Anomalies and accidental symmetries: charging the scalar leptoquark under Lμ − Lτ

While the S3 scalar leptoquark presents a possible tree-level explanation of the b → sll flavour anomalies, it suffers from two conceptual problems which are often disregarded by model-builders. Firstly, the quantum numbers of the S3 allow for a renormalisable diquark operator that would trigger rapid proton decay unless its coupling were tuned away. Secondly, one expects the leptoquark to have generic couplings to leptons, which require tuning to avoid stringent experimental bounds on lepton flavour violation. By gauging a U(1) current that acts as Lμ − Lτ on the Standard Model (SM) fermions, and under which the leptoquark has charge −1, one can remedy both these problems. The additional U(1), which is spontaneously broken at some high scale, is associated with a massive Z′ gauge boson and a scalar SM singlet Φ, which play no direct role in mediating the anomalous B meson decays. By computing one- and two-loop mass corrections, we show that this pair of particles can be hidden away at much higher mass scales without destabilising either the Higgs or the leptoquark masses. The only low-energy relic of gauging Lμ − Lτ is thus the accidental global symmetry structure of the lagrangian. On the other hand, we find quite generally that an S3 leptoquark that mediates the b → sll anomalies cannot be much heavier than a few TeV without itself inducing large Higgs mass corrections.