Dynamics of heavy flavor in a weakly magnetized hot QCD medium

We obtain the spatial and momentum-diffusion coefficients (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>D</a:mi></a:mrow><a:mrow><a:mi>s</a:mi></a:mrow></a:msub></a:mrow></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>κ</c:mi></c:math>) and the collisional energy loss (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>d</e:mi><e:mi>E</e:mi><e:mo>/</e:mo><e:mi>d</e:mi><e:mi>x</e:mi></e:math>) of a heavy quark (HQ) traversing through a thermal medium of quarks and gluons in a weak magnetic field (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>B</g:mi></g:math>), for the two cases of the HQ moving either parallel or perpendicular to <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi mathvariant="bold-italic">B</i:mi></i:math>. For that purpose, we consider Coulomb scatterings (<l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>t</l:mi></l:math>-channel) of the HQ with the light quarks, obtained from the imaginary part of the HQ self-energy via the cutting rules. Both the normalized (by <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msup><n:mi>T</n:mi><n:mn>3</n:mn></n:msup></n:math>) <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>κ</p:mi></p:math>, and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>d</r:mi><r:mi>E</r:mi><r:mo>/</r:mo><r:mi>d</r:mi><r:mi>x</r:mi></r:math>, for charm quarks are larger than that for bottom quarks due to the larger mass of the latter. Also, the effect of <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>B</t:mi></t:math> is more feeble on the bottom quark, compared to the charm quark. Comparatively, the magnitudes of both <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>κ</v:mi></v:math> and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi>d</x:mi><x:mi>E</x:mi><x:mo>/</x:mo><x:mi>d</x:mi><x:mi>x</x:mi></x:math> are significantly smaller for the case of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi mathvariant="bold-italic">v</z:mi><z:mo>⊥</z:mo><z:mi mathvariant="bold-italic">B</z:mi></z:math>. For both the cases, our results show that the momentum transfer between the HQ and the medium takes place preferentially along the direction of HQ velocity, thus leading to a significant increase in the momentum-diffusion anisotropy, compared to <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>B</db:mi><db:mo>=</db:mo><db:mn>0</db:mn></db:math>. We also calculate the (scaled) spatial diffusion coefficient, which we find to be independent of the heavy flavor mass and is almost unaffected by changes in <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi>B</fb:mi></fb:math>. Published by the American Physical Society 2024