>K'-)T<I>. 2014, TOM 146, Bbin. 1 (7), rip. 60 64
© 2014
ON HIGGS-EXTENDED MSSM MODELS
R. Ahl Laamaraa'h, S.-E. Ennadifia* M. A. Loualidia
" Laboratory of High Energy Physics, Modeling and Simulation, Faculty of Science, University Mohammed V-Agdal 10000, Rabat, Morocco
b Centre of Physics and Mathematics, CPM-CNESTEN 1014, Rabat, Morocco
Received January 13, 2014
Motivated by the LHC results revealing the SM scalar sector as well as by its possible revision, we consider an MSSM scalar extension consisting of two Higgs triplets generating the observed neutrino and Higgs masses. The latter constrains their suppressed vevs and sizable couplings, which slightly influences the extended neutralino sector and the LSP emergence.
DOI: 10.7868/S0044451014070062
1. INTRODUCTION
Despite the undeniable success of the SM of particle physics in describing the matter building blocks and their interactions below the weak scale fl, 2], it is now known to be rather complicated and incomplete. The past and the recent data continue to brighten the spectrum and dynamics of the electroweak symmetry breaking sector responsible for major problems in the SM, mostly the Higgs IIlclSS hierarchy problem. The su-persymmetry is the well-known simple model curing the Higgs problem without fine tuning. In the MSSM, the mass of the lightest Higgs boson is close the Z-boson mass at tree level, but could be raised to the value best motivated theoretically and experimentally by considering large radiatve corrections.
Recently, with the LHC observation of a new scalar boson around 125 126 GeV with a diphoton rate excess [3, 4], the consideration of MSSM extended models has become appealing. In particular, the extended Higgs sector could reproduce such a result by generating sizeable tree-level correction to the Higgs mass as well as enhancement of its diphoton decay rate through charged new degrees of freedom, whose possible detection would be a clear evidence of a Higgs sector beyond that of the MSSM [5 7]. The most considered scalar extended models often include extra singlets or triplets, which have been seen to affect the Higgs sector
* E-mail: ennadifis'fflgmail.com
phenomenology, thereby providing a large landscape where, in addition to the observed Higgs results, more famous open questions in the SM can be studied, due to the new involved parameters. Indeed, the associated parameters of the extra singlets or triplets, such as coupling constants and vevs present in the superpotential of the model within new mass and interaction terms, might be helpful in discussing more known problems such as neutrino masses and the dark matter sector in the large parameter space. However, models with an extended Higgs boson are strongly constrained by the electroweak precision tests, in particular by the p parameter [8], imposing constraints 011 the extra scalar vevs that affect the model phenomenology.
In the light of the recent Higgs observation and the deployed theoretical efforts, we consider a Higgs-triplet-extended MSSM and discuss its phenomenological implications for the mass spectrum. Specifically, we study the contribution of two extra 1" = ±2 complex triplets AU:d to the neutrino and Higgs masses by means of their vevs VAm,d and coupling parameters Awhich are constrained from the known and the electroweak precision data. We then investigate the neutralino sector extended by the fermionic triplet neutral states and discuss its compositeness and the LSP emergence according to the scale of the triplet parameters.
2. MODEL AND CONSTRAINTS
Signals for physics beyond the SM, mostly neutrinos and dark matter sectors [9 12], have been largely
m-h, GeV
160
150
140 -
130 -
120 -
110 -
100
90 -
SO
0.2
Plots of the nth as a function of A,,. a — tg B = \/3, Ad = 0.8 (thick line) and for t%3 = v/3/3,\d = 0.2 (thin line). b — tgB = >/3. A„ = 0.1 (thick line) and for tgB = \/3/3, A„ = 0.8 (thin line)
investigated and led to several extensions of the SM. Most of tlieni are based on the supersymmetry and/or extended scalar sectors. Recently, with the discovered resonance at 125.5 GeV [3, 4], the hunt for one or more Higgs boson(s) has given a big boost to the search for such directions where most studied models involve extra scalar fields. Here, for the aforementioned reasons, we extend the MSSM Higgs sector by two Y = ±2 triplets given by
The scalar triplets are described in terms of a 2 x 2 matrix representations: 6° d are the complex neutral fields and ¿>++, ¿>+, , denote the charged fields. This is one of the MSSM extensions that allows realizing some of its outstanding fragments. An implication of this emerges in the superpotential extension
W = WMSSM + WA, (2)
where W"A comprises all possible new mass and an interaction terms involving the triplet fields. Indeed, roughly, the most general gauge-invariant and renor-malizable superpotential that can be written for the extra scalars is given by
W'A = A'//.,A,//,,-—//.a Tr (A„A,/) +XUHUAUHU +
+ XdHdAdHd, (3)
Wll01'° Hu = (h+,hau), Hd = (h°dJ>d),
and Li are the MSSM Higgs and lepton doublets, and t = 1,2,3 is the generation index. The first piece is a neutrino-generated mass term and the others are the scalar-sector interaction terms. After the electroweak symmetry breaking, when the triplet Ad acquires a vacuum expectation value in its neutral compenent, the neutrinos acquire Majorana masses, restricting the value of cj,,. In fact, for A^ < 1 and neutrino masses <0.1 eV, v>\d is expected to be
'•a, = ^ < liT10 GeV, (4)
A L
which is more than 12 orders of magnitude less than the elect roweak symmetry breaking scale
V = yjvl + 4 ~ 102 GeV.
