Lepton-Jets and Low-Mass Sterile Neutrinos at Hadron Colliders

Sourabh Dube,1, ∗ Divya Gadkari,1, 2, † and Arun M. Thalapillil1, ‡

1Indian Institute of Science Education and Research,Homi Bhabha road, Pashan, Pune 411008, India.

2Department of Physics, LEPP, Cornell University, Ithaca, NY 14853, USA.(Dated: September 27, 2017)

Sterile neutrinos, if they exist, are potential harbingers for physics beyond the Standard Model.They have the capacity to shed light on our flavor sector, grand unification frameworks, dark mattersector and origins of baryon anti-baryon asymmetry. There have been a few seminal studies thathave broached the subject of sterile neutrinos with low, electroweak-scale masses (i.e. ΛQCD �mNR � mW±) and investigated their reach at hadron colliders using lepton jets. These preliminarystudies nevertheless assume background-free scenarios after certain selection criteria which are overlyoptimistic and untenable in realistic situations. These lead to incorrect projections. The uniquesignal topology and challenging hadronic environment also make this mass-scale regime ripe for acareful investigation. With the above motivations, we attempt to perform the first systematic studyof low, electroweak-scale, right-handed neutrinos at hadron colliders, in this unique signal topology.There are currently no active searches at hadron colliders for sterile neutrino states in this massrange, and we frame the study in the context of the 13 TeV high-luminosity Large Hadron Colliderand the proposed FCC-hh/SppC 100 TeV pp-collider.

I. INTRODUCTION

With the discovery of the Higgs-boson-like resonanceat the LHC [1, 2], we are very quickly approaching a de-tailed understanding of electroweak symmetry break-ing and mass generation in the SM. The presenceof fermion mass hierarchies (i.e. hierarchies amongthe Yukawa coupling constants) nevertheless remain amystery. The Yukawa couplings that span across manyorders of magnitude and the appearance of mass ratiosthat are seemingly very close to powers of the Cabibboangle (see for instance [3] and references therein) alongwith patterns in the quark and lepton mixing matricesseem to suggest that the flavor sector of the SM mayhave a rich underlying structure.

All the current experiments are largely consistentwith the existence of three neutrino electroweak eigen-states (νe, νµ, ντ ). Nevertheless, there have been a fewtantalising discrepancies from various short-baselineneutrino experiments [4–7] over the years. They haveoccasionally been very hard to accommodate in thethree active-neutrino picture, leading to many stud-ies incorporating additional singlet neutrino states tothe framework [8–22]. For instance, trying to accom-modate the LSND [4] and MiniBooNE [5] anomalies

∗ sdube@iiserpune.ac.in† divya.gadkari@students.iiserpune.ac.in‡ thalapillil@iiserpune.ac.in

with observations from solar and atmospheric neutrinomeasurements require ∆m2

sterile ∼ O(1) eV2. A similarmass squared difference is also seemingly required toreconcile the reactor anti-neutrino flux deficit [7], butthis interpretation has been weakened recently [23].On the other hand, embedding frameworks leadingnaturally to light neutrino masses, such as the see-sawmechanism [24], into grand unified models [25–33] fur-nishes singlet neutrino states that are extremely heavywith a mass O(1012−1016) GeV. These have the addedbenefit of mitigating, to some extent, fine-tuning of theneutrino Yukawa coupling constants. In these modelsYukawa couplings may be O(1) and the large hierar-chy in mass is subsequently generated, after mass diag-onalization. There are also intriguing models [34–37]with sterile neutrino states below the ΛQCD scale withmasses O(1) keV that may simultaneously be able toexplain structures in the lepton sector, provide dark-matter candidates as well as furnish a solution to thebaryon anti-baryon asymmetry observed in the uni-verse. Along with these considerations perhaps thereis also another aspect to be kept in mind – a smallright-handed neutrino mass (mM

νR) must be consideredtechnically natural, as emphasised by [38, 39], sincein the limit mM

νR → 0 one regains U(1)B-L as a globalsymmetry of the Lagrangian.

The above considerations suggest that a priori thereare perhaps no immutable reasons to expect the right-handed neutrino mass-scale to be at a particular value.Motivated by this realization it is reasonable to devise

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search strategies for sterile neutrinos that cover all pos-sible mass-scales.

There has indeed been endeavours to directly andindirectly search for sterile neutrino states across var-ious mass scales (see for instance [40–52] and associ-ated references). For instance, in [53] the sensitivity ofa future lepton collider to displaced vertex searcheswere investigated in final states e+e− → ν(N →l±jj, l+l−ν, . . .). A similar, earlier study [54] based ondisplaced vertices at the LHC investigated processessuch as pp → l±(N → l±X). Another study in [55]advocated looking for processes W+ → e+µ−e+νe andW+ → e+e+µ−νµ initiated by sterile neutrinos at theLHC; the latter being initiated only in the case of Ma-jorana sterile neutrinos. Studies such as [56] focusedon left-right symmetric models with a heavy WR, lead-ing to ‘neutrino-jet’ final states WR → l(N → ljj);where the N decay-products are collimated even formN � mW± . Recently, there have also been interest-ing studies attempting to constrain electroweak-scalesterile neutrinos through precision Higgs data [57] andhiggs decays [58]. A more complete discussion of cur-rent theoretical studies and limits, across various mass-scales, is contained in [43–47] and associated refer-ences.

