Search for Charged Lepton Flavour Violation at CMS

. Lepton ﬂavour is a conserved quantity in the standard model of particle physics, but it does not follow from an underlying gauge symmetry. After the discovery of neutrino oscillation, it has been established that lepton ﬂavour is not conserved in the neutral sector. Thus the lepton sector is an excellent place to look for New Physics, and in this perspective the Charged Lepton Flavour Violation is interesting. Various extensions of the standard model predict lepton ﬂavour violating decays that can be observed at LHC. This report summarises several searches for lepton ﬂavour violation with data collected by the CMS detector.


Introduction
Lepton flavour conservation in the standard model (SM) of particle physics does not follow from any underlying gauge symmetry.From neutrino oscillation, its violation in the neutral sector is already known.Neutrino oscillation allows, in principle, charged lepton flavour violation (LFV) but the large mass di↵erence between neutrinos and heavy gauge bosons suppresses such interactions to orders of magnitude, which is immeasurable by any existing experimental setup.However, extensions of the SM can lead to significant enhancements of processes involving charged LFV.Charged LVF processes can be directly related to neutrino masses and mixing and therefore are very promising to find evidence for physics beyond the SM.At CMS [1], several searches for charged LFV have been performed in di↵erent channels and final state topologies.Search for heavy majorana neutrinos and R-parity violating (RPV) supersymmetry (SUSY) are particularly important.Another interesting scenario is where LFV Higgs boson decays become amplified in models assuming the validity of the SM only up to a finite scale.Other possibilities are models involving more than one Higgs doublet or models predicting leptoquarks.
During LHC Run-I, a multitude of searches for the charged LFV have been performed by the CMS collaboration at proton-proton centre-of-mass energies of 7 and 8 TeV.The increase of the energy in Run-II to p s = 13 TeV has lead to a substantial increase in sensitivity.As a consequence, the mass reach for some of the searches was substantially extended after the analysis of data taken in 2015.However, this was not true for all models since the integrated luminosity recorded in 2015 was only about 1/10th of the one of Run-I.In 2016, the LHC did a fantastic job, exceeding expectations, reaching an instantaneous luminosity of 1.5 ⇥ 10 34 cm −2 sec −1 .The CMS experiment collected data with more than 92% efficiency and approximately 36 fb −1 of integrated luminosity were collected for physics.The high instantaneous luminosity comes at the price of pileup, the number of overlapping proton-proton interactions in one bunch crossing.In 2016 an average of 24 pileup interactions was observed.However, CMS have developed sophisticated tools to mitigate the e↵ect of pileup at the trigger and object reconstruction level.
In this report, some of the important searches related to charged LFV with the CMS experiment is described in brief.

Lepton flavour violating decays of Higgs boson
In SM, the LFV decays are forbidden if the theory has to be renormalizable.If this requirement is relaxed, so the theory is valid only to a finite mass scale, then LFV couplings may be introduced.LFV decays can occur naturally in models with more than one Higgs doublet without abandoning renormalizability.They also arise in supersymmetric models, composite Higgs boson models, models with flavour symmetries, Randall-Sundrum(RS) models and many others.The presence of LFV couplings would allow µ !e, ⌧ !µ and ⌧ ! e transitions to proceed via a virtual Higgs boson.

