Measurement of the local and nonlocal amplitudes in $B^{+}\to K^{+}μ^{+}μ^{-}$ decays

Abstract

This paper presents a thorough study of the local and nonlocal amplitudes in $B^+ \to K^+μ^+μ^-$ transitions through an amplitude analysis of the dimuon mass spectrum of the decay. The analysis is based on $pp$ collision data corresponding to an integrated luminosity of 8.4fb$^{-1}$ collected by the LHCb experiment. This measurement employs a model that describes both one-particle and two-particle nonlocal amplitudes across the entirety of the dimuon mass spectrum, enabling the determination of both short- and long-distance contributions to the decay. The compatibility of the Wilson coefficient combinations $C_9+C_9'$ and $C_{10}+C_{10}'$ with the Standard Model prediction is found to vary between $1.6\,σ$ and $4\,σ$, depending on the choice of local form factors.

Figures (6)

• Figure 1: The efficiency functions $\mathcal{E}_{+C_{A}\xspace}$, $\mathcal{E}_{0C_{A}\xspace}$, and $\mathcal{E}_{+C_{V}\xspace}$ given in Eqs. \ref{['eq:eff_fpc10']}, \ref{['eq:eff_fzc10']}, and \ref{['eq:eff_fpc9']} respectively. The bands represent the statistical uncertainty due to the size of the simulation sample.
• Figure 2: The fit to the reconstructed $m_{K\mu\mu}$ mass distribution in (top left) region-1, (top right) region-2, and (bottom) region-3 corresponding to the $m_{\mu\mu}$ ranges defined in Table \ref{['tab:conv_regions']}.
• Figure 3: Fit to the $m^{\rm rec}_{\mu\mu}$ distribution using form factors from the HPQCD collaboration Parrott:2022rgu for: (top left) negative ${\mathrm{J}\xspace / \uppsi\xspace}$ phase, positive $\uppsi\xspace{(2S)}$ phase; (top right) positive ${\mathrm{J}\xspace / \uppsi\xspace}$ phase, positive $\uppsi\xspace{(2S)}$ phase; (bottom left) negative ${\mathrm{J}\xspace / \uppsi\xspace}$ phase, negative $\uppsi\xspace{(2S)}$ phase; (bottom right) positive ${\mathrm{J}\xspace / \uppsi\xspace}$ phase, negative $\uppsi\xspace{(2S)}$ phase.
• Figure 4: Likelihood profiles of $C_{V}$ and $C_{A}$ resulting from a fit to the data using the $B^+\rightarrow\xspace K^+$ local form-factor determination from (left) the HPQCD collaboration Parrott:2022rgu and (right) the FNAL/MILC collaboration Bailey:2015dka. The different curves correspond to the 68.3%, 95.4% and 99.7% confidence intervals that include systematic uncertainties. The SM point is shown as a star.
• Figure 5: Likelihood profile of (left) $C_{9}\xspace$ while fixing $C_{10}\xspace$ to the SM value, and (right) $C_{10}\xspace$ while fixing $C_{9}\xspace$ to the SM value. In both cases, $C_{9}\xspace'$ and $C_{10}\xspace'$ are set to their SM value of zero, and the HPQCD local form-factor computations are used. The 68.3%, 95.4% and 99.7% confidence intervals are indicated as green bands and include systematic uncertainties. The SM point (star) is also shown.