(O 5 ) ij = L ciL φ ˜ ∗ φ ˜ † L jL

arXiv:0808.2468v2 [hep-ph] 12 Sep 2008

with multi-lepton signals

F. del Aguila, J.A. AguilarSaavedra

Departamento de Físi a Teóri a y del Cosmos and CAFPE,

Universidad de Granada, E-18071 Granada, Spain

Abstra t

We investigate the LHCdis overy potential for ele troweak s ale heavy neu-

trino singlets (seesaw I), s alar triplets (seesaw II) and fermion triplets (seesaw

III). For seesaw I we onsider a heavy Majorana neutrino oupling to the ele -

tron or muon. For seesaw II we on entrate on the likely s enario where the

new s alars de ay to two leptons. For seesaw III we restri t ourselves to heavy

Majorana fermiontriplets de aying to light leptons plus gaugeor Higgs bosons,

whi h are dominant ex ept for unnaturally small mixings. The possible signals

are lassied in termsof the harged lepton multipli ity, studying nine dierent

nal statesranging from one to six harged leptons. Using afast dete torsimu-

lation of signals and ba kgrounds, itis found thatthe trilepton hannel

ℓ ^± ℓ ^± ℓ ^∓

is byfar the bestone for s alar tripletdis overy,and for fermiontripletsit isas

good as the like-sign dilepton hannel

ℓ ^± ℓ ^±

^{. For heavy neutrinos with a mass}

O(100)

^{GeV, this trilepton hannel is also better than the usually studied like-}

sign dileptonmode. In addition to evaluating the dis overy potential, we make

spe ial emphasis onthe dis rimination amongseesaw models ifa positive signal

is observed. This ould be a omplished not only by sear hing for signals in

dierent nal states, but also by re onstru ting the mass and determining the

harge of the new resonan es, whi h is possible inseveral ases. For high lumi-

nosities, further eviden e is provided by the analysis of the produ tion angular

distributions inthe leanest hannels withthreeor four leptons.

1 Introdu tion

The near operation of the Large Hadron Collider (LHC) represents a remarkable op-

portunity to explore physi s beyond the ele troweak s ale. In parti ular, physi s at

highers ales anbeexploredintheleptonse tor[1℄,wheretheonlyeviden eofphysi s

beyond the Standard Model (SM) has been found up to now, namely massive neutri-

nos. Manytheories have been proposedtoenlarge theSM in orporatingtiny neutrino

masses, as required by experimental data [2℄. Among them, seesaw models explain

heavy elds, the leptonnumberviolating (LNV) dimension ve operator [3℄

(O 5 ) _ij = L ^c _iL φ ˜ ^∗ φ ˜ ^† L _jL

⁽¹⁾

is generated, where

L iL = ν _iL l iL

!

, i = 1, 2, 3

⁽²⁾

aretheSMleft-handedleptondoublets,

φ

^{theSMHiggsand}

φ = iτ ˜ 2 φ ^∗

^,with

τ i

^thePauli

matri es. This operator yields Majorana masses for the neutrinos after spontaneous

symmetry breaking. Athigher energies neutrino masses an begenerated from higher

dimension operatorsinvolvingextra elds(seeforexampleRef.[4℄) butwhenallheavy

degrees of freedom are integrated the operatorin Eq. (1)is re overed.

Thereare threetypesof tree-levelseesawme hanismswhi horiginatethe operator

inEq.(1),whi histheonlyve-dimensionaloneallowedbytheSU

(3)×

^SU

(2) L ×

^U

(1) Y

gauge symmetry. The originalseesaw [58℄,alsoknown asseesawof typeI,introdu es

right-handed neutrino singlets

N

^{at a high s ale. Type II seesaw [913℄ enlarges the}

SM with a omplex s alar triplet

∆

^with hyper harge

Y = 1

^{, and seesaw III [14,15℄}

introdu es olourlessfermioni triplets

Σ

^with

Y = 0

^{. BothseesawIand IIarepresent}

in left-right models [16,17℄. Combinations of seesaw I and III are predi ted in some

granduniedtheories[1820℄,and anbeimplementedinleft-rightmodelsaswell[21℄.

Thethreetypesofseesawme hanismgeneratenot onlythedimension veoperator

whi hgiveslightneutrinomasses,butalsoadditionalleptonnumber onserving(LNC)

dimension six operators, whi h are dierent in ea h seesaw s enario [22,23℄ (see also

Ref.[24℄). Therefore,seesawmodelsmayinprin iplebedis riminated,albeitindire tly,

with pre ise low-energymeasurements sensitiveto thesedimension six operators. The

seesaw messengers

N

^,

∆

^,

Σ

^{an alsobe produ ed atLHC if their masses are not very}

large but of the order of the ele troweak s ale and, in the ase of neutrino singlets, if

their mixing with the SM leptons is of order

10 ⁻²

^{or larger. Therefore, LHC gives a}

unique han e to un over the me hanism of neutrino mass generation if these heavy

states are dire tly observed.

The produ tion of heavy neutrinos [2530℄, s alar triplets [3136℄ and fermion

triplets [37℄ and their possible signals have been extensively studied in the literature.

Inthispaperwetakeanovelapproa htotheiranalysis. Insteadof lassifyingsignalsin

termsoftheparti lesprodu edinthehardpro essandstudyingoneormoreparti ular

hannels, we lassifythem by the signatures a tually seen atthe experiment,generat-

ing all the signal ontributions. As the number of jets in the nal state is not a good

lepton multipli ity,and the number ofhard jetsis onsidered onlyinfewspe ial ases

as an extra information for the kinemati al re onstru tion. We believe that this is a

more appropriate hoi efromthe experimentalpointofview. Anessentialfeatureof a

real experiment is that the observed nal states re eive in general ontributions from

several signalpro esses and, onversely,one given signalpro ess ontributestoseveral

nal states if, for example, one or more harged leptons are missed by the dete tor.

Both ee ts are taken into a ount in our analysis, whi h in ludes the ee ts of ra-

diation, pile-up and hadronisation, performed by a parton shower Monte Carlo, and

uses a fast dete tor simulation. Within a given seesaw s enario we simulate all signal

pro esses and then examinethoroughly the relevant nal states,nine intotal, ranging

from one to six hargedleptons.

