Phenomenology of light Higgs bosons in supersymmetric left-right models

Abstract

We carry out a detailed analysis of the light Higgs bosons in supersymmetric left-right models (SLRM). This includes models with minimal particle content and those with additional Higgs superfields. We also consider models with non-renormalizable higher-dimensional terms. We obtain an upper bound on the mass of the lightest CP-even neutral Higgs boson in these models. The upper bound depends only on the gauge couplings, and the vacuum expectation values of those neutral Higgs fields which control the spontaneous breakdown of the $SU(2)_L \times U(1)_Y$ gauge symmetry. We calculate the one-loop radiative corrections to this upper bound, and evaluate it numerically in the minimal version of the supersymmetric left-right model. We consider the couplings of this lightest CP-even Higgs boson to the fermions, and show that in a phenomenologically viable model the branching ratios are similar to the corresponding branching ratios in the minimal supersymmetric standard model (MSSM). We then study the most promising particle for distinguishing the SLRM from other models, namely the doubly charged Higgs boson. We obtain the mass of this doubly charged Higgs boson in different types of supersymmetric left-right models, and discuss its phenomenology.

Full text

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arXiv:hep-ph/9904388v1 19 Apr 1999
HIP-1999-16/TH
Phenomenology of light Higgs bosons in
supersymmetric left-right models
K. Huitua, P. N. Panditaa,b,cand K. Puolam¨ akia
aHelsinki Institute of Physics, P.O.Box 9, FIN-00014 University of Helsinki,
Finland
bDeutsches Elektronen-Synchrotron DESY, Notkestrasse 85, D-22603 Hamburg,
Germany
cDepartment of Physics, North Eastern Hill University, Shillong 793022, India1
Abstract
We carry out a detailed analysis of the light Higgs bosons in supersymmetric left-
right models (SLRM). This includes models with minimal particle content and those
with additional Higgs superfields. We also consider models with non-renormalizable
higher-dimensional terms. We obtain an upper bound on the mass of the lightest
CP-even neutral Higgs boson in these models. The upper bound depends only on
the gauge couplings, and the vacuum expectation values of those neutral Higgs fields
which control the spontaneous breakdown of the SU(2)L×U(1)Y gauge symmetry.
We calculate the one-loop radiative corrections to this upper bound, and evaluate
it numerically in the minimal version of the supersymmetric left-right model. We
consider the couplings of this lightest CP-even Higgs boson to the fermions, and
show that in a phenomenologically viable model the branching ratios are similar to
the corresponding branching ratios in the minimal supersymmetric standard model
(MSSM). We then study the most promising particle for distinguishing the SLRM
from other models, namely the doubly charged Higgs boson. We obtain the mass
of this doubly charged Higgs boson in different types of supersymmetric left-right
models, and discuss its phenomenology.
Key words: Supersymmetry; left-right symmetry; Higgs boson; doubly charged
Higgs boson
PACS: 12.60.Jv; 11.30.Fs; 14.80.Cp
1Permanent address
Preprint submitted to Elsevier Preprint1 February 2008

