Studies of beauty hadron and nonprompt charm hadron production in pp collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msqrt> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msqrt> <mml:mo>=</mml

In high-energy proton-proton ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>p</a:mi> <a:mi>p</a:mi> </a:math> ) collisions at the LHC, nonprompt charm hadrons, originating from beauty hadron decays, provide a valuable probe for beauty quark dynamics, particularly at low transverse momentum where direct beauty measurements are challenging. We employ a multiphase transport (AMPT) model of string melting version coupled with 8 initial conditions to study the beauty hadron and nonprompt charm hadron productions in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>p</c:mi> <c:mi>p</c:mi> </c:math> collisions at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msqrt> <e:mi>s</e:mi> </e:msqrt> <e:mo>=</e:mo> <e:mn>13</e:mn> <e:mtext> </e:mtext> <e:mtext> </e:mtext> <e:mi>TeV</e:mi> </e:math> . In this work, the beauty quark mass during the generation stage has been increased to reproduce the measured <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>b</g:mi> <g:mover accent="true"> <g:mi>b</g:mi> <g:mo stretchy="false">¯</g:mo> </g:mover> </g:math> cross section, and a beauty flavor-specific coalescence parameter <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:msubsup> <k:mrow> <k:mi>r</k:mi> </k:mrow> <k:mrow> <k:mi>B</k:mi> <k:mi>M</k:mi> </k:mrow> <k:mrow> <k:mi>b</k:mi> </k:mrow> </k:msubsup> </k:mrow> </k:math> is introduced to match LHCb measurements of beauty baryon-to-meson ratios. With these refinements, the AMPT model achieves a reasonable agreement with experimental data on beauty hadron yields and nonprompt charm hadron production from ALICE and LHCb. We present the transverse momentum and multiplicity dependence of nonprompt-to-prompt charm hadron ratios, providing new insights into the interplay between beauty quark production and the hadronization process. We emphasize that the multiplicity dependence of the nonprompt to prompt charm hadron productions can be useful to constrain the flavor dependences of the coalescence dynamics. This work establishes a unified framework for future studies of heavy quark transport and collective flow behavior in small collision systems.