Ase onddieren ewithrespe ttopreviousliterature on ernstheguidingprin iple

of the analyses performed. Due to the profusion of new physi s s enarios to be tested

at the LHC it is expe ted that, at least in a rst phase, sear hes will be in lusive to

some extent and rather model-independent, inorder tobe sensitive to dierent types

ofnewphysi s ontributingtoagiven hannel. Forexample,itisnotlikelythat,inthe

absen e of a strongphysi s ase, a nal state with two like-signleptons, large missing

energy,twojetswithaninvariantmass onsistentwiththe

W

^{massandtwoadditional}

jets will be examined right from the beginning of LHC operation. On the ontrary,

sear hes are expe ted, forexample,for in lusive nalstates withtwolike-signleptons,

as it has already been done at Tevatron [38℄. (With this philosophy,our lassi ation

of signals interms of leptonmultipli ityis perfe tlysuited.) Then,in our analyses we

will not set ne-tuned kinemati al uts onmany variablesto enhan e the signals, but

our riteria for variable sele tion and ba kground suppression will be rather general,

and in most ases valid for seesaw I, II and III signals. In this way, our results and

pro edures will be adequate for model-independent sear hes in the multi-lepton nal

states. Of ourse, if some hint of new physi s is found the analyses an be rened

and adapted to someparti ular s enario, inorder tore onstru t the resonan e masses

and/or enhan e the sensitivity.

Finally,we payaspe ialattentiontothedis riminationamongmodelsif apositive

signal isfound. Thisstudy isfar moreinvolved thanthe simple observation ofanew

physi ssignalfromseesawmessengers inone orfewparti ular hannels, towhi hmost

previous literature has been devoted. On the ontrary, model dis rimination requires

a systemati analysis of all possible nal states and the re onstru tion of the new

resonan es when possible. The three types of seesaw an give signals with one, two

and three harged leptons,plus avariablenumber ofjets (whi h, asstressed before, is

re onstru tion in hadroni hannels). Finalstates with four hargedleptons

ℓ ⁺ ℓ ⁺ ℓ ⁻ ℓ ⁻

(with

ℓ = e, µ

^{, in luding all avour} ombinations of the four leptons) only arise in seesaw II and III s enarios, and

ℓ ^± ℓ ^± ℓ ^± ℓ ^∓

^{signals only in seesaw III, as well as ve}

and six lepton nal states. Therefore, a rst straightforward dis rimination of seesaw

models results from onsidering the nal states in whi h the signals an be seen and

their statisti alsigni an e,whi hare not thesame forseesawI, IIand III.Moreover,

if a positive signal is found in a given hannel, the mass re onstru tion of the heavy

resonan e anbeoftenperformedandits hargemeasured, giving leardire teviden e

for the produ tion of the new parti le. For example, doubly harged s alars

∆ ⁺⁺

produ ed in seesaw II models often give from their de ay a signal onsisting of two

like-sign leptons with an invariantmass very lose to

M ∆ ⁺⁺

^{, whereas the spe trumof}

like-sign dilepton invariant masses in seesaw I and III does not exhibit any peak. For

high integrated luminosities, the opening angle distribution an also be tested in the

leanest hannels, givingeviden eforthe s alarorfermioni natureoftheheavy states

produ ed.

Wealsohavetopointoutthat,sin ethe maininterestinthearrivaloftheLHCera

is in early dis overies (and a luminosity of 300 fb

−1

willnot be available until several

years of LHC operation, in the optimisti s enarios), we have on entrated our study

on seesaw messengers with masses lose tothe ele troweak s ale, whi h in the ase of

seesaw II and III would be qui kly dis overed after quality data are available. Thus,

for heavy neutrino singlets we have assumed a mass

m N = 100

^{GeV, while for s alar}

and tripletfermionsthe masshasbeentakenas300 GeV.Wehavefound thatthe best

hannel for dis overy, balan ing large signal bran hing ratios and small ba kgrounds,

is the trilepton one

ℓ ^± ℓ ^± ℓ ^∓

^{. For s alar triplets of this mass,}

5σ

^{dis overy would be}

possiblewithonly3.6fb

−1

of luminosityfornormalneutrino masshierar hy (NH)and

0.9 fb

−1

forinverted hierar hy (IH).Forfermioni tripletsthe luminosityneeded is2.5

fb

−1

, while for heavy neutrino singlets it is mu h larger, around 180 fb

−1

. A lean

modeldis riminationwould be possible within the rst LHC year with 10fb

−1

.

In this paperwework out the minimalseesawIIII s enarios without newintera -

tions. It is worth mentioningthat the latter an mediate new produ tionme hanisms

of seesawmessengers,forexample,heavy neutrinosinmodelswithleft-rightsymmetry

and anadditional

W R

^{boson [3942℄, modelswith anadditional}

Z ^′

^{[43,44℄orwithnew}

s alardoublets[45,46℄. Thesametypeofsignals analsobeprodu edbyfourthgenera-

tion neutrinos[47℄. New intera tions analsoleadtopredi tiveindire tseesawsignals,

as for exampleintypeII seesawin the ontextof supersymmetri models[4850℄. Al-

ternativestothe seesawme hanismarealsopossible,forexamplein

R

^{-parityviolating}

and olliderobservables [5153℄ (for reviews see Refs. [54,55℄ and referen es there in).

The rest of this paper is organised as follows. In se tion 2 we write down the rele-

vant Lagrangianterms for the three seesaw types. We on entrate onthe intera tions

mediatingtheprodu tionandde ay pro esses onsideredinthisworkusinganotation

that, while being general, is intended to be standard and of easy use for readers not

familiar with the models introdu ed. In se tion 3 we des ribe in detail the ommon

features of the analyses, whi h are performed in se tions 4, 5 and 6 for heavy neutri-

nos, s alar triplets and fermion triplets, respe tively. We begin these se tions with a

short introdu tion, and on lude them with a summary highlighting the main results,

so thatthereadermay skipthe details. Our on lusions aredrawn inse tion7. Inthe

Appendix we give the Feynman rules used inthe MonteCarlo generators.

2 General framework

In this se tionweintrodu ethe dierentseesawmodels, set our onventions and write

the Lagrangiantermsrelevanttothe produ tionand de ay pro essesstudiedhere. We

keep the notationassimpleaspossible andsimilarfor thethree typesofseesawme h-

anism. Constraintsonthe mixingof the newfermions and s alarsare briey reviewed

at the end of ea h subse tion. The Feynman rules are olle ted in the Appendix.

2.1 Seesaw I

Type-Iseesawisusuallyimplementedbyaddingthreeright-handed urrenteigenstates

N _iR ^′

^,

i = 1, 2, 3

^, transforming as singlets under the SM gauge group. This allows to write a Yukawa intera tion for neutrinos analogous tothe one for harged leptons,

L

^Y

= −Y ^ij L ^′ _iL N _jR ^′ φ + ˜

^{H. .}

,

⁽³⁾

where

Y

^{is a}

3 × 3

^{matrix of ouplings and}

L ^′ _iL

^{the SM lepton doublets (in the weak}

eigenstate basis). Thisintera tion generatesa masstermuponspontaneoussymmetry

breaking

φ = φ ⁺ φ ⁰

!

→ 1

√ 2 0 v

!

, φ ≡ iτ ˜ ² φ ^∗ → 1

√ 2 v 0

!

