Eur. Phys. J. C (2024) 84:245
https://doi.org/10.1140/epjc/s10052-024-12574-3

Regular Article - Theoretical Physics

A novel experimental search channel for very light higgs bosons
in the 2HDM type I
S. Moretti1,2 , S. Semlali1,3,a , C. H. Shepherd-Themistocleous3
1 School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK
2 Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden
3 Particle Physics Department, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK

Received: 13 October 2023 / Accepted: 18 February 2024 / Published online: 8 March 2024
© The Author(s) 2024

Abstract We present a reinterpretation study of existing
results from the CMS Collaboration, specifically, searches
for light Beyond the Standard Model (BSM) Higgs pairs
produced in the chain decay pp → HSM → hh(aa) intoa variety of final states, in the context of the CP-conserving
2-Higgs Doublet Model (2HDM) Type-I. Through this, wetest the Large Hadron Collider (LHC) sensitivity to a possible new signature, pp → HSM → Z A → Z Z h, withZ Z → j jμ+ μ− and h → bb̄. We perform a systematic scan over the 2HDM Type-I parameter space, by taking
into account all available theoretical and experimental constraints, in order to find a region with a potentially visible
signal. We investigate the significance of it through a fullMonte Carlo simulation down to the parametrised detector
level. We show that such a signal is an alternative promisingchannel to standard four-body searches for light BSM Higgs
bosons at the LHC already with an integrated luminosity of
L = 300 fb−1 . For a tenfold increase of the latter, discovery
should be possible over most of the allowed parameter space.

1 Introduction
One of the main goals of the LHC machine is to investigate theindividual properties (mass, width, spin, CP quantum numbers) of the Higgs boson as well as its interactions (with bothmatter and forces) and to look into evidence for new physics.
These features have been probed by the ATLAS and CMS
collaborations in different production and decay channels,
using proton-proton ( pp) collision data collected at centreof-mass energies of 7, 8 [1] and 13 TeV [2,3]. More recently,
there have been observations involving the rare decay of
the Higgs boson into a Z -boson and a photon (H → Z γ )a e-mail: souad.semlali@soton.ac.uk (corresponding author)

with a significance of 3.4σ [4], which could provide insights
into the Higgs boson’s coupling to both the electroweak
gauge bosons and photons, contributing to our comprehension of the dynamics and interplays within the Higgs sector.
Although the current measurements of the Higgs mass, spin,
width and couplings to SM fermions and vector bosons [2,3]are all indeed in good agreement with the SM theoretical predictions, the small deviations in the SM-like Higgs couplings
probed in various production modes for the five key decay
channels H → γ γ , Z Z ∗ , W W ∗ , τ τ and bb [2,3] still
provide signs of possible potential BSM contributions to thetotal Higgs width and hints of new physics through the invisible and/or undetected decays. The indirect constraints fromthe current fit of couplings measurements and direct searches
for H → inv (i.e., to‘invisible’ final states) performed by
ATLAS and CMS collaborations have placed upper limits on
the Branching Ratio (BR) of Higgs boson to invisible particles and undetected BSM particles at 95% C.L. (Confidence
Level) [5–8].
The quest to uncover the trilinear couplings also holds
a prominent position on the LHC’s research agenda. Suchinteractions can be probed with sufficient luminosity, although,at present (i.e., at the end of Run 2), they are not determinedyet. A measurement of this interaction is one of the highest priority goals during, possibly, Run 3 and, certainly, atthe High Luminosity LHC (HL-LHC), both of which would,
therefore, start shedding light on the nature of the Higgs
boson and the shape of the Higgs potential, which in turnhas implications for the vacuum metastability, the hierarchy
problem as well as the strength of the Electro-Weak (EW)
phase transition. However, probing Higgs’s self-interactions,both trilinear and quartic couplings, in multi-Higgs production is experimentally very challenging. From the theory sideon the other hand, many models with an extended scalar
sector, like the 2-Higgs Doublet model (2HDM) [9–13], the123245 Page 2 of 16

Next-to-2HDM(N2HDM) [14–17] and a variety of both minimal and nonminimal Supersymmetric (SUSY) models [18–24] motivate
additional features of new di-Higgs final states, as they allpresent with additional CP-even and/or -odd Higgs states,
which can be accessible by the LHC experiments in a variety
of signatures. Among the prominent processes are searches
for exotic Higgs decays to a pair of light scalars or pseudoscalars, e.g. H → aa, hh, which then decay to SM particles.
This paper focuses on the popular 2HDM. After EW Symmetry Breaking (EWSB), the scalar sector of the 2HDM predicts five physical Higgs states, two CP-even Higgs bosons(h, H , with m h < m H ), one CP-odd one (a) and a pairof charged ones (H ± ). The rich (pseudo)scalar sector of the
2HDM and the different sets of Yukawa couplings that can berealised then offer a very interesting production and decay
phenomenology of neutral and charged Higgs states at the
LHC, even after scrutinising the 2HDM parameter space byconsidering different theoretical (vacuum stability, perturbativity, unitarity, etc.) and experimental (from SM-like Higgs
data and null searches for companion states, flavour physics
and low energy observables, etc.) constraints. Furthermore,
the 2HDM is also attractive because one can impose a simple
Z 2 discrete symmetry to the Yukawa sector in order to suppress Flavour Changing Neutral Currents (FCNCs) at treelevel [25,26], which then forces one doublet to couple to agiven type of fermions and leading as a result to four Yukawa
interactions (termed, Type-I, Type-II, Type-X and Type-Y).
In fact, in order to realise EWSB in such a way that the 2HDM
is compliant with all experimental data, it is finally customary
to allow for a soft breaking of this Z 2 symmetry. Herein, we
will use the latter setup with a Type-I Yukawa structure. Thisparticular scenario can accommodate both light neutral (10–100 GeV) and charged scalars (100–200 GeV), while one can
not obtain such light Higgs states within the 2HDM TypeII or Type-Y configuration due ot the significant constraints
arising from flavour physics, specifically from B → X s γ
which enforces a lower bound of 800 GeV on the charged
Higgs mass [27].
In the present study, we plan to take advantage of the directaccess to some trilinear Higgs couplings that the LHC canaccess, entering multi-Higgs processes such as H → hh(aa)and H ± → W ± a, to test the sensitivity of the parameter
space combination of 2HDM Type-I to light Higgs searches
in cascade (or chain) decays. As the analysis progress, we aim
to explore the scope of a new search for light Higgs bosons at
the LHC Run 3 (with an integrated luminosity of 300 fb−1 ) as
well as the HL-LHC (with an integrated luminosity of 3000
fb−1 ), on the basis of the knowledge acquired from the studyof the aforementioned signatures. We focus mainly on theconfiguration of Type-I with inverted scenario, which in turnoffers an alternative and new promising signal, in the formof the following cascade decays H → Z ∗ a → Z ∗ Z ∗ h →123Eur. Phys. J. C (2024) 84:245

bbμ− μ+ j j. The main Higgs production process is via gluon
fusion gg → H .

