# Addendum to: Combined Constraints on First Generation Leptoquarks

Andreas Crivellin<EMAIL_ADDRESS>CERN Theory Division, CH–1211
Geneva 23, Switzerland  Physik-Institut, Universität Zürich,
Winterthurerstrasse 190, CH-8057 Zürich, Switzerland  Paul Scherrer Institut,
CH–5232 Villigen PSI, Switzerland  Luc Schnell<EMAIL_ADDRESS>Laboratoire de Physique Théorique et Hautes Énergies, LPTHE, Sorbonne
Université, CNRS, 4 place Jussieu, FR-75252 Paris Cedex 05, France
Departement Physik, ETH Zürich, Otto-Stern-Weg 1, CH-8093 Zürich, Switzerland
Département de Physique, École Polytechnique, Route de Saclay, FR-91128
Palaiseau Cedex, France

###### Abstract

In this addendum to Ref. Crivellin et al. (2021a) we discuss the implications
of the recent CMS analysis of lepton flavour universality violation in non-
resonant di-lepton pairs for first generation leptoquarks. As CMS finds more
electron events than expected from background, this analysis prefers the LQ
representations
$\tilde{S}_{1},S_{2},S_{3},\tilde{V}_{1},V_{2}\,(\kappa_{2}^{RL}\neq 0)$ and
$V_{3}$ which lead to constructive interference with the SM. In principle the
excess could also be (partially) explained by the representations
$\tilde{S}_{2},V_{1}\,(\kappa_{1}^{R}\neq 0),V_{2}\,(\kappa_{2}^{LR}\neq
0),\tilde{V}_{2}$ which are interfering destructively, as this would still
lead to the right effect in bins with high invariant mass where the new
physics contribution dominates. However, in these cases large couplings would
be required which are excluded by other observables. The representations
$S_{1},V_{1}\,(\kappa_{1}^{L}\neq 0)$ cannot improve the fit to the CMS data
compared to the SM.

