Dark-sector physics in the search for the rare decays $$K^+\rightarrow \pi ^+ \nu {\bar{\nu }}$$ and $$K_L\rightarrow \pi ^0 \nu {\bar{\nu }}$$

Abstract

We compute the contribution of the decays K L → π 0 QQ and K + → π + QQ, where Q is a dark fermion of the dark sector, to the measured widths for the rare decays K + → π + νν and K L → π 0 νν. The recent experimental limit for Γ (K + → π + νν) from NA62 sets a new and very strict bound on the dark-sector parameters. A branching ratio for K L → π 0 QQ within the reach of the KOTO sensitivity is possible. The Grossman-Nir bound is weakened by the asymmetric effect of the different kinematic cuts enforced by the NA62 and KOTO experiments. This last feature holds true for all models where the decay into invisible states takes place through a light or massless intermediate state.

Explaining (g−2)μ,e , the KOTO anomaly, and the MiniBooNE excess in an extended Higgs model with sterile neutrinos

“…Thus, the new physics explanation for the KOTO anomaly is required to generate three anomalous events and satisfy the GN bound. Several such solutions have been proposed in the literature [80,[130][131][132][133][134][135][136][137][138][139][140][141][142][143].…”

Three exceptions to the Grossman-Nir bound

“…In contrast, ref. [13] relies on the fact that the available phase space is larger for neutral kaon decays due to m K L − m π 0 > m K + − m π + and thus K + → π + X inv decays can be forbidden by a finely tuned choice for the mass of the invisible final state X inv . Ref.…”

Pair production of dark particles in meson decays

“…(62). One can immediately discard scenarios where m K þ − m π þ < 2m Y < m K L − m π 0 , as the pion would have virtually no phase space [17]. Scenarios with m Y ¼ m π are also disfavored, as the maximum j ⃗p T π j is precisely around the minimum j ⃗p T π j in the signal region.…”

“…Our paper is inspired, in part, by a recent report by the KOTO Collaboration that addressed four unexplained events after unblinding their data, at a level much larger than the SM neutrino channel, which prompts theoretical investigations of beyond-SM (BSM) physics that may lead to such a signature. In many recent studies the focus has been primarily on K L decays to a pion plus new invisible particles [16][17][18][19][20][21][22][23][24]. Other recent alternatives include new particles produced at the target that decay to γγ inside the KOTO detector [16], direct K L decay to γγ plus invisible states [25], and heavy new physics operators with flavor violation or ΔI ¼ 3=2 structure [16,[26][27][28].…”