Higgs phenomenology in the minimal $B-L$ extension of the Standard Model at LHC
ABSTRACT We present some phenomenology of the Higgs sector of the Minimal $B-L$ U(1)
Extension of the Standard Model at the Large Hadron Collider. In this model,
the existence of an extra gauge boson ($Z'$) and an extra scalar (heavy Higgs)
are predicted as naturally related with the breaking of the $B-L$ (baryon minus
lepton number) symmetry. For this, we have started by deriving the unitarity
bounds in the high energy limit for the Minimal $B-L$ Model parameter space.
This was accomplished by analysing the full class of Higgs and would-be
Goldstone boson two-to-two scatterings at tree level (exploiting the
Equivalence Theorem). Hence, we studied some peculiar signature that could be
observed at the CERN machine in the search of both light and heavy Higgs
arXiv:1009.6095v2 [hep-ph] 1 Nov 2010
December 22, 2010
Higgs phenomenology in the minimal B − L
extension of the Standard Model at LHC
L. Basso, A. Belyaev, S. Moretti and G. M. Pruna1
School of Physics and Astronomy, University of Southampton,
Highfield, Southampton SO17 1BJ, UK.
We present some phenomenology of the Higgs sector of the Minimal B − L U(1)
Extension of the Standard Model at the Large Hadron Collider. In this model,
the existence of an extra gauge boson (Z′) and an extra scalar (heavy Higgs) are
predicted as naturally related with the breaking of the B −L (baryon minus lepton
number) symmetry. For this, we have started by deriving the unitarity bounds in
the high energy limit for the Minimal B − L Model parameter space. This was
accomplished by analysing the full class of Higgs and would-be Goldstone boson
two-to-two scatterings at tree level (exploiting the Equivalence Theorem). Hence,
we studied some peculiar signature that could be observed at the CERN machine
in the search of both light and heavy Higgs bosons.
Despite there is no experimental evidence of a Higgs boson, the Higgs mechanism is still
considered one of the favourite means for generating the masses of particles.
In the Standard Model (SM) framework this mechanism is realised by one Higgs dou-
blet consisting of four degrees of freedom, three of which, after spontaneous Electro-Weak
Symmetry Breaking (EWSB), turn out to be absorbed in the longitudinal polarisation
component of each of the three weak gauge bosons, W±and Z, while the fourth one gives
the physical Higgs state h.
It is clear that the SM represents a minimal choice that is completely arbitrary (as
far as we know), and in the past years a big effort has been devoted to explore the
implication of more complicated Higgs models, both in the context of the SM and in
Beyond the Standard Model (BSM) extended theories.
One of the possible BSM scenarios is the minimal B−L (Barion minus Lepton number)
gauge extension of the SM, which has been recently explored (see ) as one of the
candidates in the description of a rather simple phenomenological framework.
This model has an augmented B − L gauge symmetry, that results in the natural
presence of a new vector boson Z′, a new Higgs field (related to the B − L symmetry
breaking) and, in order to preserve the theory from anomalies, one right-handed neutrino
field per fermionic family (related to three heavy neutrinos as particle contents of the
In the present work we present a brief analysis of the phenomenology of the B−L Higgs
sector at the Large Hadron Collider (LHC), with emphasis on one distinctive signature of
the model: the heavy neutrino pair production mediated by a light Higgs in proton-proton
Firstly, in order to give a consistent picture of the allowed parameter space of the
Higgs sector, we will briefly present the results of Reference [2, 3] where the Higgs pa-
rameter space of the minimal B − L model was studied in detail by accounting for both
experimental and theoretical constraints.
Thereafter, we will present the production cross-sections and Branching Ratios (BRs),
in order to use these results to introduce some peculiar Higgs signatures at the LHC that
are not allowed by the SM assumption, and therefore they could be the hallmark of the
B − L model.
