Article

Chiral Phase Transition in Linear Sigma Model with Nonextensive Statistical Mechanics

K. ShenKey Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, ChinaHui ZhangKey Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, ChinaDefu HouKey Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, ChinaBen-Wei ZhangKey Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, ChinaEnke WangKey Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China

2017lv

ABI

Abstract

From the nonextensive statistical mechanics, we investigate the chiral phase transition at finite temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:math> and baryon chemical potential <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> in the framework of the linear sigma model. The corresponding nonextensive distribution, based on Tsallis’ statistics, is characterized by a dimensionless nonextensive parameter, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>, and the results in the usual Boltzmann-Gibbs case are recovered when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi>q</mml:mi><mml:mo>→</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:math>. The thermodynamics of the linear sigma model and its corresponding phase diagram are analysed. At high temperature region, the critical temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> is shown to decrease with increasing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math> from the phase diagram in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> plane. However, larger values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math> cause the rise of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> at low temperature but high chemical potential. Moreover, it is found that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M10"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math> different from zero corresponds to a first-order phase transition while <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M11"><mml:mi>μ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:math> to a crossover one. The critical endpoint (CEP) carries higher chemical potential but lower temperature with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M12"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math> increasing due to the nonextensive effects.

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Identifiers

DOI: 10.1155/2017/4135329

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Cited by 20 references

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