Radiative decays of charged leptons as constraints of unitarity polygons for active-sterile neutrino mixing and CP violation

Abstract

We calculate the rates of radiative β − → α − + γ decays for (α, β) = (e, µ), (e, τ ) and (µ, τ ) by taking the unitary gauge in the (3 + n) active-sterile neutrino mixing scheme, and make it clear that constraints on the unitarity of the 3 × 3 Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix U extracted from β − → α − + γ decays in the minimal unitarity violation scheme differ from those obtained in the canonical seesaw mechanism with n heavy Majorana neutrinos by a factor 5/3. In such a natural seesaw case we show that the rates of β − → α − + γ can be used to cleanly and strongly constrain the effective apex of a unitarity polygon, and compare its geometry with the geometry of its three sub-triangles formed by two vectors U αi U * βi and U αj U * βj (for i = j) in the complex plane. We find that the areas of such sub-triangles can be described in terms of the Jarlskog-like invariants of CP violation J ij αβ , and their small differences signify slight unitarity violation of the PMNS matrix U .

Radiative Decays of Charged Leptons in the Seesaw Effective Field Theory with One-loop Matching

“…As expected, our result in Eq. ( 29) is in perfect agreement with that obtained in the full theory [71,[76][77][78] in the limit of m i M W M j (for i, j = 1, 2, 3), as recently demonstrated in Ref. [71].…”

“…The experimental searches for radiative β − → α − + γ decays have placed the ever most stringent bound on lepton flavor violation in the charged-lepton sector, and the discovery of such rare decays will definitely point to new physics beyond the SM [64][65][66]. The null signal of β − → α − + γ decays has been used to constrain the unitarity violation of Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix [67][68][69] in both the minimal unitarity violation (MUV) scheme (with only one tree-level dim-6 operator besides the unique dim-5 operator) [49,58] and the type-I seesaw model [70,71]. The discrepancy between the constraints in these two cases has been noticed [70,71].…”

“…The null signal of β − → α − + γ decays has been used to constrain the unitarity violation of Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix [67][68][69] in both the minimal unitarity violation (MUV) scheme (with only one tree-level dim-6 operator besides the unique dim-5 operator) [49,58] and the type-I seesaw model [70,71]. The discrepancy between the constraints in these two cases has been noticed [70,71]. In fact, one has to perform the one-loop matching and take into account new dimension-six operators emerging only at the one-loop level, as will be shown and clarified in this work.…”

One-loop Matching of the Type-II Seesaw Model onto the Standard Model Effective Field Theory

“…In the previous work [52], we have initiated a program of performing a complete one-loop matching of the seesaw models onto the SMEFT. For the type-I seesaw model [55][56][57][58][59], the one-loop matching has been achieved and shown to be useful to investigate the radiative decays of charged leptons l − α → l − β + γ in a self-consistent way [43,60]. In the present paper, we continue to carry out the complete one-loop matching for the effective operators up to dim-6 by integrating out the heavy Higgs triplet in the type-II seesaw model [61][62][63][64][65][66] with the functional approach [67][68][69].…”

A full parametrization of the $9\times 9$ active-sterile flavor mixing matrix in the inverse or linear seesaw scenario of massive neutrinos

“…To constrain the shortest side of each effective unitarity quadrangle, one may study those leptonflavor-violating processes such as neutrino oscillations and radiative decays of charged leptons. In the latter case the new degrees of freedom can mediate the one-loop α − → β − + γ transitions for (α, β) = (µ, e), (τ, e) and (τ, µ), and the relevant loop functions depend on the masses of three sterile neutrinos and three extra neutral fermions (i.e., M i and M i for i = 1, 2, 3) [24,53,54]. A systematic analysis of such lepton-flavor-violating processes in the inverse and linear seesaw scenarios will be done elsewhere.…”