Moreover, strong constraints on models with triplets conies from the electroweak precision tests. Due to the addition of the triplets, the full Higgs kinetic La-grangian is given by
L = \DtlHti\ + \DtlHd\ + Tr WD^W +
- Tr ]/•>;, A,; [. (5)
from which we can derive the contribution of these extra fields to the gauge bosons. In particular, the Zand W"-bosons receive the masses
, 2 (6) M2, = | (,2 + 2,|„ + 2,|;) .
and hence would redefine the p parameter [8] as
R. Ahl Laamara, 5.-E. Ennadifí, M, A. Loualidi
>K3TO, TOM 146, Bbin. 1 (7), 2014
P =
2(4„+4,
4 ivj
(7)
icant effects, the SM-like Higgs boson mass can be expressed as
mh
Because the experimental value of the p parame- ~ \/mz cos2(2/?)+6i'2(AJ sin4(/?)+A¿ cos4(/?)), (10)
tor is near unity, the factor (r^ + r^ () /v'2 is required to be much smaller than unity at the tree level. This constraint with (4) means that the ¿1 „-triplet vev «a„ should also bo much smaller than the eloctroweak scale ~ v, whence such a deviation is found to be Sp < 10-24, thus keeping the experimental p parameter near unity. We finally obtain the scalar vev bound
<-'A„ d < <-' ~ 102 GeV.
(8)
Wo now turn to the Higgs boson sector, which consists of four states, with two from the ordinary doublets H.U:d and the other two from the triplets For that, we need to write the scalar potential of the model. Gathering all the contributions from F, D and soft terms, the neutral part of the scalar potential can be written as
VH = >i>
\H
0 12
l/'l J lJJdl (bHH°dH°u + H.c.) + (1^616° + H.c.
+ m"ÍJódí2 +m"ÍJóuí2 +
0 12
which is slightly above the MSSM tree-level mass owing to the new contributions of the triplets parameterized by their coupling constants AU:d- Thus, a sufficiently large tree-level Higgs boson mass requires sizable strengths of the AU:d for each value of the angle /? (0 < 3 < 7t/2) defined by
tg/i = — , 'I'd
which is not fixed by present experiments. We illustrate this by plotting the Higgs mass m/, as a function of AU:d in the Figure.
As we can see from the Figure, the constraint m/, = = 125 126 GeV requires small Xu ~ 0.1 0.25 and large Ad ~ 0.8 for large tg /? values, while large Xu ~ 0.8 0.9 and small Ad ~ 0.2 0.25 for small tg /? values. Therefore, regardless of tg/?, one of the two Higgs triplets AU:d has to be significantly coupled to the MSSM Higgs sector XU(Xd) ~ 1. This scenario, on top of raising the SM-like Higgs boson mass, can at the same time enhance the Higgs decay width to the diphoton [8,13,14] and the Higgsino mixing in the neutralino sector.
+ (Au IH^ % -Ad\H»\~ % + H.c.) + + 4i<XuH%H°6°u - 4i<XdH%H°X + + 4A2 \H°U\2 |á°uI2 + 4A2 \H¡\2 |á°|2 + +/'A Kl" l-^dl +2/'aAuSd
m
SÍ + S-2
SV
d I
x \\H°,\
si - S-2
(9)
The triplets are expected to nearly decouple from the doublets because their mixings are induced by the triplet vevs, which however should be much smaller than a few GeVs, because otherwise the p parameter would deviate from unity beyond the experimentally allowed level [8]. In this picture, ignoring the insignif-
3. NEUTRALINO AND LSP
In the present model, after the eloctroweak symmetry breaking, the neutral gauginos B and M"° combine with the two neutral MSSM Higgsinos h^, and the neutral Higgsino triplets (triplinos) 6®, d~d to form six mass eigenstates, called neutralinos. Wo lot them be denoted by Arj=i;2,... conventionally labeled in the ascending order, such that in eigonstate basis
< m?} • In the gauge-
the neutralino-mass part of the Lagrangian is
(ID
where the neutralino mass matrix takes the form
l) We use the abbreviations ,
O: = ß, 0\Y .
sin a and ca = coso: for
Ml 0 -Mzcpsw Mzsfisw 0 0
0 M-2 MZ(-fi(-w -MzHfiCw 0 0
-MzCfiHw MZ(-fi(-W 0 A dt'Cfi 0
MzSf}Sw -MzHfiCw 0 0 -Kviip
0 0 A d't'Cfi 0 0 /'■A
0 0 0 -Kviip /'■A 0
The entries Mi and M2 in this matrix come directly from the MSSM soft Lagrangian, while the entries —//. are the supersymmetric Higgsino mass terms. The terms proportional to Mz are the result of Higgs Higgsino gaugino couplings, with the Higgs scalars replaced by their vevs after some rearranging, and the zero entries refer to the neglegted terms MzVAu,d8w/v and MzVAu,dCw/v proportional the suppressed triplet vevs t^ as constrained by the elec-troweak data [7].
The analytic analysis of the resu
Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.