,

⁽⁴⁾

with

v = 246

^{GeV.Sin e}

N _iR ^′

^{areSMsinglets,gaugesymmetryallowsaMajoranamass}

term

L

^M

= − 1

2 M ij N _iL ^′ N _jR ^′ +

^{H. .}

,

⁽⁵⁾

with

M

^a

3 × 3

^{symmetri matrix and}

N _iL ^′ ≡ N iR ^{′ c}

^.

1

Dening

ν _iR ^′ ≡ ν iL ^{′ c}

^{, where}

ν _iL ^′

^are

the SMneutrino eigenstates, the fullneutrino mass term reads

L ^mass = − 1

2 ν ¯ _L ^′ N ¯ _L ^′
0 ^{√ v} ₂ Y

√ v

2 Y ^T M

! ν _R ^′ N _R ^′

!

+ H.c. .

⁽⁶⁾

The neutrino gauge intera tions are the same as inthe SM,

L W = − g

√ 2 ¯l _iL ^′ γ ^µ ν _iL ^′ W _µ ⁻ + ¯ ν _iL ^′ γ ^µ l _iL ^′ W _µ ⁺
, L ^Z = − g

2c W

¯

ν _iL ^′ γ ^µ ν _iL ^′ Z µ ,

⁽⁷⁾

with

l _iL ^′

^{the harged lepton weak} eigenstates and

c W

^{the osine of the weak mixing}

angle. The intera tion with the Higgs boson

H

^{, with the usual} normalisation

φ ⁰ = (v + H + iχ)/ √

2

^{, is}

L ^H = − 1

√ 2

 ν ¯ _iL ^′ Y ij N _jR ^′ + ¯ N _jR ^′ Y _ji ^† ν _iL ^′ 

H .

⁽⁸⁾

Then, the relevant intera tion terms for the heavy neutrino mass eigenstates

N i ≃ N _iR ^′

^{an be obtained by} diagonalising the mass matrix in Eq. (6) and rewriting the intera tionsinthemass eigenstatebasis(fordetailssee forexampleRefs.[56,57℄). For

a heavy Majorana neutrino

N

^{(dropping the subindex)and}

l = e, µ, τ

^{we have}

L ^W = − g

√ 2 V lN ¯lγ ^µ P L N W _µ ⁻ + V _lN ^∗ Nγ ¯ ^µ P L l W _µ ⁺
, L Z = − g

2c W

V _lN ν ¯ _l γ ^µ P _L N + V _lN ^∗ Nγ ¯ ^µ P _L ν _l
Z _µ , L H = − g m N

2M W

V _lN ν ¯ _l P _R N + V _lN ^∗ N P ¯ _L ν _l
H ,

⁽⁹⁾

where

m N

^{isthe heavy neutrino mass and}

V lN ≃ Y lN v

√ 2m N

(10)

is the mixing between the harged lepton

l

^{and the heavy neutrino}

N

^{. Due to the}

Majorana hara ter of

N

^and

ν l

^{, the last terms in the}

Z

^,

H

Lagrangians an be rewritten,

L ^Z = − g 2c W

¯

ν l γ ^µ (V lN P L − V lN ^∗ P R ) N Z µ , L ^H = − g m N

2M W

¯

ν l (V lN P R + V _lN ^∗ P L ) N H .

⁽¹¹⁾

1

Weavoidwritingparenthesesin harge onjugateeldstosimplifythenotation,andwrite

ψ ^c _L ≡

(ψ L ) ^c

^,

ψ ^c _R ≡ (ψ R ) ^c

^.

masses

m _ν

^{are of the order}

Y ² v ² /2m _N

^{, and the heavy neutrino mixings are}

V _lN ∼ pm ν /m N

^{. Hen e, for aheavy neutrino withinLHCrea h,say with amass}

m N ∼ 100

GeV,itsseesaw-type ontributiontolightneutrinomassesisoftheorderof

300 Y ²

^GeV,

requiring very smallYukawas

Y ∼ 10 ⁻⁶

^{to reprodu e light neutrino masses}

m _ν ∼ 0.1

eV. Moreover, the natural order of magnitude of the mixings is

O(10 ⁻⁶ )

^{, too small}

to give observable signals. In models with approximate avour symmetries the to-

tal

Y ² v ² /2m _N

ontributiontolightneutrinomasses anbesuppressed [5861℄andthe mixingsde oupledfromthelight/heavymassratio[62℄. Inthespe i realisations on-

sideredintheliterature,the symmetryadvo atedtonaturallyreprodu elightneutrino

masses withele troweak s aleheavy neutrinosisleptonnumber[63℄, inwhi h asethe

heavy neutrinos are quasi-Dira instead ofMajorana parti lesand the phenomenology

is dierent,inparti ular their de ays. In this work we willnot addresshow tobuild a

realisti modelinwhi hheavy Majorana neutrinosappearwithnon-negligiblemixings,

but wewillsimplytakethe LagrangianinEqs. (9)asaphenomenologi alone, inorder

toinvestigatetheLHCpotentialtodis overheavyMajorana neutrinos. The prospe ts

for Dira neutrinos at the ele troweak s ale, whi h appear more naturally in seesaw

models, are dis ussed elsewhere [64℄.

Even if we put aside the onne tionbetween heavy neutrino mixingand lightneu-

trino masses, the former must besmalldue topresent experimental onstraints. Ele -

troweak pre isiondata set limitson mixingsinvolvinga single hargedlepton [6569℄.

Usingthelatestexperimentaldata,the onstraintsat90% onden elevel(CL)are[69℄

3

X

i=1

|V ^eN i | ² ≤ 0.0030 ,

3

X

i=1

|V ^µN i | ² ≤ 0.0032 ,

3

X

i=1

|V ^{τ N} i | ² ≤ 0.0062 ,

⁽¹²⁾

whi hinparti ularimply onstraintsonthe individualmixings

V _lN

^{ofaheavyneutrino}

N

^{. These} onstraints are parti ularlyimportant sin e they determine the heavy neu- trinoprodu tion rossse tionsatLHC(seenextse tion). Fromleptonavour-violating

(LFV) pro esses [62,7072℄ one has onstraints involving two harged leptons,

    

3

X

i=1

V eN i V _µN ^∗ _i     

≤ 0.0001 ,     

3

X

i=1

V eN i V _{τ N} ^∗ _i     

≤ 0.01 ,     

3

X

i=1

V µN i V _{τ N} ^∗ _i     

≤ 0.01 .

⁽¹³⁾

In the absen e of some an ellation amongheavy neutrino ontributions (whi h ould

bepossible[73℄)thisboundimpliesthataheavy neutrino annothavesizeablemixings

with the ele tron and muon simultaneously. Noti e that the onstraints in Eqs. (13)

anbeeasilyevaded,forexample,ifea hheavyneutrinomixeswithadierent harged

lepton.

trinoless doublebeta de ay also onstrains their dire t ex hange [74℄

    

3

X

i=1

V _eN ² _i 1 m N i

    

< 5 × 10 ⁻⁸ GeV ⁻¹ .

