# Hints of a new leptophilic Higgs sector?

Yoav Afik1,2,, P. S. Bhupal Dev3,, Anil Thapa4, 0000-0001-8102-356X
0000-0003-4655-2866 0000-0003-4471-2336 1Enrico Fermi Institute, University of
Chicago, Chicago, Illinois 60637, USA
2Experimental Physics Department, CERN, 1211 Geneva, Switzerland
3Department of Physics and McDonnell Center for the Space Sciences, Washington
University, St. Louis, Missouri 63130, USA
4Department of Physics, University of Virginia, Charlottesville, Virginia
22904-4714, USA

###### Abstract

We show that a new leptophilic Higgs sector can resolve some intriguing
anomalies in current experimental data across multiple energy ranges.
Motivated by the recent CMS excess in the resonant $e\mu$ channel at 146 GeV,
we consider a leptophilic two-Higgs-doublet model, and propose a novel
resonant production mechanism for the neutral components of the second Higgs
doublet at the LHC using the lepton content of the proton. Interestingly, the
same Yukawa coupling $Y_{e\mu}\sim 0.65-0.81$ that explains the CMS excess
also addresses the muon $(g-2)$ anomaly. Moreover, the new Higgs doublet also
resolves the recent CDF $W$-boson mass anomaly. The relevant model parameter
space will be completely probed by future LHC data.

##  I Introduction

Using the Higgs boson as the keystone for new physics searches is well-
motivated [1], as an extended Higgs sector could potentially address some of
the pressing issues plaguing the Standard Model (SM), including the gauge
hierarchy problem, stability of the electroweak vacuum, mechanism of
electroweak symmetry breaking, origin of the fermion masses and mixing,
matter-antimatter asymmetry, and the nature of dark matter. Therefore, even
though the measured properties of the 125-GeV Higgs boson discovered at the
LHC [2, 3] are thus far consistent with the SM expectations [4, 5], further
precision Higgs studies, as well as direct searches for additional Higgs
bosons, must continue.

An interesting aspect of beyond-the-SM (BSM) physics is lepton flavor
violation (LFV), which is forbidden in the SM by an accidental global
symmetry. In fact, the observation of neutrino oscillations [6, 7, 8, 9, 10]
necessarily implies LFV. However, despite intense experimental efforts, no
corresponding LFV in the charged lepton sector has been observed [11].
Therefore, alternative searches for LFV involving exotic Higgs decays ($h\to
e\mu,e\tau,\mu\tau$) could be powerful probes of BSM physics [12, 13, 14, 15,
16, 17, 18]. Both ATLAS and CMS Collaborations have performed such LFV Higgs
searches with the $\sqrt{s}=13$ TeV LHC Run-2 data [19, 20, 21, 22, 23].
Although no evidence for LFV decays of the 125 GeV Higgs boson was found, CMS
has reported an intriguing $3.8\sigma$ local ($2.8\sigma$ global) excess in
the resonant $e\mu$ search around 146 GeV, with a preferred cross section of
$\sigma(pp\to H\to e\mu)=3.89^{+1.25}_{-1.13}$ fb [23]. If confirmed, this
would be a clear sign of BSM physics. In this letter, we take the CMS $e\mu$
excess at face value and provide the simplest possible interpretation in terms
of leptophilic neutral scalars within a two-Higgs-doublet model (2HDM). In
this context, we propose a novel resonant production channel for the
leptophilic neutral (pseudo)scalars at the LHC using the lepton parton
distribution function (PDF) of the proton [24, 25, 26, 27]; see Fig. 1. We
show that this scenario can explain the CMS excess with a Yukawa coupling
$Y_{e\mu}\sim 0.55-0.81$, while being consistent with all existing
constraints.

Another interesting feature of our solution is its intimate connection to two
other outstanding anomalies in current experimental data, namely, the
$(g-2)_{\mu}$ anomaly [28, 29, 30] and the CDF $W$-mass anomaly [31]. We
emphasize that the prospects of probing a leptophilic light Higgs sector at
the energy and intensity frontiers is a worthwhile study in its own right,
irrespective of the future status of these anomalies.

##  II Model Setup

Figure 1: A representative Feynman diagram for resonant production of
leptophilic scalar fields at hadron colliders through lepton PDF.

Here we propose an economical scenario with a leptophilic 2HDM to explain the
CMS excess. We work in the Higgs basis [32], where only one neutral Higgs
acquires a nonzero vacuum expectation value, $v$. In this basis, the scalars
fields can be parameterized as

$H_{1}=\left(\begin{array}[]{c}G^{+}\\\
\frac{1}{\sqrt{2}}\left(v+H_{1}^{0}+iG^{0}\right)\end{array}\right),\
H_{2}=\left(\begin{array}[]{c}H^{+}\\\
\frac{1}{\sqrt{2}}\left(H_{2}^{0}+iA\right)\end{array}\right),$ (1)

where $(G^{+},G^{0})$ are the Goldstone modes, eaten up by $W$ and $Z$ after
electroweak symmetry breaking, $(H^{0}_{1},H^{0}_{2})$ and $A$ are the neutral
$\mathcal{CP}$-even and $\mathcal{CP}$-odd scalars respectively, and $H^{+}$
is a charged scalar field. In the alignment/decoupling limit [33, 34, 35, 36],
we identify $H_{1}^{0}\equiv h$ as the observed $125$ GeV SM-like Higgs boson,
whereas the $H_{2}$-sector does not couple to the SM gauge bosons. This is in
agreement with the LHC data [37, 38, 39]. We assume the mixing angle $\theta$
between the $\mathcal{CP}$-even scalar $H_{2}^{0}\equiv H$ and the SM Higgs
boson is small, and the only relevant production mechanism for $H$ (and $A$)
at colliders is via its leptonic Yukawa interactions:

$-{\cal L}_{Y}\supset Y_{\alpha\beta}\bar{L}_{\alpha}H_{2}\ell_{\beta,R}+{\rm
H.c.}$ (2)

For either $Y_{e\mu}\neq 0$ or $Y_{\mu e}\neq 0$, with all other
$Y_{\alpha\beta}$ involving electrons or muons assumed to be small, the
dominant contribution to the $pp\to H/A\to e\mu$ signal comes from the
$s$-channel Feynman diagram shown in Fig. 1, where the $H/A$ is produced
resonantly using the lepton PDF of the proton, and then decays to
$e^{\mp}\mu^{\pm}$ final states with a branching ratio (BR) determined by the
structure of the Yukawa coupling matrix $Y$ in Eq. (2). There is a sub-
dominant contribution to the same final-state from a $t$-channel exchange of
$H/A$, not shown in Fig. 1, but included in our calculation.

