Effective field theory approach to lepton number violating decays $$ {K}^{\pm}\to {\pi}^{\mp }{l}_{\alpha}^{\pm }{l}_{\beta}^{\pm }: $$ long-distance contribution

Abstract

This is a sequel to our recent work [1] in which we calculated the lepton number violating (LNV) K ± decays due to contact dimension-9 (dim-9) quark-lepton effective interactions that are induced at a high energy scale. In this work we investigate the longdistance contribution to the decays arising from the exchange of a neutrino. These decays can probe LNV interactions involving the second generation of fermions that are not reachable in nuclear neutrinoless double-β decays. Our study is completely formulated in the framework of effective field theories (EFTs), from the standard model effective field theory (SMEFT) through the low energy effective field theory (LEFT) to chiral perturbation theory (χPT). We work to the first nontrivial orders in each effective field theory, collect along the way the matching conditions and renormalization group effects, and express the decay branching ratios in terms of the Wilson coefficients associated with the dim-5 and dim-7 operators in SMEFT. Our result is general in that it does not depend on dynamical details of physics at a high scale that induce the effective interactions in SMEFT and in that it does not appeal to any hadronic models. We find that the long-distance contribution overwhelmingly dominates over the contact or short-distance one. Assuming the new physics scale to be around a TeV, the branching ratios are predicted to be below the current experimental upper bounds by several orders of magnitude.

Extending low energy effective field theory with a complete set of dimension-7 operators

“…where V pr is the CKM matrix coming from the SM charged current weak interactions. These matching results can contribute to nuclear neutrinoless double β decays and LNV meson decays via the long distance mechanism [19,[35][36][37].…”

“…[5] and further refined in ref. [37]. This result will be necessary for a consistent study of new physics effects at low energy beyond the leading order.…”

“…We adopt for the dim-6 operators in SMEFT the Warsaw basis [3], and for the dim-7 operators the basis in ref. [37] that is refined from the previous one [5] and reproduced in table 3. The bases of dim-5 and dim-6 operators in LEFT are taken from ref.…”

“…Basis of dim-7 operators in SMEFT[37]. Here L, Q are the left-handed lepton and quark doublet fields, u, d, e the right-handed up-type quark, down-type quark and charged lepton singlet fields, and H the Higgs doublet withH i = ij H j .…”

General neutrino interactions with sterile neutrinos in light of coherent neutrino-nucleus scattering and meson invisible decays

“…Compared to the pure QCD running effect in [21], we find the QED correction is almost negligible. We can see the scalar-type operators are enhanced while the tensor-type operators are suppressed when evolving from the high scale Λ EW down to the low scale Λ χ .…”