arXiv:0704.1395v1  [hep-ph]  11 Apr 2007
Preprint typeset in JHEP style - HYPER VERSION
Higgs and Z ′ Phenomenology in B − L extension of
the Standard Model at LHC
W. Emam and S. Khalil
Center for Theoretical Physics at the British University in Egypt, Sherouk City, Cairo
11837, Egypt.
Faculty of Science, Ain Shams University, Cairo 11566, Egypt.
Abstract: The phenomenology of the low scale U(1)B−L extension of the standard model
and its implications at LHC is presented. In this model, an extra gauge boson corresponding
to B−L gauge symmetry and an extra SM singlet scalar (heavy Higgs) are predicted. We
show a detailed analysis of both heavy and light Higgses decay and production in addition
to the possible decay channels of the new gauge boson. We find that the cross sections
of the SM-like Higgs production are reduced by ∼ 20% − 30%, while its decay branching
ratios remain intact. The extra Higgs has relatively small cross sections and the branching
ratios of Z ′ → l+l− are of order ∼ 20% compared to ∼ 3% of the SM resuls. Hence, the
search for Z ′ is accessible via a clean dilepton signal at LHC.
Keywords: Low scale B − L, Higgs production, Higgs decays, Z ′ gauge boson.
http://arxiv.org/abs/0704.1395v1
http://jhep.sissa.it/stdsearch
Contents
1. Introduction 1
2. B − L extension of the SM 2
2.1 Symmetry breaking 2
2.2 Higgs sector 3
3. Higgs Production and Decay at Hadron Colliders 5
3.1 Higgs Production 5
3.2 Higgs Decay 9
4. Z ′ decay in B − L extension of the SM 12
5. Light H ′ Scenario 14
6. Conclusions 14
1. Introduction
The Standard Model (SM) of elementary particles has been regarded only as a low energy
effective theory of the yet-more-fundamental theory. Several attempts have been proposed
to extend the gauge symmetry of the SM via one or more U(1) gauge symmetries beyond
the hypercharge gauge symmetry, U(1)Y [1–3]. The evidence for non-vanishing neutrino
masses, based on the apparent observation of neutrino oscillation, strongly encourages this
type of extensions. In this class of models [1, 2], three SM singlet fermions arise quite
naturally due to the anomaly cancellation conditions. These three particles are accounted
for right handed neutrinos, and hence a natural explanation for the seesaw mechanism is
obtained.
A low scale B − L symmetry breaking, based on the gauge group GB−L ≡ SU(3)C ×
SU(2)L × U(1)Y × U(1)B−L, has been considered recently [2]. It was shown that this
model can account for the current experimental results of the light neutrino masses and
their large mixing. Therefore, it can be considered as one of the strong candidates for
minimal extensions of the SM. In addition, one extra neutral gauge boson corresponding
to B − L gauge symmetry and an extra SM singlet scalar (extra Higgs) are predicted.
In fact, the SM Higgs sector can be generally extended by adding extra singlet scalars
without enlarging its gauge symmetry group [4, 5]. In Ref.[2], it has been emphasized that
these new particles may have significant impact on the SM phenomenology, hence lead to
interesting signatures at Large Hadron Collider (LHC).
– 1 –
The aim of this paper is to provide a comprehensive analysis for the phenomenology of
such TeV scale extension of the SM, and its potential discovery at the LHC. The production
cross sections and the decay branching ratios of the SM like Higgs, H, and the extra Higgs
boson H ′ are analyzed. We also consider the decay branching ratios of the extra gauge
boson, Z ′.
We show that the cross sections of the Higgs production are reduced by ∼ 20%− 30%
in the interesting mass range of ∼ 120− 250 GeV relative to the SM predictions. However,
its decay branching ratios remain intact. In addition, we find that the extra Higgs (∼
TeV) is accessible at LHC, although it has relatively small cross sections. We also examine
the availability of the decay channel H ′ → HH, which happens to have very small partial
decay width. Concerning the Z ′ gauge boson, the branching ratios of Z ′ → l+l− are found
to be of order ∼ 20% compared to ∼ 3% of the SM BR(Z → l+l−).
This paper is organized as follows. In section 2 we review the Higgs mechanism and
symmetry breaking within the minimal B − L extension of the SM. We also discuss the
mixing between the SM-like Higgs and the extra Higgs boson. Section 3 is devoted for
the phenomenology of the two Higgs particles. The production cross sections and decay
branching ratios of these Higgs particles at LHC are presented. In section 4 we study the
decay of the extra gauge boson Z ′. In section 5 we briefly discuss the scenario of very light
Higgs. Finally we give our concluding remarks in section 6.
2. B − L extension of the SM
2.1 Symmetry breaking
The fermionic and kinetic sectors of the Lagrangian in the case of B − L extension are
given by
LB−L = i l̄Dµγµl + i ēRDµγµeR + i ν̄RDµγµνR
µν − 1
µν − 1
µν . (2.1)
The covariant derivative Dµ is different from the SM one by the term ig
′′YB−LCµ, where g
is the U(1)B−L gauge coupling constant, YB−L is the B−L charge, and Cµν = ∂µCν−∂νCµ
is the field strength of the U(1)B−L. The YB−L for fermions and Higgs are given in Table 1.
particle l eR νR q φ χ
YB−L −1 −1 −1 1/3 0 2
Table 1: B − L quantum numbers for fermions and Higgs particles
The Higgs and Yukawa sectors of the Lagrangian are given by
LB−L = (Dµφ)(Dµφ) + (Dµχ)(Dµχ)− V (φ, χ)
λe l̄φeR + λν l̄φ̃νR +
λνR ν̄
RχνR + h.c.
. (2.2)
– 2 –
Here, λe, λν and λνR refer to 3 × 3 Yakawa matrices. The interaction terms λν lφ̃νR and
λνR ν̄
RχνR give rise to a Dirac neutrino mass term: mD ≃ λνv and a Majorana mass term:
MR = λνRv
′, respectively. The U(1)B−L and SU(2)L × U(1)Y gauge symmetries can be
spontaneously broken by a SM singlet complex scaler field χ and a complex SU(2) doublet
of scalar fields φ, respectively. We consider the most general Higgs potential invariant
under these symmetries, which is given by
V (φ, χ) = m21φ
†φ+m22χ
†χ+ λ1(φ
†φ)2 + λ2(χ
+λ3(χ
†χ)(φ†φ), (2.3)
where λ3 > −2
λ1λ2 and λ1, λ2 ≥ 0, so that the potential is bounded from below. For
non-vanishing vacuum expectation values (vev’s), we require λ23 < 4λ1λ2 , m
1 < 0 and
m22 < 0. The vev’s, |〈φ〉| = v/
2 and |〈χ〉| = v′/
2, are then given by
1 − 2λ3m22
λ23 − 4λ1λ2
, v′2 =
−2(m21 + λ1v2)
Depending on the value of the λ3 coupling, one can have v
′ ≫ v or v′ ≈ v. Therefore, the
symmetry breaking scales, v and v′, can be responsible for two different symmetry breaking
scenarios. In our analysis we take v = 246 GeV and constrain the other scale, v′, by the
lower bounds imposed on the mass of the extra neutral gauge boson.
