Neutral pion masses within a hot and magnetized medium in a lattice-improved soft-wall AdS/QCD model

We investigate chiral phase transitions and the screening masses, pole masses, and thermal widths of neutral pion mesons with finite temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>T</a:mi></a:math> and magnetic field <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>B</c:mi></c:math> in a lattice-improved <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>AdS</e:mi><e:mo>/</e:mo><e:mi>QCD</e:mi></e:mrow></e:math> model, which is constructed by fitting the lattice results of the pseudocritical temperatures <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>T</g:mi><g:mi>pc</g:mi></g:msub><g:mo stretchy="false">(</g:mo><g:mi>B</g:mi><g:mo stretchy="false">)</g:mo></g:math>. Specifically, we find that the chiral condensate <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>σ</k:mi></k:math> undergoes a crossover phase transition demonstrating distinct magnetic catalysis and inverse magnetic catalysis effects in very low- and high-temperature regions with fixed finite <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>B</m:mi></m:math>, respectively. For the screening masses, we find that the longitudinal component decreases with <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>B</o:mi></o:math> at very low and high temperatures and increases with <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>B</q:mi></q:math> near <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>T</s:mi><s:mi>pc</s:mi></s:msub></s:math>. The transverse component always increases with <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>B</u:mi></u:math> at fixed <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>T</w:mi></w:math>. However, both the longitudinal and transverse screening masses increase with <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>T</y:mi></y:math> at fixed <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>B</ab:mi></ab:math>. Furthermore, we find that the pole mass decreases with the increase of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>B</cb:mi></cb:math> or <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>T</eb:mi></eb:math>. It is interesting to note that the thermal width shows similar behavior to the longitudinal screening masses in the very-high-temperature region. Published by the American Physical Society 2024