arXiv:hep-ph/0202199v1 21 Feb 2002
Physics Opportunities at µ+µ−Higgs Factories∗
C. Bl¨ ochingera, M. Carenab, J. Ellisc, H. Fraasa, F. Frankea, D. Garciac, S. Heinemeyerd, S. Kramlc,e,
G. Moortgat-Pickf, W. Murrayg, F. von der Pahlena, A. Pilaftsisa,h, C.E.M. Wagneri,jand G. Weigleinc,k
a Inst. f. Theoretische Physik und Astrophysik, Univ. W¨ urzburg, D-97074 W¨ urzburg, Germany
b Fermilab, P.O. Box 500, Batavia IL 60510, U.S.A.
c Theory Division, CERN, CH-1211 Geneva 23, Switzerland
d HET, Physics Department, Brookhaven Natl. Lab., Upton, NY 11973 USA
e Inst. f. Hochenergiephysik,¨Osterr. Akademie d. Wissenschaften, A-1050 Vienna, Austria
f DESY, Deutsches Elektronen-Synchrotron, D-22603 Hamburg, Germany
g RAL, Chilton, Didcot, Oxon., OX11 0QX, UK
h Department of Physics and Astronomy, Univ. of Manchester, Manchester M13 9PL, U.K.
i High Energy Physics Division, Argonne National Lab., Argonne IL 60439, U.S.A.
j Enrico Fermi Institute, University of Chicago, 5640 Ellis Ave., Chicago IL 60637, U.S.A.
k Institute for Particle Physics Phenomenology, University of Durham, Durham DH1 3LR, UK
We update theoretical studies of the physics opportunities presented by µ+µ−Higgs fac-
tories. Interesting measurements of the Standard Model Higgs decays into¯bb, τ+τ−and
WW∗may be possible if the Higgs mass is less than about 160 GeV, as preferred by
the precision electroweak data, the mass range being extended by varying appropriately
the beam energy resolution. A suitable value of the beam energy resolution would also
enable the uncertainty in the b-quark mass to be minimized, facilitating measurements
of parameters in the MSSM at such a first µ+µ−Higgs factory. These measurements
would be sensitive to radiative corrections to the Higgs-fermion-antifermion decay ver-
tices, which may violate CP. Radiative corrections in the MSSM may also induce CP
violation in Higgs-mass mixing, which can be probed via various asymmetries measur-
able using polarized µ+µ−beams. In addition, Higgs-chargino couplings may be probed
at a second µ+µ−Higgs factory.
Muon colliders produce Higgs bosons directly via µ+µ−annihilation in the s-channel, unaccompanied by spec-
tator particles. If the electroweak symmetry is broken via the Higgs mechanism, hadron machines, such as the
Tevatron collider  and the LHC , will presumably discover at least one Higgs boson, but in an experimental
environment contaminated by important backgrounds and accompanied by many other particles. An e+e−linear
collider (LC) [3, 4, 5] would complement the hadron colliders by providing precise studies of the Higgs boson in a
clean environment. However, the dominant production mechanisms create Higgs bosons in association with other
particles, such as a Z0, two neutrinos or an e+e−pair. Moreover, the peak cross section for a µ+µ−collider to
produce a Higgs of 115 GeV is around 60 pb, which can be compared with around 0.14 pb for an e+e−collider
operating at 350 GeV.
∗Report of the Higgs factory working group of the ECFA-CERN study on Neutrino Factory & Muon Storage Rings at CERN.
The potential of µ+µ−colliders for investigations of the Higgs system is very exciting, and has been the
subject of much work, see, e.g., [6, 7, 8]. However, if the study of an s-channel resonance is to be pursued
experimentally, the event rate must be sufficiently large. In the case of a Standard Model (SM) Higgs boson H,
this means that the mass must be somewhat less than twice MW, otherwise the large width reduces the peak cross
section. This condition need not apply to more complicated Higgs systems, for instance the heavier neutral Higgses
Since a µ+µ−collider is able to work near optimally over only a limited range of centre-of-mass energies,
knowledge of the Higgs mass is crucial in designing such a machine. A combined fit to precision electroweak
observables yields an indirect estimate for the SM Higgs boson mass of
mH = 88+53
with a one-sided 95% confidence-level upper limit of 196 GeV , including theoretical uncertainties. These
numbers are increased by about 20 GeV if one uses the estimate  of the effective value of αemat the Z0peak.
The range (1.1) should be compared with the lower limit from direct searches of 114.1 GeV , and suggests
that the most probable value for the Higgs mass is not much greater than this lower limit , as seen in Fig. 1.
