# New Higgses at the Electroweak Scale and Differential $t\bar{t}$
Distributions

Andreas Crivellin  Physik-Institut, Universität Zürich, Winterthurerstrasse
190, CH–8057 Zürich, Switzerland
Paul Scherrer Institut, CH–5232 Villigen PSI, Switzerland

###### Abstract

Indications for new Higgs bosons at 95 GeV and 152 GeV with significance of
3.8$\sigma$ and $4.3\sigma$, respectively, have been obtained. While the
former contains the inclusive $\gamma\gamma$ channel, the latter is obtained
by combining several modes of associated di-photon production, i.e.
$\gamma\gamma+X$ with $X=\ell,\,\ell b,\,{\rm MET},\,\tau,\,...$, within the
$\Delta$SM (the Standard Model extended by a real triplet). Such a triplet
predicts a positive definite shift in the $W$ mass, in agreement with the
current global electroweak fit, and its neutral component decays dominantly to
$W$ bosons (for small mixing angles). This offers a connection to $t\bar{t}$
differential distributions whose experimental signature is $WWb\bar{b}$: A
simplified model with a new scalar $H$, produced via gluon fusion and decaying
to $S$ and $S^{\prime}$ with subsequent (dominant) decays to $WW$ and
$b\bar{b}$, respectively, has the same final state. In fact, adding this new
physics polution to the Standard Model describes the leptonic $t\bar{t}$
distributions better by at least $5.8\sigma$. Furthermore, assuming that
$S^{\prime}$ is an $SU(2)_{L}$ singlet, the resulting di-photon signal
strength is compatible with the 95 GeV $\gamma\gamma$ measurements. A possible
UV completion of this simplified model is the $\Delta$2HDMS, i.e. a 2HDM
supplemented with a singlet and a real triplet, which can successfully
accommodate electroweak scale Baryogenesis.

##  1 Introduction

The Standard Model (SM) cannot be the ultimate theory of physics as, among
several shortcomings, it fails to explain the astrophysical observations of
Dark Matter and cannot account for the non-vanishing neutrino masses required
by neutrino oscillations. Also the minimality of its scalar sector with a
single $SU(2)_{L}$ doublet Higgs giving rise to the mass of all (fundamental)
fermions as well as the $W$ and $Z$ bosons is puzzling because it is not
guaranteed by any symmetry or consistency requirement. While additional Higgs
bosons must play a subleading role in the spontaneous breaking of the
electroweak (EW) symmetry due to the constraints from Higgs signal strengths
and the global EW fit, the average of the $W$ boson mass measurements is, in
fact, slightly higher than the SM prediction ($3.7\sigma$ [1]). Furthermore,
many deviations from the SM predictions point towards an extension of the SM
scalar sector [3] and interesting indications for new Higgses with electroweak
scale masses of 95 GeV and 152 GeV have emerged. This poses the question of
whether these hints for narrow resonances are related to the LHC multi-lepton
anomalies which appear in Higgs-like typologies in final states with at least
two leptons, moderate missing energy and ($b$-)jets [2]. In particular,
differential lepton distributions of top-quark pair production and decay show
strong tensions with the SM predictions which might be due to a new physics
(NP) contamination involving both the (hypothetical) 95 GeV and 152 GeV
bosons.

