Table Of ContentHU-SEFT R 1996-16,
FTUV 96/34, IFIC 96/40
(hep-ph/9606311)
7
9
DOUBLY CHARGED HIGGS AT LHC
9
1
n
a K. HUITU
J Research Institute for High Energy Physics
6 University of Helsinki, Finland
2
J. MAALAMPI
v
1 Department of Physics, Theory Division
1 University of Helsinki, Finland
3
6 A. PIETILA¨
0
Department of Applied Physics
6
9 University of Turku, Finland
/
h
and
p
-
p M. RAIDAL
e Department of Theoretical Physics
h
University of Valencia, Spain
:
v
i
X
r
a
Abstract
We have investigated production of doubly charged Higgs particles ∆++ via WW
L,R
fusion process in proton-proton collisions at LHC energies in the framework of the left-
right symmetric model. The production cross section of the right-triplet Higgs ∆++ is
R
for representative values of model parameters at femtobarn level. The discovery reach
depends on the mass of the right-handed gauge boson W . At best ∆++ mass up to 2.4
R R
TeV are achievable within one year run. For ∆++ the corresponding limit is 1.75 TeV
L
which depends on the value of the left-triplet vev v . Comparison with Drell-Yan pair
L
production processes shows that studies of the WW fusion processes extend the discovery
reachofLHCroughlybyafactoroftwo. Themainexperimentalsignalofaproduced∆++
L,R
would be a hard same-sign lepton pair. There will be no substantial background due to
theStandardModel(SM)interactions, sinceintheSMasame-signleptonpairwillalways
be associated with missing energy, i.e. neutrinos, due to lepton number conservation.
1
1 Introduction
Doubly charged scalar particles arise in many scenarios [1] extending the weak interac-
tions beyond the Standard Model (SM). In the left-right symmetric (LR) electroweak
theory [2] such a particle is a member of a triplet Higgs representation which plays a
crucial part in the model. The gauge symmetry SU(2) SU(2) U(1) of the
L R B−L
× ×
LR model is broken to the SM symmetry SU(2) U(1) due to a triplet Higgs ∆ ,
L Y R
×
whose neutral component acquires a non-vanishing expectation value in the vacuum. The
∆ , called the right-triplet, transforms according to ∆ = (1,3,2), and it consists of
R R
the complex fields ∆0, ∆+ and ∆++. If the Lagrangian is assumed to be invariant un-
R R R
der a discrete L R symmetry, it must contain, in addition to ∆ , also a left-triplet
R
↔
∆ = (∆0,∆+,∆++) = (3,1,2). Hence the LR model predicts two kinds of doubly
L L L L
charged particles with different interactions. In contrast with ∆ , the existence of ∆ is
R L
not essential from the point of view of the spontaneous symmetry breaking of the gauge
symmetry. The vacuum expectation value v of its neutral member is actually quite
L
tightly bound by the ρ parameter, i.e. by the measured mass ratio of the ordinary weak
bosons.
The triplet Higgses have the following Yukawa couplings to the leptons:
= h ΨT Cσ ∆ Ψ +h ΨT Cσ ∆ Ψ + h.c., (1)
LY R,ij iR 2 R jR L,ij iL 2 L jL
where Ψ = (ν ,l ) and i,j are flavour indices. From the point of view of phe-
iR,L iR,L iR,L
nomenology a very important fact is that the U(1) symmetry prevents quarks from
B−L
coupling to ∆ and ∆ . In the processes that involve hadrons the triplet Higgses appear
R L
thus only through higher order corrections.
TheYukawaLagrangian(1)leadstolargeMajoranamasstermsoftheformh ∆0 ν ν
R,ijh Ri iR jR
for the right-handed neutrinos. These give rise to the see-saw mechanism [3], which pro-
vides the simplest explanation to the lightness of ordinary neutrinos, if neutrinos do have
a mass. The anomalies measured in the solar [4] and atmospheric [5] neutrino fluxes seem
to require that neutrinos indeed have a mass, manifested in these phenomena through
flavour oscillations. Furthermore, the observations of COBE satellite [6] may indicate the
existence of a hot neutrino component in the dark matter of the Universe. In the frame-
work of SM these observations are difficult to explain, since there neutrinos are predicted
to be massless.
2
Apart from the question of neutrino mass, the LR model is more satisfactory than the
SM also in that it gives a better understanding of parity violation and it maintains the
lepton-quark symmetry in weak interactions.
