Baryon Electric Charge Correlation as a Magnetometer of QCD

The correlation between net baryon number and electric charge, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msubsup><a:mrow><a:mi>χ</a:mi></a:mrow><a:mrow><a:mn>11</a:mn></a:mrow><a:mrow><a:mi>BQ</a:mi></a:mrow></a:msubsup></a:mrow></a:math>, can serve as a magnetometer of QCD. This is demonstrated by lattice QCD computations using the highly improved staggered quarks with physical pion mass of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>M</c:mi></c:mrow><c:mrow><c:mi>π</c:mi></c:mrow></c:msub><c:mo>=</c:mo><c:mn>135</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>MeV</c:mi></c:mrow></c:math> on <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>N</e:mi><e:mi>τ</e:mi></e:msub><e:mo>=</e:mo><e:mn>8</e:mn></e:math> and 12 lattices. We find that <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msubsup><g:mi>χ</g:mi><g:mn>11</g:mn><g:mrow><g:mi>BQ</g:mi></g:mrow></g:msubsup></g:math> along the transition line starts to increase rapidly with magnetic field strength <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>e</i:mi><i:mi>B</i:mi><i:mo>≳</i:mo><i:mn>2</i:mn><i:msubsup><i:mrow><i:mi>M</i:mi></i:mrow><i:mrow><i:mi>π</i:mi></i:mrow><i:mrow><i:mn>2</i:mn></i:mrow></i:msubsup></i:mrow></i:math> and by a factor 2 at <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>e</k:mi><k:mi>B</k:mi><k:mo>≃</k:mo><k:mn>8</k:mn><k:msubsup><k:mi>M</k:mi><k:mi>π</k:mi><k:mn>2</k:mn></k:msubsup></k:math>. Furthermore, the ratio of electric charge chemical potential to baryon chemical potential, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>μ</m:mi><m:mi mathvariant="normal">Q</m:mi></m:msub><m:mo>/</m:mo><m:msub><m:mi>μ</m:mi><m:mi mathvariant="normal">B</m:mi></m:msub></m:math>, shows significant dependence on the magnetic field strength and varies from the ratio of electric charge to baryon number in the colliding nuclei in heavy ion collisions. These results can provide baselines for effective theory and model studies, and both <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msubsup><q:mi>χ</q:mi><q:mn>11</q:mn><q:mrow><q:mi>BQ</q:mi></q:mrow></q:msubsup></q:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>μ</s:mi><s:mi mathvariant="normal">Q</s:mi></s:msub><s:mo>/</s:mo><s:msub><s:mi>μ</s:mi><s:mi mathvariant="normal">B</s:mi></s:msub></s:math> could be useful probes for the detection of magnetic fields in relativistic heavy ion collision experiments as compared with corresponding results from the hadron resonance gas model.