2 2HDM type-I
The 2HDM is one of the simplest well-motivated extensionsof the SM. In this section, we briefly review the theoretical structure of this model. The scalar sector of the 2HDM
consists of two complex SU (2) L doublets, Φ1 and Φ2 , withhypercharge Y = +1. The most general SU (2) L × U (1)Yinvariant scalar potential can be written as follows [11–13]:
V (Φ1 , Φ2 ) = m 211 Φ1† Φ1 + m 222 Φ2† Φ2 − [m 212 Φ1† Φ2 + h.c.]
λ2
λ1+ (Φ1† Φ1 )2 + (Φ2† Φ2 )22
2††+λ3 (Φ1 Φ1 )(Φ2 Φ2 )


λ5 †
†
†
2
+λ4 (Φ1 Φ2 )(Φ2 Φ1 ) +(Φ Φ2 ) + h.c.
2 1



+ λ6 (Φ1† Φ1 ) + λ7 (Φ2† Φ2 ) Φ1† Φ2 + h.c. .
(1)Assuming CP-conservation in the 2HDM and following thehermiticity of the scalar potential, m 211 , m 222 , m 212 , λ1,2,3,4,5,6
are real parameters. Invoking the described Z 2 symmetry, toavoid tree-level Higgs-mediated FCNCs at tree level, implies
that λ6 = λ7 = 0. Also notice that the bilinear term proportional to m 212 breaks the Z 2 symmetry softly. Using the two
minimisation conditions of √the scalar potential and the combination v 2 = v12 +v22 = (2 2G F )−1 , one can then trade theLagrangian parameters of the 2HDM for a more convenient
set of variables,
α, tan β = vv21 , m h , m H , m a , m H ± and m 212 ,where α is the CP-even mixing angle, v1 and v2 are the Vaccum Expectations Values (VEVs) of the two Higgs doublets
Φ1 and Φ2 , respectively.
2.1 Yukawa couplings
The general structure of the Yukawa Lagrangian when both
Higgs fields couple to all fermions is given by [13]:LY = Q̄  L (Y1u Φ̃1 + Y2u Φ̃2 )u R + Q̄  L (Y1d Φ1 + Y2d Φ2 )d R+ L¯ (Y l Φ1 + Y l Φ2 )l  + h.c.,
(2)
L

1

2

R

where Q L and L L are the weak isospin quark and lepton doublets, u R and d R denote the right-handed quark singlets whileu , Y d and Y l are couplings matrices in flavour space.
Y1,2
1,2
1,2
This form of Yukawa interaction gives rise to large FCNCs
at tree level, which is strongly constrained by B-physics
observables. Implementing Z 2 symmetry [25,26] allows only
one doublet to couple to a given right-handed fermion field.

Eur. Phys. J. C (2024) 84:245

Page 3 of 16 245

Depending on the Z 2 assignment, one can have the four typesof models previously refered to as Type-I, Type-II, Type-X
and Type-Y. In the mass-eigenstate basis, they can be unified
and expressed as follows:−LY = +


f =u,d,m f f¯ f +

mf f
mf f
κh f¯ f h +κ f¯ f H
v
v H

mf f
−i
κ A f¯γ5 f Av√
2+ū m u V κ Au PL + V m d κ Ad PR d H +v√
2m κ Aν̄ L R H + + h.c.,+v

Experimental observations impose the following constraints:• EW precision observables, i.e., the oblique parameters,
S, T and U [33,34] are required to be within 95% C.L. of
their experimental measurements, the current fit values(with the correlation parameters) are given by [35]:S = −0.02 ± 0.10, T = 0.03 ± 0.12,
U = 0.01 ± 0.11, ρ ST = 0.92, ρ SU = −0.80,
ρT U = −0.93, χ ST, SU, T U < 5.99.

(3)

where PL ,R = (1 ± γ5 )/2 are the projection operators and V
denotes the Cabibbo–Kobayashi–Maskawa (CKM) matrix.
Here, we focus only on Type-I, where only one doublet Φ2couples to all fermions, and thus the Higgs-fermion couplings
are flavour diagonal in the fermion mass basis and depend
only on the mixing angles, α and β, as follows:u, d, l= sα /sβ ,κhu, d, l = cα /sβ , κ H