⁽¹⁴⁾

If

V eN j

^{saturate the bound in Eq. (12), this limit an be fullled either demanding}

that

m N j

^{are at the TeV s ale [75℄ and then beyond LHC rea h, or that there is}

a an ellation among the dierent terms in Eq. (14), as it may happen in denite

models [59℄, inparti ular for (quasi)Dira neutrinos.

2.2 Seesaw II

In type II seesaw light neutrinos a quire masses froma gauge-invariantYukawa inter-

a tion of the left-handedlepton doublets with as alartriplet

∆

^of hyper harge

Y = 1

(with

Q = T 3 + Y

^{). Writing the triplet in Cartesian omponents}

∆ = (∆ ~ ¹ , ∆ ² , ∆ ³ )

^,

the Yukawaintera tion reads

L

^Y

= 1

√ 2 Y ij L ˜ iL (~τ · ~∆) L ^jL + H.c. ,

⁽¹⁵⁾

with

L ˜ _jL = iτ 2

ν _jL ^c l _jL ^c

!

(16)

and

Y

^{asymmetri matrixof Yukawa ouplings. Weassumewithoutlossofgenerality}

that the harged lepton mass matrix is diagonal, and drop primes on the neutrino

elds, whi hare taken inthe avourbasis

ν e

^,

ν µ

^,

ν τ

^{. The triplet harge}eigenstatesare related to the Cartesian omponentsby

∆ ⁺⁺ = 1

√ 2 (∆ ¹ − i∆ ² ) , ∆ ⁺ = ∆ ³ , ∆ ⁰ = 1

√ 2 (∆ ¹ + i∆ ² ) .

⁽¹⁷⁾

When theneutraltriplet omponenta quiresava uumexpe tationvalue(vev)

h∆ ⁰ i = v ∆

^{, the Yukawa} intera tion in Eq. (15) indu esa neutrino mass term

L ^mass = −Y ij ^∗ v ∆ ν ¯ iL ν jR + H.c.

≡ − 1

2 M ij ν ¯ iL ν jR + H.c. ,

⁽¹⁸⁾

where we haveagain introdu edthe notation

ν _iR ≡ ν iL ^c

^{, and}

M _ij = 2Y _ij ^∗ v ∆

⁽¹⁹⁾

imply the relation

Y ij = 1 2v ∆

(V

MNS

^∗ M

^diag

V

MNS

^† ) ij

⁽²⁰⁾

whi hallowstodeterminethetripletYukawa ouplingsfromthediagonalneutrinomass

matrix

M

^{diag, the triplet vev and the} Maki-Nakagawa-Sakata mixing matrix [76,77℄

V

^MNS.

The triplet Yukawa intera tion in Eq. (15) also generates triplet ouplings to the

hargedleptons. The relevant terms for our analysis are

L ^∆ll = Y ij l ^c _iL l jL ∆ ⁺⁺ + Y _ij ^∗ l jL l ^c _iL ∆ ⁻⁻ , L ^∆lν = √

2Y ij ν iR l jL ∆ ⁺ + √

2Y ij l jL ν iR ∆ ⁻ ,

⁽²¹⁾

where

∆ ⁻⁻ = (∆ ⁺⁺ ) ^†

^and

∆ ⁻ = (∆ ⁺ ) ^†

^{, as usual.}

Thegaugeintera tionsofthetriplet omponentsareobtainedfromthekineti term

L

^K

= (D ^µ ∆) ~ ^† · (D ^µ ∆) , ~

⁽²²⁾

where the ovariant derivative is

D µ = ∂ µ + ig ~ T · ~ W µ + ig ^′ Y B µ

⁽²³⁾

with

T 1 =







0 0 0 0 0 −i 0 i 0





 , T 2 =







0 0 i 0 0 0

−i 0 0





 , T 3 =







0 −i 0 i 0 0 0 0 0





 ,

⁽²⁴⁾

and

W ~ _µ = (W _µ ¹ , W _µ ² , W _µ ³ )

^{, the SU}

(2) _L

^{gaugeelds, with}

W _µ ⁺ = 1

√ 2 (W _µ ¹ − iW µ ² ) , W _µ ⁻ = 1

√ 2 (W _µ ¹ + iW _µ ² ) .

⁽²⁵⁾

Thegaugeintera tionsmediatings alartripletpairprodu tionpro essesinouranalysis

are

L ^W = −ig (∂ ^µ ∆ ⁻⁻ )∆ ⁺ − ∆ ⁻⁻ (∂ ^µ ∆ ⁺ ) W _µ ⁺ ,

−ig (∂ ^µ ∆ ⁻ )∆ ⁺⁺ − ∆ ⁻ (∂ ^µ ∆ ⁺⁺ ) W _µ ⁻ , L Z = ig

c W (1 − 2s ² W ) (∂ ^µ ∆ ⁻⁻ )∆ ⁺⁺ − ∆ ⁻⁻ (∂ ^µ ∆ ⁺⁺ ) Z _µ

− ig c W

s ² _W (∂ ^µ ∆ ⁻ )∆ ⁺ − ∆ ⁻ (∂ ^µ ∆ ⁺ ) Z µ , L ^γ = i2e (∂ ^µ ∆ ⁻⁻ )∆ ⁺⁺ − ∆ ⁻⁻ (∂ ^µ ∆ ⁺⁺ ) A µ

+ie (∂ ^µ ∆ ⁻ )∆ ⁺ − ∆ ⁻ (∂ ^µ ∆ ⁺ ) A _µ .

⁽²⁶⁾

trinosinglets,be ausethe news alars anbeprodu edatLHCbyunsuppressed gauge

intera tions. Ele troweak pre isiondata set anupperlimiton the tripletvev

v ∆

^{. The}

most re ent bound obtained froma global tis [78℄

v ∆ < 2

^GeV

,

⁽²⁷⁾

whi hismu hlessstringentthanthe onederived fromneutrino masses,Eq.(19),if

Y _ij

are of theorderof the hargedleptonYukawa ouplings. Therelativevalues of

v ∆

^and

Y _ij

^{,whoseprodu t isxed by Eq. (19),determine the de ays of the s alars(adetailed}

dis ussion an be found in se tion 5). Limits on

Y _ij

^{arise from} four-fermion pro esses like

µ ⁻ → e ⁺ e ⁻ e ⁻

^,

τ → 3ℓ

^{,aswellasLFVpro essesas}

µ → eγ

^[23,79℄. Constraintson produ tsof two

Y _ij

^{are oftheorder}

10 ⁻²

^{orlarger[23℄,mu hweakerthantheexpe ted}

size for these ouplings,ex ept for the produ t

|Y ^ee Y _eµ ^∗ | < 2.4 × 10 ⁻⁵ ,

⁽²⁸⁾

whi h is obtained from

µ ⁻ → e ⁺ e ⁻ e ⁻

^{. These} onstraints are automati ally satisedif

Y _ij

^{are oforder}

10 ⁻³

^{, whi his onsistentwith our assumptionthat thedileptonmodes}

dominate the harged s alarde ays (see se tion 5).