We estimate the signal cross section numerically using MadGraph5_aMC@NLO [40]
at leading order (LO) parton-level with the LUXlep-NNPDF31 PDF (82400) [41,
42, 43, 25]. The default MadGraph5 cuts are applied at parton-level, and the
default LO dynamical scale is used, which is the transverse mass calculated by
a $k_{t}$-clustering of the final-state partons [44]. The cross section result
including both $H$ and $A$ contributions is shown by the blue curve in Fig. 2
left panel as a function of $|Y_{e\mu}|$ (also applicable for $|Y_{\mu e}|$)
for $m_{H/A}=146$ GeV and assuming ${\rm BR}(H/A\to e\mu)=70\%$ (explained
below), where the thickness accounts for the theory uncertainty due to scale
(${}^{+39.4\%}_{-30.3\%}$) and PDF ($\pm 4.5\%$) variation. The horizontal
green (yellow) shaded region explains the CMS excess at $1\sigma$ ($2\sigma$).
The corresponding ATLAS search [19] is not directly comparable with the CMS
analysis, but a back-of-the-envelope calculation from the sideband data mildly
disfavors a narrow-width excess at 146 GeV, and a rough scaling of background
gives a ballpark upper limit of about 3.0 fb on the cross section [45], as
shown by the horizontal dashed line in Fig. 2. We find that $Y_{e\mu}\sim
0.55-0.81$ can explain the CMS excess at $2\sigma$. For such values of the
leptonic Yukawa coupling, any quark Yukawa couplings of the second Higgs
doublet $H_{2}$ must be small; otherwise, it will be ruled out by the
chirality enhanced meson decays, such as $\pi^{+}\to e^{+}\nu$. Thus our
proposal is different from other scalar interpretations of the CMS excess [46,
47], which used quark couplings to enhance the production cross section.

Figure 2: Left: Total $e\mu$ production cross section from $H/A$ (blue band)
at $\sqrt{s}=13$ TeV LHC as a function of the Yukawa coupling $Y_{e\mu}$ (or
$Y_{\mu e}$) in our leptophilic 2HDM with $m_{H}\simeq m_{A}=146$ GeV. Right:
Same as left panel but in the $Y_{e\mu}-Y_{\mu e}$ plane. See text for
details.

##  III Constraints

The large $Y_{e\mu/\mu e}$ couplings of the neutral components, as well as the
charged component, of the leptophilic Higgs doublet, are subject to a number
of other constraints, and also give rise to other interesting phenomena, as
discussed below.

###  III.1 Neutral sector

Even if we choose only the off-diagonal entries $Y_{e\mu/\mu e}\neq 0$, small
diagonal entries $Y_{\ell\ell}\sim\sin\theta y_{\ell}$ (with $\ell=e,\mu$)
will be induced via the $h-H$ mixing and the SM Yukawa couplings
$y_{\ell}\equiv\sqrt{2}m_{\ell}/v$ (with $y_{\mu}\simeq 6\times 10^{-4}$ and
$y_{e}\simeq 3\times 10^{-6}$). But the products $Y_{e\mu}Y_{ee}$ and
$Y_{e\mu}Y_{\mu\mu}$ are subject to strong LFV constraints [48]. Using the
general LFV formula [49] and the current MEG limit on $\mu\to e\gamma$ [50],
we require $Y_{ee}\lesssim 9\times 10^{-5}$ and $Y_{\mu\mu}\lesssim 6\times
10^{-5}$, which gives an upper limit of $\sin\theta\lesssim 0.1$ on the Higgs
mixing.

The same $Y_{e\mu\ (\mu e)}$ coupling gives an additional contribution to the
$e^{+}e^{-}\to\mu^{+}\mu^{-}$ cross section via $t$-channel $H/A$ exchange,
and therefore, is constrained by LEP measurements, which are in good agreement
with the SM prediction [51, 52]. Naively, the contact interaction bounds from
LEP data would kill the parameter space for ${\cal O}(1)$ Yukawa couplings
[48]. However, this bound is not directly applicable, if neutral scalars are
lighter than the LEP center-of-mass energy $\sqrt{s}=209$ GeV. A dedicated
analysis [53] comparing the 2HDM cross section, which includes the
interference between the $H/A$-mediated diagrams with the SM processes,
against the LEP dimuon data imposes the constraint $Y_{e\mu}<0.8$, thus ruling
out the parameter space shown by the brown-shaded region in Fig. 2. The same
bounds are also applicable to the $Y_{\mu e}$ coupling; see Fig. 4 for
different masses. The LEP limit can be significantly improved at future lepton
colliders, such as the $\sqrt{s}=1$ TeV ILC [54] with integrated luminosity
$L=500~{}{\rm~{}fb}^{-1}$ (cf. the dashed curve in Fig. 4), which can probe
$Y_{e\mu}$ (or $Y_{\mu e}$) up to 0.1 [53, 55, 56].

As for the hadron collider constraints on light neutral scalars, most of the
Tevatron/LHC searches are done in the context of either MSSM or general 2HDM,
and rely on the gluon fusion or vector boson fusion production mechanisms.
None of these searches are applicable for us, because the leptophilic $H/A$
does not directly couple to the quarks, and in the alignment limit ($\theta\to
0$), also does not couple to the $W/Z$ bosons. This also suppresses other
production channels like pair-production of $HA$.

The most important constraint on the neutral scalar sector comes from low-
energy process of muonium ($M_{\mu}=e^{-}\mu^{+}$)-antimuonium
($\overline{M}_{\mu}=e^{+}\mu^{-}$) oscillation [57, 58, 59, 60]. The MACS
experiment at PSI puts an upper bound on the oscillation probability
$P(M_{\mu}\leftrightarrow\overline{M}_{\mu})<8.2\times 10^{-11}$ at $90\%$ CL
[61], while a sensitivity at the level of $\mathcal{O}(10^{-14})$ is expected
at the proposed MACE experiment [62]. In our 2HDM setup, the oscillation
probability gets contribution from both $H$ and $A$ [63, 60]; see Appendix A.
If $H$ and $A$ are highly non-degenerate, i.e. only either $H$ or $A$
dominantly contributes, the MACS bound requires $Y_{e\mu}<0.18$ for
$m_{H/A}=146$ GeV, as shown (for illustration only) by the vertical purple
line in Fig. 2 left panel, which rules out the LFV coupling needed to explain
the CMS excess with a single scalar/pseudoscalar. However, for $m_{H}\simeq
m_{A}$, there is a cancellation in the
$M_{\mu}\leftrightarrow\overline{M}_{\mu}$ amplitude which allows for either
$Y_{e\mu}$ or $Y_{\mu e}$ to be large, but not both. This is depicted by the
gray-shaded region in Fig. 2 right panel for $m_{H}\simeq m_{A}=146$ GeV. In
this limit, even the future MACE sensitivity cannot rule out the CMS excess
region.

