We revisit calculations of invisible widths of heavy mesons in the standard model, which serve as benchmarks for the studies of production of light, long-lived neutral particles in heavy meson decays. We challenge the common assumption that in the standard model these widths are dominated by meson decays into a two-neutrino final state and prove that they are dominated by decays into fourneutrino final states. We show that current estimates of the invisible widths of heavy mesons in the standard model underestimate the effect by orders of magnitude. We examine currently available experimental data on invisible widths and place constraints on the properties of dark photons. We also comment on the invisible widths of the kaons.
PACS numbers:Experimental studies of light, m ∼ O(0.1 − 10 3 ) MeV, weakly interacting long lived particles (WILLPs) have received considerable attention recently, in part due to development of new models of dark matter (DM). These particles could help resolve several problems in physics of dark matter, both by being DM states and/or serving as mediators between visible and dark sectors of our Universe [1]. As such, extensive experimental programs of searches for light WILLPs [2-5] have been put forward at several experimental centers around the world. For recent constraints on candidates for the light particles such as axion-like states or dark photons see [6,7].If these WILLP states exist, they could also be produced in the decays of mesons, such as B, D, or even K. One of the tantalizing experimental signatures of such transitions includes "invisible" decays of heavy meson states [8], as light WILLPs do not interact with the detectors. Currently operating experiments Belle II and BESIII at e + e − machines in Japan and China, as well as experiments at future flavor factories, are the ideal places for experimental studies of such decays. This is because flavor factories operate at the Υ(4S) (bb) or ψ(3770) (cc) resonances that decay into a correlated state of B 0 d (D 0 ) meson pairs. Thus, "invisible" B 0 d (D 0 ) decays into WILLPs can be tagged with non-leptonic decays of B 0 d (D 0 ) decays "on the other side." Current experimental constraints on those decays come from the analyses done at BaBar and Belle collaborations (for B 0 ) and by Belle collaboration (for D 0 ). No signals have been observed so far, so upper limits on the branching fractions of heavy mesons decaying to invisible final states B(B 0 d → / E) < 1.3 × 10 −4 (Belle) [9] and B(B 0 d → / E) < 2.4 × 10 −5 (BaBar) [10] for the b-flavored mesons and B(D 0 → / E) < 9.4 × 10 −5 (Belle) [11] for charmed mesons have been set at 90% confidence level.If measurements of invisible width of a heavy meson are to be used in placing constraints on new physics models [8], standard model (SM) backgrounds to those modes need to be estimated. While different experiments have different experiment-specific backgrounds for such processes related to "missing" particles in their detectors [9][10][11] that can be controlled with various experi...
