The scalar sector of the electroweak theory can be probed by a mu^+mu^-
collider S channel resonance machine. We give arguments for when such a machine
may be needed and when this information could be obtained by the LHC detector.
A very interesting case is the possibility that several scalar particles are in
the same mass range for the supersymmetric Higgs bosons h, H, and A, which
would definitely require such a machine. The Higgs factory could follow the
construction of a neutrino factory.Comment: 6 pages. Presented at the 5th Int. Conf. sponsored by UCLA on the
  Physics Potential and Development of mu^+mu^- Colliders (San Francisco, Dec.
  15-17, 1999) and to be published in the Proceedings by AI

Cline, D. B.

English

arXiv

D. B. Cline

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The scientific need for a scalar/Higgs factory

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1Presented at the 5th Int. Conf. Sponsored by UCLA on Physics Potential and Development of µ+µ- Coll iders (San Francisco,
December 15-17, 1999) and to be published in the Proceedings by AIP.
The Scientific Need for a Scalar/Higgs Factory*
CAA-0159-2/00
D.B. Cline
Center for Advanced Accelerators
Department of Physics and Astronomy, Box 951547
University of California, Los Angeles, CA  90095-1547 USA
Abstract. The scalar sector of the electroweak theory can be probed by a  µ+µ- colli der S channel
resonance machine.  We give arguments for when such a machine may be needed and when this
information could be obtained by the LHC detector.  A very interesting case is the possibilit y that
several scalar particles are in the same mass range for the supersymmetric Higgs bosons h, H, and
A, which would definitely require such a machine. The Higgs factory could follow the construction
of a neutrino factory.
EARLY STUDY OF THE HIGGS FACTORY
The concept of a Higgs factory µ+µ colli der was born at the first dedicated µ+µ
workshop in Napa, Cali fornia, December 1992;1,2 Figure 1 shows a schematic of the scan
for the Higgs presented at that meeting.1  The next workshop also changed the role of a µ+µ-
colli der.3  Subsequently very nice theoretical work on this issue has been carried out by
Berger, Barger, Gunion, and Han,4 and then a paper (which included Table 1) defining the
Higgs particle factory was presented at the Snowmass DPF meeting in 1996 by the author.5
At that 1996 DPF meeting, a first pass design of a µ+µ colli der was presented by the Muon
Colli der Consortium.6  We will make use of all of these materials and of more recent work
in this brief article, as well as proceedings from meetings we have organized2,3,7 and other
recent workshops.
When the Higgs factory was envisioned in 1992, there seemed to be littl e scientific
support.1
MOTIVATION FOR A HIGGS FACTORY
The major purpose of the Higgs factory is to find the exact Higgs mass (or masses) and
then measure the important parameters, such as the width(s) and the common and rare
branching fractions.  This concept is based mainly on a relatively low-mass Higgs (below
300 GeV).  In the low-mass region (below 150 GeV), the Higgs could well be
supersymmetric (SUSY), and the width measurement will be crucial.  Above 150 GeV, the
Higgs could be more of a standard-model type.  However, this will once again lead to the
issue of what keeps the scalar system stable, which might be answered by the study of rare
FIGURE 1.  The first concept of a Higgs factory µ+µ	 colli der from the Napa Workshop.1
TABLE 1.  Arguments for a Higgs-Factory µ+µ Colli der.1,5
1. The mµ\ me ratio gives coupling 40,000 times greater to the Higgs particle.  In the  SUSY model, one
Higgs mh < 120 GeV!!
2. The low radiation of the beams makes precision energy scans possible.
3. The cost of a “custom” colli der ring is a small fraction of the µ± source.
4. Feasibilit y report to Snowmass established that m ~ 1033 cm2 s1 is feasible.
decays of the Higgs particles (in progress).  In the near future, there could be evidence for
the Higgs mass obtained from precise electroweak parameter measurements and later from
the LHC.  This will be a crucial input for the development of the Higgs factory.  In addition,
