Susceptibilities and Taylor coefficients of magnetic QCD from perturbation theory

We compute the coefficients <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>c</a:mi> <a:mn>2</a:mn> </a:msub> <a:mo stretchy="false">(</a:mo> <a:mi>T</a:mi> <a:mo>,</a:mo> <a:mi>B</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>c</e:mi> <e:mn>4</e:mn> </e:msub> <e:mo stretchy="false">(</e:mo> <e:mi>T</e:mi> <e:mo>,</e:mo> <e:mi>B</e:mi> <e:mo stretchy="false">)</e:mo> </e:math> of the Taylor expansion for the pressure in powers of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>μ</i:mi> <i:mi>B</i:mi> </i:msub> <i:mo>/</i:mo> <i:mi>T</i:mi> </i:math> in the presence of a large magnetic field within perturbative quantum chromodynamics (QCD) at finite temperature and baryon density up to two-loops for <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>N</k:mi> <k:mi>f</k:mi> </k:msub> <k:mo>=</k:mo> <k:mn>3</k:mn> </k:math> flavors with physical quark masses. We also present results for the excess of pressure, baryon density, and baryon number susceptibility as functions of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>μ</m:mi> <m:mi>B</m:mi> </m:msub> </m:math> , as well as susceptibilities as functions of the temperature in the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mo stretchy="false">{</o:mo> <o:msub> <o:mi>μ</o:mi> <o:mi>B</o:mi> </o:msub> <o:mo>,</o:mo> <o:msub> <o:mi>μ</o:mi> <o:mi>Q</o:mi> </o:msub> <o:mo>,</o:mo> <o:msub> <o:mi>μ</o:mi> <o:mi>S</o:mi> </o:msub> <o:mo stretchy="false">}</o:mo> </o:math> basis. Our results can be directly compared to recent lattice QCD data. Even though current lattice results do not overlap with its region of validity, perturbative results seem to be compatible with those obtained on the lattice for large temperatures.