Dimension-Six Terms in the Standard Model Lagrangian

TL;DR

This paper revisits and refines the classification of dimension-six operators in the Standard Model Lagrangian, reducing the number of independent operators from previous counts by identifying redundancies.

Contribution

It provides an updated, complete list of dimension-six operators in the Standard Model, assuming baryon number conservation, and clarifies redundancies in earlier enumerations.

Findings

Identified 59 independent operators with baryon number conservation.

Reduced previous operator count from 80 to 59 by removing redundancies.

Discovered 4 additional operators when baryon number conservation is relaxed.

Abstract

When the Standard Model is considered as an effective low-energy theory, higher dimensional interaction terms appear in the Lagrangian. Dimension-six terms have been enumerated in the classical article by Buchmueller and Wyler [3]. Although redundance of some of those operators has been already noted in the literature, no updated complete list has been published to date. Here we perform their classification once again from the outset. Assuming baryon number conservation, we find 15 + 19 + 25 = 59 independent operators (barring flavour structure and Hermitian conjugations), as compared to 16 + 35 + 29 = 80 in Ref.[3]. The three summed numbers refer to operators containing 0, 2 and 4 fermion fields. If the assumption of baryon number conservation is relaxed, 4 new operators arise in the four-fermion sector.