Little Higgs models with a light T quark

Abstract

We study little Higgs models based on a SU1(3)×SU2(3) global symmetry and with two scales (the two vacuum expectation values f1,2) substantially different. We show that all the extra vector boson fields present in these models may be much heavier than the vectorlike T quark necessary to cancel top-quark quadratic corrections. In this case the models become an extension of the Standard Model with a light (≈500 GeV)T quark and a scalar Higgs field with a large singlet component. We obtain that the Yukawa and the gauge couplings of the Higgs are smaller than in the standard model, a fact that may reduce significantly the Higgs production rate through glu–glu and WW fusion. The T quark decay into Higgs boson becomes then the dominant Higgs production channel in hadron colliders.

Full text

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arXiv:hep-ph/0701040v3 24 May 2007
UG-FT-213/07
CAFPE-83/07
Little Higgs models with a light T quark
R. Barcel´ o, M. Masip and M. Moreno-Torres∗
CAFPE and Departamento de F´ ısica Te´ orica y del Cosmos
Universidad de Granada, E-18071, Granada, Spain
barcelo@correo.ugr.es, masip@ugr.es, miguelmtt@ugr.es
Abstract
We study Little Higgs models based on a SU(3)1× SU(3)2global symmetry and
with two scales (the two vacuum expectation values f1,2) substantially different. We
show that all the extra vector boson fields present in these models may be much heavier
than the vectorlike T quark necessary to cancel top-quark quadratic corrections. In
this case the models become an extension of the standard model with a light (≈ 500
GeV) T quark and a scalar Higgs field with a large singlet component. We obtain that
the Yukawa and the gauge couplings of the Higgs are smaller than in the standard
model, a fact that may reduce significantly the Higgs production rate through glu-glu
and WW fusion. The T-quark decay into Higgs boson becomes then a dominant Higgs
production channel in hadron colliders.
∗Present Address: Depto. de F´ ısica Moderna, Univ. de Granada, 18071 Granada, Spain.

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1Introduction
The naturalness of the electroweak (EW) scale has been the main motivation to presume
new physics below Λ ≈ 1 TeV. We have hints of a large grand unification scale, and we know
that the Planck scale is there, so we need a mechanism that cancels the quantum corrections
introduced by these large scales. The majoritary point of view has been that supersymmetry,
technicolor or, more recently, extra dimensions could do the job and rise the cutoff of the
standard model (SM) up to the fundamental scale.
This point of view, however, has become increasingly uneasy when facing the experi-
mental evidence. Flavor physics, electric dipole moments and other precision electroweak
observables suggest that, if present, the sfermion masses, the technicolor gauge bosons, or
the Kaluza-Klein excitations of the standard gauge fields are above 5 TeV [1]. To be effec-
tive below the TeV and consistent with the data these models require a per cent fine tuning,
whereas their presence at 5 TeV implies that nature deals with the Higgs mass parameter
m2
two digits. It may be more consistent either to presume that there should be another reason
explaining this little hierarchy between the EW and the scale of new physics or that there is
no dynamical mechanism that cancels any fine tuning in m2
has been seriously considered after recent astrophysical and cosmological data suggested a
non-zero vacuum energy density (the preferred value does not seem to be explained by any
dynamics at that scale), and it will be clearly favored if no physics beyond the SM is observed
at the LHC.
hfirst using a mechanim to cancel 30 digits and then playing hide and seek with the last
h[2, 3]. This second possibility
Little Higgs (LH) ideas [4, 5, 6] provide a very interesting framework with natural can-
celations in the scalar sector. New symmetries protect the EW scale and define consistent
models with a cutoff as high as Λ ≈ 10 TeV, scale where a more fundamental mechanism
(SUSY [7] or extra dimensions [8]) would manifest. Therefore, these models could describe
all the physics to be explored in the next generation of accelerators. More precisely, in LH
models the scalar sector has a (tree-level) global symmetry that is broken spontaneously at
a scale f ≈ 1 TeV. The SM Higgs doublet is then a Goldstone boson (GB) of the broken
symmetry, and remains massless and with a flat potential at that scale. Yukawa and gauge
interactions break explicitly the global symmetry. However, the models are built in such a
way that the loop diagrams giving non-symmetric contributions must contain at least two
different couplings. This collective breaking keeps the Higgs sector free of one-loop quadratic
top-quark and gauge contributions (see [9, 10] for a recent review). Two types of models
have been extensively considered in the literature: the ones based on a simple group (littlest
SU(5) model [5]) and the ones based on a product group (simplest SU(3) × SU(3) model
2