κ Au = cot β, κ Ad, l = − cot β,
where we have used the short-hand notation c and s for cos
and sin, respectively.
2.2 Theoretical and experimental constraints
We now describe briefly a set of, in turn, theoretical andexperimental constraints that must be satisfied by the parameter space of the 2HDM.
• Perturbative unitarity constraints require a variety of treelevel 2-to-2 body scatterings processes (e.g. scalar-scalar,gauge boson-gauge boson and scalar-gauge boson) toremain unitary at high energy [28–30].
• Vacuum stability [31] requires the scalar potential tobe finite at large field values, leading to the following
bounds:λ1,2 > 0, λ3 > − λ1 λ2 , λ3 + λ4 − |λ5 | > − λ1 λ2 .
• Perturbativity requires the quartic couplings to obey
|λi | < 4π (i = 1, . . . , 5).
The above constraints have been implemented in
2HDMC−1.8.0 [32]. This public code is then used to
explore the 2HDM parameter space and to compute the different Higgs BRs in each point of it. (2HDMC also provides
an interface to HiggsBounds and HiggsSignals, see
below.)• Consistency with the Z width measurement Γ Z =2.4952 ± 0.0023 GeV from LEP [36,37] is required.
• Constraints from LHC, Tevatron and LEP searches
which failed to find companion Higgs states are taken
into account via HiggsBounds−5.10.0 [38], whichallows to test the exclusion limits at 95% C.L.
• The code HiggsSignals−2.6.2 [39] is used tocheck the signal strength measurements of the SM-like
Higgs boson discovered at the LHC in 2012.
• Constraints from B meson decays are enforced bySuperiso-v1.4 [40], using the current measurements:– BR(B → X s γ )| E γ <1.6 GeV = (3.32 ± 0.15) × 10−4[41],
−9 [42,– BR(Bs → μ+ μ− )(LHCb) = 3.09+0.46−0.43 × 1043],
−9 [44],– BR(Bs → μ+ μ− ) (CMS) = 3.83+0.38−0.36 × 10
+0.8
× 10−10 [42,– BR(B 0 → μ+ μ− )(LHCb) = 1.2−0.7
43],−10 [44].
– BR(B 0 → μ+ μ− )(CMS) = 0.37+0.75−0.67 × 10

• Constraints from recent searches for light pseudoscalarstates in the mass range [15, 62.5] GeV, in proton√
proton collision at s = 13 TeV, in μ+ μ− bb [45,46],
μ+ μ− τ + τ − [47] and τ + τ − bb [48] final states, areincluded in HiggsBounds. Since no significant excess
is observed, upper limits are set on BR(H → aa →μ+ μ− bb, μ+ μ− τ + τ − , τ + τ − bb) [45–48]. However,lately, additional constraints from such Higgs cascadedecays have emerged, not included in the numerical tool,
so we had to deal with these separately. For example, the
CMS group has reported a search for H → aa → 4γ√[49], using the data collected at s = 13 TeV, withan integrated luminosity of 132 fb−1 . Upper limits canthen be set on BR(H → aa → 4γ ) at 95% C.L,
since no significant deviation is observed.1 The ATLAS
1 EasyNData [50] was used to digitise the exclusion limits fromthe published papers in order to test each point in the parameter
space against the upper limit on BR(H → hh(aa) → 4γ ) [49], a123245 Page 4 of 16
Table 1 (×)/() indicate
searches (not yet)/(already)implemented in
HiggsBounds−5.10.0

Eur. Phys. J. C (2024) 84:245

Limit

Collaboration

Range

HiggsBounds

H → aa → μ+ μ− bb [45]CMS

15 GeV < m a < 60 GeV

H → aa → μ+ μ− bb [46]ATLAS

15 GeV < m a < 60 GeV

H → aa → μ+ μ− τ + τ − [47]CMS

15 GeV < m a < 61.5 GeV

H → aa → τ + τ − bb [48]CMS

15 GeV < m a < 60 GeV

H → aa → 4γ [49]CMS

15 GeV < m a < 60 GeV×

H → aa → μ+ μ− bb [51]CMS

15 GeV < m a < 60 GeV×

H → aa → τ + τ − bb [51]CMS

15 GeV < m a < 60 GeV×

H → aa → μ+ μ− τ + τ − [52]CMS

3.6 GeV < m a < 21GeV×

H → aa → μ+ μ− bb [53]ATLAS

15 GeV < m a < 60 GeV×group [53] has also recently searched for the exotic
decay of the Higgs boson into two light pseudoscalars√
in μ+ μ− bb final state at s = 13 TeV with an integrated luminosity of 137 fb−1 , in the range of masses
varying from 15 to 60 GeV. An upper limit is placed on
BR(H → aa → μ+ μ− bb)2 at 95%C.L. Table 1 summarises several searches for exotic decays of the Higgs
bosons in various final states, performed by the two collaborations ATLAS and CMS at Run 2, targeting a different ranges of masses.

3 Numerical analyses
The (pseudo)scalar sector of the 2HDM involves two CPeven Higgs bosons, h and H . One of these scalars can be
identified as the 125 GeV state observed at the LHC. As
mentioned, in this analysis, we will assume that the heaviest
Higgs state H is the SM-like one with a mass of 125 GeV
and that h and a are lighter than H . We the perform a scanover the following ranges,m h ∈ [10 GeV, 90 GeV], m H = 125 GeV,m a ∈ [10 GeV, 90 GeV], m H ± ∈ [100 GeV, 160 GeV],tan β ∈ [2.5, 25], sin(β − α) ∈ [−0.7, 0.0],(4)

with m 212 = m a2 tan β/(1+tan2 β). Assuming m H = 125 GeV
and m h,a < 90 GeV, the decay channels H → hh, aa,a Z ∗ could be open, leading to invisible or undetected SMlike Higgs decays that are restricted by the current precision
measurements of Higgs couplings. CMS performed a com√bination of searches, using data collected at s = 7, 8, 13
TeV [7], for Higgs bosons decaying into invisible partiFootnote 1 continued
procedure which was validated against the case of BR(H → hh(aa) →μ+ μ− bb[51], τ + τ − bb̄ [51], μ+ μ− τ + τ − [52], μ+ μ− bb [53].
2 Corresponding search data and exclusion limits are available at the

HEPData database.

