#### Analysis of b quark pair production signal from neutral 2HDM Higgs bosons at future linear colliders

Eur. Phys. J. C
Analysis of b quark pair production signal from neutral 2HDM Higgs bosons at future linear colliders
Majid Hashemi 0
Mostafa MahdaviKhorrami 0
0 Physics Department, College of Sciences, Shiraz University , Shiraz 71946-84795 , Iran
In this paper, the b quark pair production events are analyzed as a source of neutral Higgs bosons of the two Higgs doublet model type I at linear colliders. The production mechanism is e+e− → Z (∗) → H A → bb¯bb¯ assuming a fully hadronic final state. The analysis aim is to identify both CP-even and CP-odd Higgs bosons in different benchmark points accommodating moderate boson masses. Due to pair production of Higgs bosons, the analysis is most suitable for a linear collider operating at √s = 1 TeV. Results show that in selected benchmark points, signal peaks are observable in the b-jet pair invariant mass distributions at integrated luminosity of 500 fb−1.
1 Introduction
One of the most significant accomplishments of standard
model (SM) of particle physics is indubitably, observation
of Higgs boson at LHC [
1,2
] based on a theoretical
framework known as the Higgs mechanism [
3–8
]. The observed
particle may belong to a single SU(2) doublet (SM Higgs
boson) or a model accommodating a larger structure such
as two Higgs doublet model (2HDM) [
9–11
] whose lightest
Higgs boson respects the observed particle properties.
In the latter scenario, one would have a light Higgs boson
(h) playing the role of the observed particle, plus additional
Higgs bosons with different parities and electric charges. The
extra Higgs bosons of the model are assumed to be heavier
than the observed one. Therefore, a center of mass energy
above the threshold of their masses is required to observe
them. Moreover there may be needs for a cleaner collider
with a dominant leptonic environment rather than LHC to
provide reasonable signature of such particles.
Apart from different scenarios already introduced as
beyond standard model (BSM), the 2HDM is considered
as a framework for supersymmetry theory, in which each
fermion (boson) particle has an associated boson (fermion)
particle known as super partner. This theory offers an
ingenious solution to the gauge coupling unification at high
energies, dark matter candidate (lightest supersymmetric particle)
and removal of quadratic divergence of the Higgs boson mass
radiative corrections by a natural parameter tuning. In such
a theory, the particle space is twice that in SM due to
introducing super partners for SM particles and therefore, two
Higgs doublets are required to give mass to the double space
of particles [
12–14
]. Here we do not go through such
supersymmetric theories, but instead work in the field of 2HDM
without supersymmetry.
There are four types of 2HDM with different scenarios of
Higgs-fermion couplings. The ratio of vacuum expectation
values of the two Higgs doublets (tan β = v2/v1) is the free
parameter of the model and is considered as a measure of the
Higgs-fermion coupling strength in all 2HDM types [
15
].
Our focus in this paper is 2HDM type I which allows for
heavy quark pair production in Higgs boson decays while
decays to light quarks and leptons are suppressed because
the relevant Higgs-fermion couplings depend on the fermion
mass. Therefore below the top quark pair production
threshold, H/ A → bb¯ is dominant as long as A → Z H is not
kinematically allowed.
In other scenarios, such as type III, the Higgs boson
coupling with down-type quarks can experience enhancement
proportional to tan β. However, the current analysis relies
on type I in which the signal cross section and Higgs boson
decays only depend on the Higgs boson and fermion masses.
In recent studies, other types of 2HDM (types II and IV)
were analyzed [
16–18
] leading to overall conclusion that
linear colliders have a prominent potential for observation of
2HDM Higgs bosons with a supreme capability over LHC.
In total five physical Higgs bosons are predicted in 2HDM.
The lightest Higgs boson, h, (sometimes denoted as h SM ) is
the SM like Higgs boson and there are two heavier neutral
Higgs bosons, H (CP-even) and A (CP-odd), and two charged
Higgs bosons, H ±. Recently the theory and phenomenology
of 2HDM has been extensively discussed in [
19
].
In addition to direct searches for the 2HDM Higgs bosons
which look for direct signals of Higgs boson decays, there
are indirect searches based on flavor Physics data. In such
searches, deviations from SM observables are looked for
when processes containing 2HDM Higgs bosons are added to
their corresponding diagrams from SM [
20
]. Limits obtained
from these type of studies have to be taken into account.
However, the current analysis focuses on points in parameter space
where there is no exclusion from flavor physics studies.