if Nature is supersymmetric, there will be additional SUSY-Higgs particles to study and,
thus, the Higgs factory concept will i nclude the search for and study of the SUSY Higgs
(H,A ...).  This is an experimental issue  theory can only take us just so far!
From all we now know about elementary particle physics, the scalar or SUSY scalar
sector is the key to future understanding.  A complete understanding of this sector is really
the goal of the Higgs factory and of nearly all elementary particle physics these days.
The Higgs factory is designed to first give the exact Higgs mass using an energy scan and
then measure the general properties of the Higgs, such as the field width, largest branching
fractions, etc.  It would produce 104 Higgs/yr and could investigate rare branching modes.
If there are more Higgs, the Higgs factory would be used to scan and find and study these
in detail as well .  A µ+µ colli der provides the Higgs factory, since scalars couple li ke
and the colli der has littl e radiative energy spreading (see Table 2).  Some importantm 2l
meetings are listed in Refs. 79, and some references to the early concept of a µ+µ colli der
can be found in Ref. 10. 
We expect the supercolli der LHC to extract the signal from background (i.e., seeing
either h0  or the very rare h0  µµµµ in this mass range, since h   is swamped bybb
hadronic background).  However, detectors for the LHC are designed to extract this signal.
Figure 2 gives a picture of the various physics thresholds that may be of interest for a µ+µ
colli der.  In this low mass region, the Higgs is also expected to be a fairly narrow resonance
and, thus, the signal should stand out clearly from the background from
µ+µ-     . (1)  bb  Ztail  bb
For masses above 180 GeV, the dominant Higgs decay is
h0  W +W    or   Z 0Z 0   , (2)
and the LHC should easily detect this Higgs particle.  Thus the µ+µ colli der is better
adapted for the low mass region.
The strongest argument for the low-energy colli der comes from the growing evidence
that the Higgs should exist in this low-mass range from recent electroweak  studies as shown
on Fig. 3.11  This evidence implies the exciting possibilit y that the Higgs mass is just beyond
the reach of LEP II and in a range that is very diff icult for the LHC to detect.3
In Fig. 2, we show a comparison of the Higgs factory µ+µ colli der and an e+e colli der
(NLC) that  could also study the Higgs.5  Note the very great differences in cross sections,
indicating that the e+e colli der must have very high luminosity.
TABLE 2.  Logic of Detailed Study of the Higgs Sector.
_____________________________________________________________________________________
If particles in the scalar sector are ever discovered, it will be essential to determine their properties, which will
give direct information about the nature of the particle and the underlying theory.  Three simple examples can
be cited:
1. Suppose a Higgs-like particle is discovered with mass 110 GeV.  This could either be the standard model
(SM) Higgs or an MSSM Higgs.  A measurement of the width of the state would presumably tell the
difference.  However, the SM width is 5 MeV  a formidable measurement!
2. Suppose a Higgs-like particle is discovered with a mass of 150 GeV.  This is presumably beyond the
MSSM bound, but it could be an NMSSM or an SM Higgs.  A measurement of the width could presumably
resolve the issue.
3. Suppose a Higgs-li ke particle of mass 165 GeV is discovered.  This is presumably even beyond the
NMSSM  limits.  If this is an SM Higgs, can we learn more by the study of the rare decay modes?
___________________________________________________________________________________
Figure 2.  The cross sections as a function of energy for e+e- and µ+µ- interactions producing a Higgs boson
and other systems.
Figure 3.  The most recent fit of the electroweak parameters from the CERN group to constrain the mass of
the Higgs boson.
THE MYTH OF THE TeV-SCALE SYMMETRY BREAKING
In the old days (e.g., the arguments for the SSC machine), it was argued that “new