123

Fig. 1 Allowed parameter space in the 2HDM Type-I at 95% C.L.
The solid red and green regions are excluded by the Z width constraint
and the LEP search for h → aa [54], respectively. The most sensitive searches for the relevant (m h , m a ) regions are shown by coloured
dots. Each coloured point in the (m h , m a ) plane satisfies all theoretical requirements and up-to-date experimental constraints. In the whitespace, any combination of masses is ruled out by current experimental
searchescles, which targets the following production channels: Vector Boson Fusion (VBF), Higgs-Strahlung (HS) and gluongluon Fusion (ggF) (allowing for initial state radiation). The
combination of all the searches, assuming these SM-like production modes, yields an observed (expected) upper limit on
BR(H → inv) of 0.19 (0.15) at 95% C.L. The ATLAS groupreported a direct search for Higgs bosons produced via VBF
with subsequent invisible decays, for 139 fb−1 of pp col√lision data at s = 13 TeV [8]. An observed (expected)
upper limit of 0.145 (0.103) is placed on BR(H → inv)
at 95% C.L., as a function of the assumed production crosssections. As for now, both ATLAS and CMS have placed,
respectively, an upper bound of 0.10 [6] and 0.15 [5] on
BR(H → invisible) at 95% CL. In our analysis, we willassume that BR(H → inv) designates the sum of the following decay rates, BR(H → hh), BR(H → aa) andBR(H → a Z ∗ ).
After performing a random scan over 2HDM Type-I
parameters, we show in Fig. 1 the allowed regions by the-Eur. Phys. J. C (2024) 84:245

Page 5 of 16 245

Fig. 2 Observed and expected upper limits on B(H → aa(hh) →τ + τ − bb) [51] at 95% C.L. in the 2HDM Type-I. Grey points are allowedby theoretical constraints. As stated above, red colour indicates the com-bination of the scanned model parameters, which is excluded by existing experimental searches checked by HiggsBounds [38], whereas blue
points satisfy both theoretical and experimental constraints

oretical and experimental constraints. The figure also captures the constraint from the Z width (bottom-left red region),
which forbids possible mass combinations (m h , m a ) whencos(β − α) → 1. Additionally, the constraint from the LEP
search for the e+ e− → (h → aa)a → (bbbb)bb process [54] excludes the bottom-right region corresponding tom h > 2m a , where the decay channel h → aa is kinematically open (bottom-right green region).
Each (coloured) point in the (m h , m a ) plane implies that
there is a combination of the scanned model parameters,
which obeys the aforementioned theoretical constraints andevades the current experimental limits in all searched modes,
whereas the white space corresponds to the case where any
possible mass combination is forbidden by an observed signature(s) in one or more existing experimental searches.
Within this region, the most sensitive channels for themodel parameter points, as determined by HiggsBounds,
are shown by coloured dots. Note that each coloured pointin the parameter space of the 2HDM is allowed by current experimental searches. Obviously, there are two distinct
regions in the figure. The one in the top left corner corresponds to low masses of h (m h < m H /2), and high massesof a (m a > m H /2), while the second one corresponds to them a, h > m H /2 scenario. It is interesting to note that there
are no acceptable points when 40 GeV < m h < m H /2 andm a > m H /2. This is due to the fact that this parameter combination is excluded by LEP searches for e+ e− → ah → bbbb
[54] and an ATLAS search for events with at least 3γ in
pp → HSM → hh → 4γ [55].
Finally, it is noteworthy that the most sensitives searches
for the region with low m h and high m a are the LEP searches
for processes such as e+ e− → ah → bbbb and e+ e− →(h)Z → (bb)Z [54]. Therefore, an update from the LHC
during Run 3 is unlikely to rule out this mass combination

over the plane (m h , m a ) of the 2HDM Type-I. We will befocusing on this region in the second part of our study.
We now turn to the reinterpretation of exotic Higgs
decay searches, i.e., H → aa in τ + τ − bb, μ+ μ− bb andμ+ μ− τ + τ − final states in the framework of the 2HDM TypeI, while taking advantage of the parameter space discussed
above. The recasting of τ + τ − bb, μ+ μ− bb and μ+ μ− τ + τ −searches for H → hh is also possible since these processes
share similar kinematics (in the same spirit as in Ref. [56]). It
is relevant to note that the constraints from the search for light
pseudoscalars in the τ + τ − bb final state are much stronger
than the ones from μ+ μ− bb and μ+ μ− τ + τ − searches.
CMS has set an upper limit, between 1.7% and 7.6%, on
BR(H → aa → τ + τ − bb) at 95% C.L. [51], assuming the
SM production of primary Higgs boson. We show in Fig. 2 theoutcome from reinterpreting the H → aa(hh) → τ + τ − bb
search [51] in the 2HDM Type-I. The yellow and green bands
represent the uncertainties at ±1σ and ±2σ associated withthe expected exclusion limits. Grey points satisfy theoretical constraints described in Sect. 2.2, whereas red points are
excluded by null searches (i.e., by HiggsBounds [38]). The
blue points satisfy both theoretical and experimental constraints. The area of sensitivity to H → aa(hh) → τ + τ − bb
is already excluded by existing experimental searches (redpoints). In this connection, the BR of Higgs SM-like Higgs
state decaying into hh and/or aa is very restricted and cannot
exceed 9% at 95% C.L., again, in the 2HDM Type-I.
One can draw a similar conclusion form reinterpreting
H → hh(aa) → μ+ μ− bb [51] in our reference framework. Figure 3 shows that the parameter space with sensitivity to this search is excluded. One should keep in mind
that the μ+ μ− bb final state is well-balanced between large
BR(h/a → bb) and a clean di-muon resonance that is easy123245 Page 6 of 16

Eur. Phys. J. C (2024) 84:245

Fig. 3 Observed and expected upper limits on B(H → aa(hh) → μ+ μ− bb) [51] at 95% C.L. in the 2HDM Type-I

