Giacomo De Pietro
Paolo Branchini
Enrico Graziani
Search for an invisibly decaying $Z^{\prime}$ dark boson at Belle II in $e^+ e^- \to \mu^+ \mu^- (e^{\pm} \mu^{\mp})$ + missing energy final states
2020
2020
The Standard Model (SM) is a successful and highly predictive theory of fundamental particles and interactions. However, it cannot be considered as a complete description of nature due to the fact that many phenomena, including Dark Matter, are not accounted for. One of the simplest ways to extend the SM is by adding an extra $U(1)^{\prime}$ gauge group to the theory. An additional gauge boson, here called $Z^{\prime}$, would rise and couple to both SM and undiscovered particles such as dark matter constituents. We consider here the invisible decays of a $Z^{\prime}$ boson in two different models: 1) a $Z^{\prime}$ in the framework of a $L_{\mu}-L_{\tau}$ symmetry; 2) a Lepton Flavour Violating (LFV) $Z^{\prime}$ which couples to all leptons. Model 1) is poorly constrained at low masses, and the specific invisible decay topology is investigated here for the first time. At the moment, the only similar measurement in the framework of the $L_{\mu}-L_{\tau}$ symmetry has been performed by the BaBar experiment for a $Z^{\prime}$ decaying to muons. Under a $L_{\mu}-L_{\tau}$ symmetry, the $Z^{\prime}$ boson would couple only to $\mu$, $\tau$ and the respective $\nu_\mu$ and $\nu_\tau$ neutrinos among the SM particles, with a coupling constant $g^{\prime}$. The expected branching fractions (BF) to neutrino decays are predicted to vary between 33\% and 100\% depending on the $Z^{\prime}$ mass. In the case of kinematically accessible decays to Dark Matter particles $\chi$, we assume BF$(Z^{\prime} \to \chi \bar{\chi}) = 1$. As far as model 2) is concerned, we address our interest here only to the LFV $e-\mu$ coupling. In this work we test the $L_{\mu}-L_{\tau}$ $Z^{\prime}$ model in $e^+e^- \to \mu^+\mu^-$ + missing energy processes and perform a model-independent search for a LFV $Z^{\prime}$ in $e^+e^- \to e^{\pm}\mu^{\mp}$ + missing energy processes using the 2018 data set of the Belle II detector. Belle II operates at the SuperKEKB electron-positron collider at the KEK laboratory in Tsukuba, Japan. Data were collected from April to July 2018 during the so called Phase~2 commissioning run at the center-of-mass energy of the $\Upsilon$(4S) resonance peak. The total integrated luminosity, collected by the Belle II detector during 2018, used in this analysis is 276~pb$^{-1}$. The signal signature is a narrow peak in the distribution of the mass recoiling against the $\mu\mu$ system in the $L_{\mu}-L_{\tau}$ $Z^{\prime}$ analysis and the $e\mu$ in the LFV case. The analysis is performed selecting events with only two tracks, identified as $\mu\mu$ or $e\mu$, and minimal activity in the electromagnetic calorimeter are selected. The selection is optimized using simulated events prior to examining data for the standard $Z^{\prime}$. The same selection, aside from an electron in the final state, is adopted for the LFV $Z^{\prime}$. Control samples are then used to check the estimate of the background and to infer correction factors and related uncertainties. Upper limits to $g^\prime$ are computed by applying a counting technique for each bin of the recoil mass distribution. We found no significant excess and set for the first time 90\% Confidence Level (CL) upper limits to $g^\prime$ in the range from $\mathcal{O}(10^{-2})$ to 1. For the LFV $Z^{\prime}$ model-independent search, upper limits are interpreted in terms of signal efficiency times cross section. We found no significant excess and set for the first time 90\% CL upper limits to the efficiency times cross section of the order of 10~fb. A paper that summarizes the results presented in this work is prepared and submitted for publication to Physical Review Letters.