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.

基于拟合结果，我们从每个横向动量（k_t）区间内提取了四种不同情景下的核芯半径（R_core）数值：(1) ART阶段前且未施加额外助推；(2) ART阶段前且施加τ∈[1.5,5] 飞米每光速（fm/c）的助推；(3) ART阶段后且未施加助推；(4) ART阶段后且施加τ∈[1,3] 飞米每光速（fm/c）的助推。在情景(2)中，其上限源自通用假设：衰变长度$c au_ ext{res}>5$ fm的共振态属于长寿命粒子；而在情景(4)中，我们刻意调整τ的取值范围以近似匹配情景(2)的结果。图~
ef{fig:FinalmTscaling}展示了核芯半径（R_core）的横向质量（m_T）标度行为。可以看到，四种情景均符合源半径随横向质量增大而减小的预期，且大致遵循如下幂律关系~cite{SourceMaxi}：$R_ ext{core} = a + bcdotlangle m_ ext{T}
angle^c$。该现象可通过部分子阶段产生的集体运动加以解释。相较于ALICE实验（ALICE，A Large Ion Collider Experiment）的测量结果（实心圆点），未施加额外助推的原始AMPT模型（AMPT，A Multi-Phase Transport Model）源（情景1与3）的核芯半径整体偏小；而经过修正的情景2与4则在低横向质量区间与实验数据吻合良好。值得注意的是，ALICE实验结果在横向质量小于0.5 GeV/c²的区间呈现平台特性，这可被解释为质子-质子（pp）碰撞中系统尺寸的限制效应。但AMPT模型并未展现出该平台特征，反而呈现出随横向质量幂律增长的趋势。总体而言，AMPT模型为探究系统尺寸与横向质量标度背后的物理机制提供了良好的研究平台，但仍需开展进一步研究以理解其具体行为细节。