Physics Letters B 794 (2019) 103–108
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Physics Letters B
www.elsevier.com/locate/physletb
Chiral constraints on the isoscalar electromagnetic spectral functions
of the nucleon from leading order vector meson couplings
Y. Ünal
a,b,∗
, Ulf-G. Meißner
a,c,d
a
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany
b
Physics Department, Çanakkale Onsekiz Mart University, 17100 Çanakkale, Turkey
c
Institute for Advanced Simulation, Institut für Kernphysik, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, Germany
d
Tbilisi State University, 0186 Tbilisi, Georgia
a r t i c l e i n f o a b s t r a c t
Article history:
Received
13 February 2019
Received
in revised form 16 April 2019
Accepted
20 April 2019
Available
online 22 May 2019
Editor: W.
Haxton
Keywords:
Electromagnetic
form factors
Baryon
chiral perturbation theory
Using baryon chiral perturbation theory including vector mesons, we analyze various continuum
contributions to the isoscalar electromagnetic spectral functions of the nucleon induced by the leading
order couplings.
© 2019 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
A premier tool to analyse the electromagnetic structure of the
nucleon are dispersion relations. The physics is encoded in the so-
called
spectral functions, which feature vector meson resonances
and continuum contributions. Much is known about the continuum
contribution to the isovector spectral function of the electric and
magnetic nucleon form factors, see e.g. Ref. [1]for the most recent
and most precise investigation. The situation for the corresponding
continuum contributions to the isoscalar spectral functions is dif-
ferent,
as discussed in detail in Ref. [2]. Chiral perturbation theory
has been used to analyze the three-pion continuum [3,4]within
the threshold region starting at t
0
= 9M
2
π
. These two-loop con-
tributions,
however, turn out to be rather small, because the po-
tential
enhancement from the anomalous threshold at t 8.9M
2
π
is efficiently masked by phase space factors. On the other hand,
earlier modelling suggests an important contribution from the πρ
continuum [5] and dispersion relations have been used to calcu-
late
the K
¯
K contribution [6,7]. In the sector with strange quarks,
there have been suggestions of cancellation between contributions
from
K
¯
K , KK
∗
and K
∗
K
∗
loops, although these have very differ-
ent
thresholds [8]. It might be worth to put our work in proper
*
Corresponding author at: Helmholtz-Institut für Strahlen- und Kernphysik and
Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany.
E-mail
addresses: unal@hiskp.uni-bonn.de (Y. Ünal), meissner@hiskp.uni-bonn.de
(U.-G. Meißner).
context: We work with a chiral Lagrangian with explicit vector
mesons, whereas in Ref. [5]a meson-exchange model was used.
In contrast to that, the approach used here can be systematically
improved. As concerns the dispersive approach used in Refs. [6,7],
it in principle contains the vector meson contributions. However,
as noted in these papers, the required data for the analytic contin-
uation
of the kaon-nucleon scattering amplitudes are not precise
enough to uniquely fix the isoscalar spectral functions. Thus, the
approach used here gives complementary information.
In
this paper, we want to re-analyze some of these continua
as well as some vector meson contributions to the isoscalar elec-
tromagnetic
spectral functions based on chiral perturbation the-
ory
with explicit vector mesons. This extends the earlier tree-level
analyses of vector meson contributions to the nucleon electromag-
netic
(em) form factors as given e.g. in Refs. [9,10]. Here, we work
at leading one-loop order and consider the vector coupling in-
duced
contributions. The paper is organized as follows: In Sec. 2,
we briefly recall the pertinent definitions for the electromagnetic
form factors and their spectral functions. The πρ contribution is
worked out and discussed in Sec. 3. The contributions involving K
and
K
∗
mesons are given in Sec. 4. We end with a summary and
outlook. Some technicalities are given in the Appendix.
2. Isoscalar electromagnetic spectral functions
The electromagnetic form factors of the nucleon are defined via
the matrix element of the electromagnetic current,
https://doi.org/10.1016/j.physletb.2019.05.029
0370-2693/
© 2019 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
.