to trigger on. This exercise emphasises that the 2HDM Type-I
may not be a good framework for reinterpreting searches forexotic Higgs decays into light pseudoscalar in “traditional”
final states such as μ+ μ− bb, τ + τ − bb and μ+ μ− τ + τ − .
We also address here light charged Higgs decay in themass ranges where m H ± < m t − m b and m h,a < 90 GeV.
In this configuration, the charged Higgs state can be be produced from top quark decays, i.e., t → bH + , followed byits bosonic decays to H ± → W ± h(a), instead of the standard fermionic decay modes like τ ν and cs. Many studies
motivated these channels as alternative modes to search forlight charged Higgs bosons that could dominate over the conventional fermionic channels, because of large BRs when
they are kinematically allowed, in models such as our 2HDM
Type-I [57–60]. ATLAS [61] and CMS [62] have considered
the ranges m a ∈ [15, 75] GeV and m H ± < m t −m b to search
for light charged Higgs bosons in pp → tt → bbH + W −√with H + → W + a and a → μ+ μ− at s = 13 TeV,
since the μ+ μ− finale state provides the aforementioned
experimental advantages, which offset the suppressed rateof BR(a → μ+ μ− ). Previously, both CDF and the LEP collaborations have searched for H ± → W ± a with a → bb
[63], a → τ + τ − [64] and a → bb [65]. In addition, LEP
experiments [66] have set a lower bound on the charged Higgs
boson mass of m H ± > 72.5 GeV in the 2HDM Type-I for
m a > 12 GeV at 95% C.L.
Figure 4 shows the CMS observed and expected exclusion
limits on the product of the BRs of t → bH ± , H ± →W ± a and a → μ+ μ− [62] as a function of m a predictedby the 2HDM Type-I, with respect to several theoretical andexperimental constraints. We adopt here m H ± = m a + 85
GeV [62], which enables us to consider H ± → W ±(∗) a,with W ±(∗) being on/off shell, by randomly sampling valuesof the charged Higgs mass between 100 GeV and 160 GeV(see Eq. (4)). A noteworthy observation is that the 2HDM
Type-I offers sufficient sensitivity, when the prediction of

123

Fig. 4 Observed and expected upper limits on BR(t → H + b) ×BR(H + → W + a) × BR(a → μ+ μ− ) [62] at 95% C.L. in the 2HDM
Type-I√
the model exceeds the expected limit produced at s = 13
with an integrated luminosity of 35.9 fb−1 (purple stars).
Such a signature could be exploited to search for a light H ±at future experiments, Run 3 and/or the HL-LHC, given theavailable energies and luminosities by then. Therefore, we
present in Table 2 some Benchmark Points (BPs) to test theactual sensitivity of these experiments to the 2HDM Type-I
parameter space.
We move now to discuss a new analysis, where we deploy
the parameter space of the 2HDM Type-I following the outcomes of reinterpreting previous searches for light Higgs
bosons, pp → HSM → hh(aa), in different final states,in order to search for a new signature.
Figure 5 shows the result of performing a scan over theparameter space of 2HDM Type I, wherein (recall) the heav-Eur. Phys. J. C (2024) 84:245
Table 2 BPs in the 2HDM
Type-I

Page 7 of 16 245

Parameters

BP1

BP2

BP3

BP4

(Masses are in GeV)
mh

62.86

75.69

75.58

77.18

mH

125

125

125

125

ma

40.37

50.73

52.90

53.44

m H±

105.19108.15110.83111.95

tan β

4.82

4.73

4.58

4.57

sin(β − α)−0.203−0.209−0.220−0.0.215

Γ (h)1.9 × 10−6

3.00 × 10−6

1.9 × 10−6

3.00 × 10−6

Γ (H )

4.54 × 10−3

4.53 × 10−3

4.47 × 10−3

4.48 × 10−3

Γ (A)5.39 × 10−5

6.79 × 10−5

7.6 × 10−5

7.7 × 10−5

Γ (H ± )3.31 × 10−4

3.330 × 10−4

3.339 × 10−4

3.339 × 10−4

2.36 × 10−4

2.42 × 10−4

2.43 × 10−4

2.43 × 10−4

86.65

90.64

88.47

89.39

Total decay width in GeV

BR(A → X Y )BR(A → μμ)BR(H ± → X Y ) in %BR(H ± → W + A)

Fig. 5 m h and m a vs. BR(H → Z ∗ a) (left) and σ (gg → H → Z ∗ a → Z ∗ Z ∗ h) (right) at 95% C.L. in the 2HDM Type-I

iest Higgs state is identified as the discovered SM-like one.
Each sampled point is required to satisfy the theoretical andexperimental constraints described in Sect. 2.2. In the left
panel, we illustrate m a vs. m h with the BR of H → a Z (∗)
on the colour gauge. Since m H /2 < m a < 125 GeV, H →a Z (∗) will proceed with Z being off-shell, which explains the
suppressed BR (< 0.2%). In this configuration, H → aa will
not be open, thus, H → hh would only contribute significantly to the undetected decays of H . It should be pointed
out that the total amount of BR(H → aa ∗ + a Z ∗ + hh)
should not exceed 12% as required by BR(H → inv) [2].
In the right panel, we show m a as a function of m h withσ (H → a Z ∗ → h Z ∗ Z ∗ → Z ∗ Z ∗ ) on the colour gauge.
Once the decay chain H → a Z ∗ is open, the subsequent
decay of a could lead to a → Z ∗ h with Z being off-shell andh decaying to fermions and/or γ γ . We use Sushi [67–69]

to compute the cross section of Higgs production at LO.3 It
is worth highlighting that Figs. 5, 6 and 14 focus particularlyon the region characterized by small m h and large m a in contrast to Fig. 1, which displays both regions. The cross-sectionof our signature, i.e., gg → H → a Z ∗ → h(→ bb)Z ∗ Z ∗ ,is remarkably negligible in the region with large m h and m a(m h > 60 GeV and m a > 40 GeV ), primarily due to thefact that the pseudoscalar decay width (Γa ) is dominated bya → bb̄ with a branching ratio of 85%, rather than a → Z ∗ h.
Note that the contribution of a → bb̄ is negligible in theregion with low m h and high m a . Instead, the predominantchannel in this region is a → Z ∗ h with Z being off-shell,boasting a branching ratio that can reach 90%. Furthermore,
3 The signal cross sections is computed at LO (i.e, tree level) here,

however, we will consider QCD corrections through K -factors later onin our study.

123245 Page 8 of 16

the decay of HS M → a Z ∗ is suppressed in the region withlarge m h and m a . In fact, HS M tends to decay to a Z ∗ in thespecific part of the region where the observation of a → Z ∗ h
is not possible.
We show in Fig. 6 the gg → H → a Z ∗ → h Z ∗ Z ∗ crosssection, where h → bb. The process could yield a crosssection of 0.006 pb. In the right panel of Fig. 6 we show theBR of h → bb in this region of the 2HDM Type-I parameter
space. Obviously, the decay width of h is dominated by the
decay mode h → bb. Thus, in what follows, we focus on thecase where h decays to bb and Z (∗) Z (∗) → μ+ μ− j j. Sucha scenario could be an alternative channel to search for light
Higgs bosons at Run 3 and the HL-LHC.