The analysis leading to Fig. 1 is valid within the Standard Model, or any new physics extension of it in which
the new physics effects decouple from the precision electroweak observables, as occurs for example in minimal
supersymmetric extensions of the Standard Model, when all supersymmetric particle masses are above the weak
Fig. 1: Probability distribution for the mass of the SM Higgs boson, estimated  by combining the available indirect information with
the LEP direct lower limit . The shaded region represents 50% of the probability distribution.
In fact, the 2000 run of the LEP collider yielded a 2.1 σ excess in the search for the SM Higgs boson, with
a preferred mass of 
mH = 115.6+1.4
The excess seen is consistent with the expectations from such a signal: the most significant candidate events have
been seen in the H →¯bb decay mode, with Z0→ ¯ qq, and the production cross section is quite compatible with that
expected for a SM Higgs boson. The mass (1.2) is highly consistent with the range (1.1). Moreover, both are also
highly compatible with the minimal supersymmetric extension of the Standard Model (MSSM), which predicts
the existence of a light Higgs boson weighing less than about 130 GeV . If the observation (1.2) were to be
confirmed, it would provide an excellent opportunity for a µ+µ−collider Higgs factory. As was outlined in , the
measurement of the H →¯bb decay mode for a mass around 100 GeV suffers from excessive background if mHis
close to the Z peak, and from the rapidly-increasing Higgs width, and therefore reduced on-peak cross section, as
mHincreases toward the W+W−threshold. The optimal Higgs mass identified in  was in fact 115 GeV.
In the coming years, first the Tevatron collider  and subsequently the LHC  will have opportunities to
discover the SM Higgs boson. In the case of the (constrained) MSSM, it has been shown that the prospects for the
lightest Higgs boson are nearly as good as for the SM . One may expect to measure the mass of the SM or
MSSM Higgs boson at the hadron colliders with a precision better than 1 GeV. Detailed follow-up measurements
would then be possible with an e+e−linear collider [3, 4, 5]. Unfortunately, the existence of a Higgs boson
weighing 115 GeV will probably not be clarified by the Tevatron collider or the LHC for several more years.
On the other hand, much work is still required before the feasibility of a µ+µ−collider can be demonstrated.
We recall that the muon collection and storage facility foreseen for a µ+µ−collider has many parameters in
common with those required for a neutrino factory , whose storage ring requires 1014muons per second to be
injected withapreferred energy of50GeV.Thisenergy isclose tothat required forafirst-generation µ+µ−collider.
However, a µ+µ−collider would need about an order of magnitude more muons than are foreseen in the neutrino
factory, and it is not yet clear what combination of higher-efficiency beam preparation and increased proton power
will be the most effective way to achieve this. Moreover, the normalised emittance envisaged for a neutrino factory
is 1.67 mm.rad, whereas 0.2 mm.rad is anticipated in µ+µ−collider designs . Thus, considerably more beam
cooling would be required for a µ+µ−collider. We recall also that the bunch structure foreseen for a neutrino
factory, namely a train of 140 bunches injected at 75 Hz, would need to be modified. The luminosity of a collider
scales with the square of the bunch current squared multiplied by the repetition rate. To convert the neutrino
factory into a muon collider, the basic repetition rate of 75 Hz is quite suitable, but one requires just one bunch in
each cycle. If this can be done, and a six-dimensional emittance of 1.7 × 10−10(πm)3can be achieved , a
luminosity of 1031cm−2s−1may be achieved, colliding beams with an energy spread of 0.01%.
In this report, we revisit first the physics prospects for µ+µ−collider SM Higgs factories, examining in
particular two effects that were overlooked in . One is the WW∗decay mode, which is rather clean and has a
branching ratio of at least 8% in the SM. The other is the effect of the beam energy spread, for which we consider
values larger than the 0.003% considered previously. In this way, the range of SM Higgs masses for which useful
measurements of the cross sections can be made extends up to about 160 GeV.
We recall that there is a richer Higgs sector in the MSSM, including three neutral Higgs bosons h, H and
A, where the first two have scalar couplings in the CP-conserving limit, and the latter pseudoscalar couplings.
As was also discussed in  there, are excellent prospects for a µ+µ−collider tuned to the similar masses of
the heavier neutral Higgs bosons H,A. If they weigh several hundred GeV or more, these might be difficult to
observe and study at the LHC or a linear e+e−collider. A Higgs boson weighing as little as 115 GeV is not only
consistent with supersymmetry, but even seems to require something very like it, if the effective Higgs potential
is not to become unstable at a relatively low energy scale . Thus, confirmation of the hint (1.2) would also be
a strong encouragement to envisage a second µ+µ−Higgs factory, even if the H and A have not been observed
directly. In this context we study the influence of supersymmetric radiative corrections on the peak cross sections
and branching ratios of h,H,A compared to a SM Higgs boson.