2.3 Seesaw III

In type III seesaw the SM is usually enlarged with three leptoni triplets

Σ j

^{, ea h}

omposed by three Weyl spinors of zero hyper harge. We hoose the spinors to be

right-handed under Lorentz transformations, following the notation in Refs. [23,80℄

to some extent. Writing the triplets in Cartesian omponents

Σ ~ j = (Σ ¹ _j , Σ ² _j , Σ ³ _j )

^and

usingstandardfour- omponentnotation,thetripletYukawaintera tionwiththelepton

doublets takes the form

L

^Y

= −Y ^ij L ¯ ^′ _iL (~ Σ j · ~τ) ˜ φ +

^{H. .}

,

⁽²⁹⁾

with

Y

^a

3 ×3

^{matrixofYukawa ouplings. ThetripletMajoranamass termmediating}

the seesaw is

L

^M

= − 1

2 M ij ~ Σ ^c _i · ~Σ ^j +

^{H. .}

,

⁽³⁰⁾

with

M

^a

3×3

^{symmetri matrix. Noti ethatallthemembers}

Σ ¹ _j

^,

Σ ² _j

^,

Σ ³ _j

^ofthetriplet

Σ j

^{havethe same mass term. Forea h triplet}

Σ j

^{, the harge}eigenstates are relatedto the Cartesian omponents by

Σ ⁺ _j = 1

√ 2 (Σ ¹ _j − iΣ ² j ) , Σ ⁰ _j = Σ ³ _j , Σ ⁻ _j = 1

√ 2 (Σ ¹ _j + iΣ ² _j ) .

⁽³¹⁾

The physi al parti les are harged Dira fermions

E _j ^′

^{and neutral Majorana fermions}

N _j ^′

^{(asbefore, we use primes for the weak} intera tion eigenstates),

E _j ^′ = Σ ⁻ _j + Σ ^+c _j , N _j ^′ = Σ ⁰ _j + Σ ^0c _j .

⁽³²⁾

Then, for our hoi e of right-handed hirality for the triplets wehave

E _jL ^′ = Σ ⁺ _j ^c , E _jR ^′ = Σ ⁻ _j , N _jL ^′ = Σ ⁰ _j ^c , N _jR ^′ = Σ ⁰ _j .

⁽³³⁾

Afterspontaneoussymmetrybreakingthe termsinEqs.(29), (30)leadtotheneutrino

mass matrix

L ^ν,mass = − 1

2 ν ¯ _L ^′ N ¯ _L ^′
0 ^{√ v} ₂ Y

√ v

2 Y ^T M

! ν _R ^′ N _R ^′

!

+ H.c. ,

⁽³⁴⁾

similar to the one for type-I seesaw in Eq. (6). The mass matrix for harged leptons,

also in ludingthe

3 × 3

^{SM Yukawa matrix}

Y ^l

^,reads

L ^l,mass = − ¯l L ^′ E ¯ _L ^′

√ v

2 Y ^l vY

0 M

! l ^′ _R E _R ^′

!

+ H.c.

⁽³⁵⁾

The gaugeintera tions of the new triplets an beobtained fromthe kineti term

L

^K

= i ~ Σ j · γ ^µ D µ ~ Σ j ,

⁽³⁶⁾

where a sum over

j = 1, 2, 3

^is understood. The ovariantderivative is

D µ = ∂ µ + ig ~ T · ~ W µ ,

⁽³⁷⁾

with the

T

^{matri es dened in Eqs. (24). The}

B µ

^{term is absent be ause the triplets}

have zero hyper harge. With the denitions inEqs. (31) and (32), the gauge intera -

tions in the weak eigenstate basis are

L ^W = −g ¯ E _j ^′ γ ^µ N _j ^′ W _µ ⁻ + ¯ N _j ^′ γ ^µ E _j ^′ W _µ ⁺
, L ^Z = gc W E ¯ _j ^′ γ ^µ E _j ^′ Z µ ,

L γ = e ¯ E _j ^′ γ ^µ E _j ^′ A _µ ,

⁽³⁸⁾

In the mass eigenstatebasis, the intera tionswith the photon are obviouslythe same.

For the

W

^and

Z

^{bosons they an be obtained after} diagonalisation of the harged lepton and neutrino mass matri es. Rewriting Eqs. (38) and the SM intera tions in

terms ofthemasseigenstates

E

^,

N

^(droppingthesubindi es)and SMleptons

l

^,

ν l

^,the

relevant terms are

L ^W = −g ¯ Eγ ^µ N W _µ ⁻ + ¯ Nγ ^µ E W _µ ⁺

− g

√ 2 V lN ¯lγ ^µ P L N W _µ ⁻ + V _lN ^∗ Nγ ¯ ^µ P L l W _µ ⁺

− g V lN Eγ ¯ ^µ P _R ν _l W _µ ⁻ + V _lN ^∗ ν ¯ _l γ ^µ P _R E W _µ ⁺
,

L ^Z = gc W Eγ ¯ ^µ E Z µ

+ g 2c W

V _lN ν ¯ _l γ ^µ P _L N + V _lN ^∗ N γ ¯ ^µ P _L ν _l
Z _µ + g

√ 2c _W V lN ¯lγ ^µ P L E + V _lN ^∗ Eγ ¯ ^µ P L l
Z µ ,

L ^γ = e ¯ Eγ ^µ E A µ ,

⁽³⁹⁾

at rst order inthe smallmixing

V lN ≃ − Y lN v

√ 2m N

.

⁽⁴⁰⁾

Noti e that the ouplings of the heavy neutrino

N

^{to the SM leptons are the same as}

inseesawIex eptforasign hangeinthe neutral urrent term. Fortheheavy harged

lepton they are similar but a fa tor

√ 2

^{larger, and the harged urrent oupling has}

opposite hirality. The intera tions with the SM Higgs an be obtained from the

Yukawa term in Eq. (29),

L ^H = − 1

√ 2

 ν ¯ _iL ^′ Y ij N _jR ^′ + ¯ N _jR ^′ Y _ji ^† ν _iL ^′  H

− ¯l _iL ^′ Y _ij E _jR ^′ + ¯ E _jR ^′ Y _ji ^† l ^′ _iL 

H .

⁽⁴¹⁾

Rewritingthe weakeigenstates asafun tionofthe mass eigenstates

E

^,

N

^,

l

^and

ν _l

^we

nd the intera tions

L ^H = g m Σ

2M W

V lN ν ¯ l P R N + V _lN ^∗ NP ¯ L ν l
H + g m Σ

√ 2M _W V lN ¯lP R E + V _lN ^∗ EP ¯ L l
H ,

⁽⁴²⁾

where

m Σ = m E = m N

^{isthe ommontripletmass. Finally,usingthe fa tthat}

N

^and

ν l

^{are Majorana fermions their neutraland s alar} intera tions an berewritten,

L ^ZνN = g 2c W

¯

ν l γ ^µ (V lN P L − V lN ^∗ P R ) N Z µ , L ^HνN = g m Σ

2M W

¯

ν l (V lN P R + V _lN ^∗ P L ) N H .

