Finite-regulator temperature and inverse-energy parameter

For the fixed model of Adopted finite-regulator polynomial model, use the SI energy-unit convention of Quantum field quantities and compatible SI normalizations. A declared temperature input is a scalar $T>0$ with unit kelvin (K). Use the SI-defining Boltzmann constant $k_B:=1.380649\times {10}^{-23}\mathrm{J}{\mathrm{K}}^{-1}\mathrm{.}$ This exact value is the one stated by the BIPM SI Brochure, 9th edition, version 4.01, §§2.2 and 2.3.1. Define the physical inverse-energy parameter

${\beta }_{\mathrm{p}\mathrm{h}\mathrm{y}\mathrm{s}}:=\frac{1}{k_{B}T}[{\mathrm{J}}^{-1}],$

and its dimensionless form

$\widehat{\beta }:=E_{\ast }{\beta }_{\mathrm{p}\mathrm{h}\mathrm{y}\mathrm{s}}\mathrm{.}$

The product $k_{B}T$ has unit joule, and $\widehat{\beta }$ is dimensionless because $E_{\ast }$ has unit joule. Since $k_B>0$ and $T>0$, both inverse parameters are defined and positive. The temperature $T$ is a declared model input; this definition does not infer it from a state or an experiment. It defines a parameter convention only and asserts no dynamical thermalization.