4 Signal vs. background analysis
We describe here the toolbox used to generate and analyse MC events. MadGraph-v.9.2.5 [70] is used to generate parton level configurations of both signal and background processes.4 The events are passed then to PYTHIA8[72] to simulate parton showering, hadronisation and decays.
Finally, we use Delphes−3.5.0 [73] with the standard
CMS card5 to perform detector simulation. We resort to
MadAnalysis [74] to apply cuts and to conduct the analysis.
The major background processes are top pair production in association with 2 Initial State Radiation (ISR) jets,6
Z Z production with additional bb quarks, Z W + bb →μ+ μ− j jbb and Drell-Yan plus jets (DY+jets). We show√
in Table 3 the corresponding cross sections at s = 13
TeV for the LHC energy. We have generated MC samplesof (106 ) events. Unsurprisingly, the irreducible backgrounds
pp → Z (∗) Z (∗) bb → bb j jμ+ μ− (from both QCD and
EW interactions) and pp → Z W bb → bb j jμ+ μ− arenegligible whereas pp → ggtt → ggμ+ μ− j jbbνμ ν μ andDY+jets are large.
We considered a few BPs for the signal given by gg →H → a Z ∗ → h Z ∗ Z ∗ → μ+ μ− j j bb to perform the MC
simulation. The input parameters of each BP are given in
4 Background and signal events are generated at LO. Higher order cor-

rections are quantified through K -factors. The NLO QCD correction
to top pair production in association with 2 jets computed at the LHC
is about −27% [71], which we adopt here. The NLO corrections to
gg → H are very large , about a facor of 2, due to the contributions from gg pairs to QCD radiation, whereas K NNLO/NLO ≈ is muchsmaller than K NLO/LO , signifying a convergence of the QCD expansion,so we renormalise the signal to the NNLO rates through the K -factor
K NNLO/LO = σ NNLO /σ LO ∼ 2.6 − 2.7.

Eur. Phys. J. C (2024) 84:245

Table 4. Note that the light Higgs width, Γ (h), is not smallenough to lead to a large lifetime and hence, long-lived particles producing displaced vertices inside the detector. The
proper decay length cτ0 is in fact only a tiny fraction of
micrometers.7 The different kinematic distributions at partonlevel in Fig. 7 show that the requirement of central pseudorapidity of the muons is generally satisfied however the pTof these can be rather small. To address this, one can invoke
the di-muon scouting trigger,8 which involves lowering theμtransverse momentum ( pT ) of muons to 4.5 GeV [77,78].
Note that the pT threshold of such trigger is reduced to 3
GeV [79] in Run 3. Figure 8 shows the invariant mass distributions of the two b-jets, m bb , and that of the full final
state, m j jμ+ μ− bb , for the signal and the irreducible background processes at parton level, noting that m bb is close
to light Higgs mass m h and m j jμ+ μ− bb is close to SM-like
Higgs mass m H (for the signal, unlike the irreducible backgrounds). We will clearly leverage these underlying partonic
shapes in our detector level9 analysis, to which we proceed
next, in the presence of the following sequence of acceptancecuts:
μpTb > 20 GeV, pT ( j) > 20 GeV, pT 1 > 10 GeV,μpT 2 > 5 GeV, |η(l, b)| < 2.5, |η( j)| < 5.0, ΔR > 0.4.
Additionally, we only consider events with two oppositely
charged muons, two b-jets and two light jets in the final state.
Events are further preselected after requiring the invariant
mass of the two b-jets (m bb̄ ), the two light jets (m j j ) and the
di-muon system10 (m μμ ) to lie within the following mass
ranges, as shown in Fig. 9,5 GeV < m bb̄ < 40 GeV, 10 GeV < m μμ < 50 GeV,
10 GeV < m j j < 50 GeV.
Figure 10 displays the distributions of the missing transverse energy (E/ T ) and the highest pT ’s of b-jets, light-jets
and muons for signal and background processes at detector level. (As mentioned previously, the irreducible backgrounds stemming from Z Z bb and Z W bb̄ processes are
negligible, so we have not emulated these at detector level.)
7 The proper decay length cτ falls within the range from 0.06μm to00.19μm, where τ0 is the light Higgs lifetime at rest [75].
8 The CMS standard dimuon triggers require the highest p

T muon topossess a transverse momentum within the range of 12-17 GeV, while
the second-highest pT muon reconstructed should exhibit a pT between
5-8 GeV [76]. This consequently leads to a significant loss of signal
acceptance in searches for dimuon masses below 40 GeV [77,78].

9 The minimum p

T algorithm to cluster final particles into jets, withmin = 20 GeV (for both light and b jets)
jet parameter ΔR = 0.5 and pT,j

T requirements for muons has been lowered to 5
GeV to cover the entire signal region effectively. This modification is
implemented in the Delphes card to simulate the CMS detector.

6 In our study, we focus mainly on ggtt which is vastly dominant over

10 Both μμ and j j originate from the decays of off-shell Z bosons

5 It adopts the anti-k

gqqtt and qqtt.

123(Z ∗ Z ∗ → μ+ μ− j j).

Eur. Phys. J. C (2024) 84:245

Page 9 of 16 245

Fig. 6 m h and m a vs. BR(h → bb) (left) and σ (gg → H → a Z ∗ → h Z ∗ Z ∗ → Z ∗ Z ∗ bb) (right) at 95% C.L. in the 2HDM Type-I
Table 3 The parton level crosssections of the backgroundprocesses at LO

Background

Cross section (pb)

pp → Z Z bbQCD → μ+ μ− j jbb

7.29 × 10−4 ± 1.9 × 10−6

pp → Z Z bbQED → μ+ μ− j jbb

8.39 × 10−5 ± 2 × 10−7

pp → ggtt → ggμ+ μ− j jbbνμ ν μDY + jets (μ+ μ− j jbb)

