Physics Letters B 738 (2014) 187–190
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Functional renormalization group approach to neutron matter
Matthias Drews
a,b,∗
, Wolfram Weise
a,b
a
Physik Department, Technische Universität München, D-85747 Garching, Germany
b
ECT*, Villa Tambosi, I-38123 Villazzano, Trento, Italy
a r t i c l e i n f o a b s t r a c t
Article history:
Received
3 April 2014
Received
in revised form 2 September 2014
Accepted
23 September 2014
Available
online 26 September 2014
Editor:
J.-P. Blaizot
Keywords:
Functional
renormalization group
Neutron
matter
Neutron
stars
The chiral nucleon-meson model, previously applied to systems with equal number of neutrons and
protons, is extended to asymmetric nuclear matter. Fluctuations are included in the framework of the
functional renormalization group. The equation of state for pure neutron matter is studied and compared
to recent advanced many-body calculations. The chiral condensate in neutron matter is computed as
a function of baryon density. It is found that, once fluctuations are incorporated, the chiral restoration
transition for pure neutron matter is shifted to high densities, much beyond three times the density of
normal nuclear matter.
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP
3
.
1. Introduction
In recent years our understanding of neutron matter has
been sharpened significantly. Empirical data as well as theoreti-
cal
progress set increasingly strong constraints for the equation of
state (EoS) at high baryon densities. The observation of two-solar
mass neutron stars [1,2] implies that the EoS must be sufficiently
stiff in order to support such dense systems against gravitational
collapse.
At
the same time different realistic calculations of neutron mat-
ter
based on purely hadronic degrees of freedom are seen to be
converging to a consistent picture of the energy per particle as a
function of neutron density. Approaches such as chiral Fermi liquid
theory [3], chiral effective field theory (ChEFT, [4–6]), or quantum
Monte Carlo (QMC) calculations [7,8] all agree with each other
within their ranges of applicability. Whereas compact stars with
a considerable “exotic” composition, such as a substantial quark
core, seem to provide not enough pressure to support a two-solar
mass neutron star unless additional strongly repulsive forces are
invoked, conventional hadronic matter is consistent with all avail-
able
mass-radius constraints [9].
In
recent publications [10,11], a successful chiral nucleon-
meson
model for symmetric nuclear matter, previously introduced
in [12], was studied beyond mean-field approximation. Fluctua-
*
Corresponding author at: Physik Department, Technische Universität München,
D-85747 Garching, Germany.
E-mail
addresses: matthias.drews@ph.tum.de (M. Drews), weise@tum.de
(W. Weise).
tions were treated within the framework of the functional renor-
malization
group (FRG). The importance of a proper handling of
fluctuations around the nuclear liquid-gas phase transition was
demonstrated. Moreover, no sign of chiral restoration was found
for temperatures below about 100 MeV and densities up to about
three times nuclear saturation density, n
0
= 0.16 fm
−3
.
In
the present letter we extend this model to asymmetric nu-
clear
matter. The equation of state for pure neutron matter is com-
puted
and compared with state-of-the-art many-body calculations.
As in symmetric nuclear matter, fluctuations tend to stabilize the
hadronic phase characterized by spontaneously broken chiral sym-
metry
and shift the chiral restoration transition to densities much
larger than those anticipated in mean-field approximation. This re-
sult
is of relevance for chiral approaches to strongly interacting,
highly compressed baryonic matter, indicating that nucleon and
meson (rather than quark) degrees of freedom are still active at
densities several times that of normal nuclear matter.
2. Chiral nucleon-meson model and fluctuations
The chiral nucleon-meson model is designed to describe nu-
clear
matter and its thermodynamics around the liquid-gas phase
transition. The relevant degrees of freedom are protons and neu-
trons
forming an isospin doublet nucleon field ψ = (ψ
p
, ψ
n
)
T
.
The nucleons are coupled to boson fields: a chiral four-component
field (σ , π) transforming under the chiral group SO(4)
∼
=
SU(2)
L
×
SU(2)
R
, an isoscalar–vector field ω
μ
and an isovector–vector field
ρ
μ
. Note that these ω and ρ fields are not to be identified
with the known omega and rho mesons. They are introduced
here to act as background mean fields representing the effects of
http://dx.doi.org/10.1016/j.physletb.2014.09.051
0370-2693/
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by
SCOAP
3
.