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

A bstract 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 $$ \overline{\textrm{MS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> scheme that mediate nucleon decay channels such as p → e + π 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 operators. 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 GeV, 10 6 GeV, and 10 9 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 ∼ 10 7 GeV, thus mitigating the need of a large desert. A Python package (Available at: https://github.com/rp-winter/Nucleon-Decay-SMEFT ) is provided to facilitate the RG evolution of nucleon-decay Wilson coefficients, allowing for the inclusion of generic BNC effects.