Nuclear modification of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>B</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> mesons in relativistic heavy-ion collisions based on a linear Boltzmann transport model

The nuclear modification factor (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>R</a:mi><a:mi>AA</a:mi></a:msub></a:math>) of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>B</b:mi><b:mi>c</b:mi></b:msub></b:math> mesons in high-energy nuclear collisions provides a novel probe of heavy quark interactions with the quark-gluon plasma (QGP). Based on a linear Boltzmann transport model that incorporates both Yukawa and string types of interactions between heavy quarks and the QGP, we study the production and evolution of heavy quarks and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>B</c:mi><c:mi>c</c:mi></c:msub></c:math> mesons within the same framework. A <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>B</d:mi><d:mi>c</d:mi></d:msub></d:math> bound state dissociates while one of its constituent heavy quarks scatters with the QGP with momentum transfer greater than its binding energy. The medium-modified charm and bottom quarks can recombine into <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>B</e:mi><e:mi>c</e:mi></e:msub></e:math> mesons, and the medium-modified bottom quarks can also fragment to <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>B</f:mi><f:mi>c</f:mi></f:msub></f:math> mesons. We find that most primordial <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi>B</g:mi><g:mi>c</g:mi></g:msub></g:math> mesons generated from the initial hard collisions dissociate inside the QGP. The production of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi>B</h:mi><h:mi>c</h:mi></h:msub></h:math> mesons is primarily driven by the recombination mechanism at low transverse momentum and fragmentation at high transverse momentum. The string interaction dominates over the Yukawa interaction in the nuclear modification of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi>B</i:mi><i:mi>c</i:mi></i:msub></i:math> mesons. The participant number dependence of the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:msub><j:mi>B</j:mi><j:mi>c</j:mi></j:msub></j:math> meson <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi>R</k:mi><k:mi>AA</k:mi></k:msub></k:math> is determined by the complicated interplay between the heavy quark yield, energy loss, and the QGP volume. We obtain a reasonable description of the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:msub><l:mi>R</l:mi><l:mi>AA</l:mi></l:msub></l:math> of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mi>B</m:mi><m:mi>c</m:mi></m:msub></m:math> mesons in <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:mrow><n:mi>Pb</n:mi><n:mo>+</n:mo><n:mi>Pb</n:mi></n:mrow></n:math> collisions at <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mrow><o:msqrt><o:msub><o:mi>s</o:mi><o:mi>NN</o:mi></o:msub></o:msqrt><o:mo>=</o:mo><o:mn>5.02</o:mn></o:mrow></o:math> TeV, and provide predictions for <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mrow><p:mi>Au</p:mi><p:mo>+</p:mo><p:mi>Au</p:mi></p:mrow></p:math> collisions at <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:mrow><q:msqrt><q:msub><q:mi>s</q:mi><q:mi>NN</q:mi></q:msub></q:msqrt><q:mo>=</q:mo><q:mn>200</q:mn></q:mrow></q:math> GeV.