Effective field theory approach to lepton number violating decays K±→ π∓l±l±: short-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 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 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. 1

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

“…while the QCD LECs determined in [34] are, in our notation [1], g 27×1 = 0.38 ± 0.08, g a 8×8 = (5.5 ± 2) GeV 2 , and g b 8×8 = (1.55 ± 0.65) GeV 2 . The complete amplitude for the decay…”

“…We first recall that the SD contribution in figure 1(c) arises at leading order from dim-9 operators involving two like-sign leptons and four quarks which have been thoroughly analyzed in ref. [1]. In the following we investigate systematically the effective operators that could finally dominate the LD contribution in figure 1(a,b).…”

“…This relative weakness originates from much smaller data samples accumulated in kaon experiments than the number of nuclei available in a ton-level experiment of 0νββ decays as we estimated roughly in ref. [1]. Thus the weak bounds should not be interpreted as if the SMEFT approach would be valid for a new particle with a mass as low as tens or JHEP03(2020)120…”

“…These decays can be best investigated with the aid of various effective theories while avoiding theoretical uncertainties associated with nuclear physics. In a recent publication [1] we started the endeavor with the decays K ± → π ∓ l ± l ± arising from effective contact interactions among light quarks and charged leptons l = e, µ. In this work we make a comprehensive analysis on the decays by incorporating the long-distance contribution due to the exchange of neutrinos.…”

“…In particular, working to the leading order in χPT and in LNV effects, lepton number violation could manifest itself through the neutrino mass (shown in figure 1(a)), effective interactions of a single meson with a charged lepton and neutrino pair (figure 1(b)) or of the two mesons with a pair of likely-charged leptons (figure 1(c)). The short-distance (SD) contribution in figure 1(c) was thoroughly studied in [1], and this work will focus on the long-distance (LD) terms in figure 1(a, b) due to the exchange of neutrinos. It is easy to parameterize the above effective interactions, but our aim is to work them out systematically in the EFT approach by matching sequentially to EFTs closer to new physics at a high scale.…”