Nevertheless, so far there has been no direct evidence of left-right symmetry in weak
interactions. This sets a lower bound to the energy scale of the breaking of that symme-
try. According to the direct searches of the CDF and D0 experiments at Tevatron, the
intermediate bosons of the right-handed interactions have the mass limits M > 652
WR
∼
GeV [7] and M > 650 GeV (720 GeV if the right-handed neutrino is assumed to be
WR
∼
much lighter than W ) [8], respectively. The mass limit for the new neutral intermediate
R
boson is M > 445 GeV [9]. Although there are some assumptions behind these bounds
Z2
∼
concerning e.g. the strength g of the right-handed gauge interactions in comparison
R
with the strength g of the left-handed interactions and the form of the CKM matrix of
L
the right-handed interactions, which may, when relaxed, degrade the boundsconsiderably
[10], it is reasonable to assume that below the scale of 0.5 TeV the left-right symmetry is
broken.
Hence, iftheright-handedelectroweak interactions exist, their discovery wouldrequire
accelerators whose capacity exceeds that of the present ones. The phenomenological
signatures of the LR model in 0.5 – 2 TeV linear colliders have been recently under
intensive study [11]. Particularly the signatures of the doubly charged scalar at e+e−
linear collider were discussed in ref. [12]. The production of a single doubly charged
Higgs in ep collisions at Hera was studied in ref. [13].
In previous works only the pair production of the left-triplet ∆++ in pp collisions at
L
SSC has been investigated [14]. In the present paper we shall investigate the prospects of
testing the production of single doubly charged Higgs scalars in high-energy pp collisions
at LHC. Our main concern will be the right-triplet ∆++ but we will also study the
R
production of the left-triplet ∆++. Comparison with Drell-Yan pair production processes
L
shows that the present study extends the discovery reach of ∆++ at LHC considerably for
most of the allowed parameter space of the model. The production of a single ∆++ in pp
L
collisions was also investigated in ref. [15] in the framework of Georgi-Machacek model,
which differs from the left-right symmetric model in some phenomenologically important
points, e.g. it has a new complex triplet with Y=0 and it is assumed that there are no
Majorana type couplings of doubly charged Higgs to leptons.
Let us briefly summarize the present experimental limits on the mass M and the
∆
3
possibly non-diagonal couplings h of the doubly charged scalar particle (see [16] and
ij
references therein). The most stringent constraint comes from the upper limit for the
flavour changing decay µ eee:
→
h h < 3.2 10−11 GeV−2 M2 . (2)
eµ ee × · ∆++
From the Bhabha scattering cross section at SLAC and DESY the following boundon the
h coupling was established:
ee
h2 < 9.7 10−6 GeV−2 M2 . (3)
ee × · ∆++
∼
For h =0.6, forexample, themass of thedoublycharged bosonshouldobeyM > 200
ee ∆++
∼
GeV, but for smaller couplings much lighter doubly charged scalars are still allowed. For
the coupling h the extra contribution to (g 2) yields the limit
µµ µ
−
h2 < 2.5 10−5 GeV−2 M2 , (4)
µµ · · ∆++
∼
and the muonium transformation to antimuonium converts into a limit
h h < 5.8 10−5 GeV−2 M2 . (5)
ee µµ · · ∆++
∼
From non-observation of the decay µ eγ follows
→
h h < 2 10−10 GeV−2 M2 . (6)
eµ µµ · · ∆++
∼
From the condition of vacuum stability one can derive upper bounds on the couplings
independent on the triplet Higgs mass [17]: h , h < 1.2.
ee µµ
∼
Thepaperproceedsasfollows. Inthenextsection wewillbrieflydescribetheleft-right
symmetric model. Section 3 contains our results for the production and decay of ∆++,
L,R
as well as a discussion on the background. Conclusions are presented in Section 4.
2 Description of the left-right symmetric model
In this section we will present the basic structure of the SU(2) SU(2) U(1) left-
L R B−L
× ×
right symmetric model. Quarks and leptons are assigned to the doublets of the gauge
groups SU(2) and SU(2) according to their chirality:
L R
ν ν
e e
Ψ = = (2,1, 1), Ψ = = (1,2, 1),
L e− ! − R e− ! −
L R
u 1 u 1
Q = = (2,1, ), Q = = (1,2, ), (7)
L R
d ! 3 d ! 3
L R
4
and similarly for the other families. The minimal set of fundamental scalars, if the theory
is symmetric under the L R transformation, consists of the following Higgs multiplets:
↔
φ0 φ+
Φ = 1 1 = (2,2,0),
φ− φ0 !
2 2
∆+ √2∆++
∆ = L L = (3,1,2), (8)
L √2∆0 ∆+ !
