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considered phenomenological phenomenological
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discussed discussed s FL FL superconducting gap ShareAlikeLicence. - . . The pairing is effect
the the C Locked) Locked) superconducting phase at zero -
taken into account by incorporating NonCommercial - taking Flavor - Attribution in in the calculation
se as the lowest energy state of the quark matter. the quark state of energy the lowest as se
rent values of the parameters used for the description of t
superconducting quark matter i matter quark superconducting
taken as the ground state of Quantum Chromodyna medium medium quark mass
- . In this work, the CFL matter is being studied in
state, Brasil state,
[1]
) stability of the of stability
1
Paraná
ce ce of the in Speaker
[email protected] [email protected]
dependen the thermodynamical potential of the system, The parameter. of state of the system for diffe model. phenomenological The employed here main purpose is to thestudy limit values of pha CFL the maintain to parameters The The strange quark matter in the CFL temperature has (Color been flavors (u, d, s approach thewhere interaction quarksbetween is 1 mail: mail: mail: mail: 10 June June 2011 10 Copyright owned by the author(s) under the terms of the Creative Commons under Copyrightownedbythe termsthe ofCreative the author(s) - -
- Physics, Nuclear on Workshop Brazilian the of edition XXXIV de Foz Iguaçu, 5 E Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, Brazil Janeiro, Rio de Urca, 150, Sigaud, Xavier Rua Dr. E S.B. Duarte, Físicas Pesquisas de Brasileiro Centro Brazil Janeiro, Rio de Urca, 150, Sigaud, Xavier Rua Dr. dependent quark mass quark dependent F.S.D.C. Assis, Físicas Pesquisas de Brasileiro Centro Domain of parameters in a model with density model in a of parameters Domain
PoS(XXXIV BWNP)110
in in
the The
order order [1] . ]. Here
taken taken as believes 4 baryonic i.e., zero , in , in arising arising
(
is is imitate imitate uark mass results results and
focused focused on
one one submitted submitted to Speaker Speaker Name cosmological cosmological is particles
is is introduced in is is phase phase - ability ability in the CFL few microseconds th supported supported by one As As a consequence,
determined determined for the where where
st
the the main ,
, a regime CFL as free
phase phase in Ref. [ dependent q , which - - been is is a function of here here theis that possibility the the
, and
Within
. mass
behave behave density situation situation is Also t Also
unpaired strange strange matter unpaired where where . already neutron neutron stars
features features a typical phase transition.
, called strangelets. The properties
degenerate degenerate gas.
of of of of quarks
high high energies
energies energies high enough to dilute its This This
has has condition quarks quarks es negligibly negligibly low temperature
state
, the the a , which establish that when
t
a more stable QGP condensed state. stable QGP condensed amore
Chakrabarty Chakrabarty
(QGP). (QGP). ear ear density composed of quarks u, d and s (antiquarks not not s (antiquarks u,of quarks and d composed
2 , rmed rmed in a process similar to that one
gated gated intensively nowadays, particularly in the . The pairing for quarks of flavors different and
a a completely
m, m, as we will see latter. The
fo
dense dense stable bubbles of strange quark with matter
nucl to to plasma
mperature
state state
s is at temperature low
te
in in deep interior of
is is presented in more detail for for the
leading to leading
s
of of density dependent quark
high high temperature
hadron hadron phase transition had occurred
occurs quarks
-
Cooper Cooper pairs asymptotic asymptotic freedom
as a Fermi gas as a Fermi ] ] and for the MIT bag model in CFL quarks quarks become extremely massive and at very high densities
equilibrium equilibrium
strange strange matter in a
3 very very high thermodynamic description description thermodynamic , the the model model
may may
Color Superconducting Quark Matter Quark Color Superconducting a
e have have been investi the the , the extreme
th
can can be reached for
Chakrabarty Chakrabarty model is applied for the superconducting quark matter
objective objective of experiments at the the parameter
= 0), where the effective mass an used used the the pair of , .
given by given section consider
,
]
using using formed formed has has
happen the happen formation of
main main the the accelerated nucleons can reach , in ] , 3 study f State State f we
2 o uark and gluon plasma
larger larger than system behaves system
condition conditions, conditions, or
because because that that the gas can be treated as establish the establish domain of the parameters model the the energy of the system system the of the energy
for for low densities a q could
hadron transition hadron to following es so so , - concept concept in QCD o , are presented are
present
t )
of of quarks confined in the hadron
system [2 system that
there there B
the the , quark phase phase ρ -
decreas is is favored
In In this paper In In Chakrabarty [ Chakrabarty Nowadays
high high density minimum minimum energy state of the system. This domain The Equation Equation The
Introduction study its properties
considered considered in the limit T density 1.1 temperature strange matter the the the unpaired strange matter in Ref. [ the idea is to determine model. In the conclusions phase electric superconductivity forming colors in CFL to such way the this tries to With mass model vanishes. the effective dependence dynamical mass regimes of confinement and asymptotic freedo after after the Big Bang scenario density few times of the strange matter CFLphase. extreme extreme density conversion The that the in the primordial universe this quark 1. demonstrating that nucleons in fundamental Short title Short PoS(XXXIV BWNP)110
:
of For and
MIT . in in the [7] [3] [4] [5] [6] [2] baryonic
.
