Higgs Bosons at Muon Colliders∗ M. S. Berger† Physics Department, Indiana University, Bloomington, IN 47405 (Dated: May 31, 2002) We review the role of a muon collider in the study of Higgs bosons via production in the s- channel. Very precise measurements of a Standard Model-like Higgs boson mass and total width can be performed, and may lead to a discrimination between a Standard Model Higgs boson and the light Higgs boson of the minimal supersymmetric theory. The heavier Higgs bosons from a supersymmetric theory or an exotic Higgs sector can be studied in the s-channel. A muon collider may play a crucial role in separating the overlapping signals for two heavy nearly degenerate Higgs bosons, and may play an important role in precision tests of radiative corrections in the Higgs sector. The measurements at a muon collider will be complementary to the Higgs studies at the Large Hadron Collider and at an electron-positron Linear Collider. I. INTRODUCTION Interesthasgrownrapidlyinmuoncollidersinthelastseveralyearsasitbecameclearthatthetechnological challenges might not be insurmountable[2]. Muon colliders are of interest to particle physics exploration for a number of reasons: a) the absence of significant bremsstrahlung allows one to contemplate circular accelerators of much higher energy than is possible with e+e− machines, b) the coupling of Higgs bosons is proportional to particle mass (see Fig. (1)), and hence there is the possibility that Higgs bosons can be produced in reasonable numbers in the s-channel[3, 4], c) there are regions of parameter space for which it will be impossible for either the Large Hadron Collider (LHC) or a Linear Collider (LC) to discover the heavier Higgs bosons of supersymmetry or, in the case of a general two-Higgs-doublet or more extended model, Higgs bosons of any mass with small or zero VV coupling, d) the neutrinos from the decays of muons can be used as a source for a neutrino factory[5, 6]. The large mass of the muon in comparison to that of the electron results in a number of advantageous features of a muon collider. The beam energy spreads of a muon collider can be very small, making them useful for studying narrow resonances like the SM Higgs boson. In addition, there is little bremsstrahlung, and the beam energy can be tuned to one part in a million through in situ spin-rotation measurements[7]. High rates of Higgs production at e+e− colliders rely on substantial VV Higgs coupling for the Higgs-strahlung process Z+Higgs or for the WW fusion process WW →Higgs (WW fusion). In contrast, a µ+µ− collider can provide a factory for producing a Higgs boson with little or no VV coupling so long as it has SM-like (or enhanced) µ+µ− couplings. Important examples of this last form of Higgs boson are the heavy neutral Higgs bosons H0 and A0 of the Minimal Supersymmetric Standard Model (MSSM). + − + − If the a light (∼< 130 GeV) Higgs boson exists, then both e e and µ µ colliders will be valuable; the Higgs boson would have been discovered at a previous higher energy collider (possibly a muon collider running at high energy), and then the Higgs factory would be built with a center-of-mass energy precisely tuned to the Higgs boson mass. The most likely scenario is that the Higgs boson is discovered at the LHC via gluon fusion (gg → H) or perhaps earlier at the Tevatron via associated production (qq¯ → WH,t tH), and its mass is determined to anaccuracyofabout100MeV.IfalinearcolliderhasalsoobservedtheHiggsviatheHiggs-strahlungprocess + − (e e → ZH), one might know the Higgs boson mass to better√ than 50 MeV with an integrated luminosity of −1 500 fb . The muon collider would be optimized to run at s ≈ mH , and this center-of-mass energy would be varied over a narrow range so as to scan over the Higgs resonance. ∗SubmittedtotheProceedingsof“TheFutureofParticlePhysics”,Snowmass2001,P1group.Anexpandedversionofthe Physics of Higgs Factories has been submitted to the E1 Group[1]. †[email protected] P114 2 µ+ b (t ) h µ− b (t ) ~mµ ~mb (mt) FIG. 1: Feynman diagram for s-channel production of a Higgs boson. II. SM-LIKE HIGGS BOSONS The production of a Higgs boson (generically denoted h)inthes-channel with interesting rates is a unique feature of a muon collider [3, 4]. The resonance cross section is √ 4πΓ(h → µµ¯)Γ(h → X) σh( s)= . (1) 2 2 2 h 2 (s − mh) + mh Γtot In practice, however, there is a Gaussian spread (σ√ ) to the center-of-mass energy and one must compute the s √ effective s-channel Higgs cross section after convolution assuming some given central value