L − L
∆+ √2∆++
∆ = R R =(1,3,2).
R √2∆0 ∆+ !
R − R
† † †
They transform according to Φ U ΦU , ∆ U ∆ U and ∆ U ∆ U , where
→ L R L → L L L R → R R R
U is an element of SU(2) . The vacuum expectation value of the bidoublet Φ is
L(R) L(R)
given by
1 κ 0
1
Φ = . (9)
h i √2 0 κ2 !
This breaks the Standard Model symmetry SU(2) U(1) . It generates masses to
L Y
×
fermionsthroughtheYukawacouplingsΨ¯i (f Φ+g Φ˜)Ψj +h.c.andQ¯i (fqΦ+gq Φ˜)Qj +
L ij ij R L ij ij R
h.c., where Φ˜ = σ Φ∗σ .
2 2
The vacuum expectation values of the scalar triplets are denoted by
1 0 0
∆ = . (10)
L,R
h i √2 vL,R 0 !
The right-triplet ∆ breaks the SU(2) U(1) symmetry to U(1) , and at the same
R R B−L Y
×
time the discrete L R symmetry, and it yields a Majorana mass to the right-handed
↔
neutrinos, as was discussed in Introduction. It was also mentioned that the vacuum
expectation value v of the left-triplet is quite tightly bound by the ρ parameter. One
L
has (κ2 = κ2+κ2)
1 2
M2 1+2v2/κ2
ρ = WL L , (11)
cos2θ M2 ≃ 1+4v2/κ2
W Z1 L
and the experimental result [9] ρ= 1.0004 0.003 then implies v < 9 GeV, a small value
L
±
∼
compared with κ 250 GeV.
≃
The Higgs potential describing the mutual interactions of Φ, ∆ and ∆ is in general
R L
quite complicated containing a great number of parameters. The most general potential
for these fields is given in ref. [18]. There are severe constraints on the model parameters,
the most crucial ones for our study concern v and flavour changing neutral currents
L
(FCNC). It was argued in ref. [18] that in phenomenologically consistent models either
5
v is exactly zero or a certain combination of the potential parameters, (2ρ ρ ), should
L 1 2
−
vanish identically. Since there is no fundamental principle requiring v 0 we assume
L
≡
the latter possibility and study how to probe the value of v in single ∆++ production
L L
at LHC. In this case one expects the splitting between ∆++ and ∆++ masses to be large
L R
leading to the relatively light ∆++.
L
Unlike in the SM, in the LR model there are FCNC interactions mediated by some
neutralHiggs fieldswhicharecertain superpositionsoftheneutralsmembersofthebidou-
blet Φ. In order to suppress FCNC one must require the Higgs potential to be such that
in the minimum κ κ or κ κ . This requirement has the consequence that the
1 2 1 2
≪ ≫
W ,W mixing ζ is necessarily small, because ζ (g /g )2κ κ /v 2. We will assume
L R L R 1 2 R
≃ | | | |
κ = 0, which leaves W and W as unmixed physical particles.
2 L R
The masses of the charged gauge bosons are given in the case of no mixing and v = 0
L
by the exact formulae
1
M2 = g2κ2, (12)
WL 4 L 1
1
M2 = g2(2v2 +κ2). (13)
WR 4 R R 1
If the L R symmetry is implemented, the gauge couplings g and g should be equal
L R
↔
(g = g 0.64). If no such symmetry is assumed, the internal consistency within the
R L
≃
model requires nevertheless g > 0.55g [21]. In order to satisfy the lower mass limits
R L
∼
of the new weak bosons W and Z , the vev of the right-handed triplet, v , should
R R R
be considerably larger than κ . Using the experimental value of the ordinary weak
1
boson M = 81 GeV and the Tevatron lower bound M > 650 GeV and assuming
WL WR
∼
g g = 0.64, we find v > 5.6 κ 1.4 TeV.
R L R 1
≃ ≃
∼
The see-saw mass matrix of neutrinos is given by
m m
L D
M = . (14)
mTD mR !
Theentriesare3 3matricesgivenbym = (fκ +gκ )/√2,m = h v andm = h v .
D 1 2 L L L R R R
×
The mass of the charged lepton is given by m = (fκ +gκ )/√2, and therefore if f and
l 2 1
g are comparable, one has m m . Unless there is an extraordinary hierarchy among
D l
≃
the couplings, one has m m m . In this case the approximate masses of the
L D R
≪ ≪
Majoranastates thatdiagonalize theneutrinoLagrangian aregiven bym mTm−1m
ν1 ≃ D R D
and m m .