Thus far, it seems either $Y_{e\mu}$ or $Y_{\mu e}$ coupling can be taken to
be large for explaining the CMS excess, while being consistent with the
current constraints. However, as discussed below, a combination of the LHC
charged Higgs constraints and the global fit to non-standard neutrino
interactions (NSI), preclude the possibility of a large $Y_{\mu e}$ coupling,
as shown by the horizontal purple-shaded region in Fig. 2 right panel.
Therefore, the only viable possibility is to have a large $Y_{e\mu}$ coupling
and small $Y_{\mu e}$ coupling (the lower right band of the CMS excess region
in Fig. 2 right panel).

###  III.2 Charged sector

At LEP, $H^{\pm}$ can be pair produced through either $s$-channel Drell-Yan
process via $\gamma/Z$, or $t$-channel via light neutrino. It can also be
singly produced either in association with a $W$ boson or through the Drell-
Yan channel in association with the leptons [48]. Once produced, the charged
scalar decays into $\nu_{\alpha}\ell_{\beta,R}$ through the Yukawa coupling
$Y_{\alpha\beta}$, which has the same signature as the right-handed slepton
decay into lepton plus massless neutralino in SUSY models:
$e^{+}e^{-}\to\tilde{\ell}_{R}^{+}\tilde{\ell}_{R}^{-}\to\ell_{R}^{+}\tilde{\chi}^{0}\ell_{R}^{-}\tilde{\chi}^{0}$.
We can therefore reinterpret the LEP slepton searches [64, 65, 66, 67, 68] to
derive a bound on light charged scalars. Depending on the branching ratio
${\rm BR}(H^{+}\to\ell^{+}\nu)$ the LEP limit on the charged scalar varies
from $80-100$ GeV [48].

Similarly at the LHC, a pair of charged scalars can be produced through
$s$-channel Drell-Yan process via $\gamma/Z$, followed by decays into
$\nu_{\alpha}\ell_{\beta,R}$. By reinterpreting the LHC searches for right-
handed sleptons, one can therefore put bounds on the charged scalar mass as a
function of BR in the massless neutralino limit. From an ATLAS analysis of the
LHC Run-2 data [69],we obtain a lower bound of $m_{H^{+}}>425$ GeV at 90% CL
for ${\rm BR}(H^{+}\to\mu^{+}\nu_{e})=1$. As we will see below, for
$m_{H}=m_{A}=146$ GeV, the charged Higgs boson cannot be too much heavier due
to the electroweak precision data (EWPD) constraints. Therefore, we would need
additional decay channels in order to make ${\rm
BR}(H^{+}\to\mu^{+}\nu_{e})<1$ and relax the LHC constraints.

##  IV Resolving the $W$-boson mass anomaly

The mass splitting between the neutral and charged components of the
$SU(2)_{L}$ doublet $H_{2}$ breaks the custodial symmetry of the SM at the
loop level. The change in the relationship between the $W$ and $Z$ boson
masses can be used to accommodate the recent CDF $W$-mass anomaly, which
currently stands at $7\sigma$ [31]. This effect can be parameterized by the
oblique parameters $S$ and $T$ [70, 71], which modifies [72]

$\displaystyle m_{W}\simeq m_{W}^{\rm
SM}\left[1-\frac{\alpha(S-2\cos^{2}{\theta_{w}}T)}{4(\cos^{2}{\theta_{w}}-\sin^{2}{\theta_{w}})}\right],$
(3)

where $\theta_{w}$ is the electroweak mixing angle. We incorporate the global
electroweak fit [73] with the new CDF data to show allowed ranges for the
scalar masses $(m_{A},m_{H^{+}})$ with the choice of $m_{H}=146$ GeV in Fig. 3
(blue band). In spite of explaining the CDF $W$ mass shift, the model is
mildly consistent with the PDG global fit [74], as can be seen from the red
region in Fig. 3. We find that the CDF anomaly prefers significant splitting
between $m_{A}$ and $m_{H^{+}}$. For $m_{H}=m_{A}=146$ GeV, we require
$m_{H^{+}}\simeq$ 228–234 GeV to explain the CDF anomaly at $2\sigma$.

Figure 3: $2\sigma$ allowed ranges from EWPD global fit for the charged and
neutral Higgs masses in the alignment limit of our 2HDM scenario.

To reconcile the CDF-preferred $m_{H^{+}}$ region with the LHC constraint
$m_{H^{+}}>425$ GeV, we reinterpret the slepton search limit as a function of
the charged Higgs mass and ${\rm BR}(H^{+}\to\mu^{+}\nu_{e})$, using the
publicly available cross section limits given as a function of the slepton
mass from the auxiliary material of Ref. [69], as well as from an earlier
ATLAS analysis [75]. We find that to lower the $m_{H^{+}}$ bound to $\sim 230$
GeV, as required by the CDF anomaly, we need ${\rm
BR}(H^{+}\to\mu^{+}\nu_{e})<0.7$ (0.95) according to the cross section limits
reported in Ref. [75] ([69]). We therefore fix ${\rm
BR}(H^{+}\to\mu^{+}\nu_{e})=0.7$ for our analysis of the CMS excess in Fig. 2.

For the purpose of our discussion here, we are agnostic about the detailed
structure of the Yukawa coupling matrix, which could account for the remaining
30% BR. Additional nonzero entries in the Yukawa matrix are viable, albeit
requiring potential adjustments to suppress LFV. One example texture that fits
our branching ratio requirement is $Y_{e\mu}=0.71$, $Y_{\tau\tau}=0.46$, and
all other Yukawa entries negligible. This choice does not lead to trilepton
LFV decays but does induce the radiative LFV decay $\mu\to e\gamma$ via a two-
loop process involving the tauon in the Barr-Zee diagram [76, 15]. However, it
is also important to consider other diagrams such as the two-loop Barr-Zee
diagram from the charged Higgs, which depends on the quartic coupling
$\lambda(H_{2}^{\dagger}H_{2})(H_{1}^{\dagger}H_{2})$, and depending on the
sign of $\lambda$, can destructively interfere with the tau-loop-induced
diagram. We find that the LFV constraints can be satisfied for the above
choice of Yukawa couplings for a relatively small quartic coupling of order
$\mathcal{O}(10^{-3})$.

We note here that instead of a large $Y_{e\mu}$ coupling, if we had allowed a
large $Y_{\mu e}$ coupling, it would imply the coupling of charged Higgs
$H^{-}$ to electrons and muon neutrinos. This leads to a $\nu_{\mu}-e$
coherent scattering in matter via $t$-channel exchange of the charged Higgs,
and hence, generates an NSI of the type $\varepsilon_{\mu\mu}=|Y_{\mu
e}|^{2}/(4\sqrt{2}G_{F}m_{H^{+}}^{2})$ [48]. From a recent global analysis of
NSI constraints, we get a 90% CL bound of $\varepsilon_{\mu\mu}<0.015$
[77].111This is derived from the bound on
$\varepsilon_{\tau\tau}-\varepsilon_{\mu\mu}$ [77] (see also Ref. [78]), which
is stronger than the individual bound on $\varepsilon_{\mu\mu}$. In our model,
both $\varepsilon_{\mu\mu}$ and $\varepsilon_{\tau\tau}$ cannot be
simultaneously large due to strong charged LFV constraints; therefore, the
bound on $\varepsilon_{\tau\tau}-\varepsilon_{\mu\mu}$ is also applicable for
$\varepsilon_{\mu\mu}$. For $m_{H^{+}}\sim 230$ GeV, this gives an upper bound
of $Y_{\mu e}\simeq 0.23$, which is shown by the purple-shaded region in Fig.
2 right panel.

