Abstract
Motivated by the measurements of $b\to s\ell^+\ell^-$ transitions, including $R(K)$ and $R(K^*)$, we examine lepton flavour (universality) violation in $B$ decays and its connections to $\mu\to e\gamma$ in generic leptoquark models. Considering all 10 representations of scalar and vector leptoquarks under the Standard Model gauge group we compute the tree-level matching for semileptonic $b$-quark operators as well as their loop effects in $\ell\to\ell^\prime\gamma$. In our phenomenological analysis we correlate $R(K)$, $R(K^*)$ and the other $b\to s\mu^+\mu^-$ data to $\mu\to e\gamma$ and $b\to s\mu e$ transitions for the three leptoquark representations that generate left-handed currents in $b\to s\ell^+\ell^-$ transitions and, therefore, provide a good fit to data. We find that while new physics contributions to muons are required by the global fit, also couplings to electrons can be sizeable without violating the stringent bounds from $\mu\to e\gamma$. In fact, if the effect in electrons in $b\to s\ell^+\ell^-$ has opposite sign than the effect in muons the bound from $\mu\to e\gamma$ can always be avoided. However, unavoidable effects in $b\to s\mu e$ transitions (i.e. $B_s\to\mu e$, $B\to K\mu e$, etc.) appear which are within the reach of LHCb and BELLE II.
Highlights
The LHC completed the Standard Model (SM) of particle physics by discovering the Higgs boson, but it did not yet directly observe any particles beyond the ones already present in the SM
Taking this approach and including the new LHCb result [4] for RðKÃÞ 1⁄4 ðB → KÃμþμ−Þ=ðB → KÃeþe−Þ, measuring lepton flavor universality (LFU) violation, the global significance for new physics (NP) increased above the 5σ level [5]
We focus on the three LQ representations that can give a good fit to b → sμþμ− data for the phenomenological analysis: Φ3, V
Summary
The LHC completed the Standard Model (SM) of particle physics by discovering the Higgs boson, but it did not yet directly observe any particles beyond the ones already present in the SM. Due to an intriguing pattern in these anomalies, it is tempting to interpret them as an indirect hint for new physics (NP) [1,2,3] Taking this approach and including the new LHCb result [4] for RðKÃÞ 1⁄4 ðB → KÃμþμ−Þ=ðB → KÃeþe−Þ, measuring lepton flavor universality (LFU) violation, the global significance for NP increased above the 5σ level [5]. The article is structured as follows: we will fix our conventions for the LQ interactions and calculate the contributions to b → slþl− transitions and μ → eγ We present the complete tree-level matching of the 10 LQ representations
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