Magnetized Strange -Quark- Matter at Finite Temperature
description
Transcript of Magnetized Strange -Quark- Matter at Finite Temperature
Magnetized Strange-Quark-Matter at Finite
Temperature
July 18, 2012
Latin American Workshop on High-Energy-Physics:
Particles and Strings
MSc. Ernesto López Fune
Institute of Cybernetics Mathematics and Physics (ICIMAF)
Motivation
• Extension to finite temperature environments of Phys. Rev. C 77, 015807 (2008).
• Study the thermodynamical parameters of SQM under strong magnetic fields.
Introduction• Neutron stars as the final stage of massive stars
result from Super Nova explosions.– First discovery by Jocelyn Bell in 1967.– Since then, around (or more) 1000 have been discovered.
• Main features: – Fast spinning compact objects– Periods of milliseconds– Strong magnetic fields– Small radius:10 km– High densities: – Low temperatures
Introduction• Several astrophysical observations discovered unusual neutron
stars.– Properties non explicable by canonic neutron star models.
• Main features: – Anomalous X-rays explosions– Faster spinning compact objects– Very strong magnetic fields– Smaller radius: 6 km– Higher densities: – Low temperatures
• Quark stars are proposed.
Itoh, Prog.Theor. Phys. 44,291(1970).
Introduction !!B-W-T’s Conjecture: at T = 0, P = 0 and finite density!!
SQM: stable phase of nuclear matter; made by deconfined quarks u, d and s with electrons.
FeSQM 56AE
AE
¿SQM contradict daily experience?
udus
sν eu
νeud
e
e
!!times comparable with the age of the Universe!!
Introduction !!B-W-T’s Conjecture: at T = 0, P = 0 and finite density!!
SQM: stable phase of nuclear matter; made by deconfined quarks u, d y s.
FeSQM 56AE
AE
udus
sν eu
νeud
e
e
!!times comparable with the age of the Universe!!
¿SQM contradict daily experience?
Introduction• Standard Model of Particle Physics.• Leptons + Quarks = spin-½
fermions: building blocks.• Leptons: • Quarks = u, d, s, c, t, b.• Barions = q + q + q.• Mesons = q + q
• QCD
)ν ,ν ,(ν τ), μ, ,(e τμe
Asymptotic Freedom
Color Confinement
SU(3)
Introduction
• Color Confinement ( 1 GeV) Non-linear Eqs.
• Lattice Models Lattice QCD• Phenomenological Models
– NJL---- Dynamic– MIT Bag Model---- Static
QCD Phase Transition
Hadron gas QGP
Tc = 170 MeV
MIT Bag Model
Sbagμνa
aμνμ
μMIT ψδψ
21
(V))BGG41
m)ψD(iγψ(L aμaμμ GigTD
μνa
aμνμμbag GG
41
ψψx
η21
B
0ψγψηjη μμ
μμ
0Gη μνaμ in S
μη
For low baryon numbers, it leads to a liquid drop model formalism
Multiple Reflection Expansion Method
Termodynamical potential
MIT Bag Model
sd,u,f
baggCf,Sf,Vf, VBΩC)ΩSΩV(ΩlnZβ1
Ω
bulk surface curvature
gluons
QCD Vacuum
Cpm
GdpSpm
GdV2π
pddpdN f
Cf,ff
Sf,f2
2ff
Corrections: Bulk Surface Curvature
R. Balian, C. Bloch, Annals Phys. 60, 401 (1970)Berger and Jaffe, Phys Rev C 35 213 (1987), 44 566 E (1991). Madsen Phys Rev D 50 3328 (1994)
pm
arctanpm
G ffSf,
pm
arctan2m3p
1pm
G f
f
fCf,
MIT Bag Model
Magnetized strangelets at finite temperature: J. Phys. G: Nucl. Part. Phys 39 (2012) 045006.
MIT Bag Model
Magnetized strangelets at finite temperature: J. Phys. G: Nucl. Part. Phys 39 (2012) 045006.
0,53AZ
2/3AZ
Magnetic field
Constant Magnetic field in z-direction.
Particle’s Spectrum
2f
2f
2z
ην,pf, mppE
1)ηB(2νqp ff
Landau levels Spin projections
High density compact objects endowed with strong magnetic fields
Termodynamic limit
sd,u,f
baggVf, VBΩVΩlnZβ1
Ω
bulk gluonsQCD Vacuum
fmaxν
0ν 1η2
f2
f2z
2
zff Vmpp2π
pddpdN
pd
e1
1-
e1
1dpdN
N 3μ)β(Eμ)-β(E
ff )(
pp
PVΩ TSNμΩEsd,u,f
ff
Magnetic field
BΩ
M
][B2qmμ
Iνf
2f
2ff
max
Anisotropic presures
Magnetic field
Spatial isotropy broken by the magnetic field
For B<6 1018 G 0.10)P(B
PP f|| f
BMPP ΩP || ||
Results:
Beta-equilibrium sdedu μμ μμμ
sd,u,f
fb N31
NFixed Baryonic density
esdu 3NNN2N
Local electric charge neutrality
Conditions on MSQM similarly to Astrophysics environments
MeV 0.5m MeV, 150m MeV, 5mm esdu
sdu NNN
P
10.0xnBN , ,P
P
5.5xnBN , ,P
P
2.0xnBN , ,P
P
1.0xnBN G, 5x10B ,P
0b||
0b||
0b||
0b17
||
•Electron’s density is decimated in the strong field regime.•This induces a transversal collapse of the local volume.•Temperature increase the s quarks formation.•Ferromagnetic-diamagnetic behavior expected is obtained.•Stable MSQM at low temperatures.•BWT conjecture proved.•The transversal pressure is dominated first by s quarks, then by gluons.•The transversal pressure minimum depends on the density.
Conclusions
!!MUCHAS GRACIAS!!!!THANKS SO MUCH!!
!!GRAZIE MILLE!!