After the B−L gauge symmetry breaking, the gauge field Cµ (will be called Z ′ in the
rest of the paper) acquires the following mass:
m2Z′ = 4g
′′v′2. (2.4)
The experimental search for Z ′ at CDF experiment leads to mZ′ >∼ O(600) GeV. However,
the strongest limit comes from LEP II [6]:
mZ′/g
′′ > 6TeV . (2.5)
This implies that v′ >∼ O(TeV). Moreover, if the coupling g
′′ is < O(1), one can still obtain
mZ′ >∼ O(600) GeV.
2.2 Higgs sector
In addition to the SM complex SU(2)L doublet, another complex scalar singlet arise in
this class of models. Out of these six scalar degrees of freedom, only two physical degrees
of freedom, (φ, χ), remain after the B − L and electroweak symmetries are broken. The
other four degrees of freedom are eaten by Z ′, Z and W± bosons.
The mixing between the two Higgs scalar fields is controlled by the coupling λ3. In
fact, one finds that for positive λ3 , the B−L symmetry breaking scale, v′, becomes much
higher than the electroweak symmetry breaking scale, v. In this case, the SM singlet
Higgs, φ, and the SM like Higgs, χ, are decoupled and their masses are given by
2λ1v, Mχ =
′. (2.6)
– 3 –
For negative λ3, however, theB−L breaking scale is at the same order of the the electroweak
breaking scale. In this scenario, a significant mixing between the two Higgs scalars exists
and can affect the SM phenomenology. This mixing can be represented by the following
mass matrix for φ and χ:
M2(φ, χ) =
vv′ λ2v
. (2.7)
Therefore, the mass eigenstates fields H and H ′ are given by
cos θ − sin θ
sin θ cos θ
, (2.8)
where the mixing angle θ is defined by
tan 2θ =
|λ3|vv′
λ1v2 − λ2v′2
. (2.9)
The masses of H and H ′ are given by
m2H,H′ = λ1v
2 + λ2v
(λ1v2 − λ2v′2)2 + λ23v2v′2. (2.10)
We call H andH ′ as light and heavy Higgs bosons, respectively. In our analysis we consider
a maximum mixing between the two Higgs bosons by taking |λ3| ≃ λmax1 λmax2 , where λmax1
and λmax2 are given by
λmax1 =
m2H +m
4m2Hm
+ 1 + 1
λmax2 =
m2H +m
4m2Hm
+ 1− 1
, (2.11)
and the maximum mixing angle is then given by
tan 2θ =
λmax1 λ
λmax1 v
2 − λmax2 v′2
. (2.12)
By considering the maximum mixing and fixing v = 246 GeV and v′ = 1 TeV, we have
reduced the number of free parameters of this model into just two, namely mH and mH′ .
In Figure 1, we present the maximum mixing as a function of the light Higgs mass, mH
for mH′ = 500 GeV and 1 TeV.
Due to the mixing between the two Higgs bosons, the usual couplings among the SM-
like Higgs, H, and the SM fermions and gauge bosons are modified. In addition, there are
new couplings among the extra Higgs, H ′, and the SM particles:
gHff = i
cos θ, gH′ff = i
sin θ,
gHV V = −2i
cos θ, gH′V V = −2i
sin θ,
gHZ′Z′ = 2i
sin θ, gH′Z′Z′ = −2i
cos θ,
gHνRνR = −i
sin θ, gH′νRνR = i
cos θ. (2.13)
– 4 –
100 200 300 400 500 600 700 800 900 1000
θ2cos
(GeV)Hm
=500(GeV)H’m
=1000(GeV)H’m
Figure 1: H −H ′ mixing angle as function of mH for m′H = 500 GeV and 1 TeV.
The Higgs self couplings are give by
gH3 = 6i(λ1v cos
3 θ −
v′ cos2 θ sin θ),
gH′3 = 6i(λ2v
′ cos3 θ +
v cos2 θ sin θ),
gH4 = 6iλ1 cos
gH′4 = 6iλ2 cos
gHH′2 = 2i(
v cos3 θ + λ3v
′ cos2 θ sin θ − 3λ2v′ cos2 θ sin θ),
gH2H′ = 2i(
v′ cos3 θ − λ3v cos2 θ sin θ + 3λ1v cos2 θ sin θ),
gH2H′2 = iλ3 cos
4 θ. (2.14)
These new couplings lead to a different Higgs phenomenology from the well known
one, predicted by the SM. The detailed analysis of Higgs bosons in this class of models and
their phenomenological implications, like their productions and decays at the LHC, will be
discussed in the next section.
3. Higgs Production and Decay at Hadron Colliders
3.1 Higgs Production
At the LHC, two 7-TeV proton beams with a center-of-mass energy of 14 TeV and a
luminosity of 1034cm−2s−1 will collide with each other. The machine is expected to start
running early 2008. The detection of the SM Higgs boson is the primary goal of the LHC
project.
– 5 –
H, H ′
H, H ′
H, H ′
H, H ′
Figure 2: The dominant Higgs boson production mechanisms in hadronic collisions.
At hadron colliders, the two Higgs bosons couple mainly to the heavy particles: the
massive gauge bosons Z ′, Z and W± and the heavy quarks t, b. The main production
mechanisms for Higgs particles can be classified into four groups [7]: the gluon–gluon
fusion mechanism[8], the associated Higgs production with heavy top or bottom quarks[9],
the associated production with W/Z/Z ′ bosons[10], and the weak vector boson fusion
processes[11]:
gg → H (3.1)
gg, qq̄ → QQ̄+H, (3.2)
qq̄ → V +H (3.3)
qq → V ∗V ∗ → qq +H. (3.4)
The Feynman diagrams of these processes are displayed in Figure 2. The cross sections
of the Higgs production in these four mechanisms are directly proportional to the the Higgs
couplings with the associated particles.
In case of the gluon–gluon fusion mechanism the Higgs production is mediated by
triangular loops of heavy quarks. Thus, the cross section of this process is proportional
to the Higgs coupling with the heavy quark mass. In case of B − L extension of the SM,
the production cross sections for the light Higgs, H, and the heavy Higgs, H ′, can be
approximated as
σH ∝ α2s
cos2 θ
, (3.5)
σH′ ∝ α2s
sin2 θ
, (3.6)
where the first bracket is due to the coupling QQH(H ′), while the second bracket corre-
sponds to an approximated loop factor. As can be seen from Equations 3.5 and 3.6, the
– 6 –
H, H ′
Figure 3: Feynman diagrams for Higgs production in association with heavy quarks in hadronic
collisions, pp → qq̄, gg → QQ̄H , at LO.
cross section of the light Higgs production is reduced respect to the SM one by the factor
of cos2 θ. On the other hand, the heavy Higgs production is suppressed by two factors: the
small sin θ, and the large mH′ . Therefore, the the heavy Higgs production is typically less
than that of the light Higgs by two orders of magnitudes, i.e.,
≃ sin θ
cos θ2
≃ O(10−2). (3.7)
Now, we consider the mechanism of Higgs production in association with heavy quark
pairs, Equation 3.2. In addition to the Feynman diagram shown in Figure 2, a set of other
diagrams that also contribute to this process is given in Figure 3. Note that although
this process shares the same coupling with the gluon-gluon fusion process, the leading
order expression of its cross section indicates that it is less by one order of magnitude, for
mH(H′) < 1 TeV. Furthermore, the typical ratio of σ(gg → H ′QQ̄) to σ(gg → HQQ̄) is of
order (sin θ/ cos θ)2 ≃ O(0.1).
