Renormalization Group Evolution of Dimension-seven Baryon- and Lepton-number-violating Operators

Abstract

We study dimension-seven operators in standard model effective field theory. These operators are classified into two sets, one violating lepton number but preserving baryon number ($\Delta L=\pm 2$, $\Delta B=0$) and the other violating both but preserving their sum ($-\Delta L=\Delta B=\pm 1$). It has been found in the previous literature that there are respectively 13 and 7 such independent operators. We show that one operator is redundant in each set so that the complete list contains only 12 and 6 operators respectively. We accomplish this by using standard model equations of motion and various Fierz identities. We calculate the one-loop anomalous dimension matrix for the 6 operators in the second set, and illustrate its possible phenomenological implications by working out renormalization group running of the Wilson coefficients that could contribute to the type of proton decays with $-\Delta L=\Delta B=\pm 1$, such as $p\to \nu {\pi }^{+}$.

arXiv commentv1: 11 pages, 2 figures, 1 table; v2: 12 pages, added a few refs, compared with previous work on counting of independent operators for general n generations, and added a few words on Fierz identities

References in corpus (15)

• Dimension-Six Terms in the Standard Model Lagrangian
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence
• Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence
• Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators
• Renormalization Group Scaling of Higgs Operators and Γ(h -> γγ)
• Low-derivative operators of the Standard Model effective field theory via Hilbert series methods
• Non-renormalization Theorems without Supersymmetry
• Dimension Seven Operators in Standard Model with Right handed Neutrinos
• Renormalization constants and beta functions for the gauge couplings of the Standard Model to three-loop order
• Neutron-Anti-Neutron Oscillation: Theory and Phenomenology
• TASI Lectures on Effective Field Theory and Precision Electroweak Measurements
• Unique Neutrino Mass Operator at any Mass Dimension
• 2, 84, 30, 993, 560, 15456, 11962, 261485, ...: Higher dimension operators in the SM EFT
• Generalized Fierz Identities and Applications to Spin-3/2 Particles

Cited by in corpus (3)

• Operators up to Dimension Seven in Standard Model Effective Field Theory Extended with Sterile Neutrinos
• Connecting Radiative Neutrino Mass, Neutron-Antineutron Oscillation, Proton Decay, and Leptogenesis through Dark Matter
• Extending low energy effective field theory with a complete set of dimension-7 operators