Determine the mass sector without an analytic thermal target

Establish whether the Wetterich flow equation for the finite-temperature $Z_2$-symmetric Higgs–singlet model, supplied with genuine ultraviolet and thermal boundary data but without an analytic one-loop ring-resummed thermal target, can uniquely determine the infrared mass-like combinations and the physically relevant solution branch.

Background

In the finite-temperature PINN runs, the mass-like combinations $a_H$ and $a_S$ are constrained using an analytic thermal target obtained by differentiating a one-loop ring-resummed thermal potential. The authors observe that the converged infrared potential remains visibly sensitive to this target and to which combinations are penalized.

Consequently, the mass-sector behavior is not yet an unconstrained prediction of the functional-renormalization-group flow. The quartic and shape sector receives only loose consistency restrictions and is described as insufficiently robust, making it necessary to determine whether the flow equation and physical boundary data alone can fix the mass sector.