Leptoquarks, LHC, non-resonant di-leptons

††preprint: CERN-TH-2021-053, PSI-PR-21-05, ZU-TH 16/21

##  I Introduction

Leptoquarks are very well motivated by the so-called “flavor anomalies”, i.e.
the discrepancies between measurements and the SM predictions which point
towards lepton flavor universality (LFU) violating new physics (NP) in
$R(D^{(*)})$ Lees et al. (2012, 2013); Aaij et al. (2015, 2018a, 2018b);
Abdesselam et al. (2019), $b\to s\ell^{+}\ell^{-}$ Khachatryan et al. (2015);
Aaij et al. (2016); Abdesselam et al. (2016); Aaij et al. (2017, 2019, 2020,
2021) and in the anomalous magnetic moment (AMM) of the muon ($a_{\mu}$)
Bennett et al. (2006); Abi et al. (2021), with a significance of
$>\\!3\,\sigma$ Amhis et al. (2017); Murgui et al. (2019); Shi et al. (2019);
Blanke et al. (2019); Kumbhakar et al. (2020), $>\\!5\sigma$ Capdevila et al.
(2018); Altmannshofer et al. (2017a); Algueró et al. (2019); Alok et al.
(2019); Ciuchini et al. (2019); Aebischer et al. (2020); Arbey et al. (2019);
Kumar et al. (2019a) and $4.2\,\sigma$ Aoyama et al. (2020), respectively. In
this context, it has been shown that LQs can explain $b\to s\ell^{+}\ell^{-}$
data Alonso et al. (2015); Calibbi et al. (2015); Hiller et al. (2016);
Bhattacharya et al. (2017); Buttazzo et al. (2017); Barbieri et al. (2016,
2017); Calibbi et al. (2018); Crivellin et al. (2018a); Bordone et al.
(2018a); Kumar et al. (2019b); Crivellin et al. (2019); Crivellin and
Saturnino (2019a); Cornella et al. (2019); Bordone et al. (2020); Bernigaud et
al. (2020); Aebischer et al. (2019); Fuentes-Martín et al. (2020); Popov et
al. (2019); Fajfer and Košnik (2016); Blanke and Crivellin (2018); de Medeiros
Varzielas and Talbert (2019); de Medeiros Varzielas and Hiller (2015);
Crivellin et al. (2020a); Saad (2020); Saad and Thapa (2020); Gherardi et al.
(2021); Da Rold and Lamagna (2020), $R(D^{(*)})$ Alonso et al. (2015); Calibbi
et al. (2015); Fajfer and Košnik (2016); Bhattacharya et al. (2017); Buttazzo
et al. (2017); Barbieri et al. (2016, 2017); Calibbi et al. (2018); Bordone et
al. (2018b, a); Kumar et al. (2019b); Biswas et al. (2020); Crivellin et al.
(2019); Blanke and Crivellin (2018); Heeck and Teresi (2018); de Medeiros
Varzielas and Talbert (2019); Cornella et al. (2019); Bordone et al. (2020);
Sahoo and Mohanta (2015); Chen et al. (2016); Dey et al. (2018); Bečirević and
Sumensari (2017); Chauhan et al. (2018); Bečirević et al. (2018); Popov et al.
(2019); Fajfer et al. (2012); Deshpande and Menon (2013); Freytsis et al.
(2015); Bauer and Neubert (2016); Li et al. (2016); Zhu et al. (2016); Popov
and White (2017); Deshpande and He (2017); Bečirević et al. (2016); Cai et al.
(2017); Altmannshofer et al. (2017b); Kamali et al. (2018); Mandal et al.
(2019); Azatov et al. (2018); Zhu et al. (2018); Angelescu et al. (2018); Kim
et al. (2019); Aydemir et al. (2020); Crivellin and Saturnino (2019b); Yan et
al. (2019); Crivellin et al. (2017); Marzocca (2018); Bigaran et al. (2019);
Crivellin et al. (2020a); Saad (2020); Bhupal Dev et al. (2020); Saad and
Thapa (2020); Altmannshofer et al. (2020); Fuentes-Martín and Stangl (2020);
Gherardi et al. (2021); Da Rold and Lamagna (2020) and/or $a_{\mu}$ Bauer and
Neubert (2016); Djouadi et al. (1990); Chakraverty et al. (2001); Cheung
(2001); Popov and White (2017); Chen et al. (2016); Biggio et al. (2016);
Davidson et al. (1994); Couture and Konig (1996); Mahanta (2001); Queiroz et
al. (2015); Coluccio Leskow et al. (2017); Chen et al. (2017); Das et al.
(2016); Crivellin et al. (2017); Cai et al. (2017); Crivellin et al. (2018b);
Kowalska et al. (2019); Doršner et al. (2020a); Crivellin et al. (2020a);
Delle Rose et al. (2020); Saad (2020); Bigaran and Volkas (2020); Doršner et
al. (2020b); Fuentes-Martín and Stangl (2020); Gherardi et al. (2021); Babu et
al. (2021); Crivellin et al. (2020b). They have been studied in direct LHC
searches Kramer et al. (1997, 2005); Faroughy et al. (2017); Greljo and
Marzocca (2017); Doršner et al. (2017); Cerri et al. (2019); Bandyopadhyay and
Mandal (2018); Hiller et al. (2018); Faber et al. (2020); Schmaltz and Zhong
(2019); Chandak et al. (2019); Allanach et al. (2020); Buonocore et al.
(2020); Borschensky et al. (2020), leptonic observables Crivellin et al.
(2021b) and oblique electroweak (EW) parameters as well as Higgs couplings to
gauge bosons Keith and Ma (1997); Doršner et al. (2016); Bhaskar et al.
(2020); Zhang et al. (2019); Gherardi et al. (2020); Crivellin et al. (2020c).
Furthermore, if the LQs couple to first generation fermions particularly many
low energy precision probes can be affected Shanker (1982a, b); Leurer (1994a,
b); Davidson et al. (1994), including the so-called “Cabibbo-Angle Anomaly”
Grossman et al. (2020); Seng et al. (2020); Belfatto et al. (2020); Coutinho
et al. (2020); Crivellin and Hoferichter (2020); Capdevila et al. (2021);
Crivellin et al. (2020d); Kirk (2021); Alok et al. (2020); Crivellin et al.
(2020e, f, 2021c); Belfatto and Berezhiani (2021); Branco et al. (2021) as
well as rare Kaon decays and/or $D^{0}-\bar{D}^{0}$ Bobeth and Buras (2018);
Doršner et al. (2020c); Mandal and Pich (2019).