Finally, we study the Higgs production in association with W/Z/Z ′ bosons and in the
weak vector boson fusion processes, Equations 3.3 and 3.4 respectively. In B−L extension
of the SM, the cross sections of these channels are proportional to the mass of the gauge
boson and the mixing angle θ of the two Higgs bosons:
V ≡ W/Z : σH ∝
cos2 θ ×
× Loop function, (3.8)
σH′ ∝
sin2 θ ×
× Loop function. (3.9)
In case of V ≡ Z ′, The production is enhanced by the HZ ′Z ′ coupling arising with
mZ′ . However, it is suppressed by a large value of v
′ and the mass of the virtual gauge
boson(s), mZ′ :
V ≡ Z ′ : σH ∝
sin2 θ ×
(g′′Y
× Loop function, (3.10)
σH′ ∝
cos2 θ ×
(g′′Y
× Loop function. (3.11)
From these equations, one can observe that the relative ratio between the light Higgs
production associated with W/Z and Z ′ gauge bosons is given by σH(W/Z)/σH(Z
– 7 –
 [pb]σ
(GeV)Hm
 H→gg
 Hqq→qq
 WH→qq
 ZH→qq
 Z’H→qq
Ht t→,ggqq
 H+X)[pb]→(ppσ
=14 TeVs
MRST/NLO
=1 TeVH’m
Figure 4: The cross sections of the light Higgs production as function of mH : 100 GeV ≤ mH ≤
1 TeV, for mH′ = 1 TeV.
cos2 θ/ sin2 θ×g′′2/g2(g′2). Therefore, σH(W/Z) can be larger than σH(Z ′) by one order of
magnitude at most. In contrary, the situation is reversed for the heavy Higgs production
and one finds that σ′H(Z
′) > σ′H(W/Z), which confirms our earlier discussion.
The cross sections for the Higgs bosons production in these channels (Equations 3.1-
3.4) have been calculated using the FORTRAN codes: HIGLU, HQQ, V2HV, and VV2HV,
respectively [12]. Extra subroutines have been added to these programs for the new cou-
plings associated with the two higgs scalars and the extra gauge boson [12]. As inputs, we
use v = 246 GeV, v′ = 1 TeV, and center of mass energy
s = 14 TeV. We also fix the
mass of the extra gauge boson at mZ′ = 600 GeV. The cross sections for the light Higgs
boson production are summarized in Figure 4. as functions of the light Higgs mass with
mH′ = 1 TeV. Figure 5, on the other hand, represents the heavy Higgs productions as
functions of mH′ with mH = 200 GeV.
As shown in Figure 4, the salient feature of this low scale B − L extension is that
all cross sections of the light Higgs production are reduced by about 25 − 35% in the
interesting mass range: mH < 250 GeV. As in the SM, the main contribution to the
production cross section comes from the gluon-gluon fusion mechanism with a few tens of
pb. The next relevant contribution is given by the Higgs production in the weak vector
boson mechanism, Equation 3.4. This contribution is at the level of a few pb, as estimated
above. Furthermore, the production associated with Z/W is dominant over the production
associated with Z ′ for mH < 300 GeV.
Now, we analyze the production of the heavy Higgs. It turns out that its cross sections
are smaller than the light Higgs ones. As shown in Figure 5, all these cross sections are
scaled down by factor O(10−2), which is consistent with the result obtained in Equation 3.7.
Unlike the light Higgs scenario, the production associated with Z ′ is dominant over the
– 8 –
 [pb]σ
(GeV)H’m
 H’→gg
 H’qq→qq
 WH’→qq
 ZH’→qq
 Z’H’→qq
H’t t→,ggqq
 H’+X)[pb]→(ppσ
=14 TeVs
MRST/NLO
=200 GeVHm
Figure 5: The cross sections of the heavy Higgs production as function of mH′ : 300 GeV ≤ mH′ ≤
1 TeV, for mH = 200 GeV.
production associated with Z/W in agrement with our previous prediction.
3.2 Higgs Decay
The Higgs particle tends to decay into the heaviest gauge bosons and fermions allowed
by the phase space. The Higgs decay modes can be classified into three categories: Higgs
decays into fermions (Figure 6), Higgs decays into massive gauge bosons (Figure 7), and
Higgs decays into massless gauge bosons (Figure 8).
H, H ′
Figure 6: The Feynman diagram for the Higgs boson decays into fermions.
The decay widths into fermions are directly proportional to the Hff couplings
Γ(H −→ ff) ≈ mH
cos2 θ, (3.12)
Γ(H ′ −→ ff) ≈ mH′
sin2 θ. (3.13)
– 9 –
H, H ′ V
H, H ′
H, H ′
Figure 7: Diagrams for the Higgs boson decays into massive gauge bosons.
H, H ′
H, H ′
H, H ′
Figure 8: Loop induced Higgs boson decays into a) two photons (Zγ) and b) two gluons.
H, H ′
H, H ′ W
Figure 9: Diagrams for the three–body decays of the Higgs boson into tbW final states.
In case of the top quark, three-body decays into on-shell and off-shell states (Figure 9)
were taken into consideration.
On the the hand, the decay widths into massive gauge bosons V = Z ′, Z,W are directly
proportional to the HV V couplings. This includes two-body, three-body, and four-body
decays
V ≡ W/Z : ΓH ≈
cos2 θ, ΓH′ ≈
sin2 θ, (3.14)
V ≡ Z ′ : ΓH ∝
sin2 θ, ΓH′ ∝
cos2 θ. (3.15)
As shown in Figure 8, the massless gauge bosons are not directly coupled to the Higgs
bosons, but they are coupled via W, charged fermions, and quark loops. This implies that
– 10 –
100 200 300 400 500 600 700 800 900 1000
(GeV)Hm
Figure 10: The branching ratios of the light Higgs decay as function of mH for mH′ = 1 TeV.
the decay widths are in turn proportional to the HV V and Hff couplings, hence they are
relatively suppressed.
From the above Equations, one finds that all decay widths of the light Higgs are
proportional to cos2 θ, except the new decay mode of Z ′Z ′. Furthermore, this channel has
a very small contribution to the total decay width. Therefore, the light Higgs branching
ratios (the ratios between the partial decay widths and the total decay width) have small
dependence on the mixing parameter θ. Thus, it is expected to see no significant difference
between the results of the light Higgs branching ratios in this model of B − L extension
and the SM ones. On the other hand, the heavy Higgs branching ratios have relevant
dependence on θ.