The ATLAS and CMS collaborations have per-formed dedicated searches for heavy Majorana neutri-nos [59–62] in various channels. The CMS collabora-tion has looked for heavy sterile neutrinos in µ±µ±jj,e±e±jj and e±µ±jj final states at

√s = 8 TeV with

19.7 fb−1 of data [59, 60]. The ATLAS collaborationhas similarly searched for heavy Majorana neutrinosin the µ±µ±jj and e±e±jj channels at

√s = 8 TeV

using 20.3 fb−1 of collected data [61]. The CMS col-laboration has also recently set preliminary limits at√s = 13 TeV [62], with 2.3 fb−1 data, for heavy com-

posite Majorana neutrinos in final states with two lep-tons and two quarks. All the current LHC constraintsfor the l±l±jj channels are summarised in Fig. 1.

We are interested in probing a regime where the ster-ile neutrino states have a mass above the bottom-quarkmass (mb) but is at the same time well below mW±

ΛQCD � mb < mNR� mW± .

In this narrow mass-region, the existing constraintsare minimal and the signal topology is unique whilebeing challenging. We shall sharpen and motivate theregion of interest in more detail in Sec. III. The pro-totypical signal event is illustrated in Fig. 2. In thisregion the sterile neutrino is usually very boosted andthe decay products get collimated into a lepton jet.

0 100 200 300 400 500mN (GeV)

10 6

10 5

10 4

10 3

10 2

10 1

100

|lN

|2

eejj [ATLAS, 8 TeV, 20.3 fb 1]jj [ATLAS, 8 TeV, 20.3 fb 1]

eejj [CMS, 8 TeV, 19.7 fb 1] jj [CMS, 8 TeV, 19.7 fb 1]

e jj [CMS, 8 TeV, 19.7 fb 1]

FIG. 1. Current constraints on sterile-active mixing (|Uln|)from the ATLAS and CMS collaborations [59–61]. Therelevant final states being searched for are like-sign lep-tons with associated jets (l±l±jj) in all the present analy-ses. Few of the CMS limits go all the way to intermediatemasses of around 50 GeV. The preliminary limit from CMSfor√s = 13 TeV with 2.3 fb−1 of data [62] is not shown.

pp→ l± + (NR → Lepton Jet) +X (1)

There have been a few hadron collider studies specif-ically focused on this region [47, 63]. The pioneeringstudy [63] assumed a background-free search, employ-ing certain selection criteria, with cosmic-ray initiatedmuon bundles estimated based on an ATLAS analy-sis [66]; the latter looked for long-lived neutral par-ticles in LHC events with two lepton jets. Based onthese estimates, limits at 13 TeV LHC are set in thisregion, assuming an integrated luminosity of 300 fb−1.Similarly, the study pertaining to this mass-scale dis-cussed in [47] for pp-colliders, assumes that there areno backgrounds for 1 mm < cτ < 1 m vertex dis-placements. With this and a few other assumptions,the study estimates preliminary limits for the high-luminosity LHC (HL-LHC) at 13 TeV and the FCC-hh/SppC pp-collider at 100 TeV [64, 65]. They con-clude by acknowledging that a realistic estimate of thebackgrounds and sensitivities is very much required in

3

FIG. 2. In the mass regime of interest, mb < mNR �mW± , the main production channel at hadron collid-ers is through single-W± production and decay. SincemNR/mW± � 1 the leptons from the NR decay are colli-mated and form a displaced lepton jet in the relevant pa-rameter space [63]. The lepton from the initial W± decayis detected as a prompt lepton.

this mass-regime.

As we shall discuss in Secs. III and IV, the abovesearch methodologies, selection criteria and consider-ations regarding signal and backgrounds have to bedrastically modified under realistic conditions. Ouraim is to perform a systematic study in this mass-scaleregime and investigate realistic selection criteria thatoptimise searches for these light sterile neutrinos athadron colliders. Towards this aim we explore the dis-covery potential at the 13 TeV LHC and the proposedFCC-hh/SppC 100 TeV pp-collider [64, 65]. In this lowmass-scale regime the decay products from the right-handed neutrino get collimated into a narrow cone [63].As we elaborate in Secs. III and IV, we will thereforeoptimise for a topology consisting of a prompt leptonand a collimated set of muons, a muon lepton-jet.

One of the main constraints in the region of interestcomes from electroweak precision data [67–71]. To verygood approximation, the limits on active-sterile mixing(|UlN |2), from electroweak precision data, are found tobe almost independent of the sterile neutrino masses inthis region. At 90% confidence level they are approxi-mately given by |UeN |2 ≤ 3×10−4 , |UµN |2 ≤ 1.5×10−4

and |UτN |2 ≤ 13× 10−4 [45, 67–71].

The other major constraint in this mass regimecomes from limits on heavy sterile states produced inZ0 decays. The L3 [72] and DELPHI [73] collabo-rations have performed a reanalysis of the LEP data

in this context. The former sets a limit |UlN |2 .(0.7 − 1.0) × 10−4, corresponding to a limit on thebranching ratio Br(Z0 → νN) . 10−5 [74], in theregion of interest. The DELPHI analysis puts a limitBr(Z0 → νN) . 1.3 × 10−6 at 95% C.L. which corre-sponded to |UlN |2 . 10−5 [73].

In Sec. II, to clarify notations and put our study incontext, we briefly discuss the well known theoreticalmotivations for sterile neutrinos. Here, we also brieflyconsider models where low-mass right-handed neutri-nos could arise in a natural way. In Sec. III we thendiscuss the unique signal topology furnished by ster-ile neutrinos in the mass regime of interest and alsodiscuss aspects of the various relevant backgrounds.Then, in Sec. IV we present our analysis methodolo-gies and main results. We summarise our pertinentfindings in Sec. V.

II. RIGHT-HANDED STERILE NEUTRINOSAND THE STANDARD MODEL

The inexplicable and large hierarchies among thefermion masses manifests in its most extreme form inthe case of neutrinos. To clarify notations and set con-text we briefly consider the theoretical underpinningsbehind sterile neutrinos and specific models where low,electroweak-scale masses could be generated for thesestates.

