The Trivial Higgs at LHC

Abstract

We further elaborate on our proposal for the Trivial Higgs that within the
Standard Model is the unique possibility to implement the spontaneous symmetry
breaking of the local gauge symmetry by elementary local scalar fields. The
Trivial Higgs boson turns out to be rather heavy with mass $m_H \simeq 750$
GeV. We discuss the experimental signatures of our Trivial Higgs and compare
with the recent data from ATLAS and CMS collaborations based on a total
integrated luminosity between 1 fb$^{-1}$ and 2.3 fb$^{-1}$. We suggest that
the available experimental data could be consistent with our scenario.

Full text

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arXiv:1109.5922v1 [hep-ph] 27 Sep 2011
The Trivial Higgs at LHC
P. Cea1,2∗and L. Cosmai1†
1INFN - Sezione di Bari, I-70126 Bari, Italy
2Physics Department, Univ. of Bari, I-70126 Bari, Italy
Abstract
We further elaborate on our proposal for the Trivial Higgs that within the Standard Model is the
unique possibility to implement the spontaneous symmetry breaking of the local gauge symmetry
by elementary local scalar fields. The Trivial Higgs boson turns out to be rather heavy with mass
mH≃ 750 GeV. We discuss the experimental signatures of our Trivial Higgs and compare with the
recent data from ATLAS and CMS collaborations based on a total integrated luminosity between
1 fb−1and 2.3 fb−1. We suggest that the available experimental data could be consistent with our
scenario.
∗Paolo.Cea@ba.infn.it
†Leonardo.Cosmai@ba.infn.it
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I. INTRODUCTION
In a previous paper [1] we have enlightened the scenario where the Higgs boson without
self-interaction (Trivial Higgs) could coexist with spontaneous symmetry breaking. Due to
the peculiar rescaling of the Higgs condensate, the relation between mH and the physical
vRis not the same as in perturbation theory. According to this picture one expects that
the ratio mH/vRwould be a cutoff-independent constant. In fact, our numerical results [1]
showed that the extrapolation to the continuum limit leads to the quite simple result:
mH ≃ π vR, (1)
pointing to a rather massive Trivial Higgs boson mH ≃ 750 GeV.
A cornerstone of the Standard Model is the mechanism of spontaneous symmetry breaking
that is mediated by the Higgs boson. In fact, the discovery of the Higgs boson is the
highest priority of the Large Hadron Collider (LHC). Recently, both the ATLAS and CMS
collaborations [2, 3] reported the experimental results for the search of the Higgs boson at
the Large Hadron Collider running at√s = 7 TeV, based on a total integrated luminosity
between 1 fb−1and 2.3 fb−1.
The aim of the present paper is to further elaborate on the production mechanisms of
our Trivial Higgs and to compare the theoretical expectations with selected available data
from LHC.
II. THE TRIVIAL HIGGS
For Higgs mass in the range 700 − 800 GeV the main production mechanism at LHC is
the gluon fusion gg → H. The theoretical estimate of the production cross section at LHC
for centre of mass energy√s = 7TeV is [4] :
σSM(gg → H) ≃ 0.06 − 0.14 pb , 700 GeV < mH < 800 GeV .(2)
The gluon coupling to the Higgs boson in the Standard Model is mediated by triangular loops
of top and bottom quarks. Since the Yukawa coupling of the Higgs particle to heavy quarks
grows with quark mass, thus balancing the decrease of the triangle amplitude, the effective
gluon coupling approaches a non-zero value for large loop-quark masses. On the other hand,
we already argued [1] that the non trivial rescaling of the Higgs condensate means that, if
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the fermions acquires a finite mass through the Yukawa couplings, then the coupling of the
physical Higgs field to the fermions could be very different from the perturbative Standard
Model Higgs boson. However, the coupling of the Higgs field to the gauge vector bosons
is fixed by the gauge symmetries, therefore the coupling of the Trivial Higgs boson to the
gauge vector bosons is the same as for the Standard Model Higgs boson. For large Higgs
masses the vector-boson fusion mechanism becomes competitive to the gluon fusion Higgs
production [4]:
σSM(W+W−→ H) ≃ 0.02 − 0.03 pb , 700 GeV < mH < 800 GeV .(3)
The main difficulty in the experimental identification of a very heavy Higgs (mH> 650 GeV)
resides in the large width which makes impossible to observe a mass peak. In fact, the
expected mass spectrum of our trivial Higgs should be proportional to the Lorentzian dis-
tribution:
LH(E) ∼
Γ
(E − 750 GeV)2+ Γ2
, (4)
