magnetized strange- quark-matter at finite temperature july 18, 2012 latin american workshop on...
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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)
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Motivation
• Extension to finite temperature environments of Phys. Rev. C 77, 015807 (2008).
• Study the thermodynamical parameters of SQM under strong magnetic fields.
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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
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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).
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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!!
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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?
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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)
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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
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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
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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,
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MIT Bag Model
Magnetized strangelets at finite temperature: J. Phys. G: Nucl. Part. Phys 39 (2012) 045006.
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MIT Bag Model
Magnetized strangelets at finite temperature: J. Phys. G: Nucl. Part. Phys 39 (2012) 045006.
0,53AZ
2/3AZ
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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
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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
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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 || ||
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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
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sdu NNN
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P
10.0xnBN , ,P
P
5.5xnBN , ,P
P
2.0xnBN , ,P
P
1.0xnBN G, 5x10B ,P
0b||
0b||
0b||
0b17
||
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•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
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!!MUCHAS GRACIAS!!!!THANKS SO MUCH!!
!!GRAZIE MILLE!!