ν2 ≃ R
6
Ignoringthemixingbetweenfamiliesandconsideringthematrix(14)topresentmixing
of left-handed and right-handed neutrino of one family, one obtains the mass eigenvalues
m m2 /m and m m , and the mixing angle η between these states is given by
ν1 ≃ D R ν2 ≃ R
2m
D
tan2η = . (15)
m
R
The mixing of left- and right-handed neutrinos is thus in general very small, and one can
identify ν with ν and ν with ν as a good approximation.
1 L 2 R
The mass of the heavier neutrino ν , the ”right-handed” neutrino, is related to the
2
mass of W via
R
h
R
m M . (16)
ν2 ≃ g WR
R
Most naturally the heavy neutrino and the heavy weak boson would have roughly the
same mass, but depending on the actual value of the Yukawa coupling constant h the
R
neutrino may also be lighter or somewhat heavier than W .
R
3 Signals of doubly charged Higgs production at
LHC
3.1 Production of doubly charged Higgses at LHC
We will assume that the doubly charged Higgs bosons ∆++ are light enough to be pro-
L,R
duced as real particles at LHC, and we will study separately their production and subse-
quent decay modes, concentrating mainly on the right-triplet ∆++. However, in the cases
R
when the situation in the left-handed sector differs from the right-handed one we will
presentthedifferences. In pp-collisions ∆++ cannot beproducedin interactions of quarks
L,R
because of the charge conservation. However, it can be produced through W W fu-
L,R L,R
sion, either by virtual or real W ’s, depending on the mass of ∆++. The WW fusion
L,R L,R
is not the only possibility, since also the physical singly charged Higgs scalars (κ = 0
2
assumed)
1 κ
h+ = (Φ+ + 1 ∆+), (17)
1+ κ21 1 √2vR R
2v2
R
r
1 √2v
δ+ = (∆++ LΦ+), (18)
1+ 2vL2 L κ1 2
κ2
r 1
7
q q q
W W F +
D ++ D ++ D ++
W F + F +
q' q' q'
Figure 1: Feynman graphs contributing to the production of doubly charged Higgs at LHC.
have tree level couplings both to the doubly charged Higgses and the quarks.
Another production mechanism of ∆++ at pp collider is via γ,Z ,Z exchange, i.e.
L,R L R
qq γ∗,Z∗ ∆++∆−− and qq γ∗,Z∗ ∆++∆−−. The latter process has been
→ R → R R → L → L L
studied at SSC energy in ref. [14]. While for low values of ∆++ mass the cross section
L,R
of the pair production is comparable with, or may even exceed, that of the WW fusion
reactions, its kinematical reach is much lower. Indeed, we are going to see that with the
present experimental constraints on model parameters the ∆++ mass reach at LHC in
L,R
the Drell-Yan processes is roughly half of the one in WW fusion processes.
TheFeynman graphs for the production processes of single ∆++ are depicted in Fig.1,
R
where φ+ stands for the scalars h+ and δ+. Let us investigate the relative importance
of the amplitudes. The WW fusion vertex W−W−∆++ follows from the gauge invariant
R R R
kinetic term (Dµ∆ )†D ∆ as a result of the spontaneous breaking of the left-right
R µ R
symmetry, and it is given by
1
g2v W−W−∆++. (19)
√2 R R R R R
The higher the symmetry breaking scale v is, the stronger the coupling is, but on the
R
otherhandtheheavierW is. Thecorrespondingvertex fortheleft-triplet∆++ ispropor-
R L
tional to the small quantity v , which suppresses the fusion production of ∆++. However,
L L
in this case the lightness of W boson enhances the production rate and, as explained
L
in Section 2, ∆++ is expected to be somewhat lighter than ∆++. If v = 0 then the
L R L
Drell-Yan process is the only possibility to produce the left-triplet Higgs boson.
The φ−φ−∆++ coupling arises from the following quadratic terms of the scalar poten-
R
tial (we use the notation of ref. [18]):
β Tr(Φ∆ Φ†∆†)+β Tr(Φ˜∆ Φ†∆†)+β Tr(Φ∆ Φ˜†∆†), (20)
1 R L 2 R L 3 R L
8
which yields the couplings
1
v ∆++(β Φ−Φ− β Φ−Φ− β Φ−Φ−). (21)
√2 L R 1 1 2 − 2 1 1 − 3 2 2
This contributes much less to the ∆++ production than the WW fusion (19) for several
R
reasons. First,thedimensionfulcouplingv istinycomparedwiththatoftheW−W−∆++
L R R R
vertex v . Second, the couplings of the bidoublet fields Φ and Φ to quarks are Yukawa
R 1 2
couplings and hence proportional to the mass ratio m /M , which is small compared
q WL
with the gauge coupling g appearing in the WW fusion amplitude. Furthermore, in
R
realistic models the coupling constants β are necessarily small [18], otherwise one would
i
face a serious fine tuning problem. In the case of δ+ there is still an extra suppression
due to the fact that the bidoublet component appears in δ+ with just a small weight of
√2v /κ < 0.04 (see Eq. (18)).
