Dimension-six terms in the Standard Model Lagrangian

TLDR

In the Standard Model as an effective low‑energy theory, higher‑dimensional interaction terms arise, and although dimension‑six operators were catalogued by Buchmüller and Wyler, no updated complete list exists, with the original classification including 16 + 35 + 29 operators across 0, 2, and 4‑fermion sectors. The authors aim to reclassify the dimension‑six operators from first principles. They re‑enumerate the operators using a systematic basis construction from first principles. Under baryon‑number conservation, the authors identify 59 independent dimension‑six operators—fewer than the 80 listed by Buchmüller and Wyler—and, without that assumption, find four additional four‑fermion operators.

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.