Searches for BSM physics in dilepton, multilepton and lepton + MET ﬁnal states at CMS

. Numerous new physics models, e.g., theories with extra dimensions and vari-ous gauge-group extensions of the standard model, predict the existence of new particles decaying to dilepton, multilepton, and lepton + MET ﬁnal states. This talk presents the recent results from searches for new physics in the leptonic ﬁnal states at CMS.


Introduction
Many Beyond Standard Model (BSM) physics models foresee the appearance of particles at high mass range, decaying into dilepton, multilepton and lepton + neutrino final states. Leptons considered in these searches are electrons and muons; neutrinos are revealed as missing transverse energy in the detector (E miss T ). The leptonic final states are historically channels of discovery and precision measurements, because they show very clean signatures; dealing with high energetic leptons coming from heavy resonances, however, implies careful studies of the objects and their properties. Generally these models predict very small branching ratio for leptonic decays: as a consequence, the statistical uncertainties dominate, so it is necessary to accurately evaluate the backgrounds. Results obtained from the LHC Run 2 data collected in 2015 by the CMS experiment [1] are presented: going up to √ s = 13 TeV makes the parton luminosities of processes qq → X increase substantially, especially at high mass region, improving the previous limits set on these models by LHC Run 1 data. [2]- [5] 2 CMS detector CMS is a multi-purpose experiment composed of many sub-systems enclosed in a superconducting magnet. Informations coming from different sub-detectors can be used together to improve the energy and momentum determination of the particles involved.

High energy objects
As a general approach, isolation requirements are applied to charged leptons, in order to reduce backgrounds coming from objects (mainly jets) misidentified as leptons. A lepton is isolated if the ratio of the energy deposits around its track divided by its transverse momentum (p T ) is below a certain threshold. a e-mail: lisa.benato@cern.ch

Muons
Muons are challenging objects to reconstruct at high energy values: in these conditions, their trajectory in the magnetic field is almost straight, complicating the determination of their p T and charge. The precision of their p T measurement, furthermore, is strongly influenced by the alignment of the external muon gas detectors and the inner silicon tracker. In addition, high energetic muons radiate in the detector materials, causing a loss of resolution at increasing p T . Many studies in this sense have been performed on the cosmic muons collected by CMS. Different high-p T muon reconstruction algorithms have been exploited: they generally combine informations from muon chambers and tracker, in order to improve the identification efficiency as much as possible and to discard the segments in the muon chambers where radiactive phenomena occurred.

Electrons
Electrons are reconstructed using informations coming from all the sub-detectors. Dedicated selections for high-p T electrons are applied in these analyses, in order to achieve the highest detection efficiency. Unlike muons, electron energy and p T resolutions are approximatively constant at increasing energy.

E miss T
The experimental signature of the presence of a non-interacting particle, the neutrino, is represented by the missing transverse energy, E miss T . The quantity p miss T is defined as the negative sum −Σ p T of all reconstructed particles; E miss T is the modulus of p miss T . Its magnitude is influenced by all the other objects, including jets and their corrections.

Heavy spin-1 BSM bosons searches in dilepton and lepton plus E miss T final states
A common feature of models admitting new physics consists into enlarging the Standard Model gauge symmetry group, S U(3) × S U(2) × U(1), into a larger one that, once broken into the SM group, will result into new residual groups: new spin-1 heavy bosons are expected to appear. The most naïf extension is the Sequential Standard Model [6], in which two W S S M and a Z S S M are expected to be the heavy replicas of W and Z bosons, with the same couplings to leptons as their standard model partners. More exotic spin-1 heavy bosons predicted by super string inspired models, like a Z Ψ coming from E(6) breaking [7]- [8], are searched for in the following analysis.

