Detecting Higgs Bosons with Muons at Hadron Colliders

We investigate the prospects for the discovery of neutral Higgs bosons with a pair of muons by direct searches at the CERN Large Hadron Collider (LHC) as well as by indirect searches in the rare decay $B_s \to \mu^+\mu^-$ at the Fermilab Tevatron and the LHC. Promising results are found for the minimal supersymmetric standard model, the minimal supergravity (mSUGRA) model, and supergravity models with non-universal Higgs masses (NUHM SUGRA). For $\tan\beta \simeq 50$, we find that (i) the contours for a branching fraction of $B(B_s \to \mu^+\mu^-) = 1 \times 10^{-8}$ in the parameter space are very close to the $5\sigma$ contours for $pp \to b\phi^0 \to b\mu^+\mu^- +X, \phi^0 = h^0, H^0, A^0$ at the LHC with an integrated luminosity ($L$) of 30 fb$^{-1}$, (ii) the regions covered by $B(B_s \to \mu^+\mu^-) \ge 5\times 10^{-9}$ and the discovery region for $b\phi^0 \to b\mu^+\mu^-$ with 300 fb$^{-1}$ are complementary in the mSUGRA parameter space, (iii) in NUHM SUGRA models, a discovery of $B(B_s \to \mu^+\mu^-) \simeq 5\times 10^{-9}$ at the LHC will cover regions of the parameter space beyond the direct search for $b\phi^0 \to b\mu^+\mu^-$ with $L = 300$ fb$^{-1}$.