The lightest neutral and doubly charged Higgs bosons of supersymmetric left-right models
ABSTRACT We review the phenomenology of light Higgs scalars in supersymmetric left-right models. We consider models with minimal particle content (with and without non-renormalizable higher-dimensional terms) and with additional Higgs superfields. The upper bound on the lightest CP-even neutral Higgs boson in these models is larger than in the minimal supersymmetric standard model, and the Higgs couplings to fermions approach those of the Standard Model. Possibly light doubly charged Higgs boson may provide the best signature of these models.
arXiv:hep-ph/9910504v1 27 Oct 1999
THE LIGHTEST NEUTRAL AND DOUBLY CHARGED HIGGS
BOSONS OF SUPERSYMMETRIC LEFT-RIGHT MODELSa
K. HUITU1, P.N. PANDITA1,2, K. PUOLAM¨AKI1
1Helsinki Institute of Physics, P.O.B. 9,
FIN-00014 University of Helsinki, Finland
2Department of Physics, North Eastern Hill University,
Shillong 793022, India
We review the phenomenology of light Higgs scalars in supersymmetric left-right
models.We consider models with minimal particle content (with and without
non-renormalizable higher-dimensional terms) and with additional Higgs super-
fields. The upper bound on the lightest CP-even neutral Higgs boson in these
models is larger than in the minimal supersymmetric standard model, and the
Higgs couplings to fermions approach those of the Standard Model. Possibly light
doubly charged Higgs boson may provide the best signature of these models.
The left-right models are interesting for many reasons, e.g. they provide a
natural way to generate light masses for the neutrinos via the see-saw mech-
anism1.An important motivation for the supersymmetric left-right mod-
els2−14is due to the fact15,16that if the gauge symmetry is extended to
SU(2)L× U(1)I3R× U(1)B−L, or to SU(2)L× SU(2)R× U(1)B−L, then R-
parity is conserved in the Lagrangian of the theory. Thus one of the major
problematic features of the MSSM is resolved by a gauge symmetry. Here we
will concentrate on the model with the SU(2)Rsymmetry, the supersymmetric
left-right model (SLRM).
While the problem of R-parity is solved, the particle content of the model
is enlarged. In addition to the new superfields containing the gauge bosons
of the SU(2)R symmetry, one has a right-handed neutrino superfield (νc
The Higgs sector in the SLRM is chosen to have triplets in the spectrum, in
which case one can have the conventional see-saw mechanism for neutrino mass
generation. The SU(2)L will be broken mainly by bidoublets which contain
the doublets of the MSSM. Thus, the Higgs sector consists of the following
, χ =
aTalk presented by K. Huitu in the International Workshop on Linear Colliders, Sitges, April
28 - May 5, 1999.
∆R∼ (1,1,3,−2), δR∼ (1,1,3,2), ∆L∼ (1,3,1,−2), δL∼ (1,3,1,2).(1)
The SU(2)Ltriplets ∆Land δLmake the Lagrangian fully symmetric under
L ↔ R. Left triplets are not needed for symmetry breaking or the see-saw
The VEVs preserving the U(1)emgauge invariance can be written as
, ?χ? =
, ?˜ νL? = σL, ?˜ νc
L? = σR,
R? = v∆R, ?δ0
R? = vδR, ?∆0
L? = v∆L, ?δ0
L? = vδL,(2)
The triplet VEVs v∆R,δRare, according to the lower bounds17on heavy W-
and Z-boson masses, in the range v∆R,δR>∼1 TeV. The VEVs κ′
to the mixing of the charged gauge bosons and to the flavour changing neutral
currents, and are usually assumed to vanish. The left-triplet VEVs v∆L,δLmust
be small, since the electroweak ρ parameter is close to unity, ρ = 0.9998±0.0008
17. With the minimal field content and renormalizable model, the only way to
preserve the U(1)emgauge symmetry is to break the R-parity by a sneutrino
An alternative to the minimal left-right supersymmetric model involves
additional triplet fields, ΩL(1,3,1,0) and ΩR(1,1,3,0)9. In these extended
models the gauge group SU(2)R×U(1)B−Lis broken first to an intermediate
symmetry group U(1)R×U(1)B−L, and at the second stage to U(1)Y at a lower
scale. In this theory the parity-breaking minimum respects the electromagnetic
gauge invariance without a sneutrino VEV.
A second option is to add non-renormalizable terms to the Lagrangian
of the minimal model16,11,10. It has been shown that the addition of terms
suppressed by a high scale such as Planck mass, M ∼ 1019GeV, with the
minimal field content ensures the correct pattern of symmetry breaking in
the SLRM with the intermediate scale MR>∼1010− 1011GeV, and R-parity
2The upper limit on the lightest CP-even Higgs
In the case of the SLRM we have many new couplings and also new scales
in the model and it is not obvious, what is the upper limit on the lightest
CP-even Higgs boson mass. This mass bound is a very important issue, since
the experiments are approaching the upper limit of the lightest Higgs boson
mass in the MSSM.
A general method to find an upper limit for the lightest Higgs mass was
presented in18. This method has been applied to the mass of the lightest
Figure 1: The upper bound on the mass of the lightest neutral Higgs boson. The bi- and
trilinear soft supersymmetry breaking parameters are 1 TeV (solid line) and 10 TeV (dashed
Higgs, mh, of SLRM14in three cases: (A) R-parity is spontaneously broken
(sneutrinos get VEVs), (B) R-parity is conserved because of additional triplets,
and (C) R-parity is conserved because of nonrenormalizable terms.
