Abstract
We study whether higher-dimensional operators in effective field theories, in particular in the Standard Model Effective Field Theory (SMEFT), can source gauge anomalies via the modification of the interactions involved in triangle diagrams. We find no evidence of such gauge anomalies at the level of dimension-6 operators that can therefore be chosen independently to each others without spoiling the consistency of SMEFT, at variance with recent claims. The underlying reason is that gauge-invariant combinations of Goldstone bosons and massive gauge fields are allowed to couple to matter currents which are not conserved. We show this in a toy model by computing the relevant triangle diagrams, as well as by working out Wess-Zumino terms in the bosonic EFT below all fermion masses. The same approach applies directly to the Standard Model both at the renormalisable level, providing a convenient and unusual way to check that the SM is anomaly free, as well as at the non-renormalisable level in SMEFT.
Highlights
Content as the SM, one would naively expect it to be free of gauge anomalies
We study whether higher-dimensional operators in effective field theories, in particular in the Standard Model Effective Field Theory (SMEFT), can source gauge anomalies via the modification of the interactions involved in triangle diagrams
Chiral triangle loops are known to potentially break gauge symmetries at the quantum level. These possible breakdown effects are RG-independent, it is anticipated that, if a UV model extending the SM at high energies is anomaly free, its EFT description at lower energies when the heavy degrees of freedom are integrated out and traded off for higher dimensional interactions among the SM fields should exhibit a full SU(3) × SU(2) × U(1) unbroken gauge symmetry
Summary
We start by considering a model that extends the SM with a heavy neutral lepton, i.e., a SM singlet Majorana fermion N with a Majorana mass MN. It is clear that no operator involving quarks can be generated and c(φ3q) = c(φ1q) = cφu = cφd = 0 This model violates both constraints in eqs. The UV renormalizable model that this EFT comes from is anomaly free because it is just the SM plus a singlet Majorana fermion, which has no anomaly. This is a vector-like extension of the SM and there cannot be non-decoupling BSM effects. It is known that those theories, when matched onto the SMEFT, always accidentally obey eqs. (1.1)–(1.2) [5, 6]
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