Neutrino oscillation experiments only furnish infor-mation about mass-squared differences [75]. Throughcareful endpoint measurements of the tritium β-decayspectrum, Troitzk [76] and Mainz [77] experimentswere able to put an upper limit at 95% C.L. of about

mν < 2 eV . (2)

Light neutrinos play a significant role in cosmology,by effecting the expansion history and the growth ofprimordial structures, which in combination with otherastrophysical and cosmological observations, lead to aneven tighter bound [78–80]∑

mν < 0.23 eV .

The KATRIN experiment [81] is expected to reacha sensitivity close to mν < 0.2 eV as well.

All these observations suggest that the neutrinos inthe SM have a mass-scale in the sub-eV regime. Theneutrinos with SM quantum numbers thus seem tohave a mass-scale at least a million times smaller thanthe next heaviest fermion, the electron. If not an acci-dent of nature, these small neutrino masses beg for anexplanation.

4

In the standard model, the neutrinos have just a sin-gle left-helicity field associated with them and there-fore one cannot directly write a Dirac mass term in theusual way. One could of course extend the frameworkminimally by adding just a right-handed helicity neu-trino field, thereby giving neutrinos a Dirac mass afterelectroweak symmetry breaking1

Lmass ⊃ mD

ν (νLνR + νRνL) ≡ mD

ν νν . (3)

If this was the only contribution, the relevantyukawa coupling here has to be fine-tuned to a verysmall value, to be consistent with the sub-eV mass-scale of the neutrinos. The interesting observation isthat, since the right-handed neutrino field carries noSM charges, one is allowed to also write an additionalcontribution to the mass of the form

Lmass ⊃ mM

νR (νc

RνR + νRνc

R) ≡ mM

νR χχ , (4)

i.e. a Majorana mass term. Here, the charge con-jugation is defined as ψc = iγ2ψ∗, with the notationψc

R = (ψR)c and the Majorana field χ is defined to beχ = νR + νc

R. Note that a similar term with νL wouldbe forbidden in this minimal scheme due to SM gaugeinvariance – the νL field is part of the SU(2)L doubletwith non-zero hypercharge.

This additional contribution enables a novel way inwhich the very-small neutrino masses could be gener-ated – the so called see-saw mechanism [24]. As moti-vated above, in its simplest form it leads to a neutrinomass-matrix of the form

Mν =

(0 1

2mDν

12m

D Tν mM

νR

). (5)

Taking for example the simplest 1-flavor case, with a2× 2 mass-matrix, leads to mass-eigenvalues

m1,2 =1

2

[mM

νR ±√mM 2νR +mD 2

ν

], (6)

with two Majorana eigenstates

ν1 = χ cos θ − χ sin θ (7)

ν2 = χ sin θ + χ cos θ .

Here, χ = νR + νc

R as before, χ = νL + νc

L and themixing angle is defined as

tan 2θ = − mDν

mMνR

. (8)

1 Flavor indices are suppressed in the following discussions forclarity.

If one assumes that mMνR � mD

ν , then one obtains alight and heavy neutrino state, as is well known,

νl ∼ χ , νh ∼ χ , (9)

with masses

ml ∼ −mD 2ν

mMνR

, mh ∼ mM

νR . (10)

Observe that the heavier state is a right-handed majo-rana fermion.

Note also from the above discussions that the mix-ing matrix elements |UlN |, between active and right-handed (sterile) states, roughly scale like mD

νmM−1νR .

If one had mDν ∼ O(EW-scale), hence seemingly mit-

igating to some extent the relative hierarchy amongYukawa couplings, then this would imply mM

νR ∼O(1012−1015 GeV) to get viable light neutrino massesin this simplest framework. This right-handed Ma-jorana scale is also attractive from the point of viewgrand unified theories [82], specifically left-right sym-metric grand unified models such as the Pati-Salammodel [83]. The above discussions may be extended tothe case of two or more sterile neutrinos. The inclusionof additional sterile neutrinos to the three active onesadds more structure to the neutrino sector.

On the other hand, as we alluded to before, it mustbe noted that low mM

νR scales must be considered tech-nically natural [38, 39] – since in the limit mM

νR → 0one regains U(1)B-L as a global symmetry of the La-grangian. In this context, the presence of additionalstates in a k-neutrino framework furnishes new pos-sibilities. One could now have novel flavor struc-tures, under seesaw or non-seesaw scenarios, some-times augmented by lepton-number-like family sym-metries. In many of these models the right-handedneutrino mass-scale is unconstrained and could in gen-eral be small, leading to interesting observational con-sequences [38, 39, 41, 84–95].

All of these thus imply, as we mentioned earlier, thata priori it is prudent to be agnostic about the exactmMνR scale and devise search strategies that would span

the full range of possibilities. We will be specificallyinterested in scenarios where mM

νR � mW± , i.e. in thelow, electroweak-scale regime. In these scenarios themixing between the active-sterile states could be largerthan naive expectations and potentially unsuppressed.For instance, in inverse seesaw models [85, 86] – thesimplest realization of which has three extra standardmodel singlet neutral fermions (Ψ) in addition to threegenerations of sterile (NR) and active neutrinos (νL)–

5

the Lagrangian takes the form

Linv. see-saw

mass ⊃ −MDνLNR −MΨLNR −δ

2ΨLΨc

L ,(11)

which leads to a neutrino mass-matrix

Mν =

0 MD 0M T

D 0 M0 M T δ

. (12)

Note that as δ → 0 one regains the lepton-number-like protection symmetry, and hence a small δ is tech-nically natural.

