Pion scattering, light resonances, and chiral symmetry restoration at nonzero chiral imbalance and temperature

We calculate the pion scattering amplitude at nonzero temperature and nonzero <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>μ</a:mi><a:mn>5</a:mn></a:msub></a:math>, the chemical potential associated to chiral imbalance in a locally <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>P</c:mi></c:math>-breaking scenario. The amplitude is calculated up to next-to-leading order in Chiral Perturbation Theory and is unitarized with the Inverse Amplitude Method to generate the poles of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>f</e:mi><e:mn>0</e:mn></e:msub><e:mo stretchy="false">(</e:mo><e:mn>500</e:mn><e:mo stretchy="false">)</e:mo></e:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>ρ</i:mi><i:mo stretchy="false">(</i:mo><i:mn>770</i:mn><i:mo stretchy="false">)</i:mo></i:math> resonances. Within the saturation approach, the thermal <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>f</m:mi><m:mn>0</m:mn></m:msub><m:mo stretchy="false">(</m:mo><m:mn>500</m:mn><m:mo stretchy="false">)</m:mo></m:math> pole allows to determine <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>T</q:mi><q:mi>c</q:mi></q:msub><q:mo stretchy="false">(</q:mo><q:msub><q:mi>μ</q:mi><q:mn>5</q:mn></q:msub><q:mo stretchy="false">)</q:mo></q:math>, the transition temperature for chiral symmetry restoration. Our results confirm the growing behavior of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>T</u:mi><u:mi>c</u:mi></u:msub><u:mo stretchy="false">(</u:mo><u:msub><u:mi>μ</u:mi><u:mn>5</u:mn></u:msub><u:mo stretchy="false">)</u:mo></u:math> found in previous works and, through a fit to lattice results, we improve the uncertainty range of the low-energy constants associated to <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>μ</y:mi><y:mn>5</y:mn></y:msub></y:math> corrections in the chiral Lagrangian. The results for the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>ρ</ab:mi><ab:mo stretchy="false">(</ab:mo><ab:mn>770</ab:mn><ab:mo stretchy="false">)</ab:mo></ab:math> pole are compatible with previous works regarding the dilepton yield in heavy-ion collisions.