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[11]) of global symmetries.
Of course, an important point is then if the new physics that these models introduce is
consistent with the data. In [12] it is shown that in general this is not the case, and the
degree of fine tuning that they require is not below the one, for example, in the MSSM. LH
models include an extra T quark (that cancels quadratic top quark corrections) and massive
gauge boson fields (that cancel quadratic gauge contributions and absorb extra GBs that
otherwise would be massless). It is this later type of fields, the extra gauge bosons, the one
giving large corrections to EW observables through mixing with the standard gauge bosons
and through direct couplings with the light fermions. In models based on a global SU(5)
symmetry this problem can be solved imposing a Z2symmetry known as T parity [13, 14].
This symmetry is analogous to the R parity of SUSY models: under T all the extra fields
except for the T quark are odd, whereas the standard fields are even. As a consequence, the
mixing of standard and extra gauge bosons as well as the tree level exchange of extra bosons
by standard fermions are forbidden. This keeps the corrections under control and allows T
quarks as low as 500 GeV, as required for an effective cancelation of quadratic corrections
in the Higgs sector. Unfortunately, in the simplest SU(3) × SU(3) model it is not possible
to implement a T parity.
In this paper we explore the simplest LH model [11, 15, 16] and find that it can also
accommodate a relatively light T quark together with suppressed extra gauge boson contri-
butions. This is achieved when the two VEVs f1and f2in these models are substantially
different. We analize this case and show that it has important phenomenological implications
in Higgs physics. As we will argue, analogous results would be obtained in any LH model
with a relatively low scale of global symmetry breaking.
2The model
Let us start describing in some detail the model. The scalar sector contains two triplets, φ1
and φ2, of a global SU(3)1× SU(3)2symmetry:
φ1→ eiθa
where Taare the generators of SU(3). It is assumed that the scalar triplets get vacuum
expectation values (VEVs) f1,2and break the global symmetry to SU(2)1× SU(2)2. The
spectrum of scalar fields at this scale consists then of 10 massless modes (the GBs of the
broken global symmetry) plus two massive fields (with masses of order f1and f2). If one
combination of the two global SU(3) is made local, some of the GBs will be eaten by massive
gauge bosons and the rest will define the SM Higgs sector.
1Taφ1,φ2→ eiθa
2Taφ2,(1)
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In particular, if the two VEVs are
?φ1? =




0
0
f1



,?φ2? =




0
0
f2



,(2)
and the diagonal combination of SU(3)1× SU(3)2is made local,
φ1→ eiθa(x)Taφ1,φ2→ eiθa(x)Taφ2,(3)
then the VEVs break SU(3) ×U(1)χto the standard SU(2)L× U(1)Y, a process that takes
5 GBs. The other 5 GBs (the complex doublet (h0h−) and a CP-odd singlet η) can be
parametrized non-linearly [17]:
φ1= e+i
f2
f1Θ




0
0
f1



,
η/√2
0
h0†
φ2= e−i
f1
f2Θ




0
0
f2



,(4)
where
Θ =1
f




0h0
h−
η/√2
h+
η/√2




(5)
and f =
?
f2
1+ f2
2.
If the global symmetry were exact, the Higgs boson would be massless. However, the
symmetry is just approximate (it is broken by top-quark and gauge-boson loops), so we
expect that the non-symmetric operators will appear just suppressed by a loop factor. This
may (should) give an acceptable VEV and a mass to the Higgs [18]. Let us then assume
that the real component of h0gets a VEV,
?h0? = u/√2 ,(6)
and gives mass to the standard fermions and gauge bosons. This Higgs VEV implies the
triplet VEVs


f1c1
?φ1? =


if1s1
0



,?φ2? =




−if2s2
0
f2c2



,(7)
where
s1≡ sin
uf2
√2ff1
,s2≡ sin
uf1
√2ff2
.(8)
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To obtain the observed W and Z masses one needs
?
f2
1s2
1+ f2
2s2
2=
v
√2= 174 GeV . (9)
Notice that using this non-linear realization of φithe Higgs VEV u is not 246 GeV, although
it goes to this value in the limit of large f1and f2(small s1and s2).
In the unitary gauge all the GBs except for the singlet η and the standard neutral Higgs
h are eaten by massive gauge bosons. In particular, it is easy to deduce the relation between
φ1,2and these fields:
φ1 = exp
?
i
f2η
f1f√2
?








if1(s1cos
hf2
√2ff1
+ c1sin
hf2
√2ff1
)
0
f1(c1cos
hf2
√2ff1
− s1sin
hf2
√2ff1
)








,
φ2 = exp
?
−i
f1η
f2f√2
?








−if2(s2cos
hf1
√2ff2
+ c2sin
hf1
√2ff2
)
0
f2(c2cos
hf1
√2ff2
− s2sin
hf1
√2ff2
)








.(10)
3A light T quark
As explained in the introduction, we are interested in models where the extra gauge bosons
are heavy while the vectorlike T quark that cancels quadratic corrections is lighter. The
first requirement fixes the scale f =
f2
top-quark Yukawa sector includes a triplet ΨT
described by the Lagrangian
?
1+ f2
2, as the gauge boson masses are ≈ gf. The
Q= (t b T) and two singlets (tc
1, tc
2), and it is
− Lt= λ1φ†
1ΨQtc
1+ λ2φ†
2ΨQtc
2+ h.c. , (11)
where all the fermion fields are two-component spinors. In the limit of exact symmetry (i.e.,
s1= 0 = s2) the top quark is massless and the extra T quark has a mass mT:
− Lt⊃ λ1f1Ttc
1+ λ2f2Ttc
2+ h.c. = mTTTc+ h.c. ,(12)
where mT=
?
λ2
1f2
1+ λ2
2f2
2and Tc= sαtc
1+ cαtc
2, with sα= λ1f1/
?
λ2
1f2
1+ λ2
2f2
2.
Once the Higgs VEV u is included, it is easy to see that in order to have mTsignificantly
smaller than f we need f1≪ f2and λ2≪ λ1. If we define f1≡ ǫf2, λ1≡ λ and λ2≡ ǫ′λ
5