In Ref. Crivellin et al. (2021a) we studied the interplay of low and high
energy constraints on first generation leptoquarks (LQs). In this addendum we
update this analysis by including the recent CMS measurement of lepton flavour
universality violation (LFUV) in non-resonant di-leptons Sirunyan et al.
(2021). The CMS data points towards constructively interfering new physics in
the electron channel which can improve the fit compared to the SM by more than
$3\,\sigma$ Crivellin et al. (2021d).

##  II Setup

Let us briefly review our conventions. For details, the interested reader is
referred to Ref. Crivellin et al. (2021a). All 10 possible LQ representations
under the SM gauge group are listed in Table 1 with the convention that the
electric charge $Q$ is given by $Q=\frac{1}{2}Y+T_{3}$, where $Y$ is the
hypercharge and $T_{3}$ the third component of the weak isospin. These
representations allow for couplings to SM quarks and leptons as given in Table
2. In the following, we denote the LQ masses according to their representation
and use small $m$ for the scalar LQs and capital $M$ for the vector LQs.

Field | $\Phi_{1}$ | $\tilde{\Phi}_{1}$ | $\Phi_{2}$ | $\tilde{\Phi}_{2}$ | $\Phi_{3}$ | $V_{1}$ | $\tilde{V}_{1}$ | $V_{2}$ | $\tilde{V}_{2}$ | $V_{3}$
---|---|---|---|---|---|---|---|---|---|---
$SU(3)_{c}$ | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3
$SU(2)_{L}$ | 1 | 1 | 2 | 2 | 3 | 1 | 1 | 2 | 2 | 3
$U(1)_{Y}$ | $-\frac{2}{3}$ | $-\frac{8}{3}$ | $\frac{7}{3}$ | $\frac{1}{3}$ | $-\frac{2}{3}$ | $\frac{4}{3}$ | $\frac{10}{3}$ | $-\frac{5}{3}$ | $\frac{1}{3}$ | $\frac{4}{3}$
Table 1: The ten possible representations of scalar and vector LQs under the
SM gauge group.

| $L$ | $e$
---|---|---
${\bar{Q}}$ | ${\kappa_{1}^{L}{\gamma_{\mu}}V_{1}^{\mu}+\kappa_{3}{\gamma_{\mu}}\left({\tau\cdot V_{3}^{\mu}}\right)}$ | ${\lambda_{2}^{LR}{\Phi_{2}}}$
${\bar{d}}$ | ${\tilde{\lambda}_{2}\tilde{\Phi}_{2}^{T}i{\tau_{2}}}$ | ${\kappa_{1}^{R}{\gamma_{\mu}}V_{1}^{\mu}}$
${\bar{u}}$ | ${\lambda_{2}^{RL}\Phi_{2}^{T}i{\tau_{2}}}$ | ${\tilde{\kappa}_{1}{\gamma_{\mu}}\tilde{V}_{1}^{\mu}}$
${\bar{Q}^{c}}$ | ${\lambda_{3}i{\tau_{2}}{{\left({\tau\cdot{\Phi_{3}}}\right)}^{\dagger}}+\lambda_{1}^{L}i{\tau_{2}}\Phi_{1}^{\dagger}}$ | $\kappa_{2}^{LR}{\gamma_{\mu}}{V_{2}^{\mu{\dagger}}}$
${\bar{d}^{c}}$ | ${\kappa_{2}^{RL}{\gamma_{\mu}}V_{2}^{\mu{\dagger}}}$ | ${\tilde{\lambda}_{1}\tilde{\Phi}_{1}^{\dagger}}$
${\bar{u}^{c}}$ | $\tilde{\kappa}_{2}{{\gamma_{\mu}}\tilde{V}_{2}^{\mu{\dagger}}}$ | ${\lambda_{1}^{R}\Phi_{1}^{\dagger}}$
Table 2: Interaction terms of the LQ representations listed in Table 1, where
$Q$ and $L$ represent the left-handed quark and lepton $SU(2)_{L}$ doublets,
$e$, $d$ and $u$ the right-handed $SU(2)_{L}$ singlets, the superscript $c$
stands for charge conjugation and $\tau_{i}$ are the Pauli matrices.