⁽⁴³⁾

As in the ase of heavy neutrino singlets, limits on the mixing of new fermion

triplets arise from ele troweak pre isiondata. The most re ent onstraintsare [69℄

3

X

i=1

|V ^eN i | ² ≤ 0.00036 ,

3

X

i=1

|V ^µN i | ² ≤ 0.00029 ,

3

X

i=1

|V ^{τ N} i | ² ≤ 0.00073

⁽⁴⁴⁾

µ → eγ

^,

τ → eγ

^and

τ → µγ

^{. Aglobaltallowstoobtainthe 90%CLbounds[23,80℄}

    

3

X

i=1

V eN i V _µN ^∗ _i     

≤ 1.1 × 10 ⁻⁶ ,     

3

X

i=1

V eN i V _{τ N} ^∗ _i     

≤ 0.0012 ,     

3

X

i=1

V µN i V _{τ N} ^∗ _i     

≤ 0.0012 ,

(45)

althoughthe limitsinEqs.(44)and the S hwarz inequalityimplystronger onstraints

by afa tor oftwofor the produ ts of the mixingwith the tau lepton and the ele tron

or muon,

    

3

X

i=1

|V ^eN i V _{τ N} ^∗ _i     

≤ 0.0005 ,     

3

X

i=1

|V ^µN i V _{τ N} ^∗ _i     

≤ 0.0005 .

⁽⁴⁶⁾

These limits are not relevant for heavy triplet produ tion at LHC, whi h takes pla e

through gaugeintera tionsof orderunity. Forthe de ay,the boundsonthe mixingare

six orders of magnitude above the riti al values

V lN ∼ O(10 ⁻⁸ )

^{for whi h the gauge}

boson de ay modes begin to be suppressed withrespe t toother de ays.

3 General features of the analyses

Our estimations of the dis overy potential for seesaw messengers are performed by

simulating their produ tion at LHC, together with the SM pro esses whi h may on-

stituteaba kground. Thesignalsandba kgroundsare al ulatedwithmatrix element

generators, whi hprodu eeventsampleswhi harefeededintoPythia 6.4[81℄ toadd

initialandnal state radiation(ISR,FSR) andpile-up,and perform hadronisationfor

ea h event. Afterthis, afast dete tor simulationprogram [82℄ isused, whose purpose

is tosimulate how the event would be seen in the ATLAS dete tor. The tagging of

b

and

τ

^{jets is performed with the ATLFASTB pa kage, sele ting e ien ies of 60% and}

50%, respe tively, and the orresponding mistag rates: for

b

^{tagging, it is about 1%}

for lightjetsand 15% for

c

^{jets, and for}

τ

^{taggingitis about 1%for non-taujets. The}

analysis of the events is then performed in terms of harged leptons, jets and missing

energy.

The heavy neutrino singlet signals, des ribed further in se tion 4, are generated

with theAlpgenextensionofRef.[29℄. Fors alarandfermiontripletprodu tionanew

generator Triada has been developed. For seesaw II it al ulates

∆ ⁺⁺ ∆ ⁻⁻

^,

∆ ^±± ∆ ^∓

and

∆ ⁺ ∆ ⁻

^{produ tion with subsequent leptoni de ays}

∆ ^±± → l ^± i l ^± _j

^,

∆ ^± → l ^± i ν

^(see

se tion5),where

l i = e, µ, τ

^{. (Wewilluse}

l

^{whenreferringtoele trons,muonsandtau}

leptons, reserving

ℓ

^{for ele trons and muons only.) For seesaw III it al ulates}

E ⁺ E ⁻

and

E ^± N

^{produ tion with all de ays to light leptons and gauge or Higgs bosons, as}

nal states with 128 dierent matrix elements for

E ⁺ E ⁻

^{and 748 nal states with 72}

matrixelementsfor

E ^± N

^{,whi hhavetobegeneratedwiththeir} orrespondingweights.

Matrixelementsforthe

2 → n

^{pro esses(}

n = 4

^{fors alartripletand}

n = 6

^forfermion

triplet produ tion) are al ulated using HELAS [83℄, in ludingallspin and nite width

ee ts. Integration in phase spa e is performed with VEGAS [84℄. The output of the

program, in the form of unweighted events, in ludesthe olour stru ture ne essary to

interfa e itwith Pythia.

Anequally importantingredient fora orre testimation ofthe dis overypotential

of a signal is the ba kground evaluation. Re ent parton-level al ulations [28,3537℄

underestimateSMba kgroundsbe ausethey annota ountforseveralphysi alee ts

presentinreal experiments. Onesu hee t isthe appearan e ofextra jets inthenal

state fromISR,FSRandespe iallypile-up. Inthisway,pro esseswithasmallnumber

of partons (and typi ally larger ross se tions) give important ontributions to nal

states with a larger number of jets, due to pile-up. An illustrative example will be

found inse tion6.9:

4/5

^ofthetotal ontributionof

W nj

^{produ tion(where}

nj

^stands

for

n

^{jetsatthepartoni level)toanalstatewithfourhardjetsisdueto}multipli ities

n = 0, 1, 2

^{at the partoni level. Another physi al ee t whi h annot be in luded}

in parton-level al ulationsis the produ tion of isolated hargedleptons from

b

^quark

de ays. Aswefoundinpreviouswork[29℄,

t¯ tnj

^and

b¯bnj

^arethemainSMba kgrounds givingtwolike-signleptons

ℓ ^± ℓ ^±

⁽

ℓ = e, µ

^{). Inthe former ase,this happens whenthe}

t¯ t

^{pair de ays} semileptoni ally, and one

b

^{quark gives the se ond lepton, while in the}

latter both harged leptons result from

b

^{de ays. Likewise, three leptons}

ℓ ^± ℓ ^± ℓ ^∓

^an

beprodu edinthedileptonde ay of a

t¯ t

^{pair,the thirdlepton omingfroma}

b

^quark.