The decay widths and branching ratios of the Higgs bosons in these channels have
been calculated using the FORTRAN code: HDECAY with extra subroutines for the new
couplings associated with the two higgs scalars and the extra gauge boson [12, 13]. As in
the Higgs production analysis, we use the following inputs: v = 246 GeV, v′ = 1 TeV,
mZ′ = 600 GeV, and c.m. energy
s = 14 TeV.
The decay branching ratios of the light and heavy Higgs bosons are shown in Figures 10
and 11, respectively, as functions of the Higgs masses. As expected, the branching ratios
of the light Higgs are very close to the SM ones. In the “low mass”range: 100 GeV
< MH < 130 GeV, the main decay mode is H → bb̄ with a branching ratio of ∼ 75 − 50%
. The decays into τ+τ−and cc̄ pairs come next with branching ratios of order ∼ 7 − 5%
and ∼ 3 − 2%, respectively. The γγ and Zγ decays are rare, with very small branching
ratios. In the “High mass ”range: mH > 130 GeV, the WW , ZZ, and to some extent
the tt̄ decays give the dominant contributions. The Z ′Z ′ decay arises for quite large Higgs
mass with a small branching ratio <∼ 1%.
– 11 –
200 400 600 800 1000 1200 1400 1600 1800 2000
(GeV)H’m
Figure 11: The branching ratios of the heavy Higgs decay as function of mH′ for mH = 200 GeV
Regarding the heavy Higgs decay branching ratio, one finds that H ′ → WW and ZZ
are the dominant decay modes, with a branching ratio of ∼ 70% and ∼ 20%, respectively.
To a lower extent, the tt̄ and Z ′Z ′ account for the remaining branching ratios. Note that
these two decay modes are in particular sensitive to the running mixing angles. Thus, they
have the behaviors shown in Figure 11. The other modes give very tiny contributions and
hence they are not shown in this figure.
It is useful to mention that the heavy Higgs may decay to a pair of the lighter Higgs.
The partial decay width of this channel, which can be expressed by
Γ(H ′ −→ HH) ≈
4m2H′
, (3.16)
is suppressed by the tiny gH2H′ coupling (Equation 2.14) and the relatively large mH′ . In
fact, the resulting branching ratio of this decay mode is at the level of 10−8, and hence
does not appear in Figure 11.
4. Z ′ decay in B − L extension of the SM
In this section we study the decay of the extra gauge boson predicted by the B−L extension
of the SM at LHC. In fact, there are many models which contain extra gauge bosons [6, 14].
These models can be classified into two categories depending on whether or not they arise
in a GUT scenario. In some of these models, the Z ′ and the SM Z are not true mass
eigenstates due to mixing. This mixing induces the couplings between the extra Z ′ boson
and the SM fermions. However, there is a stringent experimental limit on the mixing
parameter. In our model of B−L extension of the SM, there is no tree-level Z−Z ′mixing.
– 12 –
500 600 700 800 900 1000 1100 1200 1300 1400
(GeV)Z’m
 l→Z’
s,sc,cb b→Z’
t t→Z’
Figure 12: The decay branching ratios of the extra gauge boson Z ′ as function of mZ′ .
Nevertheless, the extra B − L Z ′ boson and the SM fermions are coupled through the
non-vanishing B − L quantum numbers.
The interactions of the Z ′ boson with the SM fermions are described by
LZ′int =
B−L g
′′ Z ′µ fγ
µf. (4.1)
The decay widths of Z ′ → f f̄ are then given by [6]
Γ(Z ′ → l+l−) ≈
(g′′Y lB−L)
Γ(Z ′ → qq̄) ≈
(g′′Y
, q ≡ b, c, s
Γ(Z ′ → tt̄) ≈
(g′′Y
(4.2)
Figures 12 shows the decay branching ratios of Z ′ as a function of mZ′ . Contrarily to
the SM Z decay, the branching ratios of Z ′ → l+l− are relatively high compared to Z ′ → qq̄.
This is due to the fact that |Y lB−L| = 3|Y
B−L|. Thus, one finds BR(Z ′ → l+l−) ≃ 20%
compared with BR(Z → l+l−) ≃ 3%. Therefore, searching for Z ′ can be easily accessible
via a clean dilepton signal, which can be one of the first new physics signatures to be
observed at the LHC.
– 13 –
5. Light H ′ Scenario
In this section we discuss the possibility of having mH′ <∼ mH and the phenomenological
implications of this scenario. As shown in section two, the mass of the non-SM Higgs mH′
receives a dominant contribution from the vev of the B − L symmetry breaking v′ and
the self coupling λ2. The Z
′ searches and the neutrino masses impose a lower limit on
v′: v′ >∼ 1 TeV. The self coupling λ2 is essentially unconstrained parameter. If λ2 ∼ O(1),
then mH′ is of order TeV as assumed in the previous sections.
There are two other interesting possibilities which have recently received some attention
in the literature. The first one corresponds to the case of λ1v
2 ∼ λ2v′2, i.e., λ2 ∼ O(10−2).
Therefore, one finds mH ∼ mH′ and the mixing angle is given by θ ∼ π/4. Hence, the
two Higgs H and H ′ couple similarly to the fermion and gauge fields, giving the same
production cross section and decay branching ratio. Therefore, the distinguish between H
and H ′ at LHC in this type of models is rather difficult. This scenario is usually known as
intense Higgs coupling [15].
The second possibility concerns the case of λ2 <∼ 10
−3, in which one obtains mH′ ≪
mH . In fact, LEP and Tevatron direct searches do not exclude a light Higgs boson with a
mass below 60 GeV. Such light Higgs may have escaped experimental detection due to the
suppression of its cross sections. Therefore, a window with a very light Higgs mass still
exist.
Having λ2 <∼ 10
−3 implies that λ3 is also less than 10
−3. In this respect, the Higgs
masses are approximately given by
λ1v, (5.1)
mH′ ≃ O
≃ O(10−2)GeV, (5.2)
and the coupling gHH′H′ in Equation 2.14 becomes very small. Thus, the decay H → H ′H ′
is not comparable to the decay into other SM particles. The phenomenology of this scenario,
derived from different SM extensions, has been studied in details [4],[16]. In addition, this
light scalar particle has been considered as an interesting candidate for dark matter [17].
6. Conclusions
In this paper we have considered the TeV scale B − L extension of the SM. We provided
a comprehensive analysis for the phenomenology of the SM like Higgs, the extra Higgs
scalar, and the extra gauge boson predicted in this model, with special emphasize on their
potential discovery at the LHC.
We have shown that the cross sections of the SM-like Higgs production are reduced
by ∼ 20% − 30% in the mass range of ∼ 120 − 250 GeV compared to the SM results.