On diagonalizing the mass matrix, assuming a hier-archy among the scales δ �MD .M , the mass of thelight neutrinos scale as

mν ∼ δM2

D

M2, (13)

while the active-sterile mixing matrix elements stillscale as

|UlN | ∼MD

M. (14)

Owing to the presumably small δ and the differ-ence in scaling behavior between masses and mix-ing angles, we have the possibility of getting verysmall SM neutrino masses, while retaining the possi-bility of relatively light sterile neutrinos. The lattercould also have significant mixing with active neutri-nos (|UlN | ∼ MD/M . O(1)). This could lead toeffective couplings between the sterile states and theW±, Z0 vector gauge bosons that are relatively un-suppressed. Thus, the relatively large mixing anglesalong with the lighter masses open the way for theseright-handed sterile states to be searched for in particlecollider experiments.

In the mass-range we are interested in, mb <mNR

� mW± , the dominant production mode for asterile neutrino are through W± charged-current andZ0 neutral-current interactions, mediated through themixings with active-neutrino states,

pp → W± +X → l±NR +X ,

↪→ Z0 +X → νNR +X .

For higher mNRand energies, other production modes

also become relevant [96–100]. For masses below thebottom-quark mass, mNR

< mb, production throughB-meson decay channels also open up.

The right-handed neutrinos after being producedsubsequently decay, again through W± charged-current or Z0 neutral-current interactions mediated by

active-sterile mixing. The partial widths to leptonic fi-nal states are given by [44, 101]

Γ(NRW∗

−−→ l−a l+b νb) =

G2F

192π3m5N |UaN |2 , (15)

Γ(NRW∗/Z∗

−−−−−→ l−a l+a νa) =

G2F

96π3m5N |UaN |2 ,(

g2L + gLgR + g2R + 2gL + 2gR + 1),

Γ(NRZ∗

−−→ νal+b l−b ) =

G2F

96π3m5N |UaN |2

(g2L + gLgR + g2R

),

Γ(NRZ∗

−−→ νaνbνb) =G2F

768π3m5N |UaN |2 .

Here the SM couplings are defined as gL = 12 + sin2 θW

and gR = sin2 θW.We are interested in devising an optimal search

strategy for low, electroweak-scale sterile neutrinosproduced at pp-colliders; dominantly via decays of W±

and which decay through their charge-current interac-tions. The typical process of interest is therefore

pp→W± +X → l±a (NR → l±a l∓a νa) +X , (16)

as shown in Fig. 2.In the next section we will take a closer look at the

event and background toplogies to be expected anddiscuss considerations that must be taken into accountfor an effective search at the LHC and the proposed100 TeV pp-colliders.

III. EVENT TOPOLOGY ANDBACKGROUNDS

Traditional multilepton searches (for exampleRef. [102, 103]) can have high sensitivity for sterile neu-trinos with masses above ∼100 GeV. These searchesrely on prompt, well-separated (and isolated) leptonsin the final state, and typically require lepton trans-verse momenta (pT) to satisfy pT > 20 GeV. Withcareful selection of isolation criteria, and lowering ofthe lepton pT threshold, or by considering final stateswith dileptons and jets, the sensitivity can be extendedto sterile neutrino masses as low as 50 GeV [59, 60].

However as the mass of the sterile neutrino becomeslighter, which is the case of interest in our current in-vestigation, new search strategies need to be explored.One such interesting final state involves a prompt lep-ton along with a lepton-jet [63]. In a lepton-jet, twoor more leptons lie very close to each other in the de-tector. Such a signature will be rejected by standard

6

isolation criteria, and needs a separate, special selec-tion criteria. Lepton-jet searches have been carriedout by the LHC experiments in the context of differ-ent new physics models. ATLAS searches for pairsof lepton-jets [104] which might or might not be sig-nificantly displaced from the interaction point. CMSsearches for a pair of leptons [105] which may lie closeto each other, but which are displaced and need tosatisfy m`` > 15 GeV. The CMS search also has stiffrequirements on lepton pT.

A different approach is needed to probe for sterileneutrinos that lie in the range mb < mNR

� mW± .We choose a final state that consists of a lepton-jet ac-companied by the presence of a prompt, well-isolatedlepton. This choice of final state dictates the analysisstrategy, since it significantly affects which standardmodel processes will act as a background to the search.Further selections to optimize the sensitivity are thengoverned by the interplay between the signal of inter-est, the backgrounds and the specific selections.

The particular decay chain we probe is W± →`±NR → `±`′±`′′∓ν. Here the ` arises promptly fromthe decay of the W±, and has relatively high pT. Onthe other hand, the `′ and `′′, which arise from thedecay of the sterile neutrino (NR), are not necessarilyprompt and can have low pT, depending on the massand lifetime of the NR. Moreover, depending on theboost of the NR, the `′ and `′′ can also come close toeach other forming a lepton-jet. Let us now considereach aspect of this signal topology carefully.

The separation between the decay products of Nscale as ∆R ∼ mNR

/pNR

T while in the rest frame ofthe W± the momentum of the sterile neutrino scalesas pNR

T ∼ (m2W± − m2

NR)/mW± . This implies that

around mNR∼ 20 GeV the opening angle for the decay

products will exceed ∆R ∼ 0.5. At around this massthe lepton-jet selection criteria will therefore becomeless efficient and one expects that the limits obtainednear mNR

∼ 20 GeV should be weaker than those fromother experiments [67–73]. On the other hand, belowmNR

. 4 GeV there are already very strong limitson active-sterile mixing angles from other searches –lepton number violating meson decays, peak searchesin meson decays, beam dump experiments and so on(Please see for instance [45] and references therein).Some of the planned experiments in this mass range,such as DUNE [106, 107] and SHiP [108, 109], are pro-jected to have the capability to probe mixing anglesall the way down to |UµN |2 ∼ 10−10. We thereforesharpen our mass-regime of interest to be between

4 GeV < mNR< 25 GeV . (17)

FIG. 3. A possible background from heavy flavor decays.Here, a J/ψ resonance is produced in association with aW±. The decay products from the boosted J/ψ fake alepton-jet while the W± furnishes a prompt lepton. A rel-atively significant fraction of such events could still surviveafter a naive selection. They must therefore be accountedfor more carefully while making an optimised analysis.