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1Introduction
One of the central problems of particle physics is to understand how the electroweak
scale associated with the mass of the W boson is generated, and why it is so small as
compared to the Planck scale associated with the Newton’s constant. In the Standard
Model (SM) the electroweak scale is generated through the vacuum expectation value
(VEV) of the neutral component of a Higgs doublet [1]. Apart from the fact that this
VEV is an arbitrary parameter in the SM, the mass parameter of the Higgs field suffers
from quadratic divergences, making the weak scale unstable under radiative corrections.
Supersymmetry is at present the only known framework in which the weak scale is stable
under radiative corrections [2], although it does not explain how such a small scale arises in
the first place. As such, considerable importance attaches to the study of supersymmetric
models, especially the Minimal Supersymmetric Standard Model (MSSM), based on the
gauge group SU(2)L× U(1)Y, with two Higgs doublet superfields. It is well known that,
because of underlying gauge invariance and supersymmetry (SUSY), the lightest Higgs
boson in MSSM has a tree level upper bound of MZ(the mass of Z boson) on its mass [3].
Although radiative corrections [4] to the tree level result can be appreciable, these depend
only logarithmically on the SUSY breaking scale, and are, therefore, under control. This
results in an upper bound of about 125 − 135 GeV on the one-loop radiatively corrected
mass [5] of the lightest Higgs boson in MSSM2. Because of the presence of the additional
trilinear Yukawa couplings, such a tight constraint on the mass of the lightest Higgs boson
need not a priori hold in extensions of MSSM based on the gauge group SU(2)L×U(1)Y
with an extended Higgs sector. Nevertheless, it has been shown that the upper bound
on the lightest Higgs boson mass in these models depends only on the weak scale, and
dimensionless coupling constants (and only logarithmically on the SUSY breaking scale),
and is calculable if all the couplings remain perturbative below some scale Λ [7–13]. This
upper bound can vary between 150 GeV to 200 GeV depending on the Higgs structure of
the underlying supersymmetric model. Thus, nonobservation of such a light Higgs boson
below this upper bound will rule out an entire class of supersymmetric models based on
the gauge group SU(2)L× U(1)Y.
The existence of the upper bound on the lightest Higgs boson mass in MSSM (with
arbitrary Higgs sectors) has been investigated in a situation where the underlying super-
symmetric model respects baryon (B) and lepton (L) number conservation. However, it
is well known that gauge invariance, supersymmetry and renormalizibility allow B and L
violating terms in the superpotentioal of the MSSM [14]. The strength of these lepton and
baryon number violating terms is, however, severely limited by phenomenological [15,16],
and cosmological [17] constraints. Indeed, unless the strength of baryon-number violating
term is less than 10−13, it will lead to contradiction with the present lower limits on the
lifetime of the proton. The usual strategy to prevent the appearance of B and L violating
2The two-loop corrections to the Higgs boson mass matrix in the MSSM are significant, and
can reduce the lightest Higgs boson mass by up to ∼ 20 GeV as compared to its one-loop value
[6].
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couplings in MSSM is to invoke a discrete Z2symmetry [18] known as matter parity, or
R-parity. The matter parity of each superfield may be defined as
(matter parity) ≡ (−1)3(B−L). (1)
The multiplicative conservation of matter parity forbids all the renormalizable B and L
violating terms in the superpotential of MSSM. Equivalently, the R-parity of any com-
ponent field is defined by Rp = (−1)3(B−L)+2S, where S is the spin of the field. Since
(−1)2Sis conserved in any Lorentz-invariant interaction, matter parity conservation and
R-parity conservation are equivalent. Conservation of R-parity then immediately implies
that superpartners can be produced only in pairs, and that the lightest supersymmetric
particle (LSP) is absolutely stable.
Although the Minimal Supersymmetric Standard Model with R-parity conservation can
provide a description of nature which is consistent with all known observations, the as-
sumption of Rpconservation appears to be ad hoc, since it is not required for the internal
consistency of MSSM. Furthermore, all global symmetries, discrete or continuous, could
be violated by the Planck scale physics effects [19]. The problem becomes acute for low
energy supersymmetric models, because B and L are no longer automatic symmetries
of the Lagrangian, as they are in the Standard Model. It is, therefore, more appealing
to have a supersymmetric theory where R-parity is related to a gauge symmetry, and
its conservation is automatic because of the invariance of the underlying theory under
this gauge symmetry. Fortunately, there is a compelling scenario which does provide for
exact R-parity conservation due to a deeper principle. Indeed, Rp conservation follows
automatically in certain theories with gauged (B − L), as is suggested by the fact that
matter parity is simply a Z2subgroup of (B − L). It has been noted by several authors
[20,21] that if the gauge symmetry of MSSM is extended to SU(2)L×U(1)I3R×U(1)B−L,
or SU(2)L× SU(2)R× U(1)B−L, the theory becomes automatically R-parity conserving.
Such a left-right supersymmetric theory (SLRM) solves the problems of explicit B and
L violation of MSSM, and has received much attention recently [22–28]. Of course left-
right symmetric theories are also interesting in their own right, for among other appealing
features, they offer a simple and natural explanation for the smallness of neutrino mass
through the so called see-saw mechanism [29].
Such a naturally R-parity conserving theory necessarily involves the extension of the
Standard Model gauge group, and since the extended gauge symmetry has to be broken,
it involves a “new scale”, the scale of left-right symmetry breaking, beyond the SUSY
and SU(2)L× U(1)Y breaking scales of MSSM. In [30] we showed that in the SLRM
with minimal particle content the upper bound on the mass of the lightest neutral Higgs
boson depends only on gauge couplings and those VEVs which break the SU(2)L×U(1)Y
symmetry. Here we will present a detailed analysis of the Higgs sector of the left-right
supersymmetric models, and consider some of the distinguishing features of the lightest
Higgs boson in these models. In the SLRMs there are typically also other light Higgs
particles. The light doubly charged Higgs boson, which we will consider in detail as well,
should provide a clear signal in experiments.
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The plan of the paper is as follows. In section 2, we review the various left-right supersym-
metric models that we consider in this paper. In section 3, we obtain the tree level upper
bound on the mass of the lightest CP-even Higgs boson for the various SLRMs considered
in section 2. We use a general procedure to obtain this (tree-level) upper bound on the
mass of the lightest CP-even Higgs boson in models with extended gauge groups, such
as SLRMs. We show that the upper bound so obtained in the renormalizable models is
independent of the supersymmetry breaking scale, as well as the left-right breaking scale.
In the case of models containing non-renormalizable terms, although the upper bound de-
pends on the left-right breaking scale, the dependence is extremely weak, being suppressed
by powers of Planck mass.
In section 4 we calculate the radiative corrections to the upper bound on the mass of the
lightest Higgs boson, and show that the most important radiative corrections arising from
quark-squark loops are of the same type as in the MSSM based on SU(2)L×U(1)Y. The
radiatively corrected upper bound so obtained is numerically considerably larger than the
corresponding bound in the MSSM, but for most of the parameter space is below 200 GeV.
In section 5 we consider the branching ratios of the lightest neutral Higgs boson, and find
that its couplings are similar to the corresponding Higgs couplings in the Standard Model
in the decoupling limit.
In section 6 we discuss the mass of the lightest doubly charged Higgs boson and the
possibility of its detection at colliders. In section 7, we present our conclusions. The
full scalar potential of the minimal supersymmetric left-right model is presented in the
Appendix A.
2The Higgs sector of the left-right supersymmetric models
In this section we briefly review the minimal supersymmetric left-right model, and then
discuss models which have an extended Higgs sector, and finally discuss models with
non-renormalizable interaction terms in the superpotential.
The minimal SLRM is based on the gauge group SU(3)C×SU(2)L×SU(2)R×U(1)B−L.
The matter fields of this model consist of the three families of quark and lepton chiral
superfields with the following transformation properties under the gauge group:
Q =


