Scalar Three Body Decays and Signals for New Physics

If massive invisible particles are pair-produced in a three-body decay, then the energy distribution of the other (visible) product is sensitive to the mass of the invisible pair. We use this fact in the contexts of a Higgs boson decaying into (i) a Z-boson and two massive neutrinos of a fourth generation, and (ii) a Z and two lightest supersymmetric particles in the minimal supersymmetric standard model. We discuss how the Z-energy spectrum in each case can reflect the values of the parameters of such models. PACS number(s): 13.85.Qk., 14.80.Gt., 14.80. Cp. E −mail : [email protected] E −mail : [email protected] ∗Permanent Address : Mehta Research Institute, 10 Kasturba Gandhi Marg, Allahabad− 211002, INDIA It is a known fact that if a pair of invisible particles are produced in some three-body decay, then the energy distribution of the third particle is sensitive to the masses of the invisible particles. This sensitivity has been utilised earlier in the context of rare decays like K−→πνν̄ to study the dependence of the resulting pion spectrum on the mass of the τ neutruino [1]. Also, it has been claimed that the decay spectra in such cases are different for Dirac and Majorana neutrinos respectively, thereby suggesting a method for distinguishing between these two kinds of fermion masses [2]. The essential argument in the above works is as follows. If all the neutrinos have masses that are negligible compared to mπ, then the differential decay rate dΓ/dEπ in the centreof-mass frame will be a monotonically increasing function of Eπ over the allowed region of phase space, as can be seen from straightforward kinematics. If, on the other hand, one of the neutrino species is significantly massive, then the decay distribution for the corresponding channel attains a peak and then falls with increasing Eπ, due to the unavailability of phase space. As a result, ∑ i dΓi dEπ exhibits a kink (i is the generation label). With increasingly higher mass of the invisible pair, the kink is displaced progressively to lower energy regions. However, as higher mass implies more phase space suppression for the channel under question, the consequent distortion in the decay spectrum also tends to be less and less conspicuous. In between, there is an optimal region where one expects the highest sensivity to the mass of the invisible pair. Since the current upper bound on the τ -neutrino mass from laboratory measurements [3, 4] is as low as 35MeV , the idea summarised above is of little potential use in its original context; the kink in the π-spectrum in K−→πνν̄ can barely occur at the very edge of the phase space even if ντ has a mass close to its upper limit. However, because of its essentially kinematic origin, a similar effect in the decay distributions of heavier particles can also be expected. This should have interesting applications in obtaining the signatures of new particles which may be invisible in character. As an example, we consider in this note