##  III CMS Analysis of non-resonant di-lepton pairs

In Ref. Sirunyan et al. (2021) CMS presented an analysis of non-resonant high-
mass di-lepton events at the LHC. Since in our framework of first generation
LQs we only get effects in electrons, we can make use of the ratio

$R_{\mu\mu/ee}\equiv\frac{d\sigma(q\overline{q}\to\mu^{+}\mu^{-})/dm_{\mu\mu}}{d\sigma(q\overline{q}\to
e^{+}e^{-})/dm_{ee}}\,,$ (1)

of differential cross sections, measuring lepton flavour universality (which
reduces the uncertainties Greljo and Marzocca (2017)), to derive bounds on the
LQ masses and couplings. Here, $m_{\ell\ell}$ ($\ell=\mu,e$) is the invariant
mass of the lepton pair. In Ref. Sirunyan et al. (2021) $R_{\mu\mu/ee}$ was
measured for nine bins in an invariant mass range between 200 and 3,500 GeV
($R_{\mu\mu/ee}^{\text{Data}}$) and normalized to the same ratio calculated
via SM Monte-Carlo routines ($R_{\mu\mu/ee}^{\text{MC}}$). This ratio in turn
was normalized to unity in the bin from 200 to 400 GeV in order to correct for
differences in acceptance and efficiency between the di-electron and di-muon
channels. The resulting data points are shown in Fig. 1 where gray (black)
represents the cases where none (at least one) of the final state leptons were
observed in the detector endcaps.

We calculated the ratio
$R_{\mu\mu/ee}^{\text{LQ}}(m,\lambda)/R_{\mu\mu/ee}^{\text{SM}}$ for the
different LQ models (at leading order in perturbation theory) using the PDF
set NNPDF23LO, also employed e.g. in the ATLAS analysis to generate the signal
DY process Aad et al. (2020), with the help of the Mathematica package
ManeParse Clark et al. (2017). We then integrated this ratio over the
invariant mass ranges of the corresponding bins and compared the resulting
signal strength to the data. Here a complication arises if the LQ mass is not
much higher than the energy of the lepton pair such that the 4-Fermi
approximation is no longer appropriate. In this case we replaced the effective
interaction by the LQ propagator as described in Sec. 4 in Ref. Bessaa and
Davidson (2015). Therefore, $R_{\mu\mu/ee}^{\text{LQ}}$ is dependent both on
the LQ mass $m$ and the LQ coupling strength $\lambda$111Here we consider
scalar LQ parameters for simplicity, it works analogously for vector LQs with
the parameters $m$, $\lambda$ replaced by $M,\kappa$.. We also estimated the
relative sensitivities of the CMS detector to the LR/RL vs LL/RR channels,
resulting from their different angular distributions, based on the CI limits
stated in Ref. Sirunyan et al. (2021). We found a small enhancement of 10% for
the LR/RL channels and therefore decided to neglect this effect, obtaining a
conservative estimate of the LR/RL LQ contributions in our calculations.

Then we performed a $\chi^{2}$ statistical analysis with two degrees of
freedom, defining

$\chi^{2}(m,\lambda)\equiv\sum_{i=1,\dots,18}\dfrac{\left(\dfrac{R_{\mu\mu/ee,i}^{\text{Data}}}{R_{\mu\mu/ee,i}^{\text{MC}}}-\dfrac{R_{\mu\mu/ee,i}^{\text{SM+LQ}}(m,\lambda)}{R_{\mu\mu/ee,i}^{\text{SM}}}\right)^{2}}{\sigma_{i}^{2}}\,,$
(2)

where $i$ runs over the data points available from the nine bins with and
without leptons detected in the CMS endcaps and $\sigma_{i}$ are the
corresponding uncertainties reported in Ref. Sirunyan et al. (2021).
Minimizing the $\chi^{2}$ function with respect to $(m,\lambda)$ we find the
best fit points $\hat{m}$ and $\hat{\lambda}$ given in Tab. 3. The
corresponding values of
$R_{\mu\mu/ee}^{\text{SM+LQ}}/R_{\mu\mu/ee}^{\text{SM}}$ for the different
bins are shown in Fig. 1, together with the CMS measurement.