of s: √ √ 2 √ − − √ √ √ s s s=mh → → √ 1 4π BF(h µµ¯) BF(h X) σh( s)= σh( s) exp 2 d s 2 . (2) √ 2σ√ m 2 1/2 2πσs s h σ√ 8 s 1+ π Γtot h √ It is convenient to express σ s in terms of the root-mean-square (rms) Gaussian spread of the energy of an individual beam, R: √ R s σ√ = (2 MeV) . (3) s 0.003% 100 GeV √ < tot It is clear from Eq. (1) that a resolution σ s ∼ Γh is needed to be sensitive to the Higgs width. Furthermore, Eq. (2) indicates that BF(h → µµ) must not be extremely suppressed for there to be large event rates for Higgs ∼ production. The width of a light SM-like Higgs is very small (e.g. a few MeV for mhSM 110 GeV), implying the need for R values as small as ∼ 0.003% for studying a light SM-like h. In addition to the very small beam energy spread, one must also be able to determine very accurately the beam energy to perform a scan over such a narrow resonance. This can be accomplished utilizing the spin precession of the muon noted above. A sample scan is illustrated in Fig. 2 for a mhSM = 110 GeV SM Higgs boson. The SM Higgs cross sections and backgrounds as well as the integrated luminosity required for a 5σ signal are shown in Fig. 3 for R =0.003% and mhSM values such that the dominant decay mode is bb. The significance of the signal is impacted by two physical processes: 1) For a Higgs mass near the Z-pole there is a significant background from µ+µ− → Z → bb. However the most recent experimental results from LEP have pushed the tot SM Higgs mass bound well above 91 GeV. 2) For a Higgs mass ∼> 130 GeV, the Higgs width Γh becomes much larger as the WW decay channel opens up. The Higgs bosons in supersymmetric models are in general detectable at muon colliders. If the masses of the supersymmetric particles are large, the Higgs sector typically exhibits decoupling behavior in which the 0 lightest supersymmetric Higgs boson h will be very similar to the hSM when the other Higgs bosons are heavy, 0 and the h rates will be very similar to hSM rates. On the other hand, the heavier Higgs bosons in a typical supersymmetric model decouple from pairs of gauge bosons VV at large mass and remain reasonably narrow P114 3 √ FIG. 2: Number of events and statistical errors in the bb final state as a function of s in the vicinity of mhSM = 110 GeV, assuming R =0.003%, and L =0.00125 fb−1 at each data point. (< 1 GeV unless the tt decay mode is open). As a result, their s-channel production rates remain large, and a muon collider can avoid the production channels that depend on a sizable coupling to gauge bosons. What can a muon collider add to the LHC and LC? The LHC and quite likely a linear collider will be available already, and the Higgs boson will be detected and some of its properties determined before a muon collider will become operational. Current expectations for the luminosity at an LC are 500 fb−1 over 1-2 years. This yields a SM Higgs boson production rate of greater than 104 per year in the process e+e− → Zh. Therefore the latest estimates of the luminosity at a linear collider yield numbers of Higgs bosons that are comparable to what will be available at a muon collider/Higgs factory with its more modest integrated luminosity (expected with the current machine parameters) of the order of one inverse femtobarn. A linear collider with such high luminosity can certainly perform quite accurate measurements of certain Higgs parameters such as the Higgs mass, couplings to gauge bosons, couplings to heavy quarks, etc.[8]. The s-channel production process allows one to determine the mass, total width, and the cross sections + − σh(µ µ → h → X) for several final states X to very high precision. The Higgs mass, total width and the cross sections can be used to constrain the parameters of the Higgs sector. For example, in the MSSM their precise values will constrain the Higgs sector parameters mA0 and tan β (where tan β is the ratio of the two vacuum expectation values (vevs) of the two Higgs doublets of the MSSM). The main question is whether these constraints will be a valuable addition to LHC and LC constraints. Precise measurements of the couplings of the Higgs boson to the Standard Model particles are important tests of the mass generation mechanism. In the Standard Model with one Higgs doublet, this coupling is proportional to the particle mass. In the more general case there can be mixing angles present in the couplings. Precision measurements of the couplings can distinguish the Standard Model Higgs boson from the SM-like Higgs boson typically present in a more general model.