##  V Muon Anomalous Magnetic Moment

The same $Y_{e\mu}$ coupling also contributes to the $(g-2)_{\mu}$ via the
neutral and charged Higgs loops [79, 80]; see Appendix B. The combined result
of the Brookhaven [28] and Fermilab [29] $(g-2)_{\mu}$ experiments is
$4.2\sigma$ away from the 2020 global average of the SM prediction [81]:
$\Delta a_{\mu}({\rm WP})=(251\pm 59)\times 10^{-11}$.222This was recently
updated to $\Delta a_{\mu}({\rm WP})=(249\pm 48)\times 10^{-11}$ [30], but
there is no noticeable change in our results. This discrepancy is however
reduced to only $1.5\sigma$, if we use the ab-initio lattice calculation from
the BMW collaboration [82]333Other lattice calculations now agree with the BMW
result in the ”intermediate distance regime” [83, 84, 85, 86], but a more
thorough and complete analysis is ongoing., which gives $\Delta a_{\mu}({\rm
BMW})=(107\pm 70)\times 10^{-11}$ [87]. The extra contribution from the
neutral Higgs sector in our 2HDM scenario can explain the $(g-2)_{\mu}$
anomaly at $1\sigma$, as shown by the red (orange) shaded region in Fig. 2,
using the BMW (WP) value for the SM prediction. We find that the $1\sigma$ WP-
preferred region is excluded by LEP constraint on $Y_{e\mu}$ for $m_{H}\simeq
m_{A}=146$ GeV, whereas part of the $1\sigma$ BMW-preferred region is still
allowed, while simultaneously explaining the CMS excess and the CDF $W$-mass
anomaly.

Fig. 4 shows the range of the $(g-2)_{\mu}$ anomaly-preferred region at
$1\sigma$ in the neutral Higgs mass-coupling plane. For comparison, the green
bar at 146 GeV shows the CMS excess region, whereas the purple shaded region
around it is the exclusion region derived from CMS data [23]. The gray-shaded
region shows the LEP exclusion from $e^{+}e^{-}\to\mu^{+}\mu^{-}$ data [53].
The magenta region is excluded at $2\sigma$ from the precision $Z$-width
measurements [74], because for $m_{H/A}<m_{Z}$, an additional decay mode
$Z\to\ell_{\alpha}^{+}\ell_{\beta}^{-}H/A\to 4\ell$ opens up. The vertical
cyan (blue) line is the indirect lower bound on the neutral Higgs mass,
derived using a combination of the electroweak precision constraint on the
mass splitting between the neutral and charged Higgs sectors using the CDF
(PDG) value of $m_{W}$, and the LEP lower limit of $\sim 100$ GeV on the
charged Higgs mass.

Figure 4: The CMS excess at $1\sigma$ (green) and 95% CL exclusion (purple) in
the mass-coupling plane, contrasted with the $1\sigma$ regions preferred by
$(g-2)_{\mu}$. Also shown are the constraints from LEP dilepton, $Z\to 4\ell$,
EWPD, and the future ILC and HL-LHC sensitivities.

From Fig. 4, we find that if we use the WP value for $g-2$, only a narrow band
around $m_{H/A}\simeq 25$ GeV can explain the $g-2$ anomaly at $1\sigma$. On
the other hand, if we use the BMW value, most of the parameter space for
$m_{H/A}>25$ GeV is currently allowed. Future sensitivity projections from HL-
LHC [88] and ILC [54] can cover most of the remaining allowed parameter space,
irrespective of the status of the CMS excess. In general, a dedicated neutral
scalar search in the LFV dilepton channels beyond 160 GeV could completely
probe the $(g-2)_{\mu}$-allowed region.

##  VI Discussion and Conclusion

Both ATLAS and the CMS collaborations searched for new bosons decaying into
opposite-sign and different flavor light leptons ($e^{\pm}\mu^{\mp}$) [19,
23]. In the CMS analysis, machine-learning techniques are used to enhance the
sensitivity where an excess is observed. ATLAS, on the other hand, did not
perform such a dedicated, BDT-optimized resonance search, and did not
interpret the results for masses which are different than the SM value of
$\sim 125$ GeV. Therefore, naively, it could be that the CMS analysis is
sensitive to a signal hypothesis which was not reachable by ATLAS. Although a
similar excess at 146 GeV is disfavored by ATLAS at $1\sigma$ (as shown in our
Fig. 2) [45], it is a ballpark estimate only and not entirely conclusive; a
dedicated interpretation of the ATLAS results is required.

Both analyses generated signal samples with two mechanisms: gluon-fusion (ggH)
and vector-boson-fusion (VBF). The contribution of the ggH mechanism to the
total cross section is significantly higher [23], and therefore it has the
dominant effect on the results. In order to validate the use of the results by
simply comparing cross sections, we compared the kinematic distributions of
the leptons between the ggH mechanism and a direct production with leptons
from the proton, and found good agreement.

It is also interesting that CMS reported excesses in the diphoton [89] and
ditau [90] channels at 95 GeV, but only with $2.9\sigma$ local ($1.3\sigma$
global) and $2.6\sigma$ local ($2.3\sigma$ global) significances,
respectively. These can be accommodated with an extended Higgs sector [91, 92,
93, 94, 95], but a common explanation together with the 146 GeV $e\mu$ excess
seems difficult, and requires further investigation.

In conclusion, the leptophilic 2HDM provides the simplest explanation for the
CMS $e\mu$ excess at 146 GeV. It also simultaneously resolves the CDF $W$-mass
and the $(g-2)_{\mu}$ anomalies. A minimal extension of this 2HDM by a singlet
charged scalar leads to the Zee model of radiative neutrino mass generation
[96]. Should the CMS excess be confirmed, a detailed neutrino oscillation fit
(similar to what was done in Ref. [48]) with large $Y_{e\mu}$ entry could be
performed, which might also lead to concrete predictions in the neutrino
sector, including NSI, as well as for charged LFV decays.

###### Acknowledgements.

We thank Saurabh Nangia for valuable technical help with using lepton PDF. AT
thanks Julian Heeck for valuable discussion. BD thanks Ashutosh Kotwal and
David Toback for convincing him that the CDF $W$-mass anomaly should be taken
seriously. BD also thanks the Mitchell Institute at Texas A&M University for
local hospitality, where part of this work was done. BD is supported in part
by the US Department of Energy grant No. DE-SC 0017987 and by a URA VSP
fellowship. The work of AT is supported in part by the National Science
Foundation under Grant PHY-2210428. YA is supported by the National Science
Foundation under Grant No. PHY-2013010.