On the other hand, the implications of the B − L extension to the SM do not change
the decay branching ratios. Moreover, we found that the extra Higgs has relatively small
cross sections, but it is accessible at LHC. Finally, we showed that the branching ratios
of Z ′ → l+l− are of order ∼ 20% compared to ∼ 3% of the SM BR(Z → l+l−). Hence,
searching for Z ′ is accessible via a clean dilepton signal at LHC.
– 14 –
Acknowledgment
This work is partially supported by the ICTP under the OEA-project-30.
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– 15 –

  The phenomenology of the low scale U(1)_{B-L} extension of the standard model
and its implications at LHC is presented. In this model, an extra gauge boson
corresponding to B-L gauge symmetry and an extra SM singlet scalar (heavy
Higgs) are predicted. We show a detailed analysis of both heavy and light
Higgses decay and production in addition to the possible decay channels of the
new gauge boson. We find that the cross sections of the SM-like Higgs
production are reduced by ~ 20%-30%, while its decay branching ratios remain
intact. The extra Higgs has relatively small cross sections and the branching
ratios of Z'-> l^+ l^- are of order ~20% compared to ~ 3% of the SM resuls.
Hence, the search for Z' is accessible via a clean dilepton signal at LHC.

Introduction 1
2. B − L extension of the SM 2
2.1 Symmetry breaking 2
2.2 Higgs sector 3
3. Higgs Production and Decay at Hadron Colliders 5
3.1 Higgs Production 5
3.2 Higgs Decay 9
4. Z ′ decay in B − L extension of the SM 12
5. Light H ′ Scenario 14
6. Conclusions 14
1. Introduction
The Standard Model (SM) of elementary particles has been regarded only as a low energy
effective theory of the yet-more-fundamental theory. Several attempts have been proposed
to extend the gauge symmetry of the SM via one or more U(1) gauge symmetries beyond
the hypercharge gauge symmetry, U(1)Y [1–3]. The evidence for non-vanishing neutrino
masses, based on the apparent observation of neutrino oscillation, strongly encourages this
type of extensions. In this class of models [1, 2], three SM singlet fermions arise quite
naturally due to the anomaly cancellation conditions. These three particles are accounted
for right handed neutrinos, and hence a natural explanation for the seesaw mechanism is
obtained.
A low scale B − L symmetry breaking, based on the gauge group GB−L ≡ SU(3)C ×
SU(2)L × U(1)Y × U(1)B−L, has been considered recently [2]. It was shown that this
model can account for the current experimental results of the light neutrino masses and
their large mixing. Therefore, it can be considered as one of the strong candidates for
minimal extensions of the SM. In addition, one extra neutral gauge boson corresponding
to B − L gauge symmetry and an extra SM singlet scalar (extra Higgs) are predicted.
In fact, the SM Higgs sector can be generally extended by adding extra singlet scalars
without enlarging its gauge symmetry group [4, 5]. In Ref.[2], it has been emphasized that
these new particles may have significant impact on the SM phenomenology, hence lead to
interesting signatures at Large Hadron Collider (LHC).
– 1 –
The aim of this paper is to provide a comprehensive analysis for the phenomenology of
such TeV scale extension of the SM, and its potential discovery at the LHC. The production
cross sections and the decay branching ratios of the SM like Higgs, H, and the extra Higgs
boson H ′ are analyzed. We also consider the decay branching ratios of the extra gauge
boson, Z ′.
We show that the cross sections of the Higgs production are reduced by ∼ 20%− 30%
in the interesting mass range of ∼ 120− 250 GeV relative to the SM predictions. However,
its decay branching ratios remain intact. In addition, we find that the extra Higgs (∼
TeV) is accessible at LHC, although it has relatively small cross sections. We also examine
the availability of the decay channel H ′ → HH, which happens to have very small partial
decay width. Concerning the Z ′ gauge boson, the branching ratios of Z ′ → l+l− are found
to be of order ∼ 20% compared to ∼ 3% of the SM BR(Z → l+l−).
This paper is organized as follows. In section 2 we review the Higgs mechanism and
symmetry breaking within the minimal B − L extension of the SM. We also discuss the
mixing between the SM-like Higgs and the extra Higgs boson. Section 3 is devoted for
the phenomenology of the two Higgs particles. The production cross sections and decay
branching ratios of these Higgs particles at LHC are presented. In section 4 we study the
decay of the extra gauge boson Z ′. In section 5 we briefly discuss the scenario of very light
Higgs. Finally we give our concluding remarks in section 6.
2. B − L extension of the SM
2.1 Symmetry breaking
The fermionic and kinetic sectors of the Lagrangian in the case of B − L extension are
given by
LB−L = i l̄Dµγµl + i ēRDµγµeR + i ν̄RDµγµνR
µν − 1
µν − 1
µν . (2.1)
The covariant derivative Dµ is different from the SM one by the term ig
′′YB−LCµ, where g
is the U(1)B−L gauge coupling constant, YB−L is the B−L charge, and Cµν = ∂µCν−∂νCµ
is the field strength of the U(1)B−L. The YB−L for fermions and Higgs are given in Table 1.
particle l eR νR q φ χ
YB−L −1 −1 −1 1/3 0 2
Table 1: B − L quantum numbers for fermions and Higgs particles
The Higgs and Yukawa sectors of the Lagrangian are given by
LB−L = (Dµφ)(Dµφ) + (Dµχ)(Dµχ)− V (φ, χ)
λe l̄φeR + λν l̄φ̃νR +
λνR ν̄
RχνR + h.c.
. (2.2)
– 2 –
Here, λe, λν and λνR refer to 3 × 3 Yakawa matrices. The interaction terms λν lφ̃νR and
λνR ν̄
RχνR give rise to a Dirac neutrino mass term: mD ≃ λνv and a Majorana mass term:
MR = λνRv
′, respectively. The U(1)B−L and SU(2)L × U(1)Y gauge symmetries can be
spontaneously broken by a SM singlet complex scaler field χ and a complex SU(2) doublet
of scalar fields φ, respectively. We consider the most general Higgs potential invariant
under these symmetries, which is given by
V (φ, χ) = m21φ
†φ+m22χ
†χ+ λ1(φ
†φ)2 + λ2(χ
+λ3(χ
†χ)(φ†φ), (2.3)
where λ3 > −2
λ1λ2 and λ1, λ2 ≥ 0, so that the potential is bounded from below. For
non-vanishing vacuum expectation values (vev’s), we require λ23 < 4λ1λ2 , m
1 < 0 and
m22 < 0. The vev’s, |〈φ〉| = v/
2 and |〈χ〉| = v′/
2, are then given by
1 − 2λ3m22
λ23 − 4λ1λ2
, v′2 =
−2(m21 + λ1v2)
Depending on the value of the λ3 coupling, one can have v
′ ≫ v or v′ ≈ v. Therefore, the
symmetry breaking scales, v and v′, can be responsible for two different symmetry breaking
scenarios. In our analysis we take v = 246 GeV and constrain the other scale, v′, by the
lower bounds imposed on the mass of the extra neutral gauge boson.