##  2 Hints for narrow resonances

###  2.1 95 GeV ($S^{\prime}$)

Combining the CMS [4] and ATLAS analyses of $pp\to{S^{\prime}\to\gamma\gamma}$
[5] a local significance of $2.9\sigma$ at 95 GeV is obtained [6]. While CMS
finds a local excess of $3.1\sigma$ in $pp\to S^{\prime}\to\tau\tau$ [7], the
side-band of the corresponding SM Higgs ATLAS analysis [8] shows no
indications of a signal at 95 GeV, which reduces the CMS significance by a
factor $\sqrt{2}$ (assuming that the ATLAS and CMS analyses have similar
sensitivity). Recasting the SM Higgs analyses of ${{pp\to S^{\prime}\to
WW^{*}}}$ [9], a preference of $\approx$2.6$\sigma$ for a non-vanishing cross
section at 95 GeV is found. Finally, LEP reported an excess in $e^{+}e^{-}\to
Z^{*}\to(S^{\prime}\to bb)+Z$ with a local significance of 2.3$\sigma$ at
$\approx$98 GeV [10]. Using the latter to reduce the search window to
$93\,{\rm GeV}<m_{S^{\prime}}<103\,$GeV (but not including it directly in the
significance calculation) and combining ${S^{\prime}\to\gamma\gamma}$,
${{S^{\prime}\to WW^{*}}}$ and $S^{\prime}\to\tau\tau$ with three degrees of
freedom gives a global significance (including the trails-factor) of
$3.8\sigma$ [11] (see left side of Fig. 1).

Figure 1: Indications for narrow resonances at the EW scale. While for the
low-mass region containing the 95 GeV excess one relies on inclusive searches,
the higher mass region with the 152 GeV excess has the most significant hints
in associated production channels. For the later, the combination is obtained
within the simplified model $H\to SS^{*}$ with $H$ produced via gluon fusion
from a top-quark loop and the decay channels $S\to WW,\,b\bar{b},\,{\rm
MET},\gamma\gamma$ as motivated by the multi-lepton anomalies.

###  2.2 152 GeV ($S$)

In this mass region, we consider the side bands of SM Higgs analyses. While an
$\approx 2\sigma$ excess in the inclusive di-photon channel exists at
$\approx$152 GeV [12], the most significant excesses appear in
$\gamma\gamma+X$ [13], i.e. the associated production of di-photons with
$X=\ell,\,{\rm MET},\,\ell b,\,\tau,\,...$. Combining these channels in a
simplified model with $pp\to H\to SS^{*}$ ($m_{H}\approx 270$ GeV) and $S\to
WW,\,b\bar{b},\,{\rm MET},\gamma\gamma$, as motivated by the the multi-lepton
anomalies [14, 15], a combined significance of $4.7\sigma$ is obtained [11]
(see right plot of Fig. 1). Note that this does not include the
$\gamma\gamma+\tau$ channel presented at Moriond EW [16] which shows a
significant excess around 152 GeV.

Going beyond a simplified model, one can consider the $SU(2)_{L}$ triplet
Higgs with hypercharge 0 [17] which contains a neutral component $\Delta^{0}$
and a charged component $\Delta^{\pm}$ which are approximately degenerate in
mass. This model predicts a positive shift in the $W$ mass and leads to
$\gamma\gamma+X$ signatures via the Drell-Yan process $pp\to
W^{*}\to\Delta^{\pm}\Delta^{0}$ [18] with a cross-section entirely governed by
the EW gauge couplings of around half a picobarn (see Fig. 2, left).
Furthermore, since the decay rates of $\Delta^{\pm}$ depend to a good
approximation only on its mass, $WZ$ is dominant for 152 GeV followed by $tb$
and $\tau\nu$ (see Fig. 2, right), one can combine all channels with a single
degree (the branching ratio of $\Delta^{0}$ to photons) for a given mass.
Including in addition to Ref. [13] the $\gamma\gamma+\tau$ channel presented
at Moriond EW [16] a combined significance of $4.3\sigma$ is obtained [19]
within this simple UV complete model.

##  3 Differential top-quark distributions

The statistically most significant multi-lepton anomaly is encoded in the
latest ATLAS analysis of the $t\bar{t}$ differential cross-sections [20], i.e.
appears in $e^{\pm}\mu^{\mp}+b$ final states. The di-lepton mass ($m^{e\mu}$)
and the angle between the leptons ($\Delta\phi^{e\mu}$) are the most relevant
observables (see Fig. 3). Several SM simulations, using different Montecarlo
generators and showering, were performed by ATLAS. However, all of them
describe data so poorly (see $\chi^{2}$ values of the SM in Table 1) that Ref.
[20] concluded: “No model (SM simulation) can describe all measured
distributions within their uncertainties.”