For the minimal model, case (A), the upper bound on mhis14
where v2= κ2
of extra triplets does not change this bound. Thus, the bound for the case
(B), can be obtained from (3) by taking the limit σL→ 0. The total number
of nonrenormalizable terms in case (C) is large. However, the contribution to
the Higgs mass bound from these terms is found to be14typically numerically
negligible. Therefore the upper bound for this class of models is essentially the
same as in the case (B).
The radiative corrections to the lightest Higgs mass are significant. For
the SLRM lightest Higgs they have been calculated in detail14. For nearly
degenerate stop masses, the radiative corrections on mhin the SLRM differ in
form from the MSSM upper bound only because of new supersymmetric Higgs
The upper bound on the mass of the lightest Higgs is plotted in Fig.1 as
a function of the scale Λ up to which the SLRM remains perturbative. The
upper bound is shown for two different values of the SU(2)Rbreaking scale,
MR= 10 TeV and MR= 1010GeV, and for two values of soft supersymmetry
2. The addition
breaking mass parameter, Ms= 1 TeV and Ms= 10 TeV. For large values of
Λ the upper bound is below 200 GeV.
2.1Couplings of the lightest neutral Higgs to fermions in the SLRM
In order to study the phenomenology of the lightest Higgs boson in the SLRM,
its couplings to fermions are needed.
In the left-right symmetric models problems with FCNC are expected if
several light Higgs bosons exist19unless mHFCNC>∼O(1 TeV). Thus the
relevant limit to discuss is the one in which all the neutral Higgs bosons,
except the lightest one, are heavy. It has been shown that in the decoupling
limit the Yukawa couplings of the τ’s are the same in the SM and the SLRM
even if the τ’s contain a large fraction of gauginos or higgsinos14.
3The lightest doubly charged Higgs
In addition to the lightest neutral CP-even Higgs, it has been known for quite
some time7that the lightest doubly charged Higgs boson in these models may
be light. Whether it is observable in the experiments is an interesting issue,
since this particle may both reveal the nature of the gauge group and help to
determine the particular supersymmetric left-right model in question.
There are four doubly charged Higgs bosons in the SLRM, of which two
are right-handed and two left-handed. The masses of the left-handed triplets
are expected to be of the same order as the soft terms. The mass matrix
for the right-handed triplets depends on the right-triplet VEV. Nevertheless,
it was noticed in7that in the SLRM with broken R-parity one right-handed
doubly charged scalar tends to be light. Also, in the nonrenormalizable case it
is possible to have light doubly charged scalars12. On the other hand, in the
nonsupersymmetric left-right model all the doubly charged scalars typically
have a mass of the order of the right-handed scale20. This is also true in the
SLRM with enlarged particle content11. Thus a light doubly charged Higgs
would be a strong indication of a supersymmetric left-right model with minimal
In Figure 2 a) an example of H++masses with broken R-parity is shown as
a function of A∆for fixed σR. The soft masses and right-handed breaking scale,
are of the order of 10 TeV. The maximum triplet Yukawa coupling allowed by
positivity of the mass eigenvalues in this case is h∆∼ 0.4. Even in the maximal
case the mass of the doubly charged scalar mH++ ∼ 1 TeV. In Fig. 2 b) mH++
is plotted in the model containing nonrenormalizable terms as a function of
the nonrenormalizable bR-parameter for v2
R/M = 102GeV.
function of the soft trilinear coupling A∆. σRvaries in the allowed range of 100 GeV to
8.45 TeV. In b) the mass is as a function of the nonrenormalizable bR-parameter. In b)
shown (dashed line). The soft supersymmetry breaking parameters and the bRparameters
are marked in the figure. tanβ = 50.
The mass mH++ of the lightest doubly charged Higgs. In a) the mass is as a
R/M = 102GeV and D = (3 TeV)2(solid line). For msoft= 10 TeV also D = 10 TeV2is
3.1Doubly charged scalars at linear colliders
The collider phenomenology of the doubly charged scalars has been actively
studied, since they appear in several extensions of the Standard Model, can be
relatively light and have clear signatures. The main decay modes for relatively
light doubly charged Higgs are21H−−→ l−
Thus the experimental signature of the decay is a same sign lepton pair with
no missing energy, including lepton number violating final states.
Since the left-right models contain many extra parameters when compared
to the MSSM, a great advantage of the pair production is that it is rela-
tively model independent. The doubly charged Higgses can be produced in
f¯f → γ∗,Z∗→ H++H−−both at lepton and hadron colliders, if kinemati-
cally allowed, even if WR is very heavy, or the triplet Yukawa couplings are
very small. The pair production cross section at a linear collider has been given
in22,23. The cross section remains sufficiently large close to the kinematical
limit for the detection to be possible.
Kinematically, production of a single doubly charged scalar would be
favoured. This option is more model dependent, but for reasonable param-
eter range the kinematical reach is approximately doubled compared to the
2, where l1,2 denote leptons.
The lightest CP even Higgs boson in SLRM can be considerably heavier as
compared to the lightest Higgs in the MSSM, and its couplings to fermions
remain similar to the couplings of the Standard Model Higgs boson. In the
SLRM with the minimal particle content one has typically also a light doubly
charged Higgs boson. If this particle is found, it is a strong indication of the
SLRM with minimal particle content.
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