Z → + − [9]
The analysis strategy consists into reconstructing the invariant mass of the heaviest + − pair, after applying adequate selections to all the leptonic candidates, in order to suppress the background contributions in favour of the expected signal. The main source of irreducible background events is represented by the Drell-Yan process, Z/γ * → + − , that is well estimated by Monte Carlo simulated events. Monte Carlo simulations also work for the second category of backgrounds, which contains real prompt leptons coming from processes like tt, tW, WW, WZ, ZZ; these predictions are validated on data in eµ control region, where no signal is expected. Non-prompt backgrounds, that are objects (mainly jets) misidentified as leptons, are predicted via data-driven methods. are suppressed applying a cut on the impact parameter with respect to the primary vertex of the hard interaction and on the 3D angle between the muons.
The observed and the predicted SM backgrounds invariant mass spectra are shown in Fig. 1 for muons (left) and electrons (right). No discrepancy is seen among the two distributions. The highest mass event is observed in the electron channel, and it is located at 2.9 TeV. The expected number of events above 2.8 TeV is 0.036 ± 0.009 ee, 1 is seen. The local p-value for the null-hypothesis calculated as the Poisson probability to observe at least one event in the electron channel above 2.8 TeV is 0.036.       Limits at 95% confidence level on the ratio between the cross-section times branching ratio for the Z divided by the same quantity for the Z are extracted: The ratio cancels the luminosity uncertainties. A Bayesian unbinned likelihood approach is applied; the likelihood is integrated using the Metropolis-Hastings algorithm. The main uncertainties related to signal efficiency and cross-section are due to lepton identification (6% for electrons, 7% for muons). The background uncertainty comes mainly from PDF uncertainties (up to 20% at 3 TeV). A mass scale uncertainty (1% for e, 3% for µ) is applied while combining the channels. The signal is modelled as the convolution of a Breit-Wigner and a Gaussian distribution, under the narrow width approximation: this means that only the on-shell region of the resonance is considered, because the interference is strongly model-dependent. In Fig. 2 (left), expected and observed limits for different signal widths are shown, ranging from 0%, to 0.6% of the expected resonance mass (as predicted by Z Ψ ), to 3% of the mass (as predicted by Z S S M ), combining the e and µ channel. The final expected and observed limits for the combination of electron and muon channels under the hypothesis of a width of 0.6% are displayed in the right panel of Fig. 2 Left: 95% confidence level observed and expected limits on the cross-section ratio for different resonance widths; they are obtained combining the electron and muon channels. Right: limits set at 95% confidence level for a Z whose natural width is the 0.6% of its mass. The theoretical curves of the discussed models are included in the plots. In this analysis, since a neutrino is expected in the final state, the discriminant variable is the transverse invariant mass, which takes into account only the transverse quantities: In order to achieve a back-to-back topology between the lepton and the neutrino, a cut is applied on their azimuthal angles, |∆φ( p T , p miss T )| > 2.5. A further selection, 0.4 < p T /E miss T < 1.5, allows to reject background contamination.
The dominant source of background is represented by the standard model W → ν process, and it is fully predicted by Monte Carlo simulations. Secondary backgrounds like Drell-Yan processes, tt, single t, WW, WZ, ZZ are also taken from simulations. QCD multijet backgrounds are estimated from data. Cosmic muons contamination is suppressed with a cut on impact parameter with regards to the primary vertex, like in the previous analysis.
In Fig. 3, the transverse mass distributions are shown for muon (left) and electron (right) channel. Data and Monte Carlo spectra are in agreement.
Limits at 95% confidence level on cross-section σ(pp → W + X → ν + X) are extracted via the modified frequentist approach (CL s method [11]- [12]). Limits are provided in a region over 1 TeV, where Run 2 data are more sensitive due to the increased center of mass energy and, consequently, increased cross-section for the considered process. The main uncertainties in the muon channel arise  from the muon momentum scale and p T resolution, that both propagate to E miss T , as pointed out in Sec. 3.1 and 3.3. The electron channel is mainly affected by PDF uncertainties, especially at high M T .
The expected and observed limits for the cross-section obtained combining the two channels are shown in Fig. 4; the final limits on the W S S M mass for each channel are summarized in Tab. 2.

