Pion emission source in pp collisions using the AMPT model with sub-nucleon structure

Based the on the fitting results, the \rcore values in each \kt interval are extracted for four different scenarios: (\rmnum{1}) before ART without further boost, (\rmnum{2}) before ART with a boost of $\tau\in[1.5,5]$ fm/$\it{c}$, (\rmnum{3}) after ART stage without boost, and (\rmnum{4}) after ART with a boost of $\tau\in[1,3]$ fm/$\it{c}$. In (\rmnum{2}), the upper limit originates from the general assumption that resonances with $\textit{c}\tau_\text{res} > 5$ fm are long-lived, while in (\rmnum{4}), the $\tau$ values are deliberately reduced to roughly match the results of (\rmnum{2}). Figure ~\ref{fig:FinalmTscaling} shows the \mt-scaling behavior of \rcore. It can be seen that all four cases are in line with the expectation that the source radii decrease as \mt increases, roughly following the power-law relationship~\cite{SourceMaxi}: $R_\text{core} = \it{a} + \it{b}\cdot\langle m_\text{T}\rangle^{\it{c}}$. This can be understood in terms of the collectivity generated since the partonic stage. Compared to the ALICE measurements (solid dots), the original AMPT sources (\rmnum{1}) and (\rmnum{3}), without additional boosting, are systematically smaller, while the modified cases of (\rmnum{2}) and (\rmnum{4}) are in good agreement with data in the low \mt ranges. Note that ALICE results also exhibit a plateau at $\mt < 0.5$~GeV/$\it{c}^\mathrm{2}$, which can be interpreted as the limitation of the system size in pp collisions. However, this feature is not observed in AMPT, which instead follows the power-law increasing tread. Generally, the AMPT provides a good environment to reveal the mechanisms behind system size and \mt-scaling, but further investigation is also required to understand the detailed behaviors.