Phase Transition in Linear Sigma model

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Phase Transition in Linear Sigma model

• -Application of Optimized Perturbation Theory

Nordic Winter School, Gausdal, 09/01-01
Kristian Berland, NTNU, Trondheim
Collaborator Jens O. Andersen
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Overview

• Introduction
• QCD phase diagram
• O(4) linear sigma model.
• Optimized perturbation theory
• Breakdown of naive perturbation theory
• Resummation strategy Optimized perturbation
  theory
• Investigation of Phase transition (of Z2 )

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QCD Phase diagram
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Crude estimate of TC

• Approximations
• All particles are massless
• MIT Bag Model
• Hot Hadron Gas

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Linear Sigma model

• Effective theories
• Two flavor massless QCD SUv(2)xSUA(2)xUv (1) x
  UA(1)
• Group Theory SUv(2)xSUA(2) O(4)
• O(4) Linear Sigma model

• Spontaneous symmetry breaking
• O(4) ? O(3) 3 broken generators
• Nature 3 pions
• Expect phase transition

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Effective potential

• For simplicity

• Infrared divergence

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Optimized pertubation theory

• Dynamics generate mass
• Interaction is not a
  perturbation!

• Solution Add zero

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Optimized perturbation theory

• Effect of new terms
• Changed mass in propagator
• New interaction

• How determine ?

Principle of minimal sensitivity
Choice

• 1- loop calculation
• PMS fails.
• FAC 1. order phase transition

Hatsuda, Chiku, Phys Rev D, 58, 076001 (1998)
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2-loop calculations

• Diagrams

• 2. order phase transition
• Critical exponent ½

• Cures infrared divergence
• HTL at high T

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Summary

• Breakdown of perturbation theory
• Resummation Optimized perturbation theory
• 2. order phase transition (2-loop order)
• Critical exponent ½ (mean field type)
• Outlook
• OPT applied to (comparison)
• O(4) Linear Sigma model
• U(2) x U(2) model

Kristian Berland krisberl_at_stud.ntnu.no
Collaborator Jens O. Andersen