Speaker Speaker Name
as in the on on the
characteristics
is is included
chemical potential chemical of the the model of
vacuum vacuum (
, therefore
asymptotic asymptotic freedom s
weak weak enough to permits
following
because because in the CFL phase
me of density interest; of of density me
is described as described is
thermodynamic potential potential thermodynamic
i
,
,
quark ]
and
1
effective effective mass
[
the
find We
in
]. the the
is the is parameter
6
given by given bulk
µ
ase has the ase has the
is
,
are are
h
i
exerted exerted by the
the the
by
confinement
and C and
flavors
)
3
, given dependence dependence of fermions fermions superconductivity in this model [ model this in
x) are are equal, with a commum Fermi momenta to dynamic
potential thermodynamic
the the g(
an additional an additional gap term
in in the
confining confining pressure
) and ) and
constant constant can not be considered
density
with different with
of confinement of
pairing
arises due to
to describe the
quarks
coupling coupling
by means by of means the the role of
he density of the of density he B*
P is
is defined by defined is
. The commom Fermi momentum ν Fermi momentum commom . The quarks quarks
plays
quark quark a situation Thus, t
.
] treatment 5
energy [
it it also the current mass of the strange quark strange the of current mass the
(
, we , get we
the pressurethe different different quark flavors are the masses are of the masses additional additional term
and
he he phase has a neutral charge eletromagnetic in ,
the the system. the free of the energy minimizes color gauge and chiral simetries are broken in the barionic reg barionic the in are broken simetries and chiral gauge color the effective calculations; pertubative T With the auxiliary functions f(x functions auxiliary the With The The The total pressure
The The effect of The color superconductor quark matter in the CFL the p in matter quark color superconductor The
is the gap the is Fermi gas Fermi
model)
i. ii. CFL iii.
and density bag this phase this where thermodynamic free Short title Short where PoS(XXXIV BWNP)110
[8] [9] [10] [11]
for three three for
e
3
- is obtained obtained is
Speaker Speaker Name
baryon baryon
by by Fig. 1
MeV fm MeV
is given is
(C = 70 70 (C =
density
superconducting phase superconducting
rks with distinct flavors, the flavors, distinct the rks with
a
qu
in a color in
4
baryon baryon number
the model parameters the model
density of density
is defined as defined is
,
i
strange matter strange
relation
the same the cold cold
as a function of as a function
has
for quark
as follows
phase
of state for of
per particle
thermodynamic of the gap, keeping constant the gap, keeping of
CFL
the
particle density particle ).
values known Energy per baryon as a function of the baryon density at zero temperature for different different for temperature at baryon zero density the of as per a function baryon Energy
can be written can
-
The energy The The equation The Since Since The
. 1
Fig the gap. of value
different the from number
Short title Short where PoS(XXXIV BWNP)110
is
CFL
This
condition
Speaker Speaker Name
thermodynamic
Fe.
56 increases, increases, the ρ
.
for the gap satisfies satisfies the ), the situation of zero
as as the ground state of the
solid points points solid Fig. in 1). on on the assumed values by the
(
pressure . This result is of fundamental
)
dependent dependent quark mass model for CFL
- CFL
baryon depends
unpaired unpaired phase in in the parameter
e e ∆
s0 the ic ic number should
system s 5
strange quark matter
for for the Fe Fe nucleus (the binding energy per nucleon is
energy per energy
56
(C, m of baryon
of of the interacting and particles the on intensity of the
together together with the condition
*, *, which appears from from 0 to 120, in steps of 10 MeV. The continuous curves as occurs domain
to to have the
strange strange matter unit unit of s , B
a minimum that that ( in in a to to ]. ].
ranging the the properties Also Also we note that a
(as shown in Fig. in 1). (as shown
10
. - ] 9 1 of of the parameters in the density [
extra extra term
energy energy density
d ) ) values
correspond ]. The high stability of the CFL 8
, the energy per , 2 we 2 show we the parameters domain of CFLfor model the stability. The lowest limit of of the Eq. [ 7 the the model parameter
and Conclusions and
gap gap ( does not does not
s important to stress tability tability window
he he calculate becomes stable becomes more S
T It’
In In Fig. The The question of stability
- ρ Results Results consequence consequence of the
a consistence phase determines pressure pressure quark quark matter of C parameter is around 70 MeV, and is fixed by the condition of having quarks confined to with in equilibrium atdensity nuclear hadrons strange non 3. parameters that characterize interaction [ maximum at A ≈ 56) requires that Short title Short phase phase with in matter the hadronic stable than is CFL more the phase where the limits mark Fig. Fig. 2 PoS(XXXIV BWNP)110
when when Speaker Speaker Name
.
hadron hadron phase transition -
) quark work progress in work
35, 858 (2005). 858 35, 178 - Phys. D16, 291 (2007). 291 D16, Phys. cs A 706 cs (2002).
od. od. 6 Phys. Phys.
M J. J. 229, 112. 229,
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Nuclear Physi Nuclear
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2, 015204. 2, B. Sinha, Phys. Lett. B Lett. Phys. Sinha, B. D 30, 272 (1984). D 272 30, rago Hovarth, A& Hovarth, , D E. E. Rev. Rev. neutron starneutron Rev. C6 Rev.
discuss discuss use rty, rty, S. Raha ia, H. Rodrigues, S. S. Rodrigues, H. ia,
to hybrid
G. Benvenuto and G. Lugones, Phys. Rev. D51, 1989 (1995 1989 D51, Rev. Phys. Lugones, G. and Benvenuto G. J. and Lugones
P. Wang, Phys. Phys. P. Wang, A. Alberico, W. M. H. Rodrigues, S. B. Duarte, J. J. Duarte, B. S. Rodrigues, H. Rodrigues, H. M. Orsaria, Phys. E. Witten, M. Orsar Chakraba O. G. Rajagopal, K., & Wilczek, F. 2001a, Phys. Rev. Lett., 86, 3492. 86, Lett., Rev. Phys. 2001a, F. Wilczek, & K., Rajagopal,
[9] [5] [6] [7] [8] [2] [3] [4] [1] [10] establishing establishing References Short title Short importance