Physics Letters B 747 (2015) 217–222
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Chiral dynamics in the
γ p → pπ
0
reaction
A.N. Hiller Blin, T. Ledwig, M.J. Vicente Vacas
∗
Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigación de Paterna, E-46071 Valencia, Spain
a r t i c l e i n f o a b s t r a c t
Article history:
Received
16 December 2014
Received
in revised form 27 February 2015
Accepted
27 May 2015
Available
online 29 May 2015
Editor:
J.-P. Blaizot
We investigate the neutral pion photoproduction on the proton near threshold in covariant chiral
perturbation theory with the explicit inclusion of degrees of freedom. This channel is specially sensitive
to chiral dynamics and the advent of very precise data from the Mainz microtron has shown the limits
of the convergence of the chiral series for both the heavy baryon and the covariant approaches. We
show that the inclusion of the resonance substantially improves the convergence leading to a good
agreement with data for a wider range of energies.
© 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
Neutral pion photoproduction on the proton at low energies
is specially sensitive to chiral dynamics. Considering the range
of energies from threshold to 500 MeV, the total cross section
appears to be clearly dominated by the magnetic dipole excita-
tion
of the (1232).
1
Its role is more important here than for
the charg ed pions photoproduction, because of the smallness of
the electric dipole contribution for the neutral pion channels. Of
course, approaching low energies, the relevance of the reso-
nance
decreases fast and may become negligible as we get far from
its mass and because of the p-wave nature of its contribution.
Close
to threshold, charged pion photoproduction has a rela-
tively
large cross section that can be well describ ed by just tree-
level
diagrams which lead to a substantial electric dipole moment.
However, the situation is quite different for the neutral pion chan-
nels
which present a much smaller cross section. Qualitatively,
this is also well understood as the theoretical models produce a
tiny s-wave amplitude, which actually vanishes in the chiral limit
(m
π
→ 0). The smallness of the lowest order tree-level contribu-
tions
offers a good opportunity for the study of higher order terms
of the chiral Lagrangian and of loop effects. In fact, one of the
important successes of Chiral Perturbation Theory (ChPT) was the
discovery in Refs. [2,3] of the importance of the loop contributions
for the π
0
channels. This allowed to solve the serious discrepancies
between data [4,5] and the Low Energy Theorems (LET) obtained
by previous theoretical models [6,7] based on current algebra and
*
Corresponding author.
E-mail
address: manuel.j.vicente@uv.es (M.J. Vicente Vacas).
1
See, e.g., Fig. 8.1 of Ref. [1].
the partial conservation of the axial current [8,9]. The model of
Refs. [2,3] was further improved in Refs. [10,11] using a more sys-
tematic
approach, heavy-baryon ChPT (HBChPT), which allows for
a proper power counting scheme. The neutral pion photoproduc-
tion
off protons was analyzed to fourth order in HBChPT in [12]
finding
a good agreement with the data that were available at the
time.
However,
the new and very precise data for the
γ +p → π
0
+p
reaction
obtained at the Mainz Microtron (MAMI) [13] have clearly
shown the limits of this approach. In Ref. [14], it has been shown
that fourth order HBChPT agrees well with data only up to around
20 MeV above threshold.
An
alternative relativistic renormalization scheme of the bary-
ons
ChPT, the Extended On Mass Shell (EOMS) ChPT [15,16] has
been successfully applied to the study of several physical observ-
ables
such as pion scattering, baryon magnetic moments and axial
form factors, baryon masses among others [17–26]. The EOMS ap-
proach
is covariant, satisfies analyticity constraints lost in the HB
formulation and usually converges relatively faster . Surprisingly,
afourth order EOMS calculation of the
γ + p → π
0
+ p process
described the experimental data even slightly worse than the HB
one [13,27].
A
possible reason for the poor agreement could be due to the
importance of the resonance, not included in the aforemen-
tioned
calculations as an explicit degree of freedom. Here, it could
be more visible than for other channels due to the smallness of
the nucleonic contributions of the lowest orders. This was already
pointed out by Hemmert et al. in Ref. [28]. Actually, they obtained
a moderate effect for the electric dipole amplitude at threshold in
their HB approach. This result was further explored in Ref. [12],
also in a HBChPT static calculation, finding a sizable cancellation
http://dx.doi.org/10.1016/j.physletb.2015.05.067
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
.