Therefore, one should consider seriously the option that these differential
distributions contain a new physics contamination. In fact, the processes
$pp\to H\to SS^{\prime}$ with $S\to WW$ and $S^{\prime}\to bb$, as shown in
Fig. 4 (right), has the same final state as $t\bar{t}$ production and decay in
the SM but with different kinematics. If we fix $m_{S}=152\,$GeV and
$m_{S^{\prime}}=95\,$GeV from the hints for narrow resonances discussed in the
last section, we can fit the cross section for $pp\to H\to SS^{\prime}\to
WWbb$ to data for a given mass of $H$. Since we checked that the impact of
varying $m_{H}$ is small, we chose 270 GeV as a benchmark point and obtained
the results given in table 1. From this, one can see that by including the NP
effect the agreement with data is significantly improved. Even for the two SM
simulations which are in best agreement with the data, the NP hypothesis is
preferred over the SM one by at least $5.8\sigma$.

Figure 2: Left: Production cross-section for $pp\to\Delta^{0}\Delta^{\pm}$ and
$pp\to\Delta^{\pm}\Delta^{\mp}$ as a function of the triplet mass. Right:
Dominant branching ratios of the charged component $\Delta^{\pm}$ as a
function of its mass. The errors are estimated from the decays for a SM Higgs
with a higher (hypothetical) mass from $h\to tt^{*},ZZ^{*}$ and $h\to cc$.

Figure 3: The dashed coloured lines show the six different SM predictions (MC)
normalized to data provided by ATLAS. The solid lines include the NP
contribution from our benchmark model obtained by a combined global fit to
$m^{e\mu}$ and $\Delta\phi^{e\mu}$ data. The black lines are obtained by
averaging the six predictions and the grey band shows the total uncertainty
(systematic and statistical). One can see that the agreement between theory
and experiment is significantly increased by adding the NP effect.

$g$$g$$\bar{b}$$W$$W$$b$$g$$t$$\bar{t}$$g$$g$$b$$\bar{b}$$W$$W$$H$$S$$S^{\prime}$

Figure 4: Feynman diagrams showing the leading SM contribution to top pair production and decay as well as the NP process $pp\to H\to SS^{\prime}$ with $S\to WW$ and $S^{\prime}\to bb$ contaminating the measurements of $t\bar{t}$ differential distributions. Monte Carlo | $\chi_{{\rm{SM}}}^{2}$ |  $\chi_{{\rm{NP}}}^{2}$ | $\sigma_{{\rm{NP}}}$ | Sig. |  $m_{S}$[GeV]
---|---|---|---|---|---
Powheg+Pyhtia8 | 213 |  102 | 9pb | 10.5$\sigma$ | $143-156$
<EMAIL_ADDRESS>| 102 |  68 | 5pb | 5.8$\sigma$ | $--$
aMC@NLO+Pythia8 | 291 |  163 | 10pb | 11.3$\sigma$ | 148-157
Powheg+Herwig7.1.3 | 261 |  126 | 10pb | 11.6$\sigma$ | 149-156
Powheg+Pythia8 (rew) | 69 |  35 | 5pb | 5.8$\sigma$ | $--$
Powheg+Herwig7.0.4 | 294 |  126 | 12pb | 13.0$\sigma$ | 149-156
Average | 182 |  88 | 9pb | 9.6$\sigma$ | 143-157
Table 1: $\chi^{2}$ values, preferred cross-section ($\sigma_{\rm NP}$)
significance (Sig.) etc. for the combined fit to $m^{e\mu}$ and
$|\Delta\phi^{e\mu}|$ distributions for the six different SM simulations and
their average. The $\chi^{2}_{\rm NP}$ is for our benchmark scenario with
$m_{S}\approx 152\,$GeV while the $m_{S}$ gives the preferred range of it from
the fit, assuming it to be a free parameter. A dash in the $m_{S}$ column
means that the preferred $1\sigma$ rage is wider than $140\,$GeV–$160\,$GeV.
The preferred NP cross-section $\sigma_{\rm NP}$ is given for
Br$[S^{\prime}\to b\bar{b}]\approx 100\%$ and Br$[S\to WW]\approx 100\%$.

