中子星中的伪南布-金石模式
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Physics Letters B 769 (2017) 14–20
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Pseudo Nambu–Goldstone modes in neutron stars
Toru Kojo
Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
19 October 2016
Received
in revised form 18 February 2017
Accepted
13 March 2017
Available
online 17 March 2017
Editor:
W. Haxton
Keywords:
Dense
QCD
Effective
models
Neutron
stars
If quarks and gluons are either gapped or confined in neutron stars (NSs), the most relevant light
modes are Nambu–Goldstone (NG) modes. We study NG modes within a schematic quark model whose
parameters at high density are constrained by the two-solar mass constraint. Our model has the color-
flavor-locked
phase at high density, with the effective couplings as strong as in hadron physics. We find
that strong coupling effects make NG modes more massive than in weak coupling predictions, and would
erase several phenomena caused by the stressed pairings in mismatched Fermi surfaces. For instance, we
found that charged kaons, which are dominated by diquark and anti-diquark components, are not light
enough to condense at strong coupling. Implications for gravitational wave signals for NS–NS mergers are
also briefly discussed.
© 2017 The Author. 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
Neutron stars are unique cosmic laboratories to study cold
dense QCD. The observations of two-solar mass (2M
) neutron
stars (NSs) [1,2] tell us that equations of state at high baryon den-
sity,
n
B
5n
0
(n
0
0.16 fm
−3
: nuclear saturation density), must
be very stiff to prevent the star from gravitational collapsing.
Meanwhile low density equations of state at n
B
2n
0
should be
softer than the previous thoughts, as suggested by studies of neu-
tron
star radii [3–7], nuclear symmetry energy, heavy ion data [8],
and predictions of chiral effective theories [9] that are combined
with sophisticated many-body calculations [10,11]. Then the theo-
retical
challenge is how to reconcile these tendencies at low and
high density [12,13]; to connect soft and stiff equations of state,
there must be a region where the sound velocity c
s
= (∂ P /∂ε)
1/2
is large, but this tends to violate the causality constraint c
s
≤ 1.
Also, soft-to-stiff equations of state does not allow us to imple-
ment
strong first order phase transitions which soften equations
of state at high density.
1
In this way the constraints from high and
low density together limit the possible classes of equations of state,
and from which one can extract useful insights into matter [14].
While
the current observations have already provided signifi-
cant
constraints, equations of state alone do not finalize our un-
derstanding
of dense matter. It is desirable to study dynamic and
E-mail address: torujj@mail.ccnu.edu.cn.
1
If we assume very stiff hadronic equations of state at low density, we may allow
strong first order phase transitions from very stiff hadronic matter to quark matter
stiff enough to pass the 2M
constraint [15].
thermal aspects of matter which originate from excitation modes
whose properties are very sensitive to the phase structure. The
predictions for thermal equations of state are very important for
the gravitational wave astronomy [16,17]; the first direct detection
of gravitational waves of a binary black-holes has been made in
September 2015 [18], and the second detection three months later
[19]. We also expect gravitational waves from NS–NS mergers in
near future. It has been argued that the patterns of gravitational
waves can discriminate different equations of state by comparing
the observations with the waveforms predicted by numerical rela-
tivity
with input equations of state [20].
The
purpose of this paper is to study the low energy modes at
high density, in a setup consistent with neutron star constraints
at zero temperature. Our underlying physical picture is based on
a 3-window description
2
for dense QCD matter which has been
studied in recent works [12,22–24]. The 3-window picture consists
of: purely nuclear matter for n
B
2n
0
; quark matter for n
B
5n
0
;
and crossover (or weak 1st order) picture
3
for 2n
0
n
B
5n
0
.
Each domain has own characteristic constraint; nuclear physics
constraint for n
B
2n
0
; the 2M
constraint for n
B
5n
0
; and
the causality and thermodynamic constraints on 2n
0
n
B
5n
0
which require 0 ≤ c
2
s
≤ 1. To express the nuclear constraints for
2
Somewhat indirect, but less model-dependent approach is to interpolate the
nuclear and perturbative quark matter equations of state. This has been carried out
with perturbative calculations to three loop order [21].
3
The crossover picture has been also discussed in an effective Lagrangian frame-
work
in [25], where matter changes its character but does not induce the first order
phase transition.
http://dx.doi.org/10.1016/j.physletb.2017.03.023
0370-2693/
© 2017 The Author. 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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