2 The Model
The model under study is the so-called “pure” or “minimal” B −L model because of the
vanishing mixing between the two U(1)Y and U(1)B−Lgroups. In this model the classical
gauge invariant Lagrangian, obeying the SU(3)C× SU(2)L× U(1)Y × U(1)B−L gauge
symmetry, can be decomposed as:
L = LY M+ Ls+ Lf+ LY. (1)
The non-Abelian field strengths in LY M are the same as in the SM whereas the
Abelian ones can be intuitively identified. In this field basis, the co-variant derivative is:
B −L model is defined by the condition ? g(EW) = 0, that implies no mixing between the
The fermionic Lagrangian is the usual SM one, apart from the presence of Right-
Handed (RH) neutrinos. The charges are the usual SM and B − L ones (in particular,
B − L = 1/3 for quarks and −1 for leptons). The B − L charge assignments of the
fields as well as the introduction of new fermionic RH-neutrinos (νR) and scalar Higgs
(χ, charged +2 under B −L) fields are designed to eliminate the triangular B −L gauge
µ+ig1Y Bµ+i(? gY +g′
µ. The “pure” or “minimal”
Z′and the SM-Z gauge bosons at the tree-level at the EW scale.
anomalies and to ensure the gauge invariance of the theory, respectively. Therefore, the
B − L gauge extension of the SM group broken at the Electro-Weak (EW) scale does
necessarily require at least one new scalar field and three new fermionic fields which are
charged with respect to the B − L group.
The scalar Lagrangian is:
Ls= (DµH)†DµH + (Dµχ)†Dµχ − V (H,χ), (2)
with the scalar potential given by
V (H,χ) = m2H†H + µ2| χ |2+λ1(H†H)2+ λ2| χ |4+λ3H†H | χ |2, (3)
where H and χ are the complex scalar Higgs doublet and singlet fields, respectively.
From this potential, with standard algebraic manipulation (see ), one finds the
explicit expressions for the Higgs bosons masses and mixing angle in terms of λ parameters.
Being h1and h2the scalar fields with masses mh1and mh2respectively (we convention-
ally choose m2
h2), we give the explicit expressions for the scalar mass eigenvalues:
= λ1v2+ λ2x2+
(λ1v2− λ2x2)2+ (λ3xv)2,
= λ1v2+ λ2x2−
(λ1v2− λ2x2)2+ (λ3xv)2, (4)
2≤ α ≤π
?(λ1v2− λ2x2)2+ (λ3xv)2.
Finally, the Yukawa interactions are: LY = −yd
jkljLνkR?H − yM
where the last term is the Majorana contribution and the others the usual Dirac ones.
jνkRχ + h.c., where˜H = iσ2H∗and i,j,k take the values 1 to 3,
Firstly, we have made an extensive study on the Higgs-sector parameter-space allowed
by theoretical constraints exploiting the well-known techniques from consideration on
vacuum stability and triviality (renormalisation group equations (RGEs) techniques, see
) and perturbative unitarity (PU) (see ). The latter, in particular, is not energy-scale
dependent, and it results in a simpler description of the mh1− mh2− α allowed space,
and we will mainly consider it in the following analysis.
By analysing the full class of Higgs and would-be Goldstone boson two-to-two scat-
terings at tree level (exploiting the Equivalence Theorem) one finds the following result:
the theory is PU-stable if mh1< 700 GeV and
where αW= αem/sin2θW.
Considering the experimental limits from LEP (which established that the safest choice
for the light Higgs boson mass is mh1> 115 GeV) we have a complete definition of the
allowed Higgs-sector parameter space.
For completeness, we have also combined the RGEs and PU techniques in order to find
a dynamical constraint on the g′
B −L symmetry breaking occurs at the TeV scale, one finds that the model is PU-stable
to the Planck scale only if g′
Thereafter, we have analysed the production mechanism channels both for h1and h2
in proton-proton colliders, with emphasis on two LHC energy-luminosity configurations:
“early discovery scenario” with√s = 7 GeV and L = 1 fb−1, “full integrated luminosity”
scenario with√s = 14 GeV and L = 300 fb−1.
As explicit example, in figure 1 we show the full set of production mechanisms for h1
in proton-proton collision at√s = 7 GeV for α = π/5: as in the SM case, the dominant
mode is represented by the gluon-gluon fusion (black line) process, while the inclusive
processes as vector boson fusion (VBF) (red line), the H-strahlung processes (blue line
for W±and violet line for Z) and the associated production of top and Higgs (green line)
represent a significantly smaller contribution. For completeness, we have superimposed
the SM-like case (α = 0) in dotted lines.