Both the first µ+µ−h factory (FMC) and the second µ+µ−(H,A) factory (SMC) will provide unique op-
portunities to study CP violation in the Higgs sector of the MSSM . There have recently been improved studies
of this possibility , in the light of which we revisit here the prospects for measuring various CP-violating ob-
servables at µ+µ−colliders. Finally, we also discuss the prospects for measuring the H,A couplings to charginos
at such a second µ+µ−(H,A) factory.
2 CP-Conserving Studies
The effective cross section for Higgs production at√s ∼ mHis obtained by convoluting the standard s-channel
Breit-Wigner resonance with the beam energy distribution, which we model as a Gaussian distribution with width
σE. At√s = mH, initial-state radiation (ISR) effects can be approximated by a constant reduction factor η, where
η is a function of the various parameters, α, mH, mµ, ..., that we do not discuss here. In the limit Γ ≪ mH, quite
a compact expression can be derived for the peak cross section:
The µ+µ−→ H → X Cross Section
σpeak= σ(√s = mH) =4π B(H → µ+µ−)B(H → X)
ηπ1/2AeA2(1 − Erf(A)),
The peak cross section depends critically on the beam-energy spread σEcompared to the resonance width Γ. There
are two important limits:
σE≪ Γ⇒σpeak=4π ηB(H → µ+µ−)B(H → X)
√2π3η Γ(H → µ+µ−)B(H → X)
Figure 2(a) shows the√s dependence of σ(µ+µ−→ H → b¯b) for a SM Higgs boson HSMweighing 115 GeV,
compared with that the lightest MSSM Higgs boson, denoted here by HMSSM, for various values of the beam-
energy resolution R ≡
Fig. 2(b). As can be seen, σpeakreaches a plateau for R ≪ Γbb/mH, in accordance with (2.5), (2.6). Note also
that the resonance is washed out in the limit Γ/σE→ 0.
√2σE/√s. ISR is neglected. The peak cross section is plotted as a function of R in
114.0 114.5 115.0115.5 116.0
CoM energy [GeV]
MH=115 GeV, µ=MSUSY=−At=1TeV, Ab=0
MH=115 GeV, µ=MSUSY=−At=1TeV, Ab=0
Fig. 2: (a) Cross sections for µ+µ−→ H → b¯b as functions of√s for SM and MSSM Higgs bosons, and (b) R dependences of the peak
cross sections, for mb(mb) = 4.15 GeV (solid lines) and mb(mb) = 4.45 GeV (dashed lines).
As has been discussed previously, not only is the beam energy spread at a µ+µ−collider potentially very
small, but also the energy can be calibrated very accurately using the decays of polarized muons in the circulating
beams. The very fine energy resolution and precision in√s expected at the µ+µ−collider would allow the
properties of the Higgs boson(s) to be determined with outstanding accuracy. One expects, for instance, to be able
to measure the mass and width of a light (mH< 2MW) Higgs boson to fractions of an MeV. If σE
procedure is to simply scan the resonance, as was studied in detail in [19, 6, 7, 8]. For a very narrow resonance,
e.g., for a light SM Higgs boson, it may, however, be that σE
luminosity. In this case it is of advantage to operate the collider at√s = mHand two different beam energy
≪ Γ and σmax
the peak cross sections:
∼Γ, the best
∼Γ can only be achieved with substantial loss of
≫ Γ . One can then determine the width of the resonance from the ratio of
) = [2√2σmin
The width of the SM Higgs boson is shown as a function of its mass in Fig. 3(a), as a line with triangles.
Also shown, with solid circles, is the spread in the centre-of-mass energy for a collider with R = 0.003%. The
open squares correspond to the spread in the centre-of-mass energy which is obtained if R is varied so that the
beam energy spread is always 40% of the Higgs width. It is assumed here that any value of R can be obtained,
and that the luminosity scales as R2/3. This procedure approximately optimises the Higgs production rate, and
hence the statistical error on the Higgs cross-section. Tighter beam energy spreads have lower luminosities, while
increasing the spread reduces the Higgs cross-section. Figure 3(b) shows how the reduction factor given in (2.3)
reduces the peak cross section in the two cases.
The decay mode H → bb was investigated in , and those results are updated in Fig. 3(c), taking account
of the loss in peak cross section. The suppression is less important as the mass, and hence the width, rises. This
means that the performance for mH = 140 GeV is almost the same as for mH = 115 GeV. We also display
results for the WW∗decay mode, which is rather clean and has at least an 8% branching ratio in the SM. The
accuracy of the width measurement obtainable at a µ+µ−collider in this channel is estimated by assuming that the
efficiency and background achieved by the DELPHI collaboration in measuring WW production at 161 GeV
can be duplicated. This includes the conservative assumption that the spin information is not used to reduce the
non-resonant WW background. We note that for MH= 115 GeV a 6% error on the bb cross-section and 32% on
the WW∗are expected per 300 pb−1, or three years of running.
