Loop effects of heavy new scalars and fermions in $b\to s\mu^+\mu^-$

Recent measurements of $b\to s\mu^+\mu^-$ processes at LHCb and BELLE have revealed tensions at the $2-3\,\sigma$ level between the Standard Model (SM) prediction and the experimental results in the channels $B\to K^*\mu^+\mu^-$ and $B_s\to\phi\mu^+\mu^-$, as well as in the lepton-flavor universality violating observable $R_K={\rm Br}(B\to K\mu^+\mu^-)/{\rm Br}(B\to Ke^+e^-$). Combined global fits to the available $b\to s\mu^+\mu^-$ data suggest that these tensions might have their common origin in New Physics (NP) beyond the SM because some NP scenarios turn out to be preferred over the SM by $4-5\,\sigma$. The fact that all these anomalies are related to muons further suggests a connection (and a common NP explanation) with the long-standing anomaly in the anomalous magnetic moment of the muon, $a_\mu$. In this article, we study the impact of a generic class of NP models featuring new heavy scalars and fermions that couple to the SM fermions via Yukawa-like interactions. We consider two different scenarios, introducing either one additional fermion and two scalars or two additional fermions and one scalar, and examine all possible representations of the new particles under the SM gauge group with dimension up to the adjoint one. The models induce one-loop contributions to $b\to s\mu^+\mu^-$ and $a_\mu$ which are capable of solving the respective anomalies at the $2\sigma$ level, albeit a relatively large coupling of the new particles to muons is required. In the case of $b\to s\mu^+\mu^-$, stringent constraints from $B_s-\overline{B}_s$ mixing arise which can be relaxed if the new fermion is a Majorana particle.