where we assume the central value of the Higgs mass according to Eq. (1) and Γ is the Higgs
total width. Note that Eq. (4) is the simplest distribution consistent with the Heisenberg
uncertainty principle and the finite lifetime τ ≃ 1/Γ.
According to the triviality and spontaneous symmetry breaking scenario the Higgs self-
coupling vanishes so that the decay width is mainly given by the decays into pairs of massive
gauge bosons:
Γ ≃ Γ(H → W+W−) + Γ(H → Z0Z0) . (5)
Since the coupling of the Trivial Higgs to the gauge vector bosons is fixed by the local
gauge symmetry, the decay width into gauge vector bosons is the same as in the case of the
perturbative Higgs boson, consequently [5]
Γ(H → W+W−) ≃ 2 Γ(H → Z0Z0) ∼ GFm3
H.(6)
Equation (6) shows that in the high mass region mH>
∼400 GeV the Higgs total width
depends strongly on mH. To take care of the energy dependence of the width in Eq. (4)
we need Γ(E) as a function of E. To this end we may follow the calculations of Higgs total
width within the Standard Model performed in Ref. [4]. In Fig. 1 (left) we show the energy
dependence of the Higgs total width Γ(E) according to Tables 28 and 29 of Ref. [4]. We
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200 400600 800 1000
E (GeV)
0
100
200
300
400
500
600
700
Γ(E) (GeV)
0 200400 600 8001000 12001400 160018002000
MH (GeV)
0
0.0005
0.0010
0.0015
0.0020
LH
FIG. 1: (Left) The energy dependence of the Higgs total width. Full points are the values of the
Standard Model Higgs total widths reported in Tables 28 and 29 of Ref. [4]. The full line is our
parameterization Eq. (7). (Right) The Lorentzian distribution Eq. (8) as a function of the Higgs
mass MH.
have fitted the tabulated values of Γ(E) with the phenomenological relation (full blue line
in Fig. 1, left):
Γ(E) ≃ 8.0 10−7E3− 1.5 10−4E2. (7)
We obtain, therefore, the following Lorentzin distribution:
LH(E) ≃
1.465
π
Γ(E)
(E − 750 GeV)2+ Γ(E)2
, (8)
where Γ(E) is given by Eq. (7), and the normalization is such that:
?∞
0
LH(E) dE = 1 . (9)
In the limit Γ → 0, LH(E) reduces to δ(E − 750 GeV). In Fig. 1 (right) we display the
Lorentzian distribution as a function of the energy E.
To evaluate the Higgs event production at LHC we need the Higgs production total cross
section. As already discussed, for large Higgs masses the main production processes are by
vector-boson fusion and gluon-gluon fusion. The Trivial Higgs production cross section by
vector-boson fusion is almost the same as in the perturbative Standard Model calculations.
In Fig. 2 (left) we show the energy dependence of the perturbative Higgs boson vector-
boson fusion cross section within the Standard Model at√s = 7 TeV reported in Table 11
of Ref. [4]. We parametrize the energy dependence of the cross section as (full blue line in
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200 400 6008001000 1200
MH (GeV)
10
100
1000
σ(pp -> qqH) [fb]
0 200400600 8001000 1200
MH (GeV)
1
10
100
1000
10000
σ(pp(gg) -> H) [fb]
FIG. 2: (Left) The energy dependence of the vector-boson fusion cross section. The full points are
the Standard Model Higgs production cross section at√s = 7 TeV reported in Table 11 of Ref. [4].
The full line is our parameterization Eq. (10). (Right) The energy dependence of the gluon-fusion
cross section. The full points are the Standard Model Higgs production cross section at√s = 7
TeV reported in Table 5 of Ref. [4]. The full line is our parameterization Eq. (11).
Fig. 2, left):
σSM(W+W−→ H) ≃
?3.0 105
MH
−
8.0 106
M2
H
?
exp(−0.0035MH) , MH in GeV . (10)
As concern the gluon fusion cross section, in Fig. 2 (right) we display the Standard Model
Higgs production cross section at√s = 7 TeV reported in Table 5 of Ref. [4]. Again we
parametrize the energy dependence of the cross section as (full blue line in Fig. 2, right):
σSM(gg → H) ≃









?
1.1 107
MH
+ 0.0097 M3
H
?
exp(−0.016MH)MH ≤ 320
320 ≤ MH ≤ 380
380 ≤ MH
2.25 103
2.30 103exp(−0.016MH)
(11)
where MHis expressed in GeV.
The gluon coupling to the perturbative Higgs boson in the Standard Model is mediated by
triangular loops of top and bottom quarks. On the other hand, as already discussed, the
coupling of the Trivial Higgs to the fermions is not fixed by the local gauge symmetry so
that there is no a priori reasons to expect that these couplings would be proportional to
the fermion masses. However, in the relevant high mass region mH>
∼400 GeV the energy
dependence of σSM(gg → H) is given essentially by the gluon distribution function. Thus,
we may safely assume that the Trivial Higgs production cross section by gluon-gluon fusion
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