H ! µ⌧
The search is based on a dataset of 35.9 fb −1 of proton-proton collisions collected with the CMS detector in 2016, at a center-of-mass energy of 13 TeV [2].The decay channel, H ! µ⌧ µ , is not  .The expected (red solid line) and observed (black solid line) limits are derived from the limit on B(H !µ⌧).The flavour diagonal Yukawa couplings are approximated by their SM values.The green (yellow) band indicates the range that is expected to contain 68% (95%) of all observed limit excursions from the expected limit.The shaded regions are derived constraints from null searches for ⌧ !3µ (dark green) and ⌧ !µγ (lighter green).The purple diagonal line is the theoretical naturalness limit.considered due to the large background contribution from Z !µµ decays.The indirect constraint, B(H !µ⌧) < O(10%) is not very stringent, hence this direct search is very important.In this search, a loose selection is first applied, and then the events are divided into categories according to the number of jets in the event.The 0-jet category enhances the gluon fusion contribution and the 1-jet category enhances gluon fusion production with initial state radiation.The 2-jet gluon fusion category has a further requirement that the invariant mass of the two jets M jj < 550 GeV while the 2-jet VBF category with the requirement M jj > 550 GeV enhances the VBF contribution.After the loose selection a set of eight kinematic variables is combined into a boosted decision tree (BDT).The signal used for training the BDT is a mixture of simulated gluon fusion and VBF events, weighted according to their respective production cross sections.In µ⌧ h channel, the background used for training is a collision data sample of misidentified lepton events.This is the dominant background in this channel.In µ⌧ e channel, the background used for training is a mixed sample of t t and Drell-Yan events weighted by their cross-sections.A binned likelihood is used to fit the distributions of the BDT output for the signal and the background contributions.No significant excess over the standard model background expectation is observed.The observed (expected) upper limits on the branching fraction of the Higgs boson are found to be B(H !µ⌧) < 0.25(0.25)%The new results exclude the branching fraction that corresponded to the best fit for the 2.4σ excess observed in the 8 TeV H ! µ⌧ channel at 95% CL.The observed and median expected 95% CL upper limits are given for each category in Figure 1-left.The constraints on branching fraction can be interpreted in terms of LFV Yukawa couplings, as shown in Figure 1  .The expected (red solid line) and observed (black solid line) limits are derived from the limit on B(H !µ⌧).The flavour diagonal Yukawa couplings are approximated by their SM values.The green (yellow) band indicates the range that is expected to contain 68% (95%) of all observed limit excursions from the expected limit.The shaded regions are derived constraints from null searches for ⌧ !3e (dark green) and ⌧ !eγ (lighter green).The purple diagonal line is the theoretical naturalness limit.

H ! e⌧
The search is based on 35.9 fb −1 data collected with CMS in 2016, at a center-of-mass energy of 13 TeV [2].The decay channel, H ! e⌧ e , is not considered due to the large background contribution from Z boson decays.The indirect constraint, B(H !e⌧) < O(10%) is not very stringent.The BDT analysis strategy is very similar to the µ⌧ analysis.The same categorisation is performed here as well.In e⌧ h channel, the similar BDT training samples as µ⌧ h analysis are used.In e⌧ µ channel, the background used for BDT training is a sample of simulated t t events.No significant excess over the standard model background expectation is observed.The observed (expected) upper limits on the branching fraction of the Higgs boson are found to be B(H !e⌧) < 0.61(0.37)%.The observed and median expected 95% CL upper limits are given for each category in Figure 2-left.The constraints on branching fraction can be interpreted in terms of LFV Yukawa couplings, as shown in Figure 2-right.for µ !eγ strongly constrains this channel, B(H !eµ) < O(10 −8 ).However, this limit can be degraded by the cancellation of lepton flavour violating e↵ects from other new physics.The direct search for H ! eµ decays presented here is therefore complementary to indirect limits obtained from searches for rare decays at lower energies.To enhance the signal sensitivity, events are categorised into nine di↵erent categories according to the region of detection of the leptons and the number of jets, and further two categories enriched in VBF production.The dominant background contributions in this search are from Drell-Yan production of ⌧ lepton pairs and electroweak diboson production.

H ! eµ
No LFV signal observed in this analysis.An exclusion limit on the branching fraction B(H !eµ) with M H = 125 GeV is derived using the CLs asymptotic model.It is shown in Figure 3-left.The expected upper limit is B(H !eµ) < 0.048% and the observed upper limit is B(H !eµ) < 0.035% at 95% confidence level.These limits are used to constrain the corresponding flavour violating Yukawa couplings, as shown in Figure 3-right.

