AI 中文总结
本研究明确了相对论重离子碰撞中中等质量双轻子测温法的物理起源与非普适特性，揭示其逆斜率与初始温度的关联机制，提出多质量窗口测量可约束热演化与电磁源组成。
AI 中文摘要
我们确定了相对论重离子碰撞中中等质量双轻子测温法的物理起源与适用范围。采用带有热双轻子产额的可控膨胀火球框架，我们证明不变质量谱的局部逆斜率参数，以百分比级精度遵循对该谱有贡献的温度的发射加权调和平均。随着热阶段初始温度升高，辐射采样的温度随整体热标度向上移动，使其调和平均紧密追踪初始温度，这为逆斜率与初始温度的强关联提供了物理基础，而所得映射仍非普适：仅缩放辐射量的变化不会改变该映射，而冷却历史或源组成的变化会在不同温度间重新分配辐射并改变响应。不过，在本文研究的温度范围内，该映射近乎线性。由于不同不变质量窗口对发射历史的权重不同，在1<M<3 GeV区间具有相同逆斜率参数的源情景，在更硬的质量窗口会呈现不同逆斜率。因此，中等质量双轻子谱是早期热历史的定量但非普适探针，结合多质量窗口测量与实际计算，可对热演化及早期电磁源组成提供额外约束。
英文摘要
We identify the physical origin and limits of intermediate-mass dilepton thermometry in relativistic heavy-ion collisions. Using a controlled expanding-fireball framework with thermal dilepton rates, we show that the local inverse-slope parameter of the invariant-mass spectrum follows, to percent-level accuracy, the emission-weighted harmonic mean of the temperatures contributing to the spectrum. As the thermal-stage initial temperature increases, the temperatures sampled by the radiation shift upward with the overall thermal scale, causing their harmonic mean to track the initial temperature closely. This provides the physical basis for the strong inverse-slope--initial-temperature correlation, while the resulting mapping remains nonuniversal: changes that only rescale the amount of radiation leave it unchanged, whereas changes in the cooling history or source composition redistribute the radiation among different temperatures and modify the response. The mapping is nevertheless nearly linear over the temperature range studied here. Because different invariant-mass windows weight the emission history differently, source scenarios with the same inverse-slope parameter in $1<M<3~{\rm GeV}$ develop different inverse slopes in harder mass windows. Intermediate-mass dilepton spectra therefore provide a quantitative but nonuniversal probe of the early thermal history, while measurements in multiple mass windows, when confronted with realistic calculations, can provide additional constraints on the thermal evolution and early electromagnetic source content.
Comments8 pages, 4 figures