After the B−L gauge symmetry breaking, the gauge field Cµ (will be called Z ′ in the
rest of the paper) acquires the following mass:
m2Z′ = 4g
′′v′2. (2.4)
The experimental search for Z ′ at CDF experiment leads to mZ′ >∼ O(600) GeV. However,
the strongest limit comes from LEP II [6]:
mZ′/g
′′ > 6TeV . (2.5)
This implies that v′ >∼ O(TeV). Moreover, if the coupling g
′′ is < O(1), one can still obtain
mZ′ >∼ O(600) GeV.
2.2 Higgs sector
In addition to the SM complex SU(2)L doublet, another complex scalar singlet arise in
this class of models. Out of these six scalar degrees of freedom, only two physical degrees
of freedom, (φ, χ), remain after the B − L and electroweak symmetries are broken. The
other four degrees of freedom are eaten by Z ′, Z and W± bosons.
The mixing between the two Higgs scalar fields is controlled by the coupling λ3. In
fact, one finds that for positive λ3 , the B−L symmetry breaking scale, v′, becomes much
higher than the electroweak symmetry breaking scale, v. In this case, the SM singlet
Higgs, φ, and the SM like Higgs, χ, are decoupled and their masses are given by
2λ1v, Mχ =
′. (2.6)
– 3 –
For negative λ3, however, theB−L breaking scale is at the same order of the the electroweak
breaking scale. In this scenario, a significant mixing between the two Higgs scalars exists
and can affect the SM phenomenology. This mixing can be represented by the following
mass matrix for φ and χ:
M2(φ, χ) =
vv′ λ2v
. (2.7)
Therefore, the mass eigenstates fields H and H ′ are given by
cos θ − sin θ
sin θ cos θ
, (2.8)
where the mixing angle θ is defined by
tan 2θ =
|λ3|vv′
λ1v2 − λ2v′2
. (2.9)
The masses of H and H ′ are given by
m2H,H′ = λ1v
2 + λ2v
(λ1v2 − λ2v′2)2 + λ23v2v′2. (2.10)
We call H andH ′ as light and heavy Higgs bosons, respectively. In our analysis we consider
a maximum mixing between the two Higgs bosons by taking |λ3| ≃ λmax1 λmax2 , where λmax1
and λmax2 are given by
λmax1 =
m2H +m
4m2Hm
+ 1 + 1
λmax2 =
m2H +m
4m2Hm
+ 1− 1
, (2.11)
and the maximum mixing angle is then given by
tan 2θ =
λmax1 λ
λmax1 v
2 − λmax2 v′2
. (2.12)
By considering the maximum mixing and fixing v = 246 GeV and v′ = 1 TeV, we have
reduced the number of free parameters of this model into just two, namely mH and mH′ .
In Figure 1, we present the maximum mixing as a function of the light Higgs mass, mH
for mH′ = 500 GeV and 1 TeV.
Due to the mixing between the two Higgs bosons, the usual couplings among the SM-
like Higgs, H, and the SM fermions and gauge bosons are modified. In addition, there are
new couplings among the extra Higgs, H ′, and the SM particles:
gHff = i
cos θ, gH′ff = i
sin θ,
gHV V = −2i
cos θ, gH′V V = −2i
sin θ,
gHZ′Z′ = 2i
sin θ, gH′Z′Z′ = −2i
cos θ,
gHνRνR = −i
sin θ, gH′νRνR = i
cos θ. (2.13)
– 4 –
100 200 300 400 500 600 700 800 900 1000
θ2cos
(GeV)Hm
=500(GeV)H’m
=1000(GeV)H’m
Figure 1: H −H ′ mixing angle as function of mH for m′H = 500 GeV and 1 TeV.
The Higgs self couplings are give by
gH3 = 6i(λ1v cos
3 θ −
v′ cos2 θ sin θ),
gH′3 = 6i(λ2v
′ cos3 θ +
v cos2 θ sin θ),
gH4 = 6iλ1 cos
gH′4 = 6iλ2 cos
gHH′2 = 2i(
v cos3 θ + λ3v
′ cos2 θ sin θ − 3λ2v′ cos2 θ sin θ),
gH2H′ = 2i(
v′ cos3 θ − λ3v cos2 θ sin θ + 3λ1v cos2 θ sin θ),
gH2H′2 = iλ3 cos
4 θ. (2.14)
These new couplings lead to a different Higgs phenomenology from the well known
one, predicted by the SM. The detailed analysis of Higgs bosons in this class of models and
their phenomenological implications, like their productions and decays at the LHC, will be
discussed in the next section.
3. Higgs Production and Decay at Hadron Colliders
3.1 Higgs Production
At the LHC, two 7-TeV proton beams with a center-of-mass energy of 14 TeV and a
luminosity of 1034cm−2s−1 will collide with each other. The machine is expected to start
running early 2008. The detection of the SM Higgs boson is the primary goal of the LHC
project.
– 5 –
H, H ′
H, H ′
H, H ′
H, H ′
Figure 2: The dominant Higgs boson production mechanisms in hadronic collisions.
At hadron colliders, the two Higgs bosons couple mainly to the heavy particles: the
massive gauge bosons Z ′, Z and W± and the heavy quarks t, b. The main production
mechanisms for Higgs particles can be classified into four groups [7]: the gluon–gluon
fusion mechanism[8], the associated Higgs production with heavy top or bottom quarks[9],
the associated production with W/Z/Z ′ bosons[10], and the weak vector boson fusion
processes[11]:
gg → H (3.1)
gg, qq̄ → QQ̄+H, (3.2)
qq̄ → V +H (3.3)
qq → V ∗V ∗ → qq +H. (3.4)
The Feynman diagrams of these processes are displayed in Figure 2. The cross sections
of the Higgs production in these four mechanisms are directly proportional to the the Higgs
couplings with the associated particles.
In case of the gluon–gluon fusion mechanism the Higgs production is mediated by
triangular loops of heavy quarks. Thus, the cross section of this process is proportional
to the Higgs coupling with the heavy quark mass. In case of B − L extension of the SM,
the production cross sections for the light Higgs, H, and the heavy Higgs, H ′, can be
approximated as
σH ∝ α2s
cos2 θ
, (3.5)
σH′ ∝ α2s
sin2 θ
, (3.6)
where the first bracket is due to the coupling QQH(H ′), while the second bracket corre-
sponds to an approximated loop factor. As can be seen from Equations 3.5 and 3.6, the
– 6 –
H, H ′
Figure 3: Feynman diagrams for Higgs production in association with heavy quarks in hadronic
collisions, pp → qq̄, gg → QQ̄H , at LO.
cross section of the light Higgs production is reduced respect to the SM one by the factor
of cos2 θ. On the other hand, the heavy Higgs production is suppressed by two factors: the
small sin θ, and the large mH′ . Therefore, the the heavy Higgs production is typically less
than that of the light Higgs by two orders of magnitudes, i.e.,
≃ sin θ
cos θ2
≃ O(10−2). (3.7)
Now, we consider the mechanism of Higgs production in association with heavy quark
pairs, Equation 3.2. In addition to the Feynman diagram shown in Figure 2, a set of other
diagrams that also contribute to this process is given in Figure 3. Note that although
this process shares the same coupling with the gluon-gluon fusion process, the leading
order expression of its cross section indicates that it is less by one order of magnitude, for
mH(H′) < 1 TeV. Furthermore, the typical ratio of σ(gg → H ′QQ̄) to σ(gg → HQQ̄) is of
order (sin θ/ cos θ)2 ≃ O(0.1).
