Collective modes in hadronic matter in a relativistic model with medium dependent coupling
R. Aguirre
Department of Physics, La Plata National University, C.C. 67 (1900) La Plata, Argentina
Received 7 September 2000; published 19 January 2001
The propagation of the lightest mesons in hadronic matter is studied at finite temperature, by including Dirac
sea effects. The meson-nucleon interaction is described in a field theory model, which exhibits a residual
interaction beyond the ground state, with a medium dependent coupling constant. The effective meson masses,
the low lying collective excitations of nuclear matter, and the giant isoscalar resonances of a system with finite
particle number are studied and compared with other theoretical predictions. The effect of different regular-
ization prescriptions is also considered.
DOI: 10.1103/PhysRevC.63.025206 PACS numbers: 21.30.Fe, 21.65.+f, 12.40.Yx, 24.80.+y
I. INTRODUCTION
Properties of hadrons are expected to vary considerably
when immersed in a dense and/or hot medium. The study of
the density dependence of meson masses can provide infor-
mation about the underlying strong interaction, as has been
suggested in 1. In that paper a qualitative expression, the
so-called Brown-Rho universal scaling law, is given for the
behavior of the in-medium hadronic masses, valid near the
chiral transition point. In later works 2,3 a relationship be-
tween the chiral picture and the hadronic language is pro-
posed. According to the scaling law, all hadrons masses de-
crease approximately at the same rate as the system
approaches the chiral phase transition with the exception of
the pseudoscalar meson masses. This fact could explain ex-
perimental results, for example on dilepton production.
Therefore it would be desirable that hadronic models that
work well far from the chiral limit, could reproduce these
features asymptotically.
In this work we intend to compare meson properties under
extreme conditions of density and temperature, and to study
collective phenomena of nuclear matter. For this purpose we
have selected a model of the quantum hadrodynamics 4,
which in its former version QHD-I has no chiral invariance.
However it has been argued 5 that the predictions of the
model are intrinsically consistent with chiral symmetry. Sub-
sequent developments have led to its present day interpreta-
tion as an effective field theory 6. Specifically we have
used the derivative scalar coupling model DSCM proposed
by Zimanyi and Moszkowski 7 and profusely applied to
describe nuclear properties 8–14.
We organize this paper by presenting the DSCM beyond
the lowest order approximation in Sec. II, the evaluation of
the meson propagators in the relativistic random phase ap-
proximation RRPA is reviewed in Sec. III, results and dis-
cussion are given in Sec. IV, and the conclusions are pre-
sented in Sec. V.
II. THE DSCM BEYOND THE MEAN FIELD
APPROXIMATION
QHD was originally outlined as a renormalizable theory
with a very restricted set of free parameters used to fit bulk
nuclear matter properties. The ground state solution is ob-
tained in the mean field approximation and assumed to be-
come more and more precise as baryon density grows. How-
ever qualitative discrepancies have shown that the inclusion
of vacuum contributions is essential even at the lowest order.
Furthermore technical difficulties in the summation of higher
order diagrams have spoiled the program of systematic cor-
rections 15. Despite these conceptual inconsistencies the
successes obtained in the description of nuclear phenomena
have encouraged its development, until its current interpre-
tation in the framework of effective field and density func-
tional theories 4,6.
In this work we have selected a quantum hadrodynamics
model which uses the same degrees of freedom as the
QHD-I, but the nucleon-scalar meson interaction is given in
a nonpolynomic parametrization. It has been used to study
many body effects in several applications 8–11, related to
an effective quark description of hadronic properties 12,
and extended to include tensor coupling 14. The DSCM
has two important features which distinguish it from the
QHD-I. First it is nonrenormalizable ab initio and there is no
immediate way to introduce vacuum corrections to the
ground state. This state is obtained in the mean field approxi-
mation, and the main properties of nuclear matter are suc-
cessfully described. A possible interpretation of this fact is
that DSCM is more efficient than QHD-I for describing low-
energy hadron physics, at this order of approximation. Sec-
ondly, a residual interaction can be extracted beyond the
lowest order solution, whose strength monotonically de-
creases with baryon density 13. This fact ensures the
ground state predominance at high density as assumed in
quantum hadrodynamics. The properties just enumerated
motivated us to use DSCM to study meson propagation in
extreme baryon density and temperature. In a first approach
we look for a qualitative description and consider only nucle-
ons, scalar meson ( ), and vector meson (
) fields. But
resonances 10, hyperons 11, and heavier mesons can also
be included in a more realistic treatment.
The DSCM model consists of nucleon and meson fields in
interaction, the simplest version 7 has a Yukawa type N -
coupling and a N - nonpolynomic term L
N
,
L
DSCM
=
¯
i ” -
M
1 +g
s
/ M
-g
v
”
+
1
2
-
1
2
m
s
2
2
-
1
4
F
F
+
1
2
m
v
2
, 1
PHYSICAL REVIEW C, VOLUME 63, 025206
0556-2813/2001/632/0252067/$15.00 ©2001 The American Physical Society 63 025206-1