Search for heavy neutral leptons in decays of W bosons produced in 13 TeV pp collisions using prompt and displaced signatures with the ATLAS detector

The problems of neutrino masses, matter-antimatter asymmetry, and dark matter could be successfully addressed by postulating right-handed neutrinos with Majorana masses below the electroweak scale. In this work, leptonic decays of W bosons extracted from 32.9 fb−1 to 36.1 fb−1 of 13 TeV proton–proton collisions at the LHC are used to search for heavy neutral leptons (HNLs) that are produced through mixing with muon or electron neutrinos. The search is conducted using the ATLAS detector in both prompt and displaced leptonic decay signatures. The prompt signature requires three leptons produced at the interaction point (either μμe or eeμ) with a veto on same-flavour opposite-charge topologies. The displaced signature comprises a prompt muon from the W boson decay and the requirement of a dilepton vertex (either μμ or μe) displaced in the transverse plane by 4–300 mm from the interaction point. The search sets constraints on the HNL mixing to muon and electron neutrinos for HNL masses in the range 4.5–50 GeV.


Introduction
T he observation of neutrino oscillations implies that neutrinos are massive [ 1] . This requires the addition of a neutrino mass-generation mechanism to the Standard M odel (S M ), which can manifest itself in the form of right-handed neutrinos, M ajorana neutrinos, or both.
A dding a right-handed M ajorana neutrino (denoted by heavy neutral lepton HNL, or simply N ) gives rise to the so-called Type-1 Seesaw mechanism [2]. A n SM neutrino then acquires a mass inversely proportional to the HNL M ajorana mass, providing a natural explanation for neutrino masses and why they are so small com pared with those of other fermions.
Heavy neutral leptons could generate the observed amount of baryon asym m etry in the universe through a process known as leptogenesis [3], and an HNL with a mass o f the order o f keV would be a valid dark-m atter candidate [4]. In fact, the addition o f three HNLs with masses below the electroweak scale, two o f which are potentially accessible by accelerator-based experiments in the range 0 .1 -9 0 G eV [5], could address the three -1 -

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fundamental questions o f the origins o f neutrino masses, baryon asymmetry, and dark matter [6 , 7] . M eeting these conditions requires small mixing angles between HNLs and neutrinos. M ixing requirements are relaxed if all three HNLs can participate in generating a baryon asym m etry [8,9] , which means however that none o f the three HNLs is available as a dark-m atter candidate. D epending on the mixing and mass parameters, the HNL may decay prom ptly or be long-lived. In this paper, searches exploiting both prom pt-decay and displaced-decay signatures are reported.
Heavy neutral leptons with masses below 5 G eV can be produced in hadron decays. In this case, sensitivity to small coupling strengths has been achieved by fixed-target experi ments with long decay volumes and by high-intensity collider experiments [10][11][12][13][14][15][16][17][18][19][20][21]. Higher HNL masses can only be directly accessed through the decays o f W , Z or H bosons, and indirectly through precision tests o f the SM. W ithin some assumptions about the relative HNL m ixing angles to the different neutrino flavours, experiments sensitive for processes such as y ^ eY or y ^ eee can provide indirect constraints which are com petitive with direct searches for HNL masses above 3 0 G e V [22]. A n analysis with the D ELPH I ex periment at LEP1 using ^1 0 6 neutrinos from Z boson decays provided the best direct constraints prior to the LH C in the HNL mass range 2-75 G eV [23]. At hadron colliders, HNLs are better sought in W rather than Z boson decays due to trigger requirements and the higher production cross section. The CM S C ollaboration presented results [24] which explore HNL masses in the range 1-1200 G eV and mixing to muon and electron neutrinos, T he uncertainty in the integrated luminosity is 2.1%, derived from the calibration o f the luminosity scale using x -y beam -separation scans, following a m ethodology similar to that detailed in ref. [30], and using the LU CID -2 detector for the baseline luminosity measure ments [31].
T he prom pt signature features three leptons originating from the interaction point, either two muons and an electron or two electrons and a muon, with same-flavour leptons o f the same charge. This latter requirement is im portant for rejecting the large backgrounds from prom pt SM processes. The displaced signature features a prom pt muon accom panied by a vertex significantly displaced from the interaction point, form ed by either two muons or a m uon and an electron. The prom pt lepton (expected to originate from a W boson decay) is essential for ensuring an efficient triggering o f such events and the displaced dilepton decay is very characteristic, rendering this signature virtually background-free. F igure 1. Feynman diagrams for N production and decay in the channels which this search is sensitive to: (a) p mixing, pe decay, LNC (probed by displaced signature); (b) p mixing, pp decay, LNC (probed by displaced signature); (c) p mixing, pe decay, LNV (probed by prompt and displaced signatures); (d) p mixing, pp decay, LNV (probed by displaced signature); (e) e mixing, ep decay, LNV (probed by prompt signature). Analogous processes involving the decay of the charge-conjugate W -boson are also included in the search, but omitted in this figure.

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The selection o f a prom pt muon and a displaced leptonic decay is chosen for the first search o f this type because requiring lepton objects (favouring muons as they are less readily affected by misidentification o f other objects than electrons) considerably reduces Q C D backgrounds, even though the same signature with a prom pt electron a n d /o r a displaced sem ileptonic decay can also be exploited at the LHC [25][26][27]. T he range 5 < m N < 5 0 G e V is explored using the prom pt signature assuming LN V. The range 4.5 < m N < 10 G eV , corresponding to decay lengths o f the order m m -c m , is probed dow n to lower |U|2 values using the displaced signature with HNL mixing to v^ without any assumption regarding LN C or LN V, as depicted in figures 1a, 1b, 1c and 1d.

