Kaon decays shedding light on massless dark photons

Abstract

We explore kaon decays with missing energy carried away by a massless dark photon, $${{\overline{\gamma }}}$$ γ ¯ , assumed to have flavor-changing dipole-type couplings to the d and s quarks. We consider in particular the neutral-kaon modes $$K_L\rightarrow \gamma {{\overline{\gamma }}}$$ K L → γ γ ¯ and $$K_L\rightarrow \pi ^0\gamma {{\overline{\gamma }}}$$ K L → π 0 γ γ ¯ and their $$K_S$$ K S counterparts, as well as the charged-kaon channel $$K^+\rightarrow \pi ^+\gamma {{\overline{\gamma }}}$$ K + → π + γ γ ¯ , each of which also has an ordinary photon, $$\gamma $$ γ , in the final state. In addition, we look at $$K_{L,S}\rightarrow \pi ^+\pi ^-{{\overline{\gamma }}}$$ K L , S → π + π - γ ¯ and $$K^+\rightarrow \pi ^+\pi ^0{{\overline{\gamma }}}$$ K + → π + π 0 γ ¯ . Interestingly, the same $$ds{{\overline{\gamma }}}$$ d s γ ¯ interactions give rise to the flavor-changing two-body decays of hyperons with missing energy and are subject to model-independent constraints that can be inferred from the existing hyperon data. Taking this into account, we obtain branching fractions $${{{\mathcal {B}}}}(K_L\rightarrow \gamma {{\overline{\gamma }}})$$ B ( K L → γ γ ¯ ) and $$\mathcal{B}(K_L\rightarrow \pi ^0\gamma {{\overline{\gamma }}})$$ B ( K L → π 0 γ γ ¯ ) which can be as high as $$10^{-3}$$ 10 - 3 and $$10^{-6}$$ 10 - 6 , respectively, one or both of which may be within the sensitivity reach of the KOTO experiment. Furthermore, we find that $${{{\mathcal {B}}}}(K^+\rightarrow \pi ^+\gamma {{\overline{\gamma }}})$$ B ( K + → π + γ γ ¯ ) and $$\mathcal{B}(K^+\rightarrow \pi ^+\pi ^0{{\overline{\gamma }}})$$ B ( K + → π + π 0 γ ¯ ) are allowed to be maximally of order $$10^{-6}$$ 10 - 6 as well, which may be probed by NA62. Complementarily, the hyperon modes can have rates which are potentially accessible by BESIII. Thus, these ongoing experiments could soon be able to offer significant tests on the existence of the massless dark photon.

New Physics Searches at Kaon and Hyperon Factories

“…-Dark photon production in charged kaon decays: The K + → π + γA and K + → π + π 0 A decays induced by the dipole operators (39) are analyzed for the massless dark photon in Refs. [188,190]. The bounds on allowed NP contribution to ∆M K in kaon mixing, assuming no cancellations with other UV contributions, limit the branching ratios to be at most B(K…”

“…for the UV model and hadronic inputs of [188] with α D ≡ e 2 /4π = 0.1. Using the same UV model and α D but the hadronic inputs of [190] one obtains, instead, the upper limits B(K…”

“…-Dark photon production in neutral kaon decays: Dark photon emission in FCNC decays of K L and K S have been explored for the massless case [112,190], in particular in the K L → γA , K L → π 0 γA and K L → π + π − A processes and their K S counterparts. The K L decays have larger branching ratios compared to K S because of the longer lifetime of the decaying state.…”

“…The K L decays have larger branching ratios compared to K S because of the longer lifetime of the decaying state. Using upper bounds on ∆M K from kaon mixing, and assuming a vanishing electric-dipole contribution in the s → dA transitions, the upper limits on branching ratios are expected to be [190]: 10) . These K L → (π 0 )γA decay rates are within the sensitivity reach of the KOTO experiment (Sections 4.3, 4.9).…”

Access to the Kaon Radius with Kaonic Atoms

“…Kaons are not elementary particles, nevertheless they are of particular interest for fundamental research as the lightest meson with non‐zero strangeness. Associated studies could give access to the strangeness sector of quantum chromodynamics, [ 1 ] CP, [ 2,3 ] and lepton number violation, [ 4 ] properties of other particles, [ 5 ] they could allow to probe dark matter, [ 6 ] and would also help in other fields. [ 7,8 ] Despite their short lifetime of the order of 10 −8 s, negatively charged kaons can be captured by a nucleus and form a kaonic atom.…”