physics”must appear at the TeV scale.  This was based on the concept that a high-mass
Higgs (TeV) becomes very “strong” and on the divergent self-interaction of the Higgs sector
requiring a cutoff at the TeV scale.  However, this need not apply if the Higgs mass is very
low, since the stabilit y conditions shown on Fig. 4 allow for a cutoff even up to the Planck
mass.  The current worldwide fits to all electroweak precision measurements strongly imply
that at least one Higgs is low mass.  Thus, there may be only one low-mass Higgs to
discover at the LHC and nothing more!
Figure 4.  Stabilit y diagram for the Higgs scalar at the divergence cutoff  and the current values of Higgs
mass from electroweak studies.
Take the example of a 170-GeV Higgs.  My SUSY theorist friends tell me this is
inconsistent with the existence of SUSY (it could also kill string theory).  But what cuts off
the divergence?  The GUT (grand unified theory) scale.
A NEUTRINO FACTORY AS THE 
FIRST STAGE OF A HIGGS FACTORY
There is great interest in a neutrino-factory muon storage ring to study neutrino mass.
A schematic of such a factory is shown in Fig. 5.  We want to point out that this storage ring
could be the first stage of a Higgs factory, with the following major differences:
(1) additional cooling is required, especially longitudinal, and
(2) the muon colli der storage ring needs to be a small as possible.
There is a certain beautiful symmetry between a study of the origins of mass (Higgs sector)
and the study of the tiny neutrino mass.
In the future, we may imagine that the scientific case for the neutrino factory increases
and that the technical obstacles are our own  the constraint of a 50-GeV muon storage ring
with a relatively small amount of cooling.  If the evidence for a low-mass Higgs is
confirmed, then the transition from the neutrino factory to a Higgs factory could be fairly
straightforward.  This could bring a unified approach to the future of particle physics in the
USA.
Figure 5.  Schematic of a neutrino factory at FNAL or BNL.
REFERENCES
 1. Cline, D., Nucl. Instrum. Methods A350, 24 (1994).
 2. See collection of papers from the First Workshop on the Physics Potential and Development of µ+µ
Colli ders (Napa, CA, 1992), in Nucl. Instrum. Methods A350, 24-56 (1994).
 3. Physics Potential and Development of µ+µ Colliders (Proc., 2nd Wksp., Sausalito, CA, 1994), edited
by D. B. Cline, AIP Conference Proceedings 352, New York, 1996.
 4. Barger, V., Berger, M. S., Gunion, J. F., and Han, T., U. Wisconsin-Madison report MAD-PH-963/hep-
ph/9702334 (1997); also Phys. Rev. Lett. 78, 3991 (1997); also ibid. 75, 1462 (1995).
 5. Cline, D.B., “A Higgs Factory µ+µ Colli der,” in New Directions for High-Energy Physics (Proc., 1996
DPF/DPB Summer Study, Snowmass, CO, June-July, 1996), edited by D. G. Cassel, L. Trindle Gennari,
and R. H. Siemann, IEEE, New York, 1997, pp. 593-597.
 6. New Directions for High-Energy Physics (Proc., 1996 DPF/DPB Summer Study, Snowmass, CO, June-
July, 1996), edited by D. G. Cassel, L. Trindle Gennari, and R. H. Siemann, IEEE, New York, 1997.
 7. Physics Potential & Development of µ+µ Colliders (Proc. 3rd Intl. Conf., San Francisco, Dec. 1995),
edited by D. B. Cline, Nucl. Phys. B (PS), 51A (1996).
 8. Beam Dynamics and Technology Issues for µ+µ Colliders (Proc., 9th Advanced ICFA Beam Dynamics
Workshop, Montauk, LI, NY, Oct. 1995), edited by J. C. Gallardo,  AIP Conference Proceedings 372,
New York, 1996.
 9. Future High Energy Colliders (Proc., Symp., Santa Barbara, CA, Oct. 1996), edited by Z. Parsa, AIP
Conference Proceedings 397, New York, 1997.
10. Early references for µµ colli ders are:  Perevedentsev, E. A. and Skrinsky, A. N., in Proc., 12th Int. Conf.
on High Energy Accelerators (Madison, WI, 1983), editors R. T. Cole and R. Donaldson, p. 485; also
Neuffer, D., Part. Accel., 14, 75 (1984);  also Neuffer, D., in Advanced Accelerator Concepts (Proc.,
Symp., Madison, WI, 1986), edited by F. E. Mill s, AIP Conference Proceedings 156, New York, 1987,
p. 201.
11. See recent LEP analysis 1999, CERN report EP 199-15.


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