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 long- distance 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 reach- able 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.
Highlights
JHEP03(2020)120 provide complementary information on underlying new physics
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 standard model effective field theory (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
Summary
For the LNV interactions, the relevant operators in LEFT involve one charged lepton, one neutrino, and a pair of quarks. These operators first appear at dimension six and have been classified in ref. 7. Considering the restrictions and reductions due to gauge symmetry, equations of motion, integration by parts, and Fierz identities, we obtain the following LNV operators relevant to our purpose here [33]: OpLrLα,βV D = (upLγμdrL)(lLαi←D→μνβC ), OpLrRα,βT D = (upLσμν drR)(lRαγ[μ←D→ν]νβC ), OpRrRα,βV D = (upRγμdrR)(lLαi←D→μνβC ), OpRrLα,βT D = (upRσμν drL)(lRαγ[μ←D→ν]νβC ),. The operators in equations (2.2)–(2.7), as well as the dim-3 Majorana mass term (2.1), make up the main body for the LD contribution These operators will be matched to those in χPT where the lepton bilinears act as external sources.
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