H N L modelling
This section details N production via mixing with an electron or muon neutrino originating from an on-shell W boson decay, as well as its leptonic decays via the same mixing, as  This calculation and calculations found in the literature [5,36,37] can yield up to 5% rela tive differences, mainly due to different treatments o f Q C D corrections. This 5% difference is considered as a relative theoretical systematic uncertainty in the branching ratio.  [40].

E vent generation and sim ulation
Background processes were generated using P o w h e g -B o x [41][42][43] with the next-toleading order (N LO ) C T10 P D F set [44] for top-quark pair (tt) (using v 2 in r3026) and single top-quark (using r2856) production, in com bination with P y t h i a [45] (v6.428, for parton showering) using the C TE Q 6L1 P D F set [46] and Perugia 2012 tune [47]. M a d - For the generation o f t t events, the top-quark mass was set to 172.5 G eV . The sam ple is normalised using the next-to-next-to-leading-order (N N LO ) cross section, including soft-gluon resummation to next-to-next-to-leading-logarithm (N NLL) [54][55][56][57][58][59][60]. For events containing a W or Z boson with associated jets simulated using S h e r p a , m atrix elements were generated with up to two additional parton emissions at NLO accuracy and up to four additional parton emissions at LO accuracy using C O M I X [61] and O p e n L o o p s [62] and merged with the S h e r p a parton shower [63] according to the M E + P S @ N L O prescrip tion [64].

The A T L A S detector
T he A TLA S experiment [69][70][71] at the LHC is a m ultipurpose particle detector with a  T he MS is the outerm ost A T L A S subdetector. It is designed to detect muons in the pseudorapidity region up to |n| = 2.7, and to provide mom entum measurements with a relative resolution better than 3% over a wide pT range and up to 10% at pT ~ 1 TeV.
A system o f three large superconducting air-core toroidal magnets, each with eight coils, A two-level trigger system is used to select events [72]. The first-level trigger is imple mented in custom electronics and uses inform ation from the muon trigger chambers and the calorimeters. This is followed by a software-based high-level trigger system, which runs reconstruction algorithms similar to those used in offline reconstruction. Com bined, the two levels reduce the 40 MHz bunch-crossing rate to approxim ately 1 kHz o f events saved for further analysis.

P rom pt-trilepton signature
T he prom pt-lepton search for HNLs is conducted in two channels: W ± ^ y ± y ± e T ve (m uon channel) and W ± ^ e ± e ± y T v^ (electron channel). It considers the case where the vertex displacement is small enough that an ID track can be reconstructed with standard A T L A S tracking algorithms. The standard reconstruction o f tracks in the ID is optimised for charged particles that originate from the beam spot, the region where the proton beams intersect. This set-up restricts the detection for decay products o f particles whose decay vertex is significantly displaced from the beam spot, especially for transverse displacements greater than approxim ately 20 mm [73]. B y requiring the final state to have three isolated leptons and no opposite-charge same-flavour lepton pairs, background events from Drell-Yan pair production, W + je ts and t t could be rejected. T he different identification criteria "loose" , "m edium " and "tight" are defined in ref. [74]. To avoid assigning a single detector response to more than one reconstructed object, a sequential overlap-removal procedure is adopted. Jets are removed if found to be within A R = 0.2 o f an electron or muon track, unless they satisfy the b-tagging requirements.
In the electron channel, jets are not removed if their p t is at least 20% higher than that

R econstru ction and selection (prom pt signature)
All selected events are required to contain leptons which must satisfy flavour and charge requirements, such that the event consists o f exactly y ± y ± e T in the muon channel and e ± e ± y T for the electron channel. Furthermore, a requirement is im posed on the three-  Table 1. Signal region selection criteria for the prompt trilepton analysis.

Backgrounds and signal extraction (prom pt signature)
The SM backgrounds that can lead to the same signature as the one from the prom pt heavy An overview o f the criteria is given in table 3.
T able 3. Signal and control region selection criteria for the prompt HNL analysis and the corre sponding distribution used in the binned maximum-likelihood fit in the SR (criterion 0) and the three CRs (criteria 1-3). In addition, estimation regions corresponding to the SR and the three CRs are defined by requiring all leptons to have the same charge. Criteria 0-3 are all used for the SR. Only one of them is inverted to define the corresponding CR.   Further checks were conducted, including a p-value test in the signal region using normal isation factors as measured in the CRs. The p-values are determined without taking into account the fit parameters associated with statistical uncertainty in the SR and found to be 7.2% for the muon channel and 13.2% for the electron channel. As this lies above the usual rejection level o f 5%, the test is considered satisfactory. U pon using the background-only hypothesis normalised in both CRs and SR very g ood com patibility was found.   isolation and identification criteria as defined in ref. [75]. Another muon, which targets a displaced muon from an HNL decay, is required to satisfy a "loose" isolation criterion and for the M S-ID track matching, as defined in ref. [75]. The x 2/d o f selection is added to recover tracks which have relatively low d0 values but still correspond to a displaced muon.

Displaced-vertex signature
For instance, it could be that, during standard reconstruction, the MS track from a muon is incorrectly m atched to an unrelated ID track.

R econstru ction and selection (displaced signature)
Large-radius tracking is perform ed on the dataset which satisfies the preselection, producing

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(3 % ) and the integrated luminosity (2.2% ) are taken into account for the interpretation. T he total system atic uncertainty, with all contributions added in quadrature, is 24%.