Second order fluctuations of conserved charges in external magnetic fields

We present a first-principles lattice QCD investigation of second-order fluctuations of and correlations among conserved charges—baryon number (B), electric charge (Q), and strangeness (S)—in the presence of external magnetic fields. Our study employs lattice simulations of (<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 QCD with physical pion masses using highly improved staggered fermions on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mn>48</c:mn><c:mn>3</c:mn></c:msup><c:mo>×</c:mo><c:mn>12</c:mn></c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mn>32</e:mn><e:mn>3</e:mn></e:msup><e:mo>×</e:mo><e:mn>8</e:mn></e:math> lattices, covering a wide range of magnetic field strengths up to <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:mrow><g:mi>GeV</g:mi></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow></g:msup></g:math>. We identify clear signals of magnetic field-induced modifications to these fluctuations and correlations, with the baryon-electric charge correlation, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msubsup><i:mi>χ</i:mi><i:mn>11</i:mn><i:mrow><i:mi>BQ</i:mi></i:mrow></i:msubsup></i:math>, exhibiting particularly strong sensitivity to the magnetic field. To bridge theoretical predictions with experimental observables, we implement systematic kinematic cuts that emulate detector acceptances of the STAR and ALICE experiments within the hadron resonance gas (HRG) model and construct proxy observables for fluctuations measurable in heavy-ion collision experiments. Our findings highlight <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msubsup><k:mi>χ</k:mi><k:mn>11</k:mn><k:mrow><k:mi>BQ</k:mi></k:mrow></k:msubsup></k:math> as a promising “magnetometer” for probing the presence of magnetic fields in QCD matter. Furthermore, we explore experimentally relevant ratios involving <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msubsup><m:mi>χ</m:mi><m:mn>11</m:mn><m:mrow><m:mi>BQ</m:mi></m:mrow></m:msubsup></m:math>, demonstrating their potential in mitigating volume effects and enhancing sensitivity to magnetic fields in collision environments. Additionally, we assess the limitations of the HRG model at strong magnetic fields, revealing deviations that indicate nontrivial modifications to hadronic degrees of freedom. These results offer new insights into the interplay between thermal and magnetic effects in the QCD phase diagram and provide experimentally relevant guidance for the detection of magnetic fields in heavy-ion collisions.