Search for muon-philic new light gauge boson at Belle II

Motivated by the long-lasting $3.5\sigma$ discrepancy in the anomalous magnetic moment of muon, we consider a new muon-specific force mediated by a light gauge boson, $X$, with mass $m_X < 2m_\mu$ and the coupling constant $g_X \sim (10^{-4}, 10^{-3})$. We show that the Belle~II experiment has a robust chance to probe such a light boson in $e^+ e^- \to \mu^+ \mu^- + X$ channel and cover the most interesting parameter space explaining the discrepancy with the planned target luminosity, $\int dt \ {\cal L}=50~{\rm ab^{-1}}$. The clean signal of muon-pair plus missing energy at Belle II can be a smoking gun for the new gauge boson. We expect that the (invisibly decaying) muon-philic light ($m_X \leq 2 m_\mu$) gauge boson can be probed down to $g_X \geq 1.5 \times 10^{-4} \ (4.6 \times 10^{-4}, \ 2.3 \times 10^{-4})$ for 50 (1, 10) ab${}^{-1}$ search.