In this mass regime of interest, for small sterile-active mixing |UµN |2, one also expects from Eq. (16),the lepton-jet to be displaced appreciably from theprimary vertex due to the large NR-boost. This dis-placement may potentially be leveraged to discrimi-nate between signal and background. Nevertheless, aswe shall explain in Sec. IV this criterion turns out tobe less significant, rather counterintuitively from naivereasoning, for overall signal sensitivity.

The presence of the prompt isolated lepton inthe signal topology significantly simplifies the triggerneeded for such a topology. Typical isolated leptontriggers at the ATLAS or CMS experiments have pTthresholds ranging from 23 GeV for muons to 35 GeVfor electrons. In addition, advanced trigger strategiessuch as those employed in Ref. [104] can also be con-structed. At a hadron collider such as the LHC, a largesource of single isolated prompt leptons is SM W± pro-duction. Along with direct production, W± also arisethrough the decay of t-quarks. The cross sections fort-quark production (tt and single-top events) are alsosignificant compared to signal at the LHC. Other stan-dard model processes that give rise to more than oneisolated prompt leptons (Z/γ∗, orWZ production) canalso lead to background to a final state with a promptlepton.

Muons generally provide cleaner lepton and lepton-

7

jet signals as compared to electrons or τ leptons.Muons are reconstructed using the tracking chambersand therefore gives a better lepton-jet discriminant.For our conservative estimates we shall therefore as-sume that there is only appreciable mixing between asingle sterile state and the muon-neutrino (νµ). Afteranalysis, this would therefore translate to a stricterlimit on |UµN |2 as a function of the sterile neutrinomass mNR

. If other channels are open then the limitsobtained in a prompt-muon and muon-lepton-jet finalstate analysis will be weaker.

The requirement of a lepton-jet should significantlyreduce the W± and top backgrounds. But at hadroncolliders, W± are typically accompanied by lighthadrons in a large fraction of events. Several lighthadrons such as the J/ψ and the Υ decay to a pair ofoppositely-charged leptons. When these light hadronsare boosted, the resultant dilepton decay may mimicthe lepton-jet of the signal (Fig. 3). This backgroundcan be reduced by raising the pT thresholds on thelepton-jet muons and placing strict requirements onhadronic activity. However given that almost 6% ofall J/ψ’s decay to a purely dimuon final state, suchrequirements will not remove this background com-pletely.

The other significant background could come fromtt events. The tt semi-leptonic decay chain results inone prompt lepton, two b-quarks, and two light quarks(tt→W±bW∓b→ `±νqq′bb). A potential decay chainfor the b-hadrons is through semileptonic decay to c-hadrons which subsequently decay semileptonically tolighter particles. Such a decay chain can also give riseto two oppositely-charged leptons. Given the boost ofthe b-quark, these two leptons can mimic the signatureof a lepton-jet. Thus both W -boson production, andtt production can result in significant background to aprompt lepton + lepton-jet final state. An example ofa final state that could arise from the tt backgroundis illustrated in Fig. 4. A requirement of low hadronicactivity in the event will supress the tt backgroundconsiderably, but not remove it completely. Furthersupression can be obtained by requiring the lepton-jetto be isolated, i.e. by requiring low hadronic activityin the immediate neighbourhood of the lepton-jet.

Other small contributions arise from single-top pro-duction, as well as low rate processes such as Z → 4`,Z + bb, or WZ/Wγ∗. The Z → 4` process where anasymmetric internal conversion takes place [110] canresult in a soft muon appearing almost collinear to oneof the muons from the Z-decay. This background aswell as background from Z + bb and WZ can be re-duced to negligible levels by vetoing events that have

FIG. 4. A prototypical background topology that may arisefrom tt events. Even vetoing for hadronic activity and im-posing isolation requirements, potentially a large fractionof such events could contaminate the signal region.

MN = 5 GeV, |UμN |2 = 5x10-6

Top pair-production + Wcc

MN = 25 GeV, |UμN |2 = 10-6

FIG. 5. The invariant mass of the µ-Jet muons is shownfor two signal points and for the combined background (ttand W+jets) for a 13 TeVcollider.

more than one isolated lepton, and by requring that theinvariant mass of all three muons in the event is be-low the W -mass. The Wγ∗ background can be furtherreduced by considering the alignment of the missingenergy with the µ-Jet.

Fig. 5 shows the invariant mass constructed from thetwo muons that form the µ-Jet. The signal distribu-tion, as expected, peaks at harder values with increas-ing mNR

. The background is concentrated at low val-ues, since it arises primarily from b-hadron as well as

8

lighter hadron decay. We do not use the invariant massin our study as we find that it inordinately affects sig-nal acceptance for low mass sterile neutrinos. We nowproceed to detail the search strategy and discuss theprospective reach attainable at hadron colliders.

IV. LEPTON JET PROBES OF STERILENEUTRINOS AT THE LHC AND FCC-hh/SppC

The signal mass-region of interest presents uniquechallenges and necessitates a careful analysis strategy,taking into consideration all the features of the signaland background topologies discussed in the previoussection. Our aim is to carefully account for the relevantbackgrounds and tailor the selection criteria to enablean optimal search strategy at a hadron machine. Wewill present our results in the context of the 13 TeVHL-LHC, and the proposed 100 TeV FCC-hh/SppCcolliders [64, 65].