The Higgs boson mass range in this analysis is 150–
250 GeV to be searched for at a future linear collider,
operating at √s = 1 TeV. Signals of heavier Higgs bosons tend
to become small when increasing the Higgs bosons masses.
All Higgs bosons are assumed to be degenerate in mass, i.e.,
m H = m A = m H± . This setting ensures that deviation from
SM, in terms of ρ, is small enough and consistent with
experimental value [
21
].
The region of interest is tan β < 50. The signal process,
i.e., e+e− → Z (∗) → H A is independent of tan β as the
Z-H-A vertex does not depend on Higgs-fermion couplings
and the 2HDM type. As will be seen in the next section, the
branching ratio of Higgs boson decay to bb¯ is also
independent of tan β for tan β < 50.
The fully hadronic final state is expected to result in two
pairs of b-jets (totally four b-jets) coming from neutral Higgs
boson H/ A decays to two b-jets. Events which contain four
identified (tagged) b-jets, are used to produce the H/ A
invariant mass distribution. The same approach is applied on
background events and a final shape discrimination is performed
to evaluate the signal significance. Before going to the details
of the analysis, a brief review of the theoretical framework
is presented in the next section.
2 Theoretical framework
Couplings of heavy neutral Higgs bosons (H and A) with
quarks in Yukawa Lagrangian of the 2HDM, as introduced
in [
22
], takes the form:
LY = D[ρ Dsβ−α − κ Dcβ−α]D H − i Dγ5ρ D D A
+ U [ρU sβ−α − κU cβ−α]U H + iU γ5ρU U A
(1)
in which U (D) are the up(down)-type quarks fields, H and
A the neutral Higgs boson fields, κq = mvq for any
up(down)type quark U (D) and sβ−α = sin(β−α) and cβ−α = cos(β−
α). The ρq parameters depend on the 2HDM type and are
proportional to κq as shown in Table 1 [
23
]. Therefore the
four types of interactions (2HDM types) depend on the values
of ρ f which is κ f (SM coupling) times a tan β or cot β factor
which makes possible deviations from SM [
24
].
In Yukawa Lagrangian of the 2HDM type I, the light
neutral Higgs (h) coupling to fermions and gauge-bosons takes
the SM value by setting sβ−α = 1. This setting suppresses the
heavy neutral Higgs (H ) coupling with gauge bosons which
is proportional to cα−β [
19
]. Therefore in our study, we set
sβ−α = 1, in respect of the correspondence principle so that
2HDM SM-like Higgs boson behaves the same as SM Higgs.
This leads to the brief form of the Lagrangian as shown in
Eq. 1:
(2)
LY = {Dρ D D + U ρU U }H
− i {Dγ5ρ D D − U γ5ρU U } A.
According to Table 1, the type I appears interesting for low
tan β as all couplings in the neutral Higgs sector are
proportional to cot β. However, the cot β factor cancels out when
calculating branching ratio of Higgs boson decays because
all Higgs-fermion couplings are proportional to the same
factor. This has two subsequences: firstly the Higgs boson decay
to fermions is independent of tan β at tree level, and secondly
the Higgs boson decays to heavy quarks become dominant
due to their larger coupling with the Higgs boson. As a result,
as long as the Higgs boson mass is below the top quark pair
production threshold, decay to bb¯ is dominant while above
the threshold (Higgs boson mass above twice the top quark
mass) decay to t t¯ starts to grow as seen from Fig. 1a, b.
It should be noted that loop diagrams such as H → gg
proceed through preferably virtual top quarks in the loop,
as seen in Fig. 2. Such decays grow when the Higgs boson
mass increases and result in the reduction of decay to b or c
quark pairs. The above conclusion is of course valid as long
as Higgs boson decay to t t¯ is kinematically impossible, i.e.,
m H/A 350 GeV.
Although the charged Higgs bosons acquire a strong limit
from flavor physics in 2HDM types II and III as reported in
[
25–27
], types I and IV receive a small excluded region at
low tan β. Since the scenario assumed in this paper assumes
degenerate Higgs boson states, one may assume the same
excluded region for neutral Higgs bosons. However, these
limits are at low tan β values and do not affect results of this
analysis.
3 Signal identification and the search scenario
The signal process, i.e., e+e− → Z (∗) → H A followed
by the Higgs bosons decays (H/ A → bb¯) depends on the
Higgs bosons masses and the cross section decreases when
the sum of the masses of the two Higgs bosons reaches the
threshold of center of mass energy provided by the collider.
