Heavy hadron production in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Au</mml:mi> <mml:mo>+</mml:mo> <mml:mi>Au</mml:mi> </mml:math> collisions at a center-of-mass energy of <mml:math xmlns:mml="http://www.w3.org/1998/Math/Math

Using the Monte Carlo <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>HYDJET</a:mi> <a:mo>+</a:mo> <a:mo>+</a:mo> </a:mrow> </a:math> model, we investigate the transverse momentum ( <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>p</b:mi> <b:mi>T</b:mi> </b:msub> </b:math> ) spectra of heavy-flavor hadrons, namely <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msup> <c:mi>D</c:mi> <c:mn>0</c:mn> </c:msup> <c:mo>,</c:mo> <c:mo> </c:mo> <c:msup> <c:mover> <c:mi>D</c:mi> <c:mo>¯</c:mo> </c:mover> <c:mn>0</c:mn> </c:msup> <c:mo>,</c:mo> <c:mo> </c:mo> <c:msup> <c:mi>D</c:mi> <c:mo>+</c:mo> </c:msup> <c:mo>,</c:mo> <c:mo> </c:mo> <c:msup> <c:mi>D</c:mi> <c:mo>−</c:mo> </c:msup> </c:math> , and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi mathvariant="normal">Λ</d:mi> <d:mi>c</d:mi> </d:msub> </d:math> , along with the nuclear modification factors of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msup> <f:mi>D</f:mi> <f:mn>0</f:mn> </f:msup> </f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msup> <g:mi>D</g:mi> <g:mo>±</g:mo> </g:msup> </g:math> in Au <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mo>+</h:mo> </h:math> Au collisions at <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:msqrt> <i:msub> <i:mi>s</i:mi> <i:mrow> <i:mi>N</i:mi> <i:mi>N</i:mi> </i:mrow> </i:msub> </i:msqrt> <i:mo>=</i:mo> <i:mn>200</i:mn> </i:mrow> </i:math> GeV RHIC energy across various centrality bins. This work extends the earlier study by relaxing the assumption of identical chemical and thermal freezeout and by exploring the effect of a higher chemical freezeout temperature relative to thermal freezeout. The study also explores the centrality and mass dependence of the charm enhancement factor ( <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:msub> <j:mi>γ</j:mi> <j:mi>c</j:mi> </j:msub> </j:math> ). Furthermore, we investigate medium-induced energy loss, particle-antiparticle asymmetry, and the role of fragmentation in the hadronization process. The <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mrow> <k:mi>HYDJET</k:mi> <k:mo>+</k:mo> <k:mo>+</k:mo> </k:mrow> </k:math> model, with its default parameters, is unable to reproduce heavy hadron yields due to their early thermal freezeout and initial state production of heavy quarks. Therefore, a systematic tuning of model parameters is performed to improve the overall agreement with experimental data. Additionally, to assess the performance of the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:mi>HYDJET</l:mi> <l:mo>+</l:mo> <l:mo>+</l:mo> </l:mrow> </l:math> model relative to other theoretical approaches, its results are compared with the TAMU, SUBATECH, Torino, and Duke models, for which corresponding simulation data are available. This study shows a decreasing trend in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>γ</m:mi> <m:mi>c</m:mi> </m:msub> </m:math> from central to peripheral collisions. Moreover, <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:msub> <n:mi>γ</n:mi> <n:mi>c</n:mi> </n:msub> </n:math> increases with increasing charm-hadron mass. The model approximately reproduces the experimental data of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:msub> <o:mi>p</o:mi> <o:mi>T</o:mi> </o:msub> </o:math> spectra at low and intermediate <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:msub> <p:mi>p</p:mi> <p:mi>T</p:mi> </p:msub> </p:math> . However, it overestimates the data at high <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:msub> <q:mi>p</q:mi> <q:mi>T</q:mi> </q:msub> </q:math> , indicating a need for improvements in modeling the energy loss of heavy quarks. The nuclear modification factors ( <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:msub> <r:mi>R</r:mi> <r:mrow> <r:mi>A</r:mi> <r:mi>A</r:mi> </r:mrow> </r:msub> </r:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:msub> <s:mi>R</s:mi> <s:mrow> <s:mi>C</s:mi> <s:mi>P</s:mi> </s:mrow> </s:msub> </s:math> ) for <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:msup> <t:mi>D</t:mi> <t:mn>0</t:mn> </t:msup> </t:math> mesons exhibit significant suppression at high <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:msub> <u:mi>p</u:mi> <u:mi>T</u:mi> </u:msub> </u:math> . At low <v:math xmlns:v="http://www.w3.org/1998/Math/MathML"> <v:msub> <v:mi>p</v:mi> <v:mi>T</v:mi> </v:msub> <v:mo>,</v:mo> <v:mo> </v:mo> <v:msub> <v:mi>R</v:mi> <v:mrow> <v:mi>A</v:mi> <v:mi>A</v:mi> </v:mrow> </v:msub> </v:math> results show deviations from the data, reflecting limitations in the model where coalescence becomes important. The antiparticle-to-particle ratios are consistent with experimental data, whereas mixed-particle ratios are underestimated, revealing the model's limitation in estimating the baryon-to-meson enhancement.