| $\lambda^{L}_{1}$ | $\lambda^{R}_{1}$ | $\tilde{\lambda}_{1}$ | $\lambda_{2}^{LR}$ | $\lambda^{RL}_{2}$ | $\tilde{\lambda}_{2}$ | $\lambda_{3}$ | $\kappa_{1}^{L}$ | $\kappa_{1}^{R}$ | $\tilde{\kappa}_{1}$ | $\kappa_{2}^{LR}$ | $\kappa_{2}^{RL}$ | $\tilde{\kappa}_{2}$ | $\kappa_{3}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
$\hat{m}$ or $\hat{M}$ [TeV] | $\infty$ | $\infty$ | 3.1 | 2.6 | 3.0 | 1.5 | 2.2 | $\infty$ | 1.0 | 4.3 | 1.0 | 2.5 | 0.6 | 3.9
$\hat{\lambda}$ or $\hat{\kappa}$ | 0 | 0 | 0.91 | 0.65 | 0.75 | 0.71 | 0.55 | 0 | 0.45 | 0.61 | 0.35 | 0.60 | 0.35 | 0.40
$\Delta\chi^{2}$ | 0 | 0 | -10.9 | -10.9 | -10.8 | -11.2 | -11.2 | 0 | -10.5 | -10.5 | -10.8 | -11.1 | -10.0 | -10.6
Table 3: Best fit points for the masses ($\hat{m},\hat{M}$) and couplings
($\hat{\lambda},\hat{\kappa}$) for the various LQ representations as well as
the corresponding minima of $\chi^{2}$ function with respect to the SM values
($\Delta\chi^{2}\equiv\chi^{2}(\infty,0)-\chi^{2}(\hat{m},\hat{\lambda})$).
The corresponding values of
$R_{\mu\mu/ee}^{\text{SM+LQ}}/R_{\mu\mu/ee}^{\text{SM}}$ in the different bins
are shown in Fig. 1.

Figure 1: The ratio $R_{\mu\mu/ee}^{\text{Data}}/R_{\mu\mu/ee}^{\text{MC}}$
measured by CMS Sirunyan et al. (2021) in the various bins compared to the
$R_{\mu\mu/ee}^{\text{SM+LQ}}/R_{\mu\mu/ee}^{\text{SM}}$ values for the best
fit of the various LQ models. The gray data points correspond to measurements
where both leptons were detected in the CMS barrel while the black dots
correspond to measurements where at least one of the leptons was detected in
the CMS endcaps. The parameters of the fit to the different LQ representations
are given in Tab. 3.

Figure 2: Limits on the parameter space of first generation scalar LQs. The
regions above the colored lines are excluded. The preferred $1\sigma$ and
$2\sigma$ regions by CMS measurement are shown in yellow. While LHC limits and
the bounds from parity violation are to a good approximation independent of
$\beta$ (for $\beta=O(\theta_{c})$) the bounds from kaon and $D$ decays depend
on it. We consider the two scenarios $\beta=\theta_{c}$ or $\beta=0$. In the
first case, the kaon limits arise for LQ representations with left-handed
quark fields while in the second case these limits are absent but bounds from
$D^{0}-\bar{D}^{0}$ arise.

Figure 3: Limits on the parameter space of first generation vector LQs. The
regions above the colored lines are excluded. The $1\sigma$ and $2\sigma$
regions that are preferred by the CMS measurement are shown in yellow. While
LHC limits and the bounds from parity violation are to a good approximation
independent of $\beta$ (for $\beta=O(\theta_{c})$) the bounds from kaon and
$D$ decays depend on it. We consider the two scenarios $\beta=\theta_{c}$ or
$\beta=0$. In the first case, the kaon limits arise for LQ representations
with left-handed quark fields while in the second case these limits are absent
but bounds from $D^{0}-\bar{D}^{0}$ arise.