As it is shown in Fig. 1a, b, the proper range of the Higgs
boson mass is basically 150–350 GeV. However at masses
above 250 GeV, the cross section and decay rates decrease
so that a reasonable signal is not observed. The Higgs boson
masses are assumed to be equal while a scenario with m A =
m H± = m H + 50 GeV is also studied.
The total cross section of the signal is ∼ 12 fb
corresponding to m H/A = 150 GeV and decreases to ∼ 9 fb
with m H = 200 GeV and m A = 250 GeV. Taking into
account the branching ratio of Higgs bosons decays, these
values decrease down to ∼ 5 fb and ∼ 1 fb respectively.
All benchmark points are checked to be consistent with the
potential stability, perturbativity and unitarity requirements
and the current experimental limits on Higgs boson masses
using 2HDMC 1.7.0 [
28,29
]. A discussion on this subject
will be presented before conclusion.
In order to identify the right pairs of b-jets, two methods
are tried. The first method is based on the special relativity
kinematics; In this method, if the Higgs bosons masses are
equal (m H = m A) which is valid in the scenario presented in
this analysis, one can distinguish the two pairs of the b-jets.
(a) H and A decays as seen in their rest frames
(b) The same decays as seen in the laboratory frame.
Figure 3a shows a typical event of H and A decays with
each decay captured in the rest frame of the decaying Higgs
boson. The axis joining the two Higgs bosons can be
considered as the preferred axis. The angle between each pair of
b-jets in the parent Higgs boson rest frame is π . The b-jet
flying closest to the axis (most collinear to its parent), has
the highest longitudinal momentum component which can
be positive or negative when projected to the axis. In the
laboratory frame, the event appears in the different form as
shown in Fig. 3b. The b-jets with smallest angle with respect
to the axis in Fig. 3b receive the highest positive or negative
Lorentz boost. The two possibilities appear as the maximum
and minimum flight angles in the laboratory frame. Due to
the momentum conservation perpendicular to the axis,
transverse momenta of the two b-jets are equal.
Adding the two longitudinal and transverse momentum
components, it is concluded that the b-jet with the smallest
angle with respect to the axis acquires the maximum total
momentum while the one with the largest angle has the
minimum total momentum among other b-jets. In extreme
relativistic limit, the energy and the momentum of a particle are
almost equal thus the conclusion holds for particle energies.
As the example, according to Fig. 3b, E1 > E4 and E2 > E3.
Due to the energy conservation, E1 + E4 = E2 + E3, and
therefore the b-jet with the maximum energy has to come
along with the b-jet with the lowest energy to keep the sum
of the two energies conserved. Without any loss of generality,
one may assume E1 to be the highest energy. Then the four
b-jets energies are sorted like E1 > E2 > E3 > E4 where
E1, E4 and E2, E3 pairs come from their own parents
separately. In order to apply this algorithm, the tagged b-jets are
sorted in terms of their energies and labeled as b1, b2, b3
and b4. Then two independent pairs, i.e., (b1, b4) and (b2, b3)
are used to calculate the invariant masses of the parent Higgs
bosons.
The second method is based on minimizing the angular
separation between the two b-jets, R = ( η)2 + ( φ)2,
in which η = − ln(tan θ2 ) is the pseudo-rapidity and φ is the
azimuthal angle. This algorithm finds the correct b-jet pair
with the minimum angular separation. One of the advantages
of this method is that it is independent of whether the Higgs
bosons masses are equal or not.
The two methods discussed above were tested separately,
however, the second method leads to better results (narrower
invariant mass peak, smaller tails and better signal to
background ratio due to the less wrong pairing). Therefore results
presented in this analysis are based on the second method.
4 Software setup and cross sections
In this work, the event generation and cross section
calculation of signal processes are handled by PYTHIA 8.2.15
[
30
] which uses 2HDM spectrum files in LHA format [
31
]
generated using 2HDMC 1.7.0 for each benchmark point
separately. The LHA files contain information about the
parameters of the model which include Higgs bosons masses,
widths and the branching ratio of decay to different channels
for each benchmark point. After multi-particle interaction
and shower production by PYTHIA, the jet reconstruction
is performed by FASTJET 3.1 [
32,33
] using anti-kt
algorithm with a jet cone size of 0.4.
The main SM background processes are t t¯, gauge boson
pair production W W, Z Z and single Z /γ ∗. These
background processes are all generated using PYTHIA and their
cross sections are also obtained using the same package
besides an additional NLO scaling which is applied on the
t t¯ cross section according to MCFM 6.1 [
34–37
]. Tables 2
and 3 indicate the signal benchmark points and background
processes and their cross sections.
