Thermomagnetic effects on light pseudoscalar meson masses within the SU(3) Nambu–Jona-Lasinio model

We calculate the screening masses of pseudoscalar mesons in a hot and strongly magnetized medium within the framework of the SU(3) Nambu-Jona–Lasinio model, using a magnetic field-independent regularization scheme. Inverse magnetic catalysis (IMC) is implemented through the use of a magnetic field-dependent coupling <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>G</a:mi><a:mo stretchy="false">(</a:mo><a:mi>B</a:mi><a:mo stretchy="false">)</a:mo></a:math>, fitted to reproduce lattice quantum chromodynamics (QCD) results for the pseudocritical chiral transition temperature <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msubsup><e:mi>T</e:mi><e:mi>c</e:mi><e:mi>B</e:mi></e:msubsup></e:math>. For the external homogeneous magnetic field considered, neutral screening masses separate in two types: perpendicular and parallel to the direction of the field, while for charged mesons only parallel energies can be defined for each Landau level. We obtain <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msub><g:mrow><g:mi>m</g:mi></g:mrow><g:mrow><g:mi>scr</g:mi><g:mo>,</g:mo><g:mrow><g:mo>⊥</g:mo></g:mrow></g:mrow></g:msub><g:mo>&gt;</g:mo><g:msub><g:mrow><g:mi>m</g:mi></g:mrow><g:mrow><g:mi>scr</g:mi><g:mo>,</g:mo><g:mrow><g:mo stretchy="false">|</g:mo><g:mo stretchy="false">|</g:mo></g:mrow></g:mrow></g:msub></g:mrow></g:math>, as expected from causality. Thermally, all screening energies are almost constant until some critical temperature, whose behavior is correlated with <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msubsup><k:mi>T</k:mi><k:mi>c</k:mi><k:mi>B</k:mi></k:msubsup></k:math>. They rapidly increase around this value, keeping a steady enhancement afterward due to thermal excitation. Magnetically, neutral parallel masses are enhanced (suppressed) at high temperatures when considering <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>G</m:mi><m:mo stretchy="false">(</m:mo><m:mi>B</m:mi><m:mo stretchy="false">)</m:mo></m:math> (<q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>G</q:mi></q:math>). Perpendicular ones display a nonmonotonic magnetic behavior for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>G</s:mi></s:math> (due to increasing <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msubsup><u:mi>T</u:mi><u:mi>c</u:mi><u:mi>B</u:mi></u:msubsup></u:math>) when <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>T</w:mi><w:mo>≲</w:mo><w:mn>500</w:mn><w:mtext> </w:mtext><w:mtext> </w:mtext><w:mi>MeV</w:mi></w:math>, but become magnetically enhanced when <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>T</y:mi><y:mo>≳</y:mo><y:mn>500</y:mn><y:mtext> </y:mtext><y:mtext> </y:mtext><y:mi>MeV</y:mi></y:math>. For <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>G</ab:mi><ab:mo stretchy="false">(</ab:mo><ab:mi>B</ab:mi><ab:mo stretchy="false">)</ab:mo></ab:math> they always increase with <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>B</eb:mi></eb:math>. Charged parallel energies are always magnetically enhanced, for both couplings. In the high-temperature limit, we show that both neutral and charged screening energies converge to <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mn>2</gb:mn><gb:mi>π</gb:mi><gb:mi>T</gb:mi></gb:math>. At <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>B</ib:mi><ib:mo>=</ib:mo><ib:mn>0</ib:mn></ib:math> the model overestimates the remaining quark interaction in this regime. At <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>B</kb:mi><kb:mo>≠</kb:mo><kb:mn>0</kb:mn></kb:math> we find that, when IMC is accounted for, the interaction is suppressed as <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>B</mb:mi></mb:math> increases, a fact that appears to be at odds with currently available lattice QCD results. Published by the American Physical Society 2024