##  Appendix A Muonium-antimuonium oscillation

The muonium-antimuonium oscillation probability in our 2HDM scenario is given
by [63, 60]

$P(M_{\mu}\to\overline{M}_{\mu})\simeq\frac{64\alpha^{6}m_{\rm
red}^{6}\tau_{\mu}^{2}}{\pi^{2}}G_{M\overline{M}}^{2}\,,$ (4)

where $\alpha$ is the fine-structure constant, $m_{\rm
red}=m_{e}m_{\mu}/(m_{e}+m_{\mu})$ is the reduced mass of the electron-muon
system, $\tau_{\mu}$ is the muon lifetime, and $G_{M\overline{M}}$ is the
Wilson coefficient which, in our 2HDM scenario, is given by [60]

$G_{M\overline{M}}^{2}\simeq
0.32\,\left|\frac{3G_{3}}{2}+\frac{G_{45}}{4}\right|^{2}+0.13\,\left|\frac{G_{45}}{4}-0.68\,G_{3}\right|^{2},$
(5)

with the following coefficients in the alignment limit:

$\displaystyle G_{45}$ $\displaystyle\equiv-\frac{Y_{e\mu}^{*2}+Y_{\mu
e}^{2}}{8\sqrt{2}}\left(\frac{1}{m_{H}^{2}}-\frac{1}{m_{A}^{2}}\right),$ (6)
$\displaystyle G_{3}$ $\displaystyle\equiv-\frac{Y_{e\mu}^{*}Y_{\mu
e}}{8\sqrt{2}}\left(\frac{1}{m_{H}^{2}}+\frac{1}{m_{A}^{2}}\right).$ (7)

We find that for $m_{H}\simeq m_{A}$, there is a cancellation in the $G_{45}$
amplitude (at the level of 6%), while the $G_{3}$ amplitude vanishes if we
consider only $Y_{e\mu}$ (or $Y_{\mu e}$).

##  Appendix B Lepton anomalous magnetic moment

The expression for one-loop contribution of neutral and charged scalars to
$(g-2)_{\mu}$ is given by

$\displaystyle\Delta a_{\mu}$
$\displaystyle\simeq\frac{m_{\mu}^{2}}{16\pi^{2}}\left[\frac{1}{m_{H}^{2}}\left\\{\frac{|Y_{e\mu}|^{2}+|Y_{\mu
e}|^{2}}{6}-2\frac{m_{e}}{m_{\mu}}\left(\frac{3}{4}+\log\left(\frac{m_{e}}{m_{H}}\right)\right)\Re(Y_{\mu
e}Y_{e\mu})\right\\}\right.$
$\displaystyle\left.\qquad\qquad+\frac{1}{m_{A}^{2}}\left\\{\frac{|Y_{e\mu}|^{2}+|Y_{\mu
e}|^{2}}{6}+2\frac{m_{e}}{m_{\mu}}\left(\frac{3}{4}+\log\left(\frac{m_{e}}{m_{A}}\right)\right)\Re(Y_{\mu
e}Y_{e\mu})\right\\}\right.$
$\displaystyle\left.\qquad\qquad-\frac{1}{m_{H^{+}}^{2}}\frac{|Y_{e\mu}|^{2}}{6}\right].$
(8)

In the limit of $m_{H}\simeq m_{A}$, the terms proportional to $m_{e}m_{\mu}$
cancel. These terms also vanish in the limit of $Y_{\mu e}\to 0$, or if the
Yukawa couplings are real. For complex Yukawa couplings, there will be
additional strong constraints from electron electric dipole moment [97]. For
our scenario with small $Y_{\mu e}$, Eq. (8) reduces to the simple expression

$\displaystyle\Delta a_{\mu}$
$\displaystyle\simeq\frac{m_{\mu}^{2}|Y_{e\mu}|^{2}}{96\pi^{2}}\left(\frac{1}{m_{H}^{2}}+\frac{1}{m_{A}^{2}}-\frac{1}{m_{H^{+}}^{2}}\right).$
(9)

The same Yukawa coupling $Y_{e\mu}$ also contributes to $(g-2)_{e}$, and
$\Delta a_{e}$ is given by Eq. (9) with the replacement
$m_{\mu}\leftrightarrow m_{e}$. Due to the $m_{e}^{2}$ suppression, the
corresponding bound on $Y_{e\mu}$ is much weaker. Moreover, it is not clear
whether the $(g-2)_{e}$ result is anomalous. Although the experimental value
of $a_{e}$ has been measured very precisely [98], the SM prediction [99]
relies on the measurement of the fine-structure constant, and currently there
is a $5.5\sigma$ discrepancy between the Paris Rb determination of $\alpha$
[100] and the Berkeley Cs determination [101]. The recent Northwestern result
sits in between [98]. Until the discrepant $\alpha$ measurements are resolved,
we cannot draw any meaningful constraints from $(g-2)_{e}$.