U


D


 ∼ (3,2,1,1


3), Qc=




Dc
Ec
Uc




 ∼ (3∗,1,2,−1
3),
L =
ν
E
 ∼ (1,2,1,−1), Lc=
νc
 ∼ (1,1,2,1), (2)
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where the numbers in the brackets denote the quantum numbers under SU(3)C×SU(2)L×
SU(2)R×U(1)B−L. The Higgs sector consists of the bidoublet and triplet Higgs superfields:
Φ =


Φ0
∆0
1Φ+
1
Φ−
2 Φ0
2


 ∼ (1,2,2,0), χ =


χ0




1χ+
1
χ−
2 χ0
2


 ∼ (1,2,2,0),
δ++
R

δ++
L

∆R=





1
√2∆−
∆−−
R
RR
−1
√2∆−
R




 ∼ (1,1,3,−2), δR=

1
√2δ+
δ0
R
R
−1
√2δ+
R

 ∼ (1,1,3,2),

 ∼ (1,3,1,2).
∆L=

1
√2∆−
∆−−
L
L
∆0
L
−1
√2∆−
L
 ∼ (1,3,1,−2), δL=

1
√2δ+
δ0
L
L
−1
√2δ+
L
(3)
There are two bidoublet superfields in order to implement the SU(2)L×U(1)Y breaking,
and to generate a nontrivial Kobayashi-Maskawa matrix. Furthermore, two SU(2)RHiggs
triplet superfields ∆Rand δRwith opposite (B − L) are necessary to break the left-right
symmetry spontaneously, and to cancel triangle gauge anomalies due to the fermionic
superpartners. The gauge symmetry is supplemented by a discrete left-right symmetry
under which the fields can be chosen to transform as
Q ↔ Qc, L ↔ Lc, Φ ↔ −τ2ΦTτ2, χ ↔ −τ2χTτ2, ∆R↔ δL, δR↔ ∆L.(4)
Thus, the SU(2)Ltriplets ∆Land δLare needed in order to make the Lagrangian fully
symmetric under L ↔ R transformation, although these are not needed phenomenologi-
cally for symmetry breaking, or the see-saw mechanism.
The most general gauge invariant superpotential involving these superfields can be written
as (generation indices suppressed)
Wmin=hΦQQTiτ2ΦQc+ hχQQTiτ2χQc+ hΦLLTiτ2ΦLc+ hχLLTiτ2χLc
+hδLLTiτ2δLL + h∆RLcTiτ2∆RLc+ µ1Tr(iτ2ΦTiτ2χ) + µ′
+µ′′
1Tr(iτ2ΦTiτ2Φ)
1Tr(iτ2χTiτ2χ) + Tr(µ2L∆LδL+ µ2R∆RδR).(5)
The scalar potential can be calculated from
V = VF+ VD+ Vsoft, (6)
where VF, VD, and Vsoftrepresent the contribution of F-terms, the D-terms, and the soft
SUSY breaking terms, respectively. The full scalar potential can be found in Appendix
A. The general form of the vacuum expectation values of the various scalar fields which
preserve the U(1)emgauge invariance can be written as
5