Finally, we study the Higgs production in association with W/Z/Z ′ bosons and in the
weak vector boson fusion processes, Equations 3.3 and 3.4 respectively. In B−L extension
of the SM, the cross sections of these channels are proportional to the mass of the gauge
boson and the mixing angle θ of the two Higgs bosons:
V ≡ W/Z : σH ∝
cos2 θ ×
× Loop function, (3.8)
σH′ ∝
sin2 θ ×
× Loop function. (3.9)
In case of V ≡ Z ′, The production is enhanced by the HZ ′Z ′ coupling arising with
mZ′ . However, it is suppressed by a large value of v
′ and the mass of the virtual gauge
boson(s), mZ′ :
V ≡ Z ′ : σH ∝
sin2 θ ×
(g′′Y
× Loop function, (3.10)
σH′ ∝
cos2 θ ×
(g′′Y
× Loop function. (3.11)
From these equations, one can observe that the relative ratio between the light Higgs
production associated with W/Z and Z ′ gauge bosons is given by σH(W/Z)/σH(Z
– 7 –
 [pb]σ
(GeV)Hm
 H→gg
 Hqq→qq
 WH→qq
 ZH→qq
 Z’H→qq
Ht t→,ggqq
 H+X)[pb]→(ppσ
=14 TeVs
MRST/NLO
=1 TeVH’m
Figure 4: The cross sections of the light Higgs production as function of mH : 100 GeV ≤ mH ≤
1 TeV, for mH′ = 1 TeV.
cos2 θ/ sin2 θ×g′′2/g2(g′2). Therefore, σH(W/Z) can be larger than σH(Z ′) by one order of
magnitude at most. In contrary, the situation is reversed for the heavy Higgs production
and one finds that σ′H(Z
′) > σ′H(W/Z), which confirms our earlier discussion.
The cross sections for the Higgs bosons production in these channels (Equations 3.1-
3.4) have been calculated using the FORTRAN codes: HIGLU, HQQ, V2HV, and VV2HV,
respectively [12]. Extra subroutines have been added to these programs for the new cou-
plings associated with the two higgs scalars and the extra gauge boson [12]. As inputs, we
use v = 246 GeV, v′ = 1 TeV, and center of mass energy
s = 14 TeV. We also fix the
mass of the extra gauge boson at mZ′ = 600 GeV. The cross sections for the light Higgs
boson production are summarized in Figure 4. as functions of the light Higgs mass with
mH′ = 1 TeV. Figure 5, on the other hand, represents the heavy Higgs productions as
functions of mH′ with mH = 200 GeV.
As shown in Figure 4, the salient feature of this low scale B − L extension is that
all cross sections of the light Higgs production are reduced by about 25 − 35% in the
interesting mass range: mH < 250 GeV. As in the SM, the main contribution to the
production cross section comes from the gluon-gluon fusion mechanism with a few tens of
pb. The next relevant contribution is given by the Higgs production in the weak vector
boson mechanism, Equation 3.4. This contribution is at the level of a few pb, as estimated
above. Furthermore, the production associated with Z/W is dominant over the production
associated with Z ′ for mH < 300 GeV.
Now, we analyze the production of the heavy Higgs. It turns out that its cross sections
are smaller than the light Higgs ones. As shown in Figure 5, all these cross sections are
scaled down by factor O(10−2), which is consistent with the result obtained in Equation 3.7.
Unlike the light Higgs scenario, the production associated with Z ′ is dominant over the
– 8 –
 [pb]σ
(GeV)H’m
 H’→gg
 H’qq→qq
 WH’→qq
 ZH’→qq
 Z’H’→qq
H’t t→,ggqq
 H’+X)[pb]→(ppσ
=14 TeVs
MRST/NLO
=200 GeVHm
Figure 5: The cross sections of the heavy Higgs production as function of mH′ : 300 GeV ≤ mH′ ≤
1 TeV, for mH = 200 GeV.
production associated with Z/W in agrement with our previous prediction.
3.2 Higgs Decay
The Higgs particle tends to decay into the heaviest gauge bosons and fermions allowed
by the phase space. The Higgs decay modes can be classified into three categories: Higgs
decays into fermions (Figure 6), Higgs decays into massive gauge bosons (Figure 7), and
Higgs decays into massless gauge bosons (Figure 8).
H, H ′
Figure 6: The Feynman diagram for the Higgs boson decays into fermions.
The decay widths into fermions are directly proportional to the Hff couplings
Γ(H −→ ff) ≈ mH
cos2 θ, (3.12)
Γ(H ′ −→ ff) ≈ mH′
sin2 θ. (3.13)
– 9 –
H, H ′ V
H, H ′
H, H ′
Figure 7: Diagrams for the Higgs boson decays into massive gauge bosons.
H, H ′
H, H ′
H, H ′
Figure 8: Loop induced Higgs boson decays into a) two photons (Zγ) and b) two gluons.
H, H ′
H, H ′ W
Figure 9: Diagrams for the three–body decays of the Higgs boson into tbW final states.
In case of the top quark, three-body decays into on-shell and off-shell states (Figure 9)
were taken into consideration.
On the the hand, the decay widths into massive gauge bosons V = Z ′, Z,W are directly
proportional to the HV V couplings. This includes two-body, three-body, and four-body
decays
V ≡ W/Z : ΓH ≈
cos2 θ, ΓH′ ≈
sin2 θ, (3.14)
V ≡ Z ′ : ΓH ∝
sin2 θ, ΓH′ ∝
cos2 θ. (3.15)
As shown in Figure 8, the massless gauge bosons are not directly coupled to the Higgs
bosons, but they are coupled via W, charged fermions, and quark loops. This implies that
– 10 –
100 200 300 400 500 600 700 800 900 1000
(GeV)Hm
Figure 10: The branching ratios of the light Higgs decay as function of mH for mH′ = 1 TeV.
the decay widths are in turn proportional to the HV V and Hff couplings, hence they are
relatively suppressed.
From the above Equations, one finds that all decay widths of the light Higgs are
proportional to cos2 θ, except the new decay mode of Z ′Z ′. Furthermore, this channel has
a very small contribution to the total decay width. Therefore, the light Higgs branching
ratios (the ratios between the partial decay widths and the total decay width) have small
dependence on the mixing parameter θ. Thus, it is expected to see no significant difference
between the results of the light Higgs branching ratios in this model of B − L extension
and the SM ones. On the other hand, the heavy Higgs branching ratios have relevant
dependence on θ.