The event selection starts from b-tagging using reconstructed
jets from FASTJET. A kinematic requirement is applied on
jets as E j > 5. GeV, |η| < 5. to reject soft jets or jets
close to the beam pipe. The b-tagging algorithm is based on
a simplified matching between the reconstructed jet and the
b-quark in the event. For each reconstructed jet, a search for
b-quarks in the jet cone is performed. If the jet accommodates
a b or c quark in the reconstruction cone, it is tagged as a
bjet with a b-tagging probability of 70% and fake rate of 10%
(from c-jets).
Each event has to have four b-jets to be analyzed. A search
among the four b-jets in the event is performed to find the
correct b-jet pair with minimum R and calculates their
invariant mass. The same algorithm is applied on background
processes. The distributions of b-jet pair invariant masses are
stored in histograms for both signal and background
processes.
In order to select events in the signal region (region of the
signal peak in the b-jet pair invariant mass distribution), a
mass window is applied on the signal plus background
distributions. The mass window enhances the signal to background
ratio leading to a higher signal purity. Figure 4a–c show the
distributions of bb¯ invariant mass from signal events on top
the background.
A polynomial fit describes the background distribution
and is used as the input probability distribution function
(PDF) for the background (the red curves shown in Fig. 4a–c).
A Gaussian fit is then added to the background PDF (the
polyTable 4 (m H = m A = m H± )
Benchmark points
nomial function) and is applied on signal plus background
distribution using the input parameter values taken from the
previous step. The result of the fits are shown as green curves
in Fig. 4a–c. The error bars are taken into account in the fit
which is based on χ 2 minimization. They are however of
statistical origin and systematic uncertainties are not taken
into account.
Table 4 shows mass windows and the total signal and
background efficiencies and the final number of signal and
background. The signal to background ratio and signal statistical
significance in different points are also included. The mass
window is set by maximizing the signal significance in a
search for the best position of the left and right sides of the
window. As seen from Table 4, the signal significance is
reasonable and above 5σ for all selected benchmark points.
It should be noted that we obtain reasonable results
only for BP1, BP2 and BP3. The fourth benchmark (BP4)
which involves different Higgs boson masses leads to smaller
branching ratio of Higgs boson decays compared to other
points. The reason is mainly due to the CP-odd Higgs decay
to ZH ( A → Z H ) which turns on when there is enough phase
space for the decay even through off-shell production of the
decay products. We examined this scenario and the result is
shown in Fig. 4d. The signal significance in this case is 7σ .
However, fitting this distribution by including two Gaussian
fits on top of a polynomial is challenging due to the small
size of the signal and large error bars.
6 Discussion
It should be noted that the theoretical space available to this
study is limited in m212 vs tan β parameter space. In order
to respect theoretical requirements, a scan over possible m212
values was performed for each tan β value resulting in a
narrow range of m212 which satisfies all requirements of
potential stability, perturbativity and unitarity. Results are
plotted in Fig. 5. As seen from Fig. 5, the available range of
m212 becomes smaller with increasing tan β for each
benchmark point. Any value of m212 in the allowed range leads
to the same branching ratio of Higgs boson decay to bb¯ for
tan β < 50. Therefore the signal significance values obtained
for tan β = 10 are valid up to tan β 50 provided that for
each value of tan β, the allowed value of m212 is taken from
the range provided in Fig. 5.
7 Conclusions
The observability of 2HDM Higgs bosons was studied at a
e+e− linear collider operating at √s = 1 TeV. Different
benchmark points were studied focusing on moderate values
of the Higgs bosons masses. The theoretical framework was
set to 2HDM type I where the Higgs (H or A) boson decay
to bb¯ is dominant as long as the Higgs boson mass is below
the threshold of on-shell decay to t t¯. The leptonic decays are
also suppressed as cot β. The signal cross section is almost
independent of tan β and therefore all results were quoted
based on a typical tan β value of 10. The collider integrated
luminosity was set to 500 fb−1. Results show that the Higgs
boson signal in bb¯ invariant mass distribution is well
observable for all benchmark points. There is also a fit possibility
for those points with equal Higgs boson masses.
Acknowledgements We would like to thank the college of sciences at
Shiraz university for providing computational facilities and maintaining
the computing cluster during the research program.
Open Access This article is distributed under the terms of the Creative
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ons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
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Commons license, and indicate if changes were made.
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