<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>MS</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \overline{\textrm{MS}} \)</EquationSource> </InlineEquation> scheme that mediate nucleon decay channels such as <i>p</i> → <i>e</i><sup>+</sup><i>π</i><sup>0</sup>, 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<sup>4</sup> GeV, 10<sup>6</sup> GeV, and 10<sup>9</sup> 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<sup>7</sup> GeV, thus mitigating the need of a large desert. A Python package (Available at: <a href="https://github.com/rp-winter/Nucleon-Decay-SMEFT">https://github.com/rp-winter/Nucleon-Decay-SMEFT</a>) is provided to facilitate the RG evolution of nucleon-decay Wilson coefficients, allowing for the inclusion of generic BNC effects.</p>

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

  • Mathew Thomas Arun,
  • M Shyam,
  • Ritik Pal

摘要

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 MS ¯ \( \overline{\textrm{MS}} \) scheme that mediate nucleon decay channels such as pe+π0, 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 104 GeV, 106 GeV, and 109 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 ∼ 107 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.