Besides, we have evaluated the BRs both for h1and h2, in the search for configurations
in which it could be possible to have any peculiar signature of the model.
Considering the h1-decay, we have analysed the role that a “light” heavy neutrino
mass (mZ/2 < mνh< mW) could play in the BRs, in order to establish if such decaying-
channel could be visible in the early discovery scenario at LHC. In particular, in figure 2
we plot the Branching ratio for h1→ 2νh(summing over the three generation of heavy
neutrinos) against the light Higgs boson mass mh1for νh= 50 GeV2and several values
of the mixing angle α in units of π/2: α = 0.2 (blue line), α = 0.4 (green line), α = 0.6
(red line), α = 0.8 (black line).
Considering the h2-decay, instead, we have analysed how the presence of a “light”
Z′-boson (the mZ′ = 210 GeV choice forces us to choose g′
limits, see ) could affect the BRs, in order to establish if such decaying-channel could
1domain (see ). From this method, assuming that the
1< 0.03 because of the LEP
2We assume that the three heavy neutrinos mass eigenstates are degenerate as this does not affect our
be visible in the full integrated luminosity scenario at LHC. Nevertheless, we have also
studied the role of a light Higgs boson (mh1= 120 GeV) in the h2’s BRs, because of
the fact that the channel h2→ 2h1represents a peculiar signature of the model, that is
distinctive with respect to supersymmetrical Models in which the mixing in the scalar
sector is forbidden.
100 200 300 400500600
ass prod, t
production at LHC (√s = 7
TeV) plotted against the light
Higgs boson mass mh1at α =
π/5 in g-g fusion (black line),
VBF (red line), Higgs-strahlung
from W±(blue line) and Z (vi-
olet line) and associated produc-
tion with top (green line). The
SM-like case has been superim-
posed in dotted lines.
Cross-section for h1
100 120 140 160 180 200 220 240
BR(h1 → 2νh)
Figure 2: Branching ratio for the
light Higgs boson decaying in two
heavy neutrinos (h1 → 2νh) in
the minimal B − L model plot-
ted against the light Higgs boson
mass mh1for νh = 50 GeV and
several values of the mixing an-
gle α in units of π/2: α = 0.2
(blue line), α = 0.4 (green line),
α = 0.6 (red line), α = 0.8 (black
Finally, by combining the two analysis (Higgses productions and BRs), we have made
a detailed study of the cross-section for some peculiar signature of the model: pp → h1→
νhνh, pp → h2→ h1h1and pp → h2→ Z′Z′. The analysis of each of these processes has
shown how there is the possibility to observe such signatures both in the early discovery
scenario (pp → νhνh) and in the full integrated luminosity scenario (pp → h1h1 and
pp → Z′Z′).
In particular, in figure 3 we show the explicit result for the pp → h1→ νhνhprocess at
LHC with√s = 7 TeV and mνh= 50 GeV: a cross-section contour “sliced” in the mh1-α
plane. Several values of the cross-section have been considered: σ = 5 fb (black line),
σ = 10 fb (red line), σ = 100 fb (green line), σ = 250 fb (blue line). The red-shadowed
region is excluded by the LEP experiments.
Even if we consider a low-luminosity scenario (L ≃ 1 fb−1), it is clear from the plot that
there is a noticeable allowed parameter space for which the rate of events is considerably
large: when the integrated luminosity reaches L = 1 fb−1(that is equivalent to 18 − 24
months of√s = 7 TeV running at LHC according to the official programme) we estimated
a collection of ∼ 10 heavy neutrino pair productions for 100 GeV< mh1< 165 GeV and
0.05π < α < 0.48π, that scales up to ∼ 102events for 110 GeV< mh1< 150 GeV and
0.15π < α < 0.46π.
This represents a clear chance to establish a heavy neutrino discovery within the next
two years at the CERN machine.
100 120 140 160 180 200 220 240
Figure 3: Cross-section contour
plot for the process pp → h1→
νhνhat LHC√s = 7 TeV, plot-
ted against mh1-α, with mνh=
50 GeV. Several values of the
cross-section have been consid-
ered: σ = 5 fb (black line), σ =
10 fb (red line), σ = 100 fb (green
line), σ = 250 fb (blue line). The
red-shadowed region is excluded
by the LEP experiments.
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