As mentioned, we will assume that there is appre-ciable mixing only between the sterile state and muon-neutrinos to set a conservative limit. This is partiallymotivated by the fact that at the LHC, muons willprovide a cleaner lepton and lepton-jet signal as com-pared to electron or tau leptons. Identifying lepton-jetswith electrons and taus require a more careful under-standing of how hadronic objects might be wronglyreconstructed or misidentified as lepton-jets. Muonson the other hand are reconstructed using the track-ing chambers and this gives a better measurement ofthe kinematics. With this consideration we will alsotake the prompt lepton and lepton-jet to be muonic.

In the 4 GeV < mNR< 25 GeV mass-range, the

dominant mode of production for NR is via an on-shell W± boson, as in Fig. 2. The NR is produced inassociation with a prompt muon

W± → NR + µ± .

The cross-sections for this production channel coulddiffer by an order of magnitude between a 13 TeV and100 TeV hadron collider. In Fig. 6 we illustrate thisvariation for the production cross-section in the case ofmNR

= 8 GeV, as a function of the mixing. As we shallsee, in the case of the backgrounds this increase can beeven more drastic presenting challenges at 100 TeV.

After production, we will consider the fully leptonicdecay of the NR, proceeding via an off-shell W±∗ orZ0∗ boson

NR → µ∓ +W±∗ → µ∓ + µ± + νµ (18)

↪→ νµ + Z0∗ → νµ + µ∓ + µ± .

FIG. 6. The production cross section for a sterile, right-handed neutrino in association with a lepton, generated viaon-shell W± decay. The plot is for mNR = 8 GeV and thevariation is shown as a function of the mixing. The twocurves are for the 13 TeV (red) and 100 TeV (green) cases.

We optimize our analysis for the case where the NRis boosted. This results in the final state muons andneutrino arising from its decay to be collimated. Thusour signal lepton-jet of specific interest is a muon-lepton-jet

µ-Jet : < µ±µ∓νµ >

where the muons and neutrino are tightly collimatedin a small cone-radius. We will require these pair ofmuons to be within a cone of radius ∆R < 0.5, where

∆R =√

∆η2 + ∆φ2. We will refer to this object as amuon-jet or µ-Jet henceforth.

Due to the boost of the NR and small mixing angles,the µ-Jet will be displaced from the prompt muon atthe primary vertex. So, the characteristic signal beingsearched for consists of a prompt muon and a displacedµ-Jet.

We generate the signal processes usingMadGraph5 aMC@NLO [111] for both 13 TeV and100 TeV. The parton showering and hadronizationare preformed using Pythia 8.219 [112] with Tune4C used to simulate the busy hadronic environment.The hadronized output is then passed through theDelphes 3.3.2 [113] detector simulation. We use thedefault CMS and FCC detector cards for 13 TeV and100 TeV respectively.

The dominant SM backgrounds arise from W± pro-duction in association with jets and from tt produc-

9

tion. The Z → 4` and WZ backgrounds are reducedby demanding the invariant mass of the µ-Jet withthe prompt muon, mµ-Jet−promptµ < 80 GeV. Theadditional vetoing of a second prompt muon helps tocompletely remove the contribution from Z, and WZprocesses. These selections do not impact the signalgiven the lack of a second prompt muon in the signal,and since the signal process begins with an on-shell Wboson.

The background processes also follow the same sim-ulation chain as the signal. The exact efficiencies ofreconstructing non-standard objects, such as muon-jets, at a future 100 TeV detector are of course lesswell understood, and must await a detailed descrip-tion of the final detector design. We do our analysisusing generator level hadronized output at both 13 TeVand 100 TeV. To assess the effect of reconstruction ef-ficiency on the signal, we consider two scenarios: aper-muon efficiency of 90%, which will result in anevent efficiency of about 70%, and a per-muon effi-ciency of 80%, which will result in an event efficiencyof about 50%. We start by making a selection for theprompt muon. We require the prompt muon to satisfypT > 22 GeV, and |η| < 2.4. We then also make ad-ditional requirements on the impact parameter of themuon to ensure promptness, while requiring the muonto be isolated. At the LHC, this prompt isolated muoncan be used to trigger the event. For the µ-Jet, westart with selections based on the unique kinematicsand topology of the signal, and subsequently imposefurther criteria that help to discriminate against dom-inant backgrounds, that may still contaminate the sig-nal region.

Overall, our signal selection criteria may be listedas:

• S0 : Require an isolated, prompt muon withpT > 22 GeV, and |η| < 2.4. Transverse im-pact parameter dXY < 0.2mm and dZ < 0.1mm.The prompt muon is required to have the relative

isolation,ΣptrkpT

< 25%. Here Σptrk is the sum

of transverse momentum of all charged particleswith ptrk > 1 GeV around a cone of ∆R < 0.4from the prompt muon.

• S1: We require the µ-Jet to be composed of apair of muons with opposite charge, and withpT > 2 GeV and |η| < 2.4. This pair of muonsshould also satisfy ∆R < 0.5. The µ-Jet 4-vectoris constructed by adding the 4-vectors of the twomuons which form the µ-Jet.

• S2: We require the invariant mass of theµ-Jet with the prompt muon, mµ-Jet−promptµ <80 GeV . We also require that there is not morethan one prompt muon per event. Both these re-quirements reduce the contribution from Z → 4`to negligible levels. In addition since the signal isproduced starting with an on-shell W -boson, wealso expect the invariant mass to not contributebeyond the W -boson mass.

• S3: The signal does not have significant hadronicactivity, while the primary backgrounds havejets. We require HT < 60 GeV, where HT isdefined as the scalar sum of pT of all AK4 jets inthe event with pT > 30 GeV. This selection re-duces both the tt and the W±+Jets background.

• S4: The azimuthal angle between the missingtransverse energy (MET) and the µ-Jet shouldsatisfy ∆φmuon-jet−MET < 0.5. This selectionsupresses the tt background and the W±+Jetsbackground, where the ∆φmuon-jet−MET has nopreferential value.

