Cold and dense perturbative QCD in a very strong magnetic background

Abstract

We compute the pressure from first principles within perturbative QCD at finite baryon density and very high magnetic fields up to two-loops and with physical quark masses. The region of validity for our framework is given by <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>m</a:mi><a:mi>s</a:mi></a:msub><a:mo>≪</a:mo><a:msub><a:mi>μ</a:mi><a:mi>q</a:mi></a:msub><a:mo>≪</a:mo><a:msqrt><a:mrow><a:mi>e</a:mi><a:mi>B</a:mi></a:mrow></a:msqrt></a:math>, where <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>m</c:mi><c:mi>s</c:mi></c:msub></c:math> is the strange quark mass, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>μ</e:mi><e:mi>q</e:mi></e:msub></e:math> is the quark chemical potential, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>e</g:mi></g:math> is the fundamental electric charge, and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>B</i:mi></i:math> is the magnetic field strength. We include the effects of the renormalization scale in the running coupling, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>α</k:mi><k:mi>s</k:mi></k:msub><k:mo stretchy="false">(</k:mo><k:msub><k:mi>μ</k:mi><k:mi>q</k:mi></k:msub><k:mo>,</k:mo><k:msqrt><k:mrow><k:mi>e</k:mi><k:mi>B</k:mi></k:mrow></k:msqrt><k:mo stretchy="false">)</k:mo></k:math>, and running strange quark mass. We also discuss the simplifications that come about in the chiral limit. The effectively negligible contribution of the exchange diagram allows for building a simple analytic model for the equation of state for pure quark magnetars and computing their mass and radius at very large values of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>B</o:mi></o:math>. These results provide constraints on the behavior of the maximum mass and associated radius from perturbative QCD. We also discuss the magnetic bag model for extreme magnetic fields. Published by the American Physical Society 2024

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