Beyond Jarlskog: 699 invariants for CP violation in SMEFT

Abstract

As SMEFT is a framework of growing importance to analyze high-energy data, understanding its parameter space is crucial. The latter is commonly split into CP-even and CP-odd parts, but this classification is obscured by the fact that CP violation is actually a collective effect that is best captured by considering flavor-invariant combinations of Lagrangian parameters. First we show that fermion rephasing invariance imposes that several coefficients associated to dimension-six operators can never interfere with operators of dimension ≤ 4 and thus cannot appear in any physical observable at $$ \mathcal{O} $$ O 1/Λ2. For those that can, instead, we establish a one-to-one correspondence with CP-odd flavor invariants, all linear with respect to SMEFT coefficients. We explicitly present complete lists of such linear CP-odd invariants, and carefully examine their relationship to CP breaking throughout the parameter space of coefficients of dimension ≤ 4. Requiring that these invariants all vanish, together with the Jarlskog invariant, the strong-CP phase, and the 6 CP-violating dimension-6 bosonic operators, provides 699(+1 + 1 + 6) conditions for CP conservation to hold in any observable at leading order, $$ \mathcal{O} $$ O (1/Λ2).

Global constraints on Yukawa operators in the standard model effective theory

“…Another approach would be to attempt to provide the constraints in terms of basis-independent, i.e., Jarlskog-type, invariants (see recent ref. [92]).…”

Adding Flavor to the SMEFT

“…The other operators, which come with the flavor-spurion suppression, will be constrained chiefly by low-energy flavor physics. For any of the symmetries in table 1, if an operator containing fermions turns out to be Hermitian, it is counted in the left column since it introduces a single real parameter, otherwise it appears both in the left and right columns for the real and imaginary parameters, respectively (some care has to be taken when connecting the imaginary parameters with CP violation [83]). Additionally, there are always 9 CP-even (added to the left column) and 6 CP-odd (added to the right column) parameters for the pure bosonic dimension-6 operators, which do not carry any flavor.…”

“…These many new operators also results in a large number of new CP-invariants[83][84][85] 2. In this work, we consider neutrinos to be massless.…”

Electric dipole moments at one-loop in the dimension-6 SMEFT

“…J. C (2022) 82:926 allow to build more flavor invariants [52] beyond the Jarlskog invariant. In this paper we study which of the new phases in the SMEFT can enter in the expressions of the lepton and neutron EDMs beyond the log contributions induced by the RG flow which have been studied in the literature.…”

“…We would like to stress that we are considering, in the SMEFT, tree and 1-loop level contributions to EDMs: in presence of new physics, these CP odd observables can be in general largely enhanced. In fact, allowing for the presence of higher dimensional operators, CP violating effects are no more encoded only by the Jarlskog invariant and a larger variety of complex flavor invariants can be built from Wilson coefficients together with Yukawa matrices [52]. The flavor structure of the effective theory is such that these invariants can indeed be generated at lower loop level with respect to the SM case.…”