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!!