## References

  * [1] S. Dawson et al., “Report of the Topical Group on Higgs Physics for Snowmass 2021: The Case for Precision Higgs Physics,” in Snowmass 2021.  9, 2022.  [2209.07510].
  * [2] ATLAS Collaboration, G. Aad et al., “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,” Phys. Lett. B 716 (2012) 1–29, [1207.7214].
  * [3] CMS Collaboration, S. Chatrchyan et al., “Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC,” Phys. Lett. B 716 (2012) 30–61, [1207.7235].
  * [4] CMS Collaboration, A. Tumasyan et al., “A portrait of the Higgs boson by the CMS experiment ten years after the discovery,” Nature 607 no. 7917, (2022) 60–68, [2207.00043].
  * [5] ATLAS Collaboration, “A detailed map of Higgs boson interactions by the ATLAS experiment ten years after the discovery,” Nature 607 no. 7917, (2022) 52–59, [2207.00092]. [Erratum: Nature 612, E24 (2022)].
  * [6] Super-Kamiokande Collaboration, Y. Fukuda et al., “Evidence for oscillation of atmospheric neutrinos,” Phys. Rev. Lett. 81 (1998) 1562–1567, [hep-ex/9807003].
  * [7] SNO Collaboration, Q. R. Ahmad et al., “Measurement of the rate of $\nu_{e}+d\to p+p+e^{-}$ interactions produced by 8B solar neutrinos at the Sudbury Neutrino Observatory,” Phys. Rev. Lett. 87 (2001) 071301, [nucl-ex/0106015].
  * [8] Double Chooz Collaboration, Y. Abe et al., “Indication of Reactor $\bar{\nu}_{e}$ Disappearance in the Double Chooz Experiment,” Phys. Rev. Lett. 108 (2012) 131801, [1112.6353].
  * [9] Daya Bay Collaboration, F. P. An et al., “Observation of electron-antineutrino disappearance at Daya Bay,” Phys. Rev. Lett. 108 (2012) 171803, [1203.1669].
  * [10] RENO Collaboration, J. K. Ahn et al., “Observation of Reactor Electron Antineutrino Disappearance in the RENO Experiment,” Phys. Rev. Lett. 108 (2012) 191802, [1204.0626].
  * [11] L. Calibbi and G. Signorelli, “Charged Lepton Flavour Violation: An Experimental and Theoretical Introduction,” Riv. Nuovo Cim. 41 no. 2, (2018) 71–174, [1709.00294].
  * [12] J. L. Diaz-Cruz and J. J. Toscano, “Lepton flavor violating decays of Higgs bosons beyond the standard model,” Phys. Rev. D 62 (2000) 116005, [hep-ph/9910233].
  * [13] G. Blankenburg, J. Ellis, and G. Isidori, “Flavour-Changing Decays of a 125 GeV Higgs-like Particle,” Phys. Lett. B 712 (2012) 386–390, [1202.5704].
  * [14] R. Harnik, J. Kopp, and J. Zupan, “Flavor Violating Higgs Decays,” JHEP 03 (2013) 026, [1209.1397].
  * [15] A. Crivellin, J. Heeck, and P. Stoffer, “A perturbed lepton-specific two-Higgs-doublet model facing experimental hints for physics beyond the Standard Model,” Phys. Rev. Lett. 116 no. 8, (2016) 081801, [1507.07567].
  * [16] J. Herrero-Garcia, N. Rius, and A. Santamaria, “Higgs lepton flavour violation: UV completions and connection to neutrino masses,” JHEP 11 (2016) 084, [1605.06091].
  * [17] M. Endo, S. Iguro, and T. Kitahara, “Probing $e\mu$ flavor-violating ALP at Belle II,” JHEP 06 (2020) 040, [2002.05948].
  * [18] R. K. Barman, P. S. B. Dev, and A. Thapa, “Constraining lepton flavor violating Higgs couplings at the HL-LHC in the vector boson fusion channel,” Phys. Rev. D 107 no. 7, (2023) 075018, [2210.16287].
  * [19] ATLAS Collaboration, G. Aad et al., “Search for the Higgs boson decays $H\to ee$ and $H\to e\mu$ in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector,” Phys. Lett. B 801 (2020) 135148, [1909.10235].
  * [20] CMS Collaboration, A. M. Sirunyan et al., “Search for lepton flavour violating decays of a neutral heavy Higgs boson to $\mu\tau$ and e$\tau$ in proton-proton collisions at $\sqrt{s}=$ 13 TeV,” JHEP 03 (2020) 103, [1911.10267].
  * [21] CMS Collaboration, A. M. Sirunyan et al., “Search for lepton-flavor violating decays of the Higgs boson in the $\mu\tau$ and e$\tau$ final states in proton-proton collisions at $\sqrt{s}$ = 13 TeV,” Phys. Rev. D 104 no. 3, (2021) 032013, [2105.03007].
  * [22] ATLAS Collaboration, G. Aad et al., “Searches for lepton-flavour-violating decays of the Higgs boson into $e\tau$ and $\mu\tau$ in $\sqrt{s}=13$ TeV $pp$ collisions with the ATLAS detector,” JHEP 07 (2023) 166, [2302.05225].
  * [23] CMS Collaboration, A. Hayrapetyan et al., “Search for the lepton-flavor violating decay of the Higgs boson and additional Higgs bosons in the e$\mu$ final state in proton-proton collisions at $\sqrt{s}$ = 13 TeV,” Phys. Rev. D 108 no. 7, (2023) 072004, [2305.18106].
  * [24] V. Bertone, S. Carrazza, D. Pagani, and M. Zaro, “On the Impact of Lepton PDFs,” JHEP 11 (2015) 194, [1508.07002].
  * [25] L. Buonocore, P. Nason, F. Tramontano, and G. Zanderighi, “Leptons in the proton,” JHEP 08 no. 08, (2020) 019, [2005.06477].
  * [26] L. Buonocore, P. Nason, F. Tramontano, and G. Zanderighi, “Photon and leptons induced processes at the LHC,” JHEP 12 (2021) 073, [2109.10924].
  * [27] H. K. Dreiner, V. M. Lozano, S. Nangia, and T. Opferkuch, “Lepton PDFs and multipurpose single-lepton searches at the LHC,” Phys. Rev. D 107 no. 3, (2023) 035011, [2112.12755].
  * [28] Muon g-2 Collaboration, G. W. Bennett et al., “Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL,” Phys. Rev. D 73 (2006) 072003, [hep-ex/0602035].
  * [29] Muon g-2 Collaboration, B. Abi et al., “Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm,” Phys. Rev. Lett. 126 no. 14, (2021) 141801, [2104.03281].
  * [30] Muon g-2 Collaboration, D. P. Aguillard et al., “Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm,” Phys. Rev. Lett. 131 no. 16, (2023) 161802, [2308.06230].
  * [31] CDF Collaboration, T. Aaltonen et al., “High-precision measurement of the $W$ boson mass with the CDF II detector,” Science 376 no. 6589, (2022) 170–176.
  * [32] S. Davidson and H. E. Haber, “Basis-independent methods for the two-Higgs-doublet model,” Phys. Rev. D 72 (2005) 035004, [hep-ph/0504050]. [Erratum: Phys.Rev.D 72, 099902 (2005)].
  * [33] J. F. Gunion and H. E. Haber, “The CP conserving two Higgs doublet model: The Approach to the decoupling limit,” Phys. Rev. D 67 (2003) 075019, [hep-ph/0207010].
