ar X iv : h ep - p h / 98 06 48 7 v 1 2 5 Ju n 19 98 On The Invisible Decays of the Υ and J / Ψ Resonances

We estimate the most important corrections to the branching ratios for the invisible decays of quarkonium states, arising from possible extensions of the Standard Model. Among the possibilities considered are the presence of extra Z-bosons, minimal supersymmetric extensions of the Standard Model with R-parity violation and decays into Goldstinos. Prospects of detecting these corrections at existing and future B-factories and τ -charm factories are discussed. ∗[email protected] †[email protected] ‡[email protected] B-meson factories under construction at KEK and at SLAC [1] can deliver 10 Υ’s and Υ’s per year, when they are tuned to run at resonance. Coupled with what is available at CLEO III, these facilities will make it possible for the first time to study in detail invisible decays of these resonances. Such decay modes can be studied by observing the decay Υ → Υ+2πs at resonance and tagging on the invariant mass of the dipion system at the Υ-mass. Invisible decays of heavy quarkonium states offer a window into what may lie beyond the Standard Model. The reason is that apart from neutrinos, the minimal Standard Model predicts no other channels that these states can decay into. The associated rates for these decays can be computed precisely, and so any observed departure can furnish hints of structures over and above those in the Standard Model. As we will show below, a more complete test of what these structures might be would require similar measurements on the J/Ψinvisible decay widths, something which could be achieved at the τ -charm factory in the future. In what follows, we concentrate on what we believe to be the largest among these effects. In particular, we will estimate the branching ratios into neutrinos in the presence of extra Z-bosons, and R-parity violating effects in supersymmetrized Standard Models, and finally decays into Goldstinos. To begin, we present the Standard Model prediction for the branching ratio of the invisible decays of Υ and J/Ψ and their observed decays into electron-positron pairs. To our knowledge the detail formulae have not been given before. Within the Standard Model the invisible mode consists solely of decays into three types of neutrino-antineutrino pairs. Neglecting polarization effects and taking into account ee production through a photon only we get Γ (Υ → νν̄) Γ (Υ → e+e−) = 27GM Υ 64π2α2 (−1 + 4 3 sin θW ) 2 (1) = 4.14× 10 , Γ(J/Ψ → νν̄)) Γ(J/Ψ → e+e−) = 27GM J/Ψ 256π2α2 (1− 8 3 sin θW ) 2 , (2) = 4.54× 10 , with G and α being the Fermi and the fine structure constants respectively. MΥ,J/Ψ are masses for the Υ and J/Ψ states. These formulas are expected to be correct up to about 2-3%. The major sources of theoretical uncertainty involved in (1) and (2) can be listed as follows: 1. corrections to the Υ and J/Ψ wave functions, including QCD corrections and polarization effects, 2. ee production through Z, 3. electroweak radiative corrections, 4. corrections due to the Higgs boson. The first correction is not expected to be significant since it similarly modifies the neutrino and electron decay widths, and so the leading order cancels in the branching ratio. The