RG evolution and effect of intermediate new-physics on $\Delta B=1$ four-fermion operators

Motivated by the stringent experimental bounds on proton lifetime and the need for precise low-energy predictions, there has been renewed interest in the renormalization group (RG) evolution of Wilson coefficients for baryon number violating (BNV) operators and their characteristic new-physics scales. In this work, we analyze the RG running of dimension-6 four-fermion operators in the $\overline{\text{MS}}$ scheme that mediate nucleon decay channels such as $p \to e^+ \pi^0$, while systematically accounting for the impact of baryon number conserving (BNC) new-physics that can enter the theory at an intermediate scale as higher-dimensional effective field theory operator. These BNC operators mix with BNV ones at 1-loop and alter the RG flow. The running is performed from the electroweak scale up to representative intermediate scales of $10^4~\text{GeV}$, $10^6~\text{GeV}$, and $10^9~\text{GeV}$, corresponding to possible thresholds for new BNC degrees of freedom. Comparing the RG evolved coefficients with current experimental bounds on nucleon decay lifetimes, we find that the inclusion of BNC-BNV mixing, dominated by top quark loops, can significantly lower the effective proton decay scale to $\sim 10^7$ GeV, thus mitigating the need of a large desert. A Python package is provided to facilitate the RG evolution of nucleon-decay Wilson coefficients, allowing for the inclusion of generic BNC effects.