• S5: We construct an isolation variable for theµ-Jet as the sum of transverse momenta of allcharged tracks with pT > 1 GeV within a cone of∆R < 0.6 from the µ-Jet. We require this sumto be less than 3 GeV. This selection stronglydiscriminates against the tt and W±+Jets back-ground since the muons in these processes areaccompanied by hadronic activity.

At 100 TeV, the fraction of signal events that areproduced in the forward direction increases as com-pared to 13 TeV. The existing LHC experiments havecoverage up to |η| < 2.5 for muons, and |η| < 5 forthe calorimeters. We have considered that the detec-tors at a future 100 TeV collider will have extendedmuon coverage, as compared to present detectors, andthus we modify our selection to |η| < 5.0 for all muonsin our 100 TeV analysis. But being in the narrow4 GeV < mNR

< 25 GeV signal regime, we find thatmost kinematic quantities of interest, such as the pTof muons, MET etc. are quite similar between 13 TeVand 100 TeV. We have therefore adopted, as evidentfrom selection criteria S0-S5 earlier, identical selectionsfor 13 TeV and 100 TeV studies. We have performedcross-checks to ensure the robustness of these assump-tions.

In Fig. 7(a) we show the azimuthal angle betweenthe missing transverse energy (MET) and the µ-Jet forsignal and the combined background (tt and W+jets)

10

for a 13 TeV collider. As expected the signal is con-centrated at the lower end, while the background hasuniformly distributed value of ∆φmuon-jet−MET on av-erage. Fig. 7(b) shows the isolation of the µ-Jet of thesignal and the combined background (tt and W+jets)for the 13 TeV collider after our signal selections S0through S2 have been imposed. The tt production(t→Wb→ `νb) and the W+jets gives rise to a muonsin a cascade decay. Hence due to their busy hadronicenvironment, the µ-Jet for the backgrounds are lesserisolated than the signal. We also consider cosmic-raysas a background. Given our topology a cosmic-ray canonly act as a background if it passes through the in-teraction point (thus acting as the prompt muon inthe event, and one of the µ-Jet muons). Following theestimate presented in Ref. [63], we consider this back-ground to be negligible.

Previous studies have considered the impact-parameter and displacement of the µ-Jet muons to bea sharp discriminating variable, against background,and have made selections for displaced muon-jets. Wefind that placing too hard a cut on these variables ac-tually reduces overall sensitivity to events where theµ-Jet is sometimes less displaced. It is also found thatafter other selection criteria it does not impact the re-maining dominant Wcc or tt backgrounds significantly.The primary backgrounds arising from tt decay involveb-hadrons. These b-hadrons have lifetimes of ordercτ ∼ 500µm, resulting in muon displacement distri-butions that appear similar to signal over a significantpart of the parameter space. Given these reasons, wedo not actually make any hard impact-parameter re-quirements or displacement requirements for the µ-Jetmuons.

Given the selections described above (S0 throughS5), Table I shows the acceptance for signal and back-ground for our 13 TeV analysis, while Table II showsthe same for the 100 TeV analysis. It is evident thatthe veto on hadronic activity, and the ∆φ requirementbetween the µ-Jet and MET reduces the backgrounddrastically while maintaining high signal sensitivity.As an alternative to the hadronic activity veto, as across-check, we also performed a separate study usingb-tagging to assess the impact on the tt background.For this study, we considered the b-tagging efficiencyfrom the CMS experiment [114]. We find, perhapsunsurprisingly, that an overall hadronic activity vetoacts as a better background discriminant than usingb-tags given the typical b-tagging efficiencies of 90%with misidentification rate of about 1%.

In Fig. 8, we compare the final estimated sensitiv-ity for our selections. Existing constraints are shown

MN = 8 GeV, |UμN |2 = 10-5

Top pair-production + Wcc

MN = 8 GeV, |UμN |2 = 10-5

Top pair-production + Wcc

FIG. 7. Depicted on top is the azimuthal angle betweenthe missing transverse energy (MET) and the µ-Jet for sig-nal and the combined background (tt and W+jets) for a13 TeV collider. As expected the ∆φmuon-jet−MET peaksat a lower value for the signal while showing no particularpreference for any value for the backgrounds. Shown onthe bottom is the isolation of the µ-Jet for the signal andcombined background. The µ-Jet for the backgrounds ismuch lesser isolated due to busy hadronic activity. Both ofthese are obtained after the selections S0 through S2 havebeen imposed.

as dotted curves. The contours are for 13 TeV LHCwith 300 fb−1 data (red) and 100 TeV FCC-hh/SppCalso assuming 300 fb−1 data (green). We show 95%CL limits on |UµN |2as a function of right-handed neu-trino masses mNR

. The limits were computed usingthe asymptotic limit method [115]-[118]. Assuming a100% event reconstruction efficiency for signal, the up-

11

TABLE I. The acceptance for signal and background forthe 13 TeVanalysis.

Selections Signal tt WccS0:Acceptance [%] 47.8 22.6 67.3S1:Acceptance [%] 18.9 3.5× 10−1 2.1× 10−2

S2:Acceptance [%] 17.9 2.6× 10−1 1.6× 10−2

S3:Acceptance [%] 16.6 6.7× 10−4 10−2

S4:Acceptance [%] 13.4 6.7× 10−4 10−3

S5:Acceptance [%] 12.2 5× 10−6 2.3× 10−4

TABLE II. The acceptance for signal and background forthe 100 TeVanalysis.

