batavia, IL, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
22 January 2015
Received
in revised form 1 June 2015
Accepted
3 June 2015
Available
online 9 June 2015
Editor:
W. Haxton
We generalize forward real Compton amplitude to the case of the interference of the electromagnetic
and weak neutral current, formulate a low-energy theorem, relate the new amplitudes to the interference
structure functions and obtain a new set of sum rules. We address a possible new sum rule that relates
the product of the axial charge and magnetic moment of the nucleon to the 0th moment of the structure
function g
5
(ν, 0). For the dispersive γ Z-box correction to the proton’s weak charge, the application of
the GDH sum rule allows us to reduce the uncertainty due to resonance contributions by a factor of two.
The finite energy sum rule helps addressing the uncertainty in that calculation due to possible duality
violations.
© 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
.
The study of Compton scattering within dispersion relation for-
malism
has led to a derivation of the celebrated sum rules that
model-independently relate low-energy properties of the nucleon
to its excitation spectrum. Forward Compton amplitude that con-
tains
parity-conserving (PC) and parity-violating (PV) interactions
is expressed in terms of scalar PC amplitudes f , g and PV ampli-
tudes
˜
f ,
˜
g, see e.g. Refs. [1,2],
T (ν) = f (ν)(
ε
∗
·
ε) + g(ν)i
σ ·[
ε
∗
×
ε]+
˜
f (ν)i
ˆ
q ·[
ε
∗
×
ε]
+
˜
g(ν)(
σ
ˆ
q)(
ε
∗
·
ε), (1)
with M the nucleon mass,
σ the nucleon spin,
ˆ
q the unit vector
pointing in the direction of the photon three momentum, and
ε
,
ε
the final (initial) photon polarization vectors. We define the elec-
tromagnetic
forward Compton amplitude as
T
γγ
=
i
8π Me
2
d
4
xe
iqx
p|Tj
μ
EM
(x) j
ν
EM
(0)|pε
μ
ε
∗
ν
, (2)
with M the nucleon mass and e related to the fine structure con-
stant
α
em
= e
2
/(4π) ≈ 1/137. Only PC amplitudes f , g are present
*
Corresponding author.
E-mail
addresses: gorshtey@kph.uni-mainz.de (M. Gorchtein), xilinz@uw.edu
(X. Zhang).
in the electromagnetic case. The γ Z-interference forward Compton
amplitude is normalized as
T
γ Z
=
i sin 2θ
W
4π Me
2
d
4
xe
iqx
p|Tj
μ
NC
(x) j
ν
EM
(0)|pε
μ
ε
∗
ν
, (3)
with θ
W
the weak mixing angle. We focus on transverse Z
0
here,
whereas the longitudinal component may be related to pion photo
production through PCAC. The vector coupling of the Z
0
con-
tributes
to the amplitudes f , g that already appeared in the elec-
tromagnetic
case. To disambiguate we will use the superscript γ Z
for
the interference case. The PV amplitudes
˜
f ,
˜
g arise from an
interference of the electromagnetic current with the axial vector
current, and correspond to nucleon spin-independent and nucleon
spin-dependent contributions, respectively. Under crossing ν →−ν
the amplitudes f ,
˜
g are even, while the amplitudes
˜
f , g are odd.
We
wish to emphasize that although we consider a Z
0
boson
in the final or initial state, the kinematics of the Compton process
that we study here is such that the on-shell Z
0
cannot be pro-
duced
since q
2
= 0. PV sum rules have been considered either in
the Compton process γ + N → γ + N with hadronic PV effects [3,4]
or
Compton-like process γ + ν → W
+
+e
−
, γ + e
−
→ Z
0
+e
−
and
such, with an on-shell weak boson produced in the final state [5,6].
In the process that we consider, the Z
0
may originate, e.g., from
neutrino or charged lepton scattering off the nucleon accompanied
with a radiation of a real photon in the final state, as, e.g., virtual
Compton scattering is accessed in a process e
−
+ N → e
−
+ N + γ .
http://dx.doi.org/10.1016/j.physletb.2015.06.009
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
.
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