Leading-order QCD equation of state in strong magnetic fields at nonzero baryon chemical potential

We present continuum-estimated ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>2</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> )-flavor lattice QCD results for the leading-order Taylor expansion coefficients of the equation of state in strong magnetic fields and at nonzero baryon chemical potential. Simulations employ the highly improved staggered quark action with physical pion masses on lattices of temporal extent <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>N</c:mi> <c:mi>τ</c:mi> </c:msub> <c:mo>=</c:mo> <c:mn>8</c:mn> </c:math> , 12, covering <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mn>145</e:mn> <e:mtext> </e:mtext> <e:mtext> </e:mtext> <e:mi>MeV</e:mi> <e:mo>≲</e:mo> <e:mi>T</e:mi> <e:mo>≲</e:mo> <e:mn>165</e:mn> <e:mtext> </e:mtext> <e:mtext> </e:mtext> <e:mi>MeV</e:mi> </e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>e</g:mi> <g:mi>B</g:mi> <g:mo>≲</g:mo> <g:mn>0.8</g:mn> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:msup> <g:mi>GeV</g:mi> <g:mn>2</g:mn> </g:msup> </g:math> , imposing strangeness neutrality with baseline results at electric charge to baryon number ratio <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>r</i:mi> <i:mo>=</i:mo> <i:mn>0.4</i:mn> </i:math> . We determine the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>T</k:mi> <k:mi>–</k:mi> <k:mi>e</k:mi> <k:mi>B</k:mi> </k:math> dependence of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>q</m:mi> <m:mn>1</m:mn> </m:msub> </m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>s</o:mi> <o:mn>1</o:mn> </o:msub> </o:math> (electric charge and strangeness chemical potential ratios), pressure coefficient <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>P</q:mi> <q:mn>2</q:mn> </q:msub> </q:math> , baryon number density coefficient <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msubsup> <s:mi>N</s:mi> <s:mn>1</s:mn> <s:mi mathvariant="normal">B</s:mi> </s:msubsup> </s:math> , and energy-related coefficients <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:msub> <v:mi mathvariant="normal">Θ</v:mi> <v:mn>2</v:mn> </v:msub> </v:math> (trace anomaly), <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msub> <y:mi>ε</y:mi> <y:mn>2</y:mn> </y:msub> </y:math> (energy density), and <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>σ</ab:mi> <ab:mn>2</ab:mn> </ab:msub> </ab:math> (entropy density). Magnetic fields induce temperature-band crossings for <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi>q</cb:mi> <cb:mn>1</cb:mn> </cb:msub> </cb:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi>P</eb:mi> <eb:mn>2</eb:mn> </eb:msub> </eb:math> and nonmonotonic structures in the energy-related coefficients, with <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msub> <gb:mi mathvariant="normal">Θ</gb:mi> <gb:mn>2</gb:mn> </gb:msub> </gb:math> at strong fields possibly vanishing or turning negative at higher <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mi>T</jb:mi> </jb:math> , indicating dominance of the pressure term over the energy contribution. We also examine the <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:mi>r</lb:mi> </lb:math> -dependence, finding that <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:mi>r</nb:mi> <nb:mo>=</nb:mo> <nb:mn>0</nb:mn> </nb:math> (charge-neutral matter) shows the most muted magnetic-field enhancement of <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"> <pb:msub> <pb:mi>P</pb:mi> <pb:mn>2</pb:mn> </pb:msub> </pb:math> despite larger <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"> <rb:mo stretchy="false">|</rb:mo> <rb:msub> <rb:mi>q</rb:mi> <rb:mn>1</rb:mn> </rb:msub> <rb:mo stretchy="false">|</rb:mo> </rb:math> , providing a useful reference for neutron-star–relevant conditions. Comparisons with the hadron resonance gas model show qualitative agreement at low <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:mi>T</vb:mi> </vb:math> and weak <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"> <xb:mi>e</xb:mi> <xb:mi>B</xb:mi> </xb:math> , with clear deviations near the crossover and at strong fields. These results provide useful input for constraining models and effective theories of QCD matter in strong magnetic fields at finite baryon density.