Search for $Z^{\prime }\to {\mu }^{+}{\mu }^{-}$ in the $L_{\mu }-L_{\tau }$ gauge-symmetric model at Belle

We search for a new gauge boson $Z^{\prime }$ that couples only to heavy leptons and their corresponding neutrinos in the process $e^{+}{e}^{-}\to Z^{\prime }(\to {\mu }^{+}{\mu }^{-}){\mu }^{+}{\mu }^{-}$, using a $643{\mathrm{fb}}^{-1}$ data sample collected by the Belle experiment at or near the $\mathrm{\Upsilon }(1S,2S,3S,4S,5S)$ resonances at the KEKB collider. While previous searches for $Z^{\prime }$ performed a data-based estimation of the initial state radiation effect, our search for the $Z^{\prime }$ is the first to include effects due to initial state radiation in the signal simulated samples that were used in estimating the detection efficiency. No signal is observed in the $Z^{\prime }$ mass range of $0.212–10\mathrm{GeV}/c^2$, and we set an upper limit on the coupling strength, $g^{\prime }$, constraining the possible $Z^{\prime }$ contribution to the anomalous magnetic dipole moment of the muon.

Figure 1

Feynman diagram for the main production channel of the $Z^{\prime }$ in $e^{+}{e}^{-}$ colliders.

Figure 2

Top: Reduced mass, $m_R$, distributions. Red points represent the data after all selection criteria are applied. Black squares represent the non-ISR MC expectation for the $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ (Diag36) [41] scaled to the data luminosity. Bottom: The ratio between data and the non-ISR $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ MC expectation. The red line represents a fit of a first order polynomial where its constant term is $0.700\pm 0.003$ and the slope term is negligible. Both: Black shaded region at $3.1\mathrm{GeV}/c^2$ represents the $J/\psi$ region which is not used in this analysis.

Figure 3

Top: Detection efficiency as a function of the reduced mass. Red points represent values with ISR correction. Open blue squares represent values without it. Bottom: Ratio between ISR and non-ISR detection efficiencies linearly fit. The average constant value from a linear and constant fit is $0.741\pm 0.001$.

Figure 4

Local signed significance values.

Figure 5

The solid blue curve represents a fit to the data of a sum of two Crystal Ball functions added to a third-order polynomial. The dashed red and green curves represent the third-order polynomial and the sum of two Crystal Ball functions, respectively.

Figure 6

Number of observed signal events ($N_{\mathrm{obs}}$) from the fit for the different $Z^{\prime }$ mass hypotheses.

Figure 7

90% C.I. upper limit on the Born cross section for $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}(Z^{\prime }\to {\mu }^{+}{\mu }^{-})$ as a function of $m_{Z^{\prime }}$.

Figure 8

90% C.I. upper limit on $g^{\prime }$ as a function of $m_{Z^{\prime }}$. The red solid is the Belle result. The black dotted line represents the BABAR results [33], the light gray shaded area is the result of CCFR, and the light purple hashed area is the result of CHARM-II over the $Z^{\prime }$ parameter space [23, 48], and the green region indicates the values of the $Z^{\prime }$ coupling needed to explain $(g-2{)}_{\mu }$ suggested by the Muon $g-2$ Collaboration [17, 20].