<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>z</mml:mi><mml:mi>g</mml:mi></mml:msub></mml:math> distribution for heavy flavor jets in dense quark-gluon plasma

We study the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>z</a:mi><a:mi>g</a:mi></a:msub></a:math> distribution for heavy flavor, i.e., bottom and charm quark, jets propagating through the dense QCD medium. We extend the late emission approximation for the Armesto-Salgado-Wiedemann formula to heavy flavors. We consider both the normalized and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>N</c:mi><c:mtext>jet</c:mtext></c:msub></c:math> normalized <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>z</e:mi><e:mi>g</e:mi></e:msub></e:math> distributions, and the ratio of the latter distributions to the vacuum ones, called the R ratio. We demonstrate that since there is no collinear singularity in the medium, there is no principal need to use the Sudakov safety technique for medium-induced emission. We see that contrary to the vacuum case, the normalized <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>z</g:mi><g:mi>g</g:mi></g:msub></g:math> distribution is sensitive to the dead-cone angle value. In particular, for the case of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>N</i:mi><i:mtext>jet</i:mtext></i:msub></i:math> normalized distribution with <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>θ</k:mi><k:mi>g</k:mi></k:msub><k:mo>≤</k:mo><k:msub><k:mi>θ</k:mi><k:mi>cut</k:mi></k:msub></k:math>, it is possible to directly probe the dead-cone gluons in the medium. Our results can be useful to guide the experimental measurements of the heavy flavor jet substructure in a dense QCD medium.