Selections Signal tt WccS0:Acceptance [%] 64.3 30.6 85.1S1:Acceptance [%] 16.0 4.1× 10−1 3.2× 10−2

S2:Acceptance [%] 11.9 2.5× 10−1 2.5× 10−2

S3:Acceptance [%] 9.2 7.4× 10−3 6× 10−3

S4:Acceptance [%] 7.2 3× 10−4 2× 10−3

S5:Acceptance [%] 6.8 3.5× 10−5 3.1× 10−4

per limit on the signal cross-section is calculated to beσLIM = 9.03 × 10−4 pb. If we consider efficiencies of70% and 50%, the upper limit worsens to 1.3 × 10−3

pb and 1.8 × 10−3 pb respectively. As expected, thereach of the experiment will depend on the efficiencywith which muons (and the signal events) are recon-structed. Note that at higher mNR

, the sensitivity de-creases since the daughter muons no longer satisfy thegeometric criteria for a µ-Jet. A high sensitivity at lowmNR

is maintained due to the extreme low momentamuons considered here.

As shown in Fig. 8, the 13 TeV LHC search opti-mised for this mass-regime is already competitive insensitivity, if not slightly better in some regions, tothe sensitivity of the proposed 100 TeV hadron col-lider. This may seem surprising and contrary to naiveexpectations. The primary reason is again the nar-row [4 GeV, 25 GeV] signal region that we are tryingto optimize over and the presence of strongly pro-duced backgrounds that disproportionately increasewhen one moves from 13 TeV to 100 TeV. Even thoughthe signal cross-section of our signal increases by anorder of magnitude at the 100 TeV collider, as ev-idenced by Fig. 6, we observe that the backgroundcross-section increases even more drastically – about5 times as rapidly as the signal. This is of course ex-

5 10 15 20 25mN (GeV)

10 10

10 8

10 6

10 4

10 2

|N|2

13 TeV LHC100 TeV FCC-hh/SppCEWPTLEP (L3)LEP (DELPHI)

FIG. 8. Exclusion contours for the 13 TeV LHC (red) andthe proposed 100 TeV FCC-hh/SppC (green), for similarselection criteria, assuming a signal efficiency of 100%. Forthe same integrated luminosity of 300fb−1, and for a simi-lar cut based analysis, the LHC is already competent witha 100 TeV collider. Constraints from electroweak precisiondata (EWPT) [67–71] and LEP data (L3 and DELPHI col-laborations) [72, 73] are also shown for comparisons.

pected as backgrounds like top-pair production feedoff the strong production modes while our signal isdominantly produced solely via the weak interaction,in this regime. The drastic increase in backgroundcross-sections at 100 TeV renders some of the signalcross-section increase and selection optimisations im-potent. Thus, if our analysis and understanding iscorrect, for a 100 TeV hadron collider to do signif-icantly better than the LHC, an increased detectorcoverage and algorithmic improvements, such as in b-tagging, might be required, along with more sophisti-cated search strategies. Based on our study, our cur-rent conclusion is therefore that the 13 TeV LHC, forthe final states of interest, can give competitive limitsin the [4 GeV, 25 GeV] sterile neutrino mass-regime.

V. SUMMARY AND CONCLUSIONS

Sterile neutrino states are well motivated in manyextensions of the Standard Model and have the po-

12

tential to cast light on many unsolved questions in ourtheoretical frameworks. With the realization that theirmasses are not a priori fixed to any particular mass-scale, it becomes crucial to have search strategies span-ning all the possible values.

We focused on a relatively unexplored mass regime(ΛQCD � mNR

� mW±), where current constraintsand experimental searches at hadron colliders are lack-ing. Also, prior theoretical studies in this signal regionseem to have missed certain subtle, albeit crucial as-pects of backgrounds and selection, while making sen-sitivity projections.

Motivated by the previous studies, unique signaltopology and challenges singular to hadron collid-ers, we specifically revisited the sterile neutrino sig-nal topology consisting of a prompt lepton and a dis-placed lepton-jet. We have attempted to make the firstsystematic study in this signal region, for the 13 TeVhigh-luminosity Large Hadron Collider and a futureFCC-hh/SppC 100 TeV pp-collider.

For the same set of selection cuts, albeit for selec-tion criteria optimised to each collider, our conclusionis that the 13 TeV HL- LHC may already be compet-itive with a future hadron collider. This is partiallydue to the fact that we are optimizing over a narrowmass-region in the low, electroweak regime for the sig-nal – so the gains in signal cross-section while goingto a higher energy machine are moderate – while therelevant backgrounds for the toplogy under consider-ation increase much more drastically. A higher de-tector coverage, algorithmic improvements and a more

sophisticated search strategy, in contrast to the simplecut and count based analysis we have performed, maypossibly improve the reach at a 100 TeV pp-collider sig-nificantly. On the other hand a future e+e− collidermay be able to significantly extend the sensitivities tovery low mixing angles (see for instance [47] and ref-erences therein). Also, during the completion of thiswork an interesting study [119] appeared that looksfor sterile neutrinos by reinterpreting displaced vertexsearches (µjj final states) for long-lived particles atLHCb, during run-1 [120]. The study recasts currentdata and makes projections for future LHCb searchesand the final limits are comparable to our study in themass regime of interest; nevertheless with a differentexclusion-limit functional profile.

A systematic and continuing program of sterile neu-trino searches at current and future colliders, in allrelevant mass ranges and topologies, would help in elu-cidating the nature of these states, if they exist, andhelp towards a complete coverage of interesting signalregions.

ACKNOWLEDGEMENTS

We would like to thank S. Chauhan, E. Izaguirre, B.Shuve, S. Somalwar and S. Thomas for discussions andcomments on the manuscript. S.D. and D.G are grate-ful to E. Izaguirre and B. Shuve for providing modelfiles from their earlier study for corroboration and to S.Chauhan for help with simulation. The computationsfor the study were performed at the High Power Com-puting facility of the EHEP group at IISER, Pune.

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