New Physics in $b\to s\mu \mu$: FCC-hh or a Muon Collider?

Abstract

Rare flavour-changing neutral-current transitions $b\to s{\mu }^{+}{\mu }^{-}$ probe higher energy scales than what is directly accessible at the LHC. Therefore, the presence of new physics in such transitions, as suggested by the present-day LHCb anomalies, would have a major impact on the motivation and planning of future high-energy colliders. The two most prominent options currently debated are a proton-proton collider at 100 TeV (FCC-hh) and a multi-TeV muon collider (MuC). In this work, we compare the discovery prospects at these colliders on benchmark new physics models indirectly detectable in $b\to s{\mu }^{+}{\mu }^{-}$ decays but beyond the reach of the high-$p_T$ searches at the HL-LHC. We consider a comprehensive set of scenarios: semileptonic contact interactions, $Z^{\prime }$ from a gauged $U(1{)}_{B_3-L_{\mu }}$ and $U(1{)}_{L_{\mu }-L_{\tau }}$, the scalar leptoquark $S_3$, and the vector leptoquark $U_1$. We find that a 3 TeV MuC has a sensitivity reach comparable to the one of the FCC-hh. However, for a heavy enough mediator, the new physics effects at a 3 TeV MuC are only observed indirectly via deviations in the highest energy bin, while the FCC-hh has a greater potential for the discovery of a resonance. Finally, to completely cover the parameter space suggested by the $bs\mu \mu$ anomalies, among the proposed future colliders, only a MuC of 10 TeV (or higher) can meet the challenge.

v2: 38 pages + references, 19 figures. Added summary plot and other minor changes. Version published in JHEP

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