Charged leptons from

b

^{quark de ays typi allyhave smalltransverse momentum, but}

the ross se tion for

t¯ tnj

^{produ tion is three orders of magnitude larger than for the}

signals onsidered and even larger for

b¯bnj

^,

1.4 µ

^{b. Besides, signals sometimes have}

leptons whi h are not very energeti , e.g. when they originate from

τ

^{de ays. In any}

ase,suppressingtheseba kgroundswithouteliminatingimportantsignal ontributions

is not easy. A third ee t whi h makes a parton level al ulation insu ient is that

sometimes a hargedleptonismissedbythe dete tor,forexamplebe auseitislo ated

inside a hadroni jet and thus it is not isolated. This is important, for instan e, for

like-sign dilepton signals, where one of the main ba kgrounds is

W Znj

^{produ tion}

when one of the leptonsfrom the

Z

^{de ay is missedby the dete tor.}

In order to have predi tions for SM ba kgrounds as a urate as possible we use

Alpgen [85℄ to generate hard events whi h are interfa ed to Pythia using the MLM

pres ription [86℄ to perform a mat hing between the soft radiation generated by

Pro ess De ay

L

^Events

t¯ tnj

^,

n = 0, . . . , 6

semileptoni 300 fb

−1

60.8 M

t¯ tnj

^,

n = 0, . . . , 6

^{dileptoni 300 fb}

⁻¹

^{15.2 M}

b¯bnj

^,

n = 0, . . . , 3

^{all 0.075fb}

⁻¹

^116M

c¯ cnj

^,

n = 0, . . . , 3

^{all 0.075fb}

⁻¹

^145M

tj W → lν

^{300 fb}

⁻¹

^{9.5 M}

t¯b W → lν

^{300 fb}

⁻¹

^{540 K}

tW

^{all 300 fb}

⁻¹

^16M

t¯ tt¯ t

^{all 300 fb}

⁻¹

^{1.6 K}

t¯ tb¯b

^{all 300 fb}

⁻¹

^{340 K}

W nj

^,

n = 0, 1, 2 W → lν

^{10 fb}

⁻¹

^{557.4 M}

W nj

^,

n = 3, . . . , 6 W → lν

^{30 fb}

⁻¹

^10M

W b¯bnj

^,

n = 0, . . . , 4 W → lν

^{300 fb}

⁻¹

^{5.2 M}

W c¯ cnj

^,

n = 0, . . . , 4 W → lν

^{300 fb}

⁻¹

^{5.5 M}

W t¯ tnj

^,

n = 0, . . . , 4 W → lν

^{300 fb}

⁻¹

^{50.6 K}

Z/γ nj

^,

n = 0, 1, 2

^,

m _ll < 120

^GeV

Z → l ⁺ l ⁻

^{10 fb}

⁻¹

^{54.9 M}

Z/γ nj

^,

n = 3, . . . , 6

^,

m _ll < 120

^GeV

Z → l ⁺ l ⁻

^{30 fb}

⁻¹

^{1.1 M}

Z/γ nj

^,

n = 0, . . . , 6

^,

m _ll > 120

^GeV

Z → l ⁺ l ⁻

^{300 fb}

⁻¹

^{17.3 M}

Zb¯bnj

^,

n = 0, . . . , 4 Z → l ⁺ l ⁻

^{300 fb}

⁻¹

^2M

Zc¯ cnj

^,

n = 0, . . . , 4 Z → l ⁺ l ⁻

^{300 fb}

⁻¹

^{1.8 M}

Zt¯ tnj

^,

n = 0, . . . , 4 Z → l ⁺ l ⁻

^{300 fb}

⁻¹

^{18.7 K}

W W nj

^,

n = 0, . . . , 3 W → lν

^{300 fb}

⁻¹

^{2.9 M}

W Znj

^,

n = 0, . . . , 3 W → lν

^,

Z → l ⁺ l ⁻

^{300 fb}

⁻¹

^{377 K}

ZZnj

^,

n = 0, . . . , 3 Z → l ⁺ l ⁻

^{300 fb}

⁻¹

^{37.4 K}

W W W nj

^,

n = 0, . . . , 3 2W → lν

^{300 fb}

⁻¹

^{14.7 K}

W W Znj

^,

n = 0, . . . , 3

^{all 300 fb}

⁻¹

^{48.7 K}

W ZZnj

^,

n = 0, . . . , 3

^{all 300 fb}

⁻¹

^{15.3 K}

ZZZnj

^,

n = 0, . . . , 3 2Z → l ⁺ l ⁻

^{300 fb}

⁻¹

¹¹⁴

Table 1: Ba kground pro esses onsidered in the simulations. The se ond olumn

indi ates the de ay modes in luded (where

l = e, µ, τ

^{), and the third olumn the}

luminosityequivalentgenerated. Thelast olumn orrespondstothe numberofevents

after mat hing,with K and M standingfor

10 ³

^and

10 ⁶

^events,respe tively.

PythiaandthehardjetsgeneratedbyAlpgenavoidingdouble ounting. Ba kground

samplesaregeneratedwithlargestatisti s,often300fb

−1

,inordertoavoidu tuations

in the nal sele ted samples. This is a demanding omputational task, whi h would

takearoundtenyearsinamodernsinglepro essorsystem. Theba kgroundsgenerated

and the orresponding luminosities are olle ted in Table 1. For

b¯bnj

^and

c¯ cnj

^the

these ba kgrounds as des ribed in detail in appendix A of Ref. [29℄. Signals are all

generated with a statisti s of 3000 fb

−1

, and all results are res aled to 30 fb

−1

in the

Tables.

The pro edure used for estimating the statisti al signi an e of a signal is onsid-

ered ase by ase. In the absen e of any systemati un ertainty on the ba kground,

the statisti al signi an e would be

S ⁰ ≡ S/ √

B

^{, where}

S

^and

B

^{are the number of}

signal and ba kground events, or its analogous from the

P

^{-number for small ba k-}

grounds where Poisson statisti s must be applied. Nevertheless, there are systemati

un ertainties inthe ba kground evaluationfromseveral sour es: the theoreti al al u-

lation, parton distribution fun tions (PDFs), the ollider luminosity, pile-up,ISR and

FSR, et . aswell assome spe i un ertainties related tothe dete tor likethe energy

s ale and

b

^{tagging e ien y. Provided that the signal manifests as a lear peak in a}

distribution (as in doubly harged s alar produ tion) or a long tail, it will be possi-

ble tonormalisethe ba kground dire tly fromdata,and extra t the peak signi an e.

In this ase, we give estimators of the sensitivity onsidering two hypotheses for the

ba kground normalisation:

(a) the SMba kground normalisationdoes not have any un ertainty;

(b) the SMba kground is normaliseddire tly from data.

In some of the ases examined the signal has a wide distribution and the SM ba k-

ground annot be normalised from data. In su h situations we in lude a 20% ba k-

groundun ertaintyinthesigni an esummedinquadrature, usingasestimator

S ²⁰ ≡ S/pB + (0.2B) ²

^.

