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In this paper, we perform a complete one-loop computation of theshort-distance Wilson coefficients for $B_{s,d}-\bar{B}_{s,d}$ mixings and$B_{s,d}\to\ell^+\ell^-$ decays in the Manohar-Wise model, which extends the SMscalar sector by a colour-octet and weak-doublet scalar. Based on thesecalculations, combined constraints on the model parameters are derived from thecurrent flavour data, including the $B_{s,d}-{\bar{B}}_{s,d}$ mixings,$B_{s,d}\to\mu^+\mu^-$, $B\to X_s\gamma$, $B\to K^{\ast}\gamma$,$B\to\rho\gamma$, and $Z\to b \bar{b}$ decays. The future sensitivity to themodel is also explored in the observables achievable with $50~{\rm fb}^{-1}$ ofLHCb and $50~{\rm ab}^{-1}$ of Belle-II data. We find that the Manohar-Wisemodel could explain the current data, especially when the couplings of thecharged colour-octet scalars to quarks are complex, with the resulting$\chi^2_{\rm min}$ being significantly smaller than that of the SM. Finally, weinvestigate correlations among the two isospin asymmetries $\Delta(K^*\gamma)$and $\Delta(\rho\gamma)$, as well as the averaged time-integrated branchingratios $\bar{{\mathcal B}}(B_{s,d}\to \mu^+\mu^-)$; some of them are found tobe quite strong and could, therefore, provide further insights into the model,once more precise experimental measurements and theoretical predictions forthese observables are available in the future.

$B_{s,d}-\bar{B}_{s,d}$ mixings and $B_{s,d}\to\ell^+\ell^-$ decays within the Manohar-Wise model