Allowing now $m_{S}$, to which the distributions are most sensitive among the
new scalar masses, to vary, we show its preferred range in Fig. 5. We can see
that the resulting interval of $\approx(144\,{\rm GeV})$-$\approx(157\,{\rm
GeV})$ is compatible with $m_{S}\approx 152\,$GeV obtained from the
$\gamma\gamma+X$ excesses. Furthermore, averaging the six different SM
predictions the resulting best fit to $t\bar{t}$ data is obtained for
$\sigma(pp\to H\to SS^{\prime}\to WWb\bar{b})\approx 9$pb. Assuming that
$S^{\prime}$ has SM-like branching ratios (e.g. is an $SU(2)_{L}$ singlet),
and thus decays to 86% to $b\bar{b}$, this results at the same time in a di-
photon signal strength in agreement with the 95 GeV $\gamma\gamma$ excess (see
Fig. 5). Similarly, $S$ should decay dominantly to $WW$ but only suppressed to
$ZZ$ (as there is no four-lepton excess at $\approx$152 GeV), which suggests
that it could be the neutral component of an $SU(2)_{L}$ triplet, further
strengthening the connection to the 152 GeV excess.

##  4 Conclusions and Outlook

Statistically significant indications for new narrow resonances with masses of
95 GeV and 152 GeV have been observed in LHC data. While the former appears in
inclusive searches, the latter is most pronounced in associated production
channels, i.e. $\gamma\gamma+X$ with $X=\ell,\,{\rm MET},\,\ell
b,\,\tau,\,...$. For the 95 GeV candidate a model-independent significance of
3.8 $\sigma$ is found, while combining the hints for associated di-photon
production within the $\Delta$SM, i.e. the SM supplemented by a Higgs triplet
with $Y=0$, results in a 4.3$\sigma$ excess at 152 GeV.

The Higgs triplet does not only predict a positive shift in the $W$ mass, as
preferred by the current global EW fit, but also provides a possible
connection to the multi-lepton anomalies. Since its neutral component decays
dominantly to $WW$ (for small mixing angles with the SM Higgs), it could be
involved in the explanation of the discrepancies between the SM predictions
and measurements of the differential top-quark distributions via the NP
contamination $pp\to SS^{\prime}\to WWbb$. In fact, if one assumes that $S$ is
the neutral component of the triplet and $S^{\prime}$ a singlet, a 95 GeV di-
photon signal strength in agreement with experimental data is obtained.

Recently, we proposed the $\Delta$2HDMS, i.e. the SM extended by a singlet, a
$Y=0$ triplet and a second $Y=1/2$ doublet, as a UV complete model that can
account for the top-quark differential distributions and the 95 GeV and 152
GeV excesses [21]. Interestingly, this model was previously studied in a very
different context; it was shown to be above to give rise to EW scale
Baryogenesis [22], i.e. explain the matter anti-matter asymmetry in the
universe.

Figure 5: Preferred regions from the $t\bar{t}$ differential distributions
(red) as a function of $m_{S}$ and the total cross section $pp\to H\to
SS^{\prime}\to WWbb$ assuming $S^{\prime}$ to be SM-like and Br$[S\to
WW]=100\%$. The blue region is preferred by the $95\,$GeV $\gamma\gamma$
signal strength.

## Acknowledgments

I thank the organizers of Moriond EW and QCD, in particular Gudrun Hiller and
Nazila Mahmoudi, for the invitation and the opportunity to present my
research. This work is supported by a professorship grant from the Swiss
National Science Foundation (No. PP00P21_76884).

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