##  IV Phenomenological Analysis

The regions allowed at the $1\sigma$ and $2\sigma$ level (with respect to the
best fit points) from the CMS measurement are shown in Fig. 2 and 3 together
with the other constraints on first generation LQs. For
$\tilde{\lambda}_{1},\lambda_{2}^{LR},\lambda_{2}^{RL},\tilde{\lambda}_{2},\lambda_{3},\kappa_{1}^{R},\tilde{\kappa}_{1},\kappa_{2}^{LR},\kappa_{2}^{RL},\tilde{\kappa}_{2}$
and $\kappa_{3}$, the model explains data better than the SM, with
$\Delta\chi^{2}\equiv\chi^{2}(\infty,0)-\chi^{2}(\hat{m},\hat{\lambda})$ being
$\approx-11$ as they provide clear effects in the high $m_{\ell\ell}$ bins.
The representations with $\lambda_{1}^{L},\lambda_{1}^{R}$ and
$\kappa_{1}^{L}$ feature a destructive LQ–SM interference term. While they can
also yield $R_{\mu\mu/ee}^{SM+LQ}/R_{\mu\mu/ee}^{SM}<1$ at large
$m_{\ell\ell}$ values for sizable LQ contributions, the destructive
interference then results in deviations
$R_{\mu\mu/ee}^{SM+LQ}/R_{\mu\mu/ee}^{SM}>1$ for intermediate invariant masses
($m_{\ell\ell}\approx 500$ GeV) leading to a fit that is worse than the one of
the SM. The representations with couplings
$\tilde{\lambda}_{2},\kappa_{1}^{R},\kappa_{2}^{LR},\tilde{\kappa}_{2}$ also
lead to destructive interference with the SM, but they feature smaller
interference terms. In these cases, $R_{\mu\mu/ee}^{SM+LQ}/R_{\mu\mu/ee}^{SM}$
is only slightly larger than 1 for intermediate $m_{\ell\ell}$, allowing still
for a good fit to the data.

Taking into account the other exclusion limits already presented in Ref.
Crivellin et al. (2021a), we see from Fig. 2 and 3 that the representations
with the couplings $\tilde{\lambda}_{1}$, $\lambda_{2}^{LR}$,
$\lambda_{2}^{RL}$, $\tilde{\kappa}_{1}$, $\kappa_{2}^{RL}$ and $\kappa_{3}$
can account for the CMS measurement without violating other bounds, since
these representations interfere constructively with the SM such that small LQ
contributions are sufficient to explain the excess in electron pairs.
$\lambda_{2}^{LR}$ and $\kappa_{3}$ are potentially in slight tension with the
neutral meson mixing or rare kaon decays, depending on the CKM mixing angle
$\beta$. However, in case of alignment to the up sector, and allowing for
fine-tuning in $D^{0}-\bar{D}^{0}$ mixing, $V_{3}$ could not only account for
the CMS data, but also explain the Cabbibo angle anomaly. Although the
representations with the couplings
$\tilde{\lambda}_{2},\lambda_{3},\kappa_{1}^{R},\kappa_{2}^{LR}$ and
$\tilde{\kappa}_{2}$ explain the CMS data, they are excluded by parity
violation, $K^{+}\to\pi^{+}\nu\bar{\nu}$, or the ATLAS Drell-Yan measurement.
Except for $\lambda_{3}$, these representations all interfere destructively
with the SM, requiring excluded lower values of $\hat{m}/\hat{\lambda}$
(corresponding to larger LQ contributions) to explain the electron excess at
high $m_{\ell\ell}$.

##  V Conclusion

In this addendum we examined the impact of the CMS measurement on LFU
violation in non-resonant di-lepton pairs. We found that the first generation
LQs with the couplings
$\tilde{\lambda}_{1},\lambda_{2}^{LR},\lambda_{2}^{RL},\tilde{\lambda}_{2},\lambda_{3},\kappa_{1}^{R},\tilde{\kappa}_{1},\kappa_{2}^{LR},\kappa_{2}^{RL},\tilde{\kappa}_{2}$
and $\kappa_{3}$ provide better fits to the CMS data than the SM with
$\Delta\chi^{2}\approx-11$. Among these, $\tilde{\lambda}_{1}$,
$\lambda_{2}^{LR}$, $\lambda_{2}^{RL}$, $\tilde{\kappa}_{1}$,
$\kappa_{2}^{RL}$, $\kappa_{3}$ feature constructive interference with the SM
and are consistent with all other available measurements. In case of alignment
to the up sector and allowing for fine-tuning in $D^{0}-\bar{D}^{0}$ mixing,
$V_{3}$ could not only account for the CMS data, but also explain the Cabbibo
angle anomaly.

###### Acknowledgements.

A.C. is grateful to Emanuele Bagnaschi for bringing the CMS analysis to his
attention. The work of A.C. is supported by a Professorship Grant
(PP00P2_176884) of the Swiss National Science Foundation. L.S. is supported by
the “Excellence Scholarship & Opportunity Programme” of the ETH Zürich. A.C.
thanks CERN for the support via the Scientific Associate program.

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