We consider irrelevant deformations of massless RSOS scattering theories by an infinite number of higher [ \( T\overline{T} \) ]s operators which introduce extra non-trivial CDD factors between left-movers and right-movers. It is shown that the resulting theories can be UV complete after bypassing typical Hagedorn-like singularities if the coefficients of the deformations are fine-tuned. By classifying all integrable cases, we have discovered a new UV complete QFT associated to the \( {\mathcal{M}}_p \) (p ≥ 3) minimal CFT based on the integrable structure of the RSOS scattering theory. This new theory is the massless ℤp−1 parafermionic sinh-Gordon (PShG) model with a self-dual coupling constant. This correspondence is confirmed by showing that the scale-dependent vacuum energies computed by the thermodynamic Bethe ansatz derived from the S-matrices match those from the quantization conditions for the PShG models using the reflection amplitudes.