L 1
∼
The∆++W−φ−vertexinthegraphsofFig.1. derivesfromthekineticterm(Dµ∆ )†D ∆ ,
R R R µ R
which yields the coupling
ig W− (∆−∂µ∆++ ∆++∂µ∆−). (22)
R Rµ R R − R R
This amplitude is possible for h−, but not for δ− which does not have a right-triplet
component. For h− the process is suppressed, in addition to the small Higgs coupling
with quarks, also due to the small weight κ /√2v of the ∆− component.
1 R R
We can conclude that the W W fusion process dominates the production of single
R R
∆++ in pp collisions, and the Higgs exchange diagrams can be safely ignored (except
R
in the unprobable case that W is orders of magnitude heavier than the singly charged
R
Higgses). The same is also true for the left-triplet Higgs boson production process.
We have performed calculations of the WW fusion process in Fig.1. without making
any simplifying assumptionstaking into account the threeparticle finalstate phasespace.
To obtain numerical values for the cross sections and final state distributions we have
convoluted thefunctionsover theinitialstate quarksmomentumspectrausingthedefault
MRS-G set of the parton distributions of CERN Library program PDFLIB [19]. All
numericalintegrations have beenperformedby the integration routineVEGAS [20] which
ensures high accuracy of the results.
The production cross sections for ∆++ in WW fusion are presented in Fig.2. by bold
L,R
lines. InFig.2. (I)thecross section of ∆++ productionis plotted for threedifferentvalues
R
of W mass as a function of ∆++ mass. For low ∆++ masses the cross section is a quite
R R R
9
rapidly falling function of M , e.g. going from 650 GeV to 1.5 TeV, the cross section
WR
for M++ = 200 GeV decreases more than an order of magnitude. If light ∆++ will be
∆R R
detected then this sensitivity can be used to obtain indirect information about W mass.
R
For heavy ∆++, however, the cross section depends on M rather weakly which allows
R WR
one to probe large Higgs masses. With the present lower value M = 650 GeV, the
WR
designed LHC luminosity of 100 fb−1 per year and assuming that ten events are needed
for discovery, ∆++ as heavy as 2.4 TeV can be found at LHC. We have also calculated
R
the Drell-Yan pair production cross section of ∆++ (assuming Z to be very heavy) and
R R
presented it by dashed line in Fig.2. (I). For M < 1 TeV and M++ > 500 GeV the
WR ∆R
∼ ∼
WW fusion cross section exceeds the Drell-Yan one which falls below the discovery limit
if M++ > 1 TeV.
∆R
∼
If v vanishes, the production of ∆++ in W+W+ fusion is not possible due to the
L L L L
proportionality of the corresponding coupling to v analogously to Eq. (19). The single
L
productionby other mechanisms is too small to beobserved as explained previously. Ifv
L
differs from zero, also ∆++ production is possible. For the allowed vev v = 9 GeV the
L L
WW fusion production cross section is shown in Fig.2. (II) by the bold line. In this case
the free parameters to be tested are the vev v and the mass of ∆++ (the cross section
L L
scales as v2). With the chosen value of v the production cross section is comparable
L L
with the ∆++ production one but it falls faster with the Higgs mass. The discovery limit
R
of ∆++ is as high as 1.75 TeV. In this case the Drell-Yan cross section, also presented in
L
Fig.2. (II), is a few percent bigger than for the right-triplet Higgs due to additional Z
L
contribution but, as seen in figure, its discovery potential is the same.
Especially for background considerations it will be interesting to study the angular
distribution of ∆++. In Fig.3. the p and E distributions are shown for m =500
R T ∆R ∆++
R
GeV and M =1 TeV. Comparing the distributions it is seen that the doubly charged
WR
Higgses are mostly transverse. As the angular distribution of the decay products of ∆++
R
is flat, the loss of events in small forward angles is not essential.
3.2 Decay of the triplet Higgs
In the lowest order the doubly charged scalar ∆++ can decay via the following channels:
R
∆++ l+l′+, (23)
R →
W+W+, (24)
→ R R
10