Search for stop pair production
Natural SUSY models feature pair production of stops that decay to a number of final states.To fully test supersymmetric naturalness, searches for all possible decay chains should be carried out.These can be broadly categorized as R-parity conserving (RPC) or violating (RPV) scenarios, where R-parity is defined by R = (−1) 3B+L+2s , where B and L are the baryon and lepton numbers, and s is the spin of the particle.All SM particle fields have R = +1 while all superpartner fields have R = −1.
When R-parity is conserved, superpartners are produced in pairs, the lightest superpartner (LSP) is stable and a dark-matter candidate, and proton stability is ensured.Supersymmetric models with RPV interactions violate either B or L but can avoid proton decay limits.The RPV interactions allow for single production of SUSY particles (sparticles) and for sparticle decay into SM only particles.
To demonstrate how natural SUSY might manifest itself with RPV couplings, a stop RPV model is examined.In this model, the stop decays to a top quark and intermediate on or o↵ shell bino.The   With the observed result, where the bino mass is 200 GeV, models with the stop mass below 1020 GeV is excluded when λ 122 is non-zero, and below 820 GeV is excluded when λ 233 is non-zero.

High mass eµ search
A search for heavy resonances decaying into eµ final states has been performed using an integrated luminosity of 2.7 fb −1 of 13 TeV proton-proton collision data recorded with the CMS detector in 2015 [5].The search is designed in a model-independent way by only requiring one prompt muon Figure 6.Left: 95% CL upper limit on the signal cross section times branching fraction for the RPV ⌧ sneutrino signal as a function of the mass of the resonance [5].Right: 95% CL upper limit on the signal cross section times branching fraction for the QBH signal as a function of the threshold mass [5].and one prompt electron in the event selection.The main sources of background are t t and WW processes.No evidence for physics beyond the SM is observed in the invariant mass spectrum of selected eµ pairs.To interpret the results, two di↵erent signal models are used.One is the RPV SUSY, where the ⌧ sneutrino signal gives rise to a narrow resonance.A mass hierarchy of supersymmetric particles, where the ⌧ sneutrino is the LSP, is assumed.In this model, the ⌧ sneutrino can decay either into the final state under study, an eµ pair, via the couplings λ 132 and λ 231 or into d d via the coupling λ 0 311 .For simplicity, we assume λ 132 = λ 231 in all the presented results.Another theoretical interpretation is the Quantum blackhole (QBH) signal that exhibits a broader signal shape with a sharp edge at the threshold mass M th .Theories that allow for a fundamental Planck scale at the TeV scale o↵er the possibility of the production of microscopic black holes at the LHC.The production of a spin-0, colourless, charge-neutral QBH is considered, in a model with lepton flavour violation.In absence of any significant excess, the 95% CL limits on the signal cross section times branching ratio are calculated.For RPV ⌧ sneutrino resonance signal, they are shown in Figure 6-left and the limits for the QBH signal are shown in Figure 6

Heavy Majorana Neutrino
Several extensions of the SM to address neutrino masses have been proposed so far, among which the seesaw mechanism is an appealing possibility.The seesaw mechanism introduces new heavy particles coupling to leptons and to the Higgs doublets, and accounts for the expected smallness of neutrino masses.Within the type-III seesaw model, the neutrino is considered a Majorana particle whose mass arises via the mediation of new massive fermions.These massive fermions are an SU(2) triplet of heavy Dirac charged leptons and a heavy Majorana neutral lepton.In proton-proton collisions, these massive fermions may be pair-produced through electroweak interactions in both charged-charged and charged-neutral pairs.A search for type-III seesaw signal in events with three or more electrons or muons is performed with 35.9 fb −1 of data at 13 TeV collected by the CMS experiment in 2016 [6].Decays of heavy fermion pairs result in 27 di↵erent production processes and can naturally lead to  [6].Right: The 95% confidence level upper limits on the cross section for production of heavy fermion pairs [6].Also shown is the theoretical prediction for the cross section of the heavy fermion pair production via the type III seesaw mechanism, with its uncertainty.In the flavour-democratic scenario (B e = B µ = B ⌧ ), heavy fermion pair production is excluded for masses below 840 GeV.multi-lepton final states, via decays of W, Z or H bosons.An example Feynman diagram for one of the most relevant processes with three leptons in the final state is shown in Figure 7-left.As can be seen from the Feynman diagram, there is no LFV in the process itself, but the existence of a heavy fermion can enhance LFV processes like µ !eγ.The selected multi-lepton events are classified into statistically independent search channels using the number of leptons, lepton flavour and charge combinations, and other kinematic quantities.The number of opposite-sign-same-flavour(OSSF) pairs are counted, where the pairs are made using each lepton only once.Events are further classified in three categories as on-Z, below-Z, and above-Z, based on the presence of at least one OSSF pair with mass in the Z-mass window, below 81 GeV, or above 101 GeV, respectively.No statistically significant excess was found in the various signal regions that was probed.Assuming a flavourdemocratic scenario, 95% confidence level upper limit on the cross section sum for the production of heavy fermion pairs is calculated, using the the CLs method.Based on the observed cross section limits, the production of heavy fermion pairs are ruled out for masses less than 850 GeV (expected 790 GeV), as presented in Figure 7-right.

