Measurements of the local and non-local contributions in $B^{\pm}\rightarrow K^{\pm}\mu^{\pm}\mu^{\mp}$ decays using LHCb data

In the study of the decay of B mesons, the observed deviations from standard model predictions could potentially be explained by underestimated non-local hadronic intermediate states. To answer this question, the local and non-local contributions to $B^{\pm}\rightarrow K^{\pm}\mu^{\pm}\mu^{\mp}$ decays are measured by analysing the invariant dimuon mass distribution in the range: $300 < m_{\mu\mu} < 4700 MeV/c^{2}$} {($0.09 < q^2 < 22.09 GeV^{2}/c^{4}$). The analysis uses pp collision data collected by the LHCb experiment between 2011 and 2018 corresponding to an integrated luminosity of 9 $fb^{-1}$. The non-local contributions are modelled using hadronic dispersion relations including a description of intermediate one-particle and two-particle states which scatter to a pair of muons. The largest one-particle states interfering with the local contribution are $J/\psi$ and $\psi (2S)$ and the two-particle states described are $DD$, $D^{*}D^{*}$ and $DD^{*}$. The interference from $J/\psi$ is observed to be small while a large component of the two-particle states, along with the $\psi (2S)$, is observed to destructively interfere with the local contribution. The effect of this interference on the vector current ($C_{9}$) and axial-vector current ($C_{10}$) Wilson coefficients, which encode heavy standard model and beyond standard model physics, are discussed. The branching fractions of the one-particle and two-particle states are also measured.