  * [34] M. Carena, I. Low, N. R. Shah, and C. E. M. Wagner, “Impersonating the Standard Model Higgs Boson: Alignment without Decoupling,” JHEP 04 (2014) 015, [1310.2248].
  * [35] P. S. B. Dev and A. Pilaftsis, “Maximally Symmetric Two Higgs Doublet Model with Natural Standard Model Alignment,” JHEP 12 (2014) 024, [1408.3405]. [Erratum: JHEP 11, 147 (2015)].
  * [36] D. Das and I. Saha, “Search for a stable alignment limit in two-Higgs-doublet models,” Phys. Rev. D 91 no. 9, (2015) 095024, [1503.02135].
  * [37] J. Haller, A. Hoecker, R. Kogler, K. Mönig, T. Peiffer, and J. Stelzer, “Update of the global electroweak fit and constraints on two-Higgs-doublet models,” Eur. Phys. J. C 78 no. 8, (2018) 675, [1803.01853].
  * [38] O. Eberhardt, A. P. n. Martínez, and A. Pich, “Global fits in the Aligned Two-Higgs-Doublet model,” JHEP 05 (2021) 005, [2012.09200].
  * [39] A. Karan, V. Miralles, and A. Pich, “Updated global fit of the ATHDM with heavy scalars,” [2307.15419].
  * [40] J. Alwall et al., “The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations,” JHEP 07 (2014) 079, [1405.0301].
  * [41] A. Manohar, P. Nason, G. P. Salam, and G. Zanderighi, “How bright is the proton? A precise determination of the photon parton distribution function,” Phys. Rev. Lett. 117 no. 24, (2016) 242002, [1607.04266].
  * [42] A. V. Manohar, P. Nason, G. P. Salam, and G. Zanderighi, “The Photon Content of the Proton,” JHEP 12 (2017) 046, [1708.01256].
  * [43] NNPDF Collaboration, V. Bertone, S. Carrazza, N. P. Hartland, and J. Rojo, “Illuminating the photon content of the proton within a global PDF analysis,” SciPost Phys. 5 no. 1, (2018) 008, [1712.07053].
  * [44] S. Catani, Y. L. Dokshitzer, M. H. Seymour, and B. R. Webber, “Longitudinally invariant $K_{t}$ clustering algorithms for hadron hadron collisions,” Nucl. Phys. B 406 (1993) 187–224.
  * [45] K. Leney, “Searches in the BSM Higgs sector.”  https://indico.in2p3.fr/event/29681/contributions/122562/attachments/76697/111308/02-KLeney-V1.pdf. 57th Rencontres de Moriond, Electroweak Interactions & Unified Theories, La Thuile, Italy (2023).
  * [46] R. Primulando, J. Julio, N. Srimanobhas, and P. Uttayarat, “A new Higgs boson with electron-muon flavor-violating couplings,” Phys. Lett. B 845 (2023) 138129, [2304.13757].
  * [47] N. Koivunen and M. Raidal, “Production and decays of 146 GeV flavons into e$\mu$ final state at the LHC,” JHEP 11 (2023) 014, [2305.00014].
  * [48] K. S. Babu, P. S. B. Dev, S. Jana, and A. Thapa, “Non-Standard Interactions in Radiative Neutrino Mass Models,” JHEP 03 (2020) 006, [1907.09498].
  * [49] L. Lavoura, “General formulae for f(1) —$>$ f(2) gamma,” Eur. Phys. J. C 29 (2003) 191–195, [hep-ph/0302221].
  * [50] MEG Collaboration, A. M. Baldini et al., “Search for the lepton flavour violating decay $\mu^{+}\rightarrow\mathrm{e}^{+}\gamma$ with the full dataset of the MEG experiment,” Eur. Phys. J. C 76 no. 8, (2016) 434, [1605.05081].
  * [51] OPAL Collaboration, G. Abbiendi et al., “Tests of the standard model and constraints on new physics from measurements of fermion pair production at 189-GeV to 209-GeV at LEP,” Eur. Phys. J. C 33 (2004) 173–212, [hep-ex/0309053].
  * [52] LEP, ALEPH, DELPHI, L3, OPAL, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavor Group Collaboration, t. S. Electroweak, “A Combination of preliminary electroweak measurements and constraints on the standard model,” [hep-ex/0312023].
  * [53] R. K. Barman, R. Dcruz, and A. Thapa, “Neutrino masses and magnetic moments of electron and muon in the Zee Model,” JHEP 03 (2022) 183, [2112.04523].
  * [54] T. Barklow, J. Brau, K. Fujii, J. Gao, J. List, N. Walker, and K. Yokoya, “ILC Operating Scenarios,” [1506.07830].
  * [55] P. S. B. Dev, R. N. Mohapatra, and Y. Zhang, “Lepton Flavor Violation Induced by a Neutral Scalar at Future Lepton Colliders,” Phys. Rev. Lett. 120 no. 22, (2018) 221804, [1711.08430].
  * [56] P. S. B. Dev, R. N. Mohapatra, and Y. Zhang, “Probing TeV scale origin of neutrino mass at future lepton colliders via neutral and doubly-charged scalars,” Phys. Rev. D 98 no. 7, (2018) 075028, [1803.11167].
  * [57] B. Pontecorvo, “Mesonium and anti-mesonium,” Sov. Phys. JETP 6 (1957) 429. http://jetp.ras.ru/cgi-bin/dn/e_006_02_0429.pdf.
  * [58] U. D. Jentschura, G. Soff, V. G. Ivanov, and S. G. Karshenboim, “The Bound mu+ mu- system,” Phys. Rev. A 56 (1997) 4483, [physics/9706026].
  * [59] T. E. Clark and S. T. Love, “Muonium - anti-muonium oscillations and massive Majorana neutrinos,” Mod.The second-order weak correction to (g - 2) of the muon in arbitrary gauge models Phys. Lett. A 19 (2004) 297–306, [hep-ph/0307264].
  * [60] T. Fukuyama, Y. Mimura, and Y. Uesaka, “Models of the muonium to antimuonium transition,” Phys. Rev. D 105 no. 1, (2022) 015026, [2108.10736].
  * [61] L. Willmann et al., “New bounds from searching for muonium to anti-muonium conversion,” Phys. Rev. Lett. 82 (1999) 49–52, [hep-ex/9807011].
  * [62] A.-Y. Bai et al., “Snowmass2021 Whitepaper: Muonium to antimuonium conversion,” in Snowmass 2021.  3, 2022.  [2203.11406].
  * [63] R. Conlin and A. A. Petrov, “Muonium-antimuonium oscillations in effective field theory,” Phys. Rev. D 102 no. 9, (2020) 095001, [2005.10276].
  * [64] ALEPH Collaboration, A. Heister et al., “Search for scalar leptons in e+ e- collisions at center-of-mass energies up to 209-GeV,” Phys. Lett. B 526 (2002) 206–220, [hep-ex/0112011].
  * [65] ALEPH Collaboration, A. Heister et al., “Absolute mass lower limit for the lightest neutralino of the MSSM from e+ e- data at s**(1/2) up to 209-GeV,” Phys. Lett. B 583 (2004) 247–263.
  * [66] DELPHI Collaboration, J. Abdallah et al., “Searches for supersymmetric particles in e+ e- collisions up to 208-GeV and interpretation of the results within the MSSM,” Eur. Phys. J. C 31 (2003) 421–479, [hep-ex/0311019].