Conclusion
Some results on searches for charged lepton flavour violation, performed by the CMS experiment, using 8 TeV and 13 TeV pp collision data is presented.No significant excess has been observed in any of the searches and no hint of BSM has been found.This could be an indication that new physics beyond the Standard Model occurs at higher scales than the TeV scale.More precise answers can come only from indirect new physics probes, like precision studies of neutrinos and their properties, muon anomalous magnetic moment and searches for forbidden or suppressed processes like charged LVF.However, from the current searches, the limits are significantly extended with respect to previously published results.Further searches in more complicated final states are underway.

Figure 1 .
Figure 1.Left: Observed and expected 95% CL upper limits on the B(H !µ⌧) for each individual category and combined [2].Right: Constraints on the flavour violating Yukawa couplings, |Y µ⌧ | and |Y ⌧µ | [2].The expected (red solid line) and observed (black solid line) limits are derived from the limit on B(H !µ⌧).The flavour diagonal Yukawa couplings are approximated by their SM values.The green (yellow) band indicates the range that is expected to contain 68% (95%) of all observed limit excursions from the expected limit.The shaded regions are derived constraints from null searches for ⌧ !3µ (dark green) and ⌧ !µγ (lighter green).The purple diagonal line is the theoretical naturalness limit.

Figure 2 .
Figure 2. Left: Observed and expected 95% CL upper limits on the B(H !e⌧) for each individual category and combined [2].Right: Constraints on the flavour violating Yukawa couplings, |Y e⌧ | and |Y ⌧e | [2].The expected (red solid line) and observed (black solid line) limits are derived from the limit on B(H !µ⌧).The flavour diagonal Yukawa couplings are approximated by their SM values.The green (yellow) band indicates the range that is expected to contain 68% (95%) of all observed limit excursions from the expected limit.The shaded regions are derived constraints from null searches for ⌧ !3e (dark green) and ⌧ !eγ (lighter green).The purple diagonal line is the theoretical naturalness limit.

AFigure 3 .
Figure 3. Left: 95% CL upper limits by category for H ! eµ decay for categories combined by number of jets, the VBF categories combined and all categories combined [3].Right: Constraints on the flavour violating Yukawa couplings |Y eµ | and |Y µe | [3].The expected (red solid line) and observed (black solid line) limits are derived from the limits on B(H !eµ) from the present analysis.The flavour diagonal Yukawa couplings are approximated by their SM values.The green (yellow) band indicates the range that is expected to contain 68% (95%) of all observed limit excursions.The shaded regions are derived constraints from null searches for µ?eγ (dark green), µ !3e (light blue) and µ ! e conversions (grey).The purple diagonal line is the theoretical naturalness limit.

Figure 4 .
Figure 4. Left: Feynman diagram for RPV coupling λ 122 .Right:The 95% confidence level limits in the stop and bino mass plane for models with RPV coupling λ 122[4].The region to the left of the curve is excluded.

Figure 5 .
Figure 5. Left: Feynman diagram for RPV coupling λ 233 .Right:The 95% confidence level limits in the stop and bino mass plane for models with RPV coupling λ 233[4].The region to the left of the curve is excluded.

Figure 7 .
Figure 7. Left: Feynman diagram example of the heavy fermion production and decay in the type-III seesaw model[6].Right: The 95% confidence level upper limits on the cross section for production of heavy fermion pairs[6].Also shown is the theoretical prediction for the cross section of the heavy fermion pair production via the type III seesaw mechanism, with its uncertainty.In the flavour-democratic scenario (B e = B µ = B ⌧ ), heavy fermion pair production is excluded for masses below 840 GeV. -right.