Measurement of Lepton Universality Ratio at Belle II

Decays mediated by the flavour-changing neutral current transition \(b \rightarrow s \ell ^+ \ell ^-\) are not allowed at tree level in the standard model (SM) and can only proceed via higher-order loop diagrams. Such suppressed decays provide an excellent avenue to search for physics beyond the SM. The \(B \rightarrow K \ell \ell \) ( \(\ell = e, \mu \) ) decays have recently sparked a lot of interest in a measurement related to the lepton-flavour-universality ratio \(R_{K}\) which is the ratio of the muon to electron channel branching fraction. Belle II, which has been recording \(e^+e^-\) collision data since 2019, provides a complementary experimental setup to confirm this discrepancy. The \(B \rightarrow J/\psi (\ell ^+ \ell ^-) K\) decays, in contrast to suppressed, charmless \(B \rightarrow K \ell \ell \) decays, involve the favoured \(b \rightarrow c\) tree-level transition, where beyond-the-SM contributions are expected to be negligible. Thus, a measurement of \(R_{J/\psi }\) and its consistency with unity would be a strong validation of the future \(R_{K}\) measurement in the charmless counterpart. We present our recent findings from Belle II data on \(R_{J/\psi }\) isospin asymmetry, and the branching fraction of \(B \rightarrow J/\psi (\ell ^+ \ell ^-) K\) decays.