effective quark models in the presence of a magnetic...
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Effective Quark Models in the Presence of a Magnetic Field
Pablo Guillermo Allen PhD Student University of Buenos Aires, Argentina Director: Dr. N.N. Scoccola Comisión Nacional de Energía Atómica
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MOTIVATION Background
Effect of magnetic fields on hadronic matter
- Generated in Heavy ion collisions
High Temperature, Low density regime
B ∼ 1. 1019
- Neutron stars (Magnetars)
Low Temperature, High density regime
B ∼ 1. 1015 - 1. 1018
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Nambu Jona Lasinio (NJL) Lagrangian
INTRODUCTION The Model - Basics
CHIRAL SYMMETRY
Effective Interaction among quark fields
Parameters: G: Coupling constant, Л Momentum Cut-off m0: Bare mass
Quark fields 2 flavours
Spontaneous symmetry breaking driven by G
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MEAN FIELD APPROXIMATION
INTRODUCTION: The Model - Treatment
CHIRAL CONDENSATE ORDER PARAMETER
Gap Equation
Self-Consistent for M
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INTRODUCTION: The Model - Extension
Chemical Potential
Introduced as Lagrange Multiplier
Dispersion Relation
Temperature
Magnetic Field
Matsubara frequency
* Flavour * Colour * 4-Momentum
Includes sum over:
Sum over Landau Levels (Constant and homogeneous)
Time component integration
Gap Equation solved for M, for different
values of T,mu and B
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Phase Diagram
INTRODUCTION: Model Behaviour
B=1.1019
Broken Symmetry
Symmetry Restored
Cross over and first order transitions
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RESULTS:
Enhancement of Symmetry Breaking for higher B
Behaviour for T=0 & mu=0
Mass dependance on Magnetic Field
More complicated behaviour for finite temperature and chemical potential
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B=0 & B=1.1018 – 1.1019 B=1.1019 – 1.1020
Phase Diagram – Distinct Ranges RESULTS:
Criticial Temp vs Magnetic field at µ=0
Criticial µ vs Magnetic field at T=0
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CRITICAL END POINT – Dependance on Magnetic Field RESULTS:
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Introduction of Polyakov Loop
Non Local Interaction
WHAT’S NEXT?
Background Colour Field
Effective coupling term with quarks
Study deconfinement transition
Interaction through Non Local Currents
Sharp cut-off Removed
Introduction of regulators
More realistic interaction
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Thanks!
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Masa vs Parámetro adimensional G*L^2
Transición de Fase – Cross over
Parámetros de ajuste
RESULTADOS:
NJL ELEMENTAL
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RESULTADOS:
TEMPERATURA Y POTENCIAL QUIMICO FINITO Mass vs Temperatura - Mu Parámetro
Diagrama de fases-
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M vs T para diferentes valores de B
mu=0 MeV
Cambio en el diagrama de fases a diferentes valores de B
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Algo vs algo a algo fijo con algo como parámetro
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m0=0 Transicion 2do orden
m0= finite Cross-over
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INTRODUCCION DE CAMPO MAGNETICO:
Acoplamiento a B externo, uniforme y constante
Derivada Covariante
Resolución de Ecuación de Dirac: Relación de Dispersión modificada
Ecuacion del gap….
Integral x-y en el propagador Suma de niveles de Landau
INTRODUCCION:
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Poner T,mu,B, resolver la ecuación del gap. En general se hace fijando dos parámetros, B,mu ponele… y corriendo sobre T. Graficar potenciales… poner algunas curvas tipo que representan la transicion de fase que nos interesa y que con los potenciales se pueden clasificar las transiciones posibles y el punto que separa las dos transiciones