The decay mode H → τ+τ−is also an important channel, which provides power to distinguish between
different Higgs models . The importance of this decay mode is discussed in more detail in  and in Sect. 2.3,
but we recall here that a measurement of the branching ratio with a 16% statistical error could be made at a µ+µ−
collider using an integrated luminosity of 100 pb−1.
We conclude that if one varies R at centre-of-mass energies above ∼145 GeV, useful cross section measure-
ments are possible up to about 160 GeV. Beyond this point, the Higgs resonance is simply too wide for a peak
cross-section measurement to be feasible. However, we can confidently expect at least one Higgs boson in the
mass range accessible to a µ+µ−collider.
The accuracies for the branching ratio measurements have to be compared with the corresponding numbers
at an e+e−linear collider [3, 4, 5], where ∆BR/BR of about 2.5%, 5%, 4% are achievable for the b¯b, τ+τ−,
WW∗modes respectively (for mH= 120 GeV,√s = 350 GeV, and?L = 500 fb−1). We emphasize that the
numbers include detailed detector simulations that are not yet available for the FMC. In addition, by combining
LC and FMC data the branching ratio of H → µ+µ−can be measured to 4% accuracy .
It was observed in  that, for certain values of R, σpeak(µ+µ−→ H → b¯b) becomes practically indepen-
dent of mb. More generally speaking, R can be chosen such that the peak cross section for a given final state X is
FMC accuracies quoted earlier for these modes are very dependent on the luminosity obtainable, and that these LC
We conclude that chargino production via s-channel Higgs exchange at a µ+µ−collider may allow a precise
determination of the Higgs-chargino couplings in the MSSM, if the resonances can be separated. We leave for a
future occasion discussions of the cases where the resonances overlap, and when CP violation is important.
We have seen in this chapter some of the physics opportunities offered by µ+µ−colliders operated as Higgs
factories. Interest in these opportunities has been stimulated by the possible existence of a light Higgs boson. The
case outlined here depends indeed upon the mass of this lightest Higgs boson, and, although all the indications are
favourable, this remains an unknown parameter.
A first muon collider (FMC) operating around the peak of the Standard Model (SM) Higgs boson, that
is expected to weigh ∼ 120 GeV, as seen in Fig. 1, offers interesting prospects for precision measurements
of properties of the SM Higgs boson, such as its mass and decay width. The mass could be measured to an
unprecedented accuracy in the sub-MeV region. A direct width determination would be possible to an accuracy of
O(1) MeV. By varying judiciously the beam-energy spread, an interesting peak event rate could be attained for a
SM Higgs mass up to about 160 GeV, and measurements of decays into¯bb, τ+τ−and WW∗may be possible. The
accuracies obtained for these branching ratios are in the same ball park as those expected at an e+e−linear collider
(LC). However, they are highly dependent on the available luminosity and the details of the detector, which are not
yet fixed for the FMC. Notice also that by combining with LC measurements the coupling of the Higgs boson to
µ+µ−could be determined with an accuracy of ∼ 4% at the FMC .
If supersymmetry plays a rˆ ole at the electroweak scale, one expects a richer Higgs sector, containing three
neutral Higgs bosons h,H,A. As we have shown, the production cross sections and branching ratios of h,H,A
are very sensitive to supersymmetric radiative corrections. As we have also shown, polarized µ+µ−beams would
offer in addition interesting opportunities to explore CP violation in decay vertices and/or Higgs-mass mixing.
The masses of H,A may already be estimated quite accurately using FMC measurements. A second Higgs factory
(SMC) tuned to the twin H,A peaks offers valuable prospects for measuring the two masses independently (due
to the fine energy resolution reachable at a µ+µ−collider), the couplings of the heavy Higgs bosons to SM and
supersymmetric particles, as well as the opportunity for further interesting measurements of possible CP violation
in the MSSM Higgs sector.
Wehave not discussed in this report the physics prospects offered by ahigh-energy µ+µ−collider. Asis well
known, this would have certain advantages over a high-energy e+e−collider, notably in the beam energy spread
and in the accuracy with which the beam energy could be calibrated using the precession of the µ±polarization.
However, it is too early to know whether these advantages would be conclusive, and a multi-TeV µ+µ−collider
would presumably need to be preceded by one or more lower-energy Higgs factories.
S.K. thanks the CERNTheory Division for financial support during a stay at CERN.The work of D.G. is supported
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