The decay widths and branching ratios of the Higgs bosons in these channels have
been calculated using the FORTRAN code: HDECAY with extra subroutines for the new
couplings associated with the two higgs scalars and the extra gauge boson [12, 13]. As in
the Higgs production analysis, we use the following inputs: v = 246 GeV, v′ = 1 TeV,
mZ′ = 600 GeV, and c.m. energy
s = 14 TeV.
The decay branching ratios of the light and heavy Higgs bosons are shown in Figures 10
and 11, respectively, as functions of the Higgs masses. As expected, the branching ratios
of the light Higgs are very close to the SM ones. In the “low mass”range: 100 GeV
< MH < 130 GeV, the main decay mode is H → bb̄ with a branching ratio of ∼ 75 − 50%
. The decays into τ+τ−and cc̄ pairs come next with branching ratios of order ∼ 7 − 5%
and ∼ 3 − 2%, respectively. The γγ and Zγ decays are rare, with very small branching
ratios. In the “High mass ”range: mH > 130 GeV, the WW , ZZ, and to some extent
the tt̄ decays give the dominant contributions. The Z ′Z ′ decay arises for quite large Higgs
mass with a small branching ratio <∼ 1%.
– 11 –
200 400 600 800 1000 1200 1400 1600 1800 2000
(GeV)H’m
Figure 11: The branching ratios of the heavy Higgs decay as function of mH′ for mH = 200 GeV
Regarding the heavy Higgs decay branching ratio, one finds that H ′ → WW and ZZ
are the dominant decay modes, with a branching ratio of ∼ 70% and ∼ 20%, respectively.
To a lower extent, the tt̄ and Z ′Z ′ account for the remaining branching ratios. Note that
these two decay modes are in particular sensitive to the running mixing angles. Thus, they
have the behaviors shown in Figure 11. The other modes give very tiny contributions and
hence they are not shown in this figure.
It is useful to mention that the heavy Higgs may decay to a pair of the lighter Higgs.
The partial decay width of this channel, which can be expressed by
Γ(H ′ −→ HH) ≈
4m2H′
, (3.16)
is suppressed by the tiny gH2H′ coupling (Equation 2.14) and the relatively large mH′ . In
fact, the resulting branching ratio of this decay mode is at the level of 10−8, and hence
does not appear in Figure 11.
4. Z ′ decay in B − L extension of the SM
In this section we study the decay of the extra gauge boson predicted by the B−L extension
of the SM at LHC. In fact, there are many models which contain extra gauge bosons [6, 14].
These models can be classified into two categories depending on whether or not they arise
in a GUT scenario. In some of these models, the Z ′ and the SM Z are not true mass
eigenstates due to mixing. This mixing induces the couplings between the extra Z ′ boson
and the SM fermions. However, there is a stringent experimental limit on the mixing
parameter. In our model of B−L extension of the SM, there is no tree-level Z−Z ′mixing.
– 12 –
500 600 700 800 900 1000 1100 1200 1300 1400
(GeV)Z’m
 l→Z’
s,sc,cb b→Z’
t t→Z’
Figure 12: The decay branching ratios of the extra gauge boson Z ′ as function of mZ′ .
Nevertheless, the extra B − L Z ′ boson and the SM fermions are coupled through the
non-vanishing B − L quantum numbers.
The interactions of the Z ′ boson with the SM fermions are described by
LZ′int =
B−L g
′′ Z ′µ fγ
µf. (4.1)
The decay widths of Z ′ → f f̄ are then given by [6]
Γ(Z ′ → l+l−) ≈
(g′′Y lB−L)
Γ(Z ′ → qq̄) ≈
(g′′Y
, q ≡ b, c, s
Γ(Z ′ → tt̄) ≈
(g′′Y
(4.2)
Figures 12 shows the decay branching ratios of Z ′ as a function of mZ′ . Contrarily to
the SM Z decay, the branching ratios of Z ′ → l+l− are relatively high compared to Z ′ → qq̄.
This is due to the fact that |Y lB−L| = 3|Y
B−L|. Thus, one finds BR(Z ′ → l+l−) ≃ 20%
compared with BR(Z → l+l−) ≃ 3%. Therefore, searching for Z ′ can be easily accessible
via a clean dilepton signal, which can be one of the first new physics signatures to be
observed at the LHC.
– 13 –
5. Light H ′ Scenario
In this section we discuss the possibility of having mH′ <∼ mH and the phenomenological
implications of this scenario. As shown in section two, the mass of the non-SM Higgs mH′
receives a dominant contribution from the vev of the B − L symmetry breaking v′ and
the self coupling λ2. The Z
′ searches and the neutrino masses impose a lower limit on
v′: v′ >∼ 1 TeV. The self coupling λ2 is essentially unconstrained parameter. If λ2 ∼ O(1),
then mH′ is of order TeV as assumed in the previous sections.
There are two other interesting possibilities which have recently received some attention
in the literature. The first one corresponds to the case of λ1v
2 ∼ λ2v′2, i.e., λ2 ∼ O(10−2).
Therefore, one finds mH ∼ mH′ and the mixing angle is given by θ ∼ π/4. Hence, the
two Higgs H and H ′ couple similarly to the fermion and gauge fields, giving the same
production cross section and decay branching ratio. Therefore, the distinguish between H
and H ′ at LHC in this type of models is rather difficult. This scenario is usually known as
intense Higgs coupling [15].
The second possibility concerns the case of λ2 <∼ 10
−3, in which one obtains mH′ ≪
mH . In fact, LEP and Tevatron direct searches do not exclude a light Higgs boson with a
mass below 60 GeV. Such light Higgs may have escaped experimental detection due to the
suppression of its cross sections. Therefore, a window with a very light Higgs mass still
exist.
Having λ2 <∼ 10
−3 implies that λ3 is also less than 10
−3. In this respect, the Higgs
masses are approximately given by
λ1v, (5.1)
mH′ ≃ O
≃ O(10−2)GeV, (5.2)
and the coupling gHH′H′ in Equation 2.14 becomes very small. Thus, the decay H → H ′H ′
is not comparable to the decay into other SM particles. The phenomenology of this scenario,
derived from different SM extensions, has been studied in details [4],[16]. In addition, this
light scalar particle has been considered as an interesting candidate for dark matter [17].
6. Conclusions
In this paper we have considered the TeV scale B − L extension of the SM. We provided
a comprehensive analysis for the phenomenology of the SM like Higgs, the extra Higgs
scalar, and the extra gauge boson predicted in this model, with special emphasize on their
potential discovery at the LHC.
We have shown that the cross sections of the SM-like Higgs production are reduced
by ∼ 20% − 30% in the mass range of ∼ 120 − 250 GeV compared to the SM results.
On the other hand, the implications of the B − L extension to the SM do not change
the decay branching ratios. Moreover, we found that the extra Higgs has relatively small
cross sections, but it is accessible at LHC. Finally, we showed that the branching ratios
of Z ′ → l+l− are of order ∼ 20% compared to ∼ 3% of the SM BR(Z → l+l−). Hence,
searching for Z ′ is accessible via a clean dilepton signal at LHC.
– 14 –
Acknowledgment
This work is partially supported by the ICTP under the OEA-project-30.
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