Seesaw type-III mechanism search in multilepton final states [13]
A remarkable puzzle left unsolved by the Standard Model is related to neutrino masses. An appealing possibility is represented by the seesaw mechanism: it introduces new heavy particles coupling to leptons and to Higgs doublets, accounting for both the neutrino masses and their smallness (six or more orders of magnitude smaller than that of the electron). In particular, in the type-III seesaw model [14], the neutrino is considered a Majorana particle whose mass arises via the mediation of a massive fermionic triplet, composed by the heavy Dirac charged Σ ± , and the heavy Majorana neutral Σ 0 . In high energy proton-proton collisions, the heavy fermions may be produced in pairs through electroweak interactions. In this search, a final state with at least three charged leptons (electrons or muons) is considered: the heavy triplet can decay into leptons via electroweak or Higgs bosons. In Fig. 5, one of the 27 possible decay modes is pictured. The decay rate of a Σ to a particular flavour is proportional to where each V represents the coupling of the heavy fermion to the considered leptonic flavour. In the flavour democratic scenario, V is the same for e, µ and τ. Figure 5. Seesaw type-III search. Feynman diagram example of the fermion Σ production and decay in leptonic final states in the context of the type-III seesaw model. The analysis strategy is based on grouping the final states in categories, depending on the number of reconstructed leptons, the number of opposite sign same flavour pairs (OSSF), zero, one or two, and on the invariant mass of the pair, on or under-above the nominal mass of the Z boson. A promising cut that has been studied to reject backgrounds is the scalar sum of the p T of all the considered leptons, L T , added to E miss T , requiring L T + E miss T > 350 GeV: this guarantees high efficiency for both channels involving decays where the momentum is carried by leptons, like Σ ± → Z ± → ± + − , and decays where there is a large amount of missing transverse energy, like Σ 0 → Hν → WWν. Considering the most significant channels in terms of expected signal given the luminosity, the analysis consists in keeping 4 distributions, depending on the lepton properties: 3 leptons without an OSSF pair, 3 leptons with one OSSF pair on-Z, 3 leptons with one OSSF pair above-Z, and 4 leptons with at least one OSSF pair. In left Fig.6, the spectrum of L T + E miss T for the category 1 OSSF pair, 3 leptons, m + − above-Z is displayed, whilst in right Fig.6 there is the spectrum for the category where there is at least 1 OSSF, 4 leptons, no requirements on m + − : it is noticeable that the statistics is very low. Data and Monte Carlo spectra are in agreement.
Backgrounds strongly depend on the categories considered. 51% of the total expected background is represented by the standard model decay WZ → and validated on data. The kinematics of the leptonic tt decays, with a misidentified lepton from a b-jet, is predicted by Monte Carlo samples; the misidentification rate, instead, is measured in data control region. Z → plus a misidentified lepton in jet is predicted with a data-driven method. Other processes, like ZZ → 4 , ttZ, ttW, H → 4 , are evaluated via Monte Carlo simulations.
Limits at 95% confidence level on the cross-section sum for the production of seesaw heavy fermionic pairs Σ 0 Σ + , Σ 0 Σ − , Σ + Σ − and on their mass are extracted with the asymptotic CL s method, under the assumptions of a degenerate m Σ , and of the flavour democratic scenario, where V e = V µ = V τ = 10 −6 . They are reported in Fig. 7 and in Tab. 3. The p-value for the observation in all the considered channels, assuming there is no new physics, is 0.93. The uncertainties are strongly dominated by statistics; systematic uncertainties are small and mainly due to PDF and to renormalization and factorization uncertainties related to E miss T range in the dominant WZ background.   [15] Many extensions of the Standard Model predict the existence of heavy resonances decaying into lepton flavour violating final states, like eµ. If a fundamental Planck scale could be observable at TeV, the production of microscopic black holes decaying into couples of particles should be possible at the LHC, once the production mass threshold M th is reached. In particular, in the considered models [16]- [17], quantum black holes (QBH) are spin-0, colourless, neutral particles, and lepton flavour violation is allowed. A search in this sense has been performed; the interpretation of the results depends on the number of extra-dimensions n involved: for n = 1, a Randall-Sundrum scenario is considered, while for n ≥ 2, we lay in the ADD scenarios.
The analysis strategy consists in reconstructing the invariant mass distribution of the eµ pairs, without requiring to the leading leptons to be opposite sign, in order to avoid an efficiency loss due to the wrong assignment of the electron charge in high energy range. The misidentification of the objects involved is reduced by rejecting all the electrons close (in a cone ∆R < 0.1) to muons that produce bremsstrahlung. In left Fig.8, the invariant mass spectrum of the eµ pairs is presented; the right plot is the cumulative distribution of the previous one. Data and Monte Carlo spectra are in agreement.
The backgrounds contributing to the final state can be divided into two categories: the first comprises events with at least two prompt, isolated leptons; the second includes jets and photons misidentified as isolated leptons or jets with non-prompt leptons coming from heavy-flavour decays. In the former category, processes like tt, WW, WZ, ZZ, single t, Drell-Yan are included, and they are estimated from Monte Carlo samples; in the latter category, the dominant contribution is represented by W + jets processes, and all these backgrounds are predicted with data-driven methods.
An upper limit at 95% confidence level on the cross-section times branching ratio is determined using a binned likelihood Bayesian approach, and it is shown in Fig. 9. The non-resonant signal is modelled as a broad shape smeared by the detector resolution, with a sharper edge at M th . The uncertainties, entering the limit extraction as nuisance parameters, are modelled with log-normal distributions. The uncertainty on the muon momentum scale (10% per TeV) propagates to an uncertainty on the background yield of 30% at 3 TeV. The dominant uncertainty in the background yield prediction is due to the uncertainty on the shape of the eµ distribution in the tt background, that ranges up to 31% at 2 TeV. The final limits on the threshold mass of the QBH are reported in Tab. 4, as a function of the extra-dimensions considered in the theoretical model.   Figure 9. Quantum black holes in eµ search. Expected and observed limits at 95% confidence level on the crosssection times branching ratio for the quantum black hole production. The theoretical curves of the discussed models are included in the plot.

Conclusions
The LHC collider is facing its "search era": searching for heavy resonances predicted by BSM models that decay into leptons and neutrinos is considered a high-priority task nowadays. Many searches have been performed during Run 2 in 2015 by the CMS collaboration: the increased √ s allowed improvements with regards to Run 1 analyses, pushing the exclusion limits to higher masses of the