Universal mechanism for near-linearity of the dilepton thermometer relation

Establish a simple universal mechanism that enforces the nearly linear relationship between the intermediate-mass dilepton spectral inverse-slope parameter and the $e\gamma$-weighted thermal-stage initial temperature.

Background

The paper explains the strong correlation between the intermediate-mass dilepton inverse slope and the thermal-stage initial temperature through approximate rescaling of the emission-temperature distribution. However, the rescaling is incomplete because fixed physical scales, the cooling history, microscopic emission rates, and source composition reshape that distribution. Consequently, the observed near-linearity over the studied temperature range emerges from the full evolution and emission response rather than from an identified universal principle. Determining whether a simple universal mechanism underlies this near-linearity remains unresolved.

References

We do not identify a simple universal mechanism that enforces the nearly linear $T_{}$--$\langle T_{\rm in}\rangle$ relation; over the range studied here, its near-linearity emerges from the full evolution and emission response.

— Origin and limits of intermediate-mass dilepton thermometry  (2608.16102 - Du, 17 Aug 2026) in Section 3, “Origin of the thermometer relation”