3.2 ± 0.0039

pp → Z W + bb, W + → j j

3.13 × 10−4 ± 7.9 × 10−7

pp → Z W − bb, W − → j j

2.84 × 10−4 ± 6.3 × 10−7

1.7 ± 0.008

Table 4 Selected BPs with parton level cross section and other observables at LO. (All masses and widths are in GeV, with m H = 125 GeV.)
BPs

mh

ma

m H±

sin(β − α)tan β Γ (h)

BP1

15.37

72.21

120.99−0.19

8.55 3.11 × 10−9 4.4 × 10−3
1.01 × 10−9

Γ (H )
4.4 × 10−3

Γ (A)Γ (H ± )Γ (Z → ha) σ (pb)1.028 × 10−4 7.88 × 10−20.00083

3.28 × 10−4

1.60 × 10−4

4.752 × 10−20.000968

4.11 × 10−40.00164

4.73 × 10−4

BP2

12.56

74.12

113.93

−0.16

5.97

BP3

11.64

73.03

104.56−0.19

5.09 3.13 × 10−9 4.49 × 10−3 1.644 × 10−4 3.96 × 10−2

Fig. 7 The transverse momentum (left) and pseudorapidity (right) of the hardest muon for the signal (all BPs)123245 Page 10 of 16

Eur. Phys. J. C (2024) 84:245

Fig. 8 The invariant mass of the bb̄ (left) and μ+ μ− j j bb (right) system for the signal (BP1) and the irreducible backgrounds (Z Z bb, Z W bb)
at parton level

Fig. 9 Correlation between E/ T and m bb (left panel), m μμ (middle panel) and m j j (right panel) for signal (BP3), at detector level

Fig. 10 The E/ T and highest pT distributions for muons, b- and light-jets (clockwise) for signal (BP3) and background processes, ggt t¯ (blue) andDY+jets (green), at detector level

123

Eur. Phys. J. C (2024) 84:245

Page 11 of 16 245

Fig. 11 ΔR distributions between the two ( pT ordered) b-jets and muons, from hardest to softest (clockwise) for signal (red) (BP3) and backgroundprocesses, ggt t¯ (blue) and DY+jets (green), at detector level

The E/ T distribution from simulated samples of background
events is mainly from di-leptonic decay of ggtt, i.e., withtt → W + bW − b → (μ+ νμ b)(μ− ν μ b) whereas the E/ T in
both signal and DY+jets events is due to the semi-leptonic
b-meson decays (alongside detector effects). Furthermore,
Fig. 11 illustrates the different angular separations between
b-quarks and muons for signal and dominant backgrounds,
where one can read that background arsing from top pair production has only a minimal component with muons comingfrom semi-leptonic b-meson decays (as intimated).
To enhance the signals and suppress the backgrounds arising from ggtt and DY+jets, we have adopted several kinematic cuts, which choice is based on comparing different
distributions of the signal and background processes at thedetector level. Specifically, this has been done through 2D
distributions correlating the missing transverse momentum toa series of kinematic variables pertaining to some of the visible objects in the final state as illustrated in Figs. 12 and 13 forsignal and background processes mentioned above. One canread that the signal and backgrounds distributions are anticorrelated. In fact, forcing the missing transverse energy to be
below 30 GeV will strongly favour the signal over the backgrounds, specifically, ggt t¯.11 Additionally, selecting eventsjμwith pT < 75 GeV and pT < 40 GeV would enhance the
11 Only 10% of t t¯gg events have survived after applying the missing
transverse energy cut, as indicated in Table 5.

signal significance and suppress both background processes.
Through similar reasoning, we require the invariant mass ofthe system to satisfy m H < 180 GeV. We show in Table 5
the event rates of the backgrounds after applying the cutflow
discussed above. Notably, DY+jets events are significantly
reduced after considering a final state with exactly 2 b-jets, 2light jets and 2 muons, while adhering to the invariant masses
requirements.12 Both backgrounds processes are completely
removed after applying the kinematic cuts and restricting theinvariant mass of the system to be below 180 GeV to further differentiate the signal from the remaining backgroundprocesses.
√= 13
We have then computed the significance (for s √S−1√
TeV and L = 300 fb ), defined as Σ = B+S = S,13
where S(B) is the signal(background) yield after the discussed cutflow, for not only our three initial BPs (whose Σ
rates are 3.05, 3.18 and 3.42 for BP1, BP2 and BP3, respectively), but also those appearing in Table 6. We have done
so in order to be able to map the 2HDM Type-I parameter
space in detail, so as to acquire a sense of the true portion ofit that can be tested by forthcoming experiments. Note thath < 40 GeV. We
therefore set a cut on the invariant mass of bb̄ to capture the light Higgsof the signal as illustrated in the right panel of Fig. 9, and to suppress
the backgrounds.
13 The major background processes, t t¯gg and DY+jets, are suppressed
once the kinematic cuts are implemented.
12 bb̄ originate from a light Higgs (h) decay with m123

245 Page 12 of 16

Eur. Phys. J. C (2024) 84:245

jFig. 12 Correlation between pT and E/ T for signal (BP3) (red), ggt t¯ (blue) and DY+jets (green) at detector levelμFig. 13 Correlation between pT and E/ T for signal (BP3) (red colour), ggt t¯ (blue colour) and DY+jets (green colour) at detector level

Table 5 Event rates of the twodominant background processes,
ggtt and DY+jets, with√s = 13 TeV and L = 300 fb−1
after applying the cutflow

Cutflowt t¯ggNumber of events (L, σ )960,000.000

534,000.000

E/ T < 30.0 GeV

743,769.811

56,336.998μ± μ∓ , m μμ ∈ [10, 50] GeV

46022.406

5521.560

2 light jets, m j j ∈ [10, 50] GeV

5952.001

1655.400

2 b-jets, m bb̄ ∈ [5, 40] GeV

19.20021.36019.20021.36019.2000.00

jpT < 70 GeV
μpT < 50 GeV

we have kept the same cutflow already illustrated for all such
new BPs too. Also, it is at this stage that we take into accountthe aforementioned QCD K -factor for the signal. Many ofthe latter can have a significance larger than 3 and up to nearly4, for Run 3 energy and luminosity. To observe their distribution over the (m h , m a ) plane, we have finally produced√
Fig. 14, indeed, assuming s = 13 TeV and L = 300 fb−1 ,where both significance (Σ) and efficiency () are mapped.
Hence, at Run 3, we can conclude that a substantial portion of
the 2HDM Type-I parameter space can offer some evidenceof the signal we have pursued. Furthermore, we notice that alarger efficiency can be obtained for small m a : this is because
the loss of efficiency with b-tagging is over-compensated bya simultaneous higher efficiency for both j- and μ-tagging.
Needless to say, at the HL-LHC, where L = 3000 fb−1 , mostof the sampled parameter space of the 2HDM Type-I would
be discoverable.