  * [67] L3 Collaboration, P. Achard et al., “Search for scalar leptons and scalar quarks at LEP,” Phys. Lett. B 580 (2004) 37–49, [hep-ex/0310007].
  * [68] OPAL Collaboration, G. Abbiendi et al., “Search for anomalous production of dilepton events with missing transverse momentum in e+ e- collisions at s**(1/2) = 183-Gev to 209-GeV,” Eur. Phys. J. C 32 (2004) 453–473, [hep-ex/0309014].
  * [69] ATLAS Collaboration, G. Aad et al., “Search for electroweak production of charginos and sleptons decaying into final states with two leptons and missing transverse momentum in $\sqrt{s}=13$ TeV $pp$ collisions using the ATLAS detector,” Eur. Phys. J. C 80 no. 2, (2020) 123, [1908.08215].
  * [70] M. E. Peskin and T. Takeuchi, “A New constraint on a strongly interacting Higgs sector,” Phys. Rev. Lett. 65 (1990) 964–967.
  * [71] M. E. Peskin and T. Takeuchi, “Estimation of oblique electroweak corrections,” Phys. Rev. D 46 (1992) 381–409.
  * [72] I. Maksymyk, C. P. Burgess, and D. London, “Beyond S, T and U,” Phys. Rev. D 50 (1994) 529–535, [hep-ph/9306267].
  * [73] C.-T. Lu, L. Wu, Y. Wu, and B. Zhu, “Electroweak precision fit and new physics in light of the W boson mass,” Phys. Rev. D 106 no. 3, (2022) 035034, [2204.03796].
  * [74] Particle Data Group Collaboration, R. L. Workman et al., “Review of Particle Physics,” PTEP 2022 (2022) 083C01.
  * [75] ATLAS Collaboration, M. Aaboud et al., “Search for electroweak production of supersymmetric particles in final states with two or three leptons at $\sqrt{s}=13\,$TeV with the ATLAS detector,” Eur. Phys. J. C 78 no. 12, (2018) 995, [1803.02762].
  * [76] V. Ilisie, “New Barr-Zee contributions to $\mathbf{(g-2)_{\mu}}$ in two-Higgs-doublet models,” JHEP 04 (2015) 077, [1502.04199].
  * [77] P. Coloma, M. C. Gonzalez-Garcia, M. Maltoni, J. a. P. Pinheiro, and S. Urrea, “Global constraints on non-standard neutrino interactions with quarks and electrons,” JHEP 08 (2023) 032, [2305.07698].
  * [78] IceCube Collaboration, R. Abbasi et al., “Non-standard neutrino interactions in IceCube,” PoS EPS-HEP2021 (2022) 245.
  * [79] J. P. Leveille, “The Second Order Weak Correction to (G-2) of the Muon in Arbitrary Gauge Models,” Nucl. Phys. B 137 (1978) 63–76.
  * [80] M. Lindner, M. Platscher, and F. S. Queiroz, “A Call for New Physics : The Muon Anomalous Magnetic Moment and Lepton Flavor Violation,” Phys. Rept. 731 (2018) 1–82, [1610.06587].
  * [81] T. Aoyama et al., “The anomalous magnetic moment of the muon in the Standard Model,” Phys. Rept. 887 (2020) 1–166, [2006.04822].
  * [82] S. Borsanyi et al., “Leading hadronic contribution to the muon magnetic moment from lattice QCD,” Nature 593 no. 7857, (2021) 51–55, [2002.12347].
  * [83] M. Cè et al., “Window observable for the hadronic vacuum polarization contribution to the muon g-2 from lattice QCD,” Phys. Rev. D 106 no. 11, (2022) 114502, [2206.06582].
  * [84] Extended Twisted Mass Collaboration, C. Alexandrou et al., “Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions,” Phys. Rev. D 107 no. 7, (2023) 074506, [2206.15084].
  * [85] Fermilab Lattice, HPQCD,, MILC Collaboration, A. Bazavov et al., “Light-quark connected intermediate-window contributions to the muon g-2 hadronic vacuum polarization from lattice QCD,” Phys. Rev. D 107 no. 11, (2023) 114514, [2301.08274].
  * [86] RBC, UKQCD Collaboration, T. Blum et al., “Update of Euclidean windows of the hadronic vacuum polarization,” Phys. Rev. D 108 no. 5, (2023) 054507, [2301.08696].
  * [87] H. Wittig, “Progress on $(g-2)_{\mu}$ from Lattice QCD,” in 57th Rencontres de Moriond on Electroweak Interactions and Unified Theories.  6, 2023.  [2306.04165].
  * [88] I. Zurbano Fernandez et al., “High-Luminosity Large Hadron Collider (HL-LHC): Technical design report,” tech. rep., CERN, Geneva, 12, 2020.
  * [89] CMS Collaboration, “Search for a standard model-like Higgs boson in the mass range between 70 and 110$~{}\mathrm{GeV}$ in the diphoton final state in proton-proton collisions at $\sqrt{s}=13~{}\mathrm{TeV}$,”. CMS-PAS-HIG-20-002.
  * [90] CMS Collaboration, A. Tumasyan et al., “Searches for additional Higgs bosons and for vector leptoquarks in $\tau\tau$ final states in proton-proton collisions at $\sqrt{s}$ = 13 TeV,” JHEP 07 (2023) 073, [2208.02717].
  * [91] T. Biekötter, S. Heinemeyer, and G. Weiglein, “The CMS di-photon excess at 95 GeV in view of the LHC Run 2 results,” Phys. Lett. B 846 (2023) 138217, [2303.12018].
  * [92] D. Azevedo, T. Biekötter, and P. M. Ferreira, “2HDM interpretations of the CMS diphoton excess at 95 GeV,” JHEP 11 (2023) 017, [2305.19716].
  * [93] P. Escribano, V. M. Lozano, and A. Vicente, “Scotogenic explanation for the 95 GeV excesses,” Phys. Rev. D 108 no. 11, (2023) 115001, [2306.03735].
  * [94] T. Biekötter, S. Heinemeyer, and G. Weiglein, “The 95.4 GeV di-photon excess at ATLAS and CMS,” [2306.03889].
  * [95] S. Bhattacharya, G. Coloretti, A. Crivellin, S.-E. Dahbi, Y. Fang, M. Kumar, and B. Mellado, “Growing Excesses of New Scalars at the Electroweak Scale,” [2306.17209].
  * [96] A. Zee, “A Theory of Lepton Number Violation, Neutrino Majorana Mass, and Oscillation,” Phys. Lett. B 93 (1980) 389. [Erratum: Phys.Lett.B 95, 461 (1980)].
  * [97] T. S. Roussy et al., “An improved bound on the electron’s electric dipole moment,” Science 381 (2023) 46, [2212.11841].
  * [98] X. Fan, T. G. Myers, B. A. D. Sukra, and G. Gabrielse, “Measurement of the Electron Magnetic Moment,” Phys. Rev. Lett. 130 no. 7, (2023) 071801, [2209.13084].
  * [99] T. Aoyama, T. Kinoshita, and M. Nio, “Theory of the Anomalous Magnetic Moment of the Electron,” Atoms 7 no. 1, (2019) 28.
  * [100] L. Morel, Z. Yao, P. Cladé, and S. Guellati-Khélifa, “Determination of the fine-structure constant with an accuracy of 81 parts per trillion,” Nature 588 no. 7836, (2020) 61–65.
  * [101] R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. Müller, “Measurement of the fine-structure constant as a test of the Standard Model,” Science 360 (2018) 191, [1812.04130].