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

Motivated by the long-lasting 3.5σ 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_μ and the coupling constant gX ∼ (10⁻⁴, 10⁻³). We show that the Belle II experiment has a robust chance to probe such a light boson in e⁺e⁻ → μ⁺μ⁻ + X channel and cover the most interesting parameter space explaining the discrepancy with the planned target luminosity, ∫dtL=50ab−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 ≲ 2m_μ) gauge boson can be probed down to g_X ≲ 1.5 × 10⁻⁴(4.6 × 10⁻⁴, 2.3 × 10⁻⁴) for 50 (1, 10) ab⁻¹ search.