123

DY+jets

5 Conclusions
In this paper, we have shown the outcome of performing some recasting over the parameter space of the 2HDM
Type I, wherein the heaviest CP-even Higgs state H is
identified with the discovered SM-like one, HSM , while hand a are lighter. After considering the available experimental data from searches for exotic Higgs decay into
two light (pseudo)scalars, we have found that the corresponding parameter space for which there is sensitivity via
HSM → hh(aa) → τ + τ − bb at Run 2 is already excluded
by existing constraints from BSM Higgs searches. Furthermore, we have shown that there are regions of the 2HDM
Type-I parameter space compliant with theoretical and experimental constraints yielding substantial BR(H ± → W ± a)and BR(H → Z ∗ Z ∗ h). The large size of the former has
been exploited in other literature. Here, concerning the lat-Eur. Phys. J. C (2024) 84:245
Table 6 Extended list of BPs
used in the MC simulation forthe 2HDM Type-I parameter
scan, highlighting the h and amasses as well as the signal LO
cross section and event rate after
the full cutflow, together with its
significance Σ and efficiency .
Recall that NNLO QCD
K -factor has been used for
Higgs
production. Here,√s = 13 TeV and L = 300 fb−1

Page 13 of 16 245

BPm h (GeV)

m a (GeV)σ (pb)

No. of events

Significance Σ

Efficiency 

BP4

11.85

72.75

4.82 × 10−4

12.94

3.59

0.033

BP5

17.15

76.24

2.54 × 10−4

6.9695

2.63

0.035
0.032

BP6

24.55

78.85

1.39 × 10−4

3.5894

1.89

BP7

15.98

82.43

1.705 × 10−4

4.8392

2.19

0.036

BP8

34.15

84.26

4.48 × 10−5

1.22

1.10

0.034

BP9

20.69

79.30

2.30 × 10−4

7.2086

2.68

0.039

BP10

16.73

71.67

3.31 × 10−4

8.7579

2.95

0.033

BP11

16.78

69.25

3.247 × 10−4

8.8105

2.96

0.034

BP12

21.82

85.56

1.42 × 10−4

3.66

1.91

0.032

BP13

22.78

77.17

1.629 × 10−4

5.34

2.31

0.041

BP14

17.09

78.40

2.038 × 10−4

5.81

2.41

0.037

BP15

19.10

72.89

2.401 × 10−4

6.94

2.63

0.043

BP16

15.87

75.0242.192 × 10−4

4.19

2.04

0.025

BP17

15.67

78.38

2.426 × 10−4

4.32

2.07

0.023

BP18

19.76

83.14

1.662 × 10−4

3.22

1.79

0.025

BP19

20.24

76.76

1.873 × 10−4

4.76

2.18

0.032

BP20

28.15

77.04

9.39 × 10−5

2.37

1.53

0.032

BP21

27.08579.40

8.134 × 10−5

1.67

1.29

0.027

BP22

11.83

74.06

4.577 × 10−4

13.34

3.65

0.036

BP23

12.28576.51

3.377 × 10−4

10.30

3.20

0.035

BP24

13.09

75.47

3.538 × 10−4

10.01

3.16

0.035

BP25

14.15

74.35

3.458 × 10−4

9.24

3.03

0.034

BP26

11.96

78.57

3.557 × 10−4

9.33

3.04

0.033

BP27

12.60

77.17

3.311 × 10−4

9.92

3.14

0.038

BP28

14.30

76.77

2.423 × 10−4

6.46

2.54

0.034

BP29

14.16

78.86

2.572 × 10−4

5.75

2.39

0.036

BP30

16.15

81.22

1.843 × 10−4

5.11

2.26

0.028

BP31

12.85

83.93

2.308 × 10−4

5.13

2.26

0.028

BP32

11.63

88.72

1.325 × 10−4

2.57

1.60

0.025

1.67

1.29

0.027

3.28

1.81

0.039

BP33

19.86

88.73

8.03 × 10−5

BP34

22.71

74.16

1.093 × 10−4

Fig. 14 Significance (left) and efficiency (right) of each BP produced in our analysis over the (m h , m a ) projection of the 2HDM Type-I parameter
space, after the full cutflow described in the text123245 Page 14 of 16ter, we have made the case for looking at the process pp →HSM → Z ∗ A → Z ∗ Z ∗ h via Z Z → μ+ μ− j j and h → bb
decays, specifically, in the region with large m a and small
m h . After performing a full MC analysis down to detector
level, we have proven that the overwhelming backgrounds
arising from both top-quark pair production in association
with 2 ISR jets and DY+jets can be suppressed after applying efficient kinematics cuts, leading to a large significanceof this hitherto unexplored light Higgs signature already atRun 3 of the LHC, where evidence of it can be seen, further
affording one with clear discovery potential at the HL-LHC.
Acknowledgements The work of SM is supported in part through theNExT Institute and the STFC Consolidated Grant No. ST/L000296/1.
SS is fully supported through the NExT Institute. SS acknowledges theuse of the IRIDIS High Performance Computing Facility, and associatedsupport services at the University of Southampton, in the completionof this work.
Data availability statement This manuscript has no associated data or
the data will not be deposited. [Authors’ comment: This is a theoretical
study that has no associated data.]
Code availability My manuscript has no associated code/software.
[Authors’ comment: This is a theoretical study that has no associatedcode/software.]Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation,
distribution and reproduction in any medium or format, as long as you
give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes
were made. The images or other third party material in this article
are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons licence and your intended
use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecomm
ons.org/licenses/by/4.0/.
Funded by SCOAP3 .

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