Abstract
Abstract The excellent experimental prospects to measure the invisible mass spectrum of the $$K^+\rightarrow \pi ^+\nu {\bar{\nu }}$$ K + → π + ν ν ¯ decay opens a new path to test generalised quark–neutrino interactions with flavour changing $$s\rightarrow d$$ s → d transitions and as such to novel probes of Physics beyond the Standard Model. Such signals can be a consequence of new lepton-number violating or lepton-number conserving interactions, with their interpretations depending on the Majorana versus Dirac nature of the neutrinos. Furthermore, the possible existence of new massive sterile neutrinos can be tested via their distinctive imprints in the invariant mass spectrum. Within the model-independent framework of the weak effective theory at dimension-six, we study the New Physics effects of Majorana and Dirac neutrinos on the differential distribution of $$K^+\rightarrow \pi ^+\nu {\bar{\nu }}$$ K + → π + ν ν ¯ allowing for lepton-number violating interactions and potential new sterile neutrinos. We determine the current and expected future sensitivity on the corresponding $$\Delta S=1$$ Δ S = 1 neutral-current Wilson coefficients using the distribution measured by the NA62 collaboration and accounting for expected improvements based on the HIKE experiment. We present single-operator fits and also determine correlations among different type of operators. Even though we focus on $$s\rightarrow d\nu \nu $$ s → d ν ν transitions, the operator bases for Majorana and Dirac and the classification of lepton-number-violating/conserving interactions is applicable also for the study of $$b\rightarrow s/d\nu \nu $$ b → s / d ν ν and $$c\rightarrow u\nu \nu $$ c → u ν ν transitions relevant in current phenomenology.