In the energy range of LHC discoveries, a lepton collider with high luminosity and high resolution will be necessary to both decifer possible intricated signals from LHC, and perform precision measurements. A muon collider has been invented and designed by the muon collider collaboration. This would be a tool of choice in this endeavour, because it has superior center-of-mass energy resolution and determination using muon g-2 spin precession. The energy spread also needs to be determined, though, for reasons that will become clear below.

A special feature of muons is that the Yukawa coupling to the Higgs is proportionnal to the muon mass, therefore much larger than with electrons. The Higgs can be produced with a useful cross-section in the s-channel! The above figure represents a scan of the Higgs resonance that was simulated by Bill Murray . This is the Jewel on the crown , as our american colleagues like to put it. He also addressed issues such as luminosity measurement and b-tagging.

Cool physics, if the Higgs happens to be in the energy range between 100 and 160 GeV. As is well known, things degrade rapidly if the Higgs mass is above twice the W mass, as all interesting decay modes are washed out by decays into W pairs and then Z pairs. See for instance the presentation by Fernand Renard on the possibility to measure the Higgs couplings. (full paper)

In supersymmetry, the precision measurement of the Higgs boson mass and width, and especially the cross-section at the top of the resonance, bring substantial constraints on the model parameters, as studied by Patrick Janot .

In a more general framework of symmetry breaking by new strong forces (technicolor type), the muon collider is a tool of choice as narrow and close by resonances often occur. Paper by Roberto Casalbuoni et al.

With muons, ISR is somewhat reduced (the big Log is halved) with respect to electrons. This sharpens narrow resonances or thresholds line shapes, see e.g. the Z line shape with muons. The effect of this, as well as the effect of the Yukawa coupling of the muon to the Higgs are clearly visible in GRACE simulations by Denis Perret-Gallix (transparencies)

Muon polarisation is limited by the requirement of a large acceptance at the muon production source. This limits its usefulness for enhancing signal over background for e.g. the Higgs resonance. Nevertheless, the fact that muons of both signs are polarised is very convenient for precision measurements at the Z peak, as studied by Alain Blondel who considered the "boring" idea of a muon collider as Z factory.

Alain Blondel