4 Seesaw I signals

Forour study we onsider the single heavy neutrino produ tion pro ess

q ¯ q ^′ → W ^∗ → l ^± N ,

⁽⁴⁷⁾

with

l = e, µ, τ

^{. Its ross se tion depends on}

m N

^{as well as on the small mixing}

V lN

^,

to whi h the amplitude is proportional. Its dependen e on

m N

^{is plotted in Fig. 1,}

normalised to

|V ^lN | ² = 1

^{.2 Heavy Majorana neutrino singletsde ay toSMleptonsplus}

2

Thetotal rossse tionplottedinFig.2ofRef.[29℄isunderestimatedbyafa toroftwo,whilethe

rossse tionswith

N

^{de ayandwith}kinemati al uts,aswellasthenumbersofeventsin ludedinall Tables,are orre t. WethankB.Gavelaforbringingthisin orre tnormalisationintoourattention.

50 100 150 200 m _N

1 10 10 ² 10 ³ 10 ⁴ 10 ⁵

σ / | V lN | 2 (pb)

Figure1: Cross se tionfor produ tionof heavy neutrino singlets

q ¯ q → l ^± N

^{at LHC.}

a gauge orHiggs boson, with partialwidths

Γ(N → l ⁻ W ⁺ ) = Γ(N → l ⁺ W ⁻ )

= g ²

64π |V lN | ² m ³ _N M _W ²



1 − M _W ² m ² _N

 

1 + M _W ²

m ² _N − 2 M _W ⁴ m ⁴ _N

 ,

Γ(N → ν ^l Z) = g ²

64πc ² _W |V ^lN | ² m ³ _N M _Z ²



1 − M _Z ² m ² _N

 

1 + M _Z ²

m ² _N − 2 M _Z ⁴ m ⁴ _N

 ,

Γ(N → ν ^l H) = g ²

64π |V ^lN | ² m ³ _N M _W ²



1 − M _H ² m ² _N

 ²

.

⁽⁴⁸⁾

For

m N < M W

^{these two body de ays are not possible and}

N

^{de ays into three}

fermions, mediated by o-shell bosons. Within any of these four de ay modes, the

bran hing fra tions for individual nal states

l = e, µ, τ

^{are in the ratios}

|V ^eN | ² :

|V ^µN | ² : |V ^{τ N} | ²

^{. However, asit an be learly seen fromEqs. (48),the total bran hing}

ratio forea h ofthe four hannelsabove (summingover

l

^)is independent ofthe heavy neutrino mixingand determined onlyby

m N

^{and the gauge and Higgsboson masses.}

Heavy neutrino produ tion ross se tions are suppressed by the small mixings

|V ^eN | ² ≤ 0.0030

^,

|V ^µN | ² ≤ 0.0032

^,

|V ^{τ N} | ² ≤ 0.0062

^{[69℄, and then the} observability of

lN

^{produ tion is limited to masses up to 150 GeV} approximately due to the large ba kgrounds [29℄.

3

In this situation, heavy neutrino de ay produ ts are not very en-

ergeti and SM ba kgrounds are important. Among the possible nal states given by

Eqs. (48), only harged urrent de ays give nal states whi h may be observable in

3

Themassrea hismu hlargerat

e ⁺ e ⁻

^[56,73℄and

eγ

^{[87℄ olliders,whose}environmentis leaner (see Ref.[57℄forareview).

q ¯ q → Z ^∗ → νN ,

gg → H ^∗ → νN

⁽⁴⁹⁾

give

ℓ ^±

^and

ℓ ⁺ ℓ ⁻

^{nal states whi h are} unobservable due to the huge ba kgrounds.

Pairprodu tion

q ¯ q → Z ^∗ → NN

⁽⁵⁰⁾

has its ross se tion suppressed by

|V lN | ⁴

^{, phase spa e and the}

Z

propagator, and is thus negligible.

In a previous work [29℄ we have studied in great detail the observability of heavy

neutrino singlets in the like-sign dilepton nal state for

m N > M W

^{as well as for}

m N < M W

^{, performing} sophisti ated likelihood analyses to ee tively suppress the ba kgrounds. We found that a heavy neutrino oupling only to the ele tron with

|V ^eN | ² = 0.0054

^{ouldbedis overedupto}

m N = 145

^{GeV,andifit ouplestothemuon}

with

|V ^µN | ² = 0.0096

^{it ouldbedis overedupto200GeV.(Ifit ouplesonlytothetau}

the signalsare swamped bythe SMba kground.) Forheavy neutrinoslighter thanthe

W

^{boson,we found that, for example,a 60GeV neutrino ouplingto the muon might}

bedis overedup to

|V ^µN | ² = 4.9 × 10 ⁻⁵

^{. Theselimits,however, are obtainedfromvery}

optimisedanalyses whi huseasinputthe heavy neutrinomasstobuildthe probability

distributions for the heavy neutrino signal. In this se tion we will take the opposite

approa h, following the philosophy of this paper: we will investigate whether with

generi  model-independent uts the heavy neutrino (as well asseesaw II and seesaw

III signals) might be observable. Of ourse, dedi ated experimental sear hes an be

arried out assumingsome value for

m N

^{and optimisingthe} kinemati al distributions for this mass toa hieve thebest sensitivity. But,atleast inarst step, LHC sear hes

are likelytobeperformedwith general and model-independent event sele tions.

Amajordieren ebetween heavy neutrinosignalsstudiedinthisse tionands alar

triplet and fermion triplet signals on erns lepton avour. For the latter, the SM

ba kgrounds involving ele trons and muons are alike at large transverse momenta,

and itmakessense to perform avour blind sear hes summingele trons and muons.

This is alsosensible from the point of view of the signals, whi h have the same ross

se tionsif thenew states oupletothe ele tron,the muon orboth,asitwillbeargued

in se tions5 and6. On the other hand,for heavy neutrino produ tionthe situationis

learly dierent. At low transverse momenta SM ba kgrounds involvingele trons are

mu h larger than those involvingmuons, as shown in Ref. [29℄, and sear hes must be

performedindependentlyinordertoavoidthatapossiblesignalinmuonnal statesis

heavy neutrino ouplesto the ele tron, the muon or both: if it ouples tothe ele tron

e ^± N

^{produ tionwilltakepla e,ifit ouplestothe muonwewillhave}

µ ^± N

produ tion, and if it ouplesto both we willhave the two pro esses simultaneously. Therefore, for

heavy neutrino sear hes it is onvenient todivide nal states by lepton avour.

In what follows we assume two s enarios: (i) a heavy neutrino oupling only to

the ele tron with

|V ^eN | ² = 0.0030

^{, labelled as s enario S1; (ii) oupling only to the}

muon with

|V ^µN | ² = 0.0032

^{, labelled as s enario S2. We will take a mass}

m N = 100

^{GeV, between the two ases previously studied. For su h a heavy neutrino mass}

the produ tion ross se tion is large, and the kinemati s of the signal is ompletely

dierent from the other ases. The de ay bran hing ratios are Br

(N → l ⁻ W ⁺ ) =

Br

(N → l ⁺ W ⁻ ) = 0.43

^{, Br}

(N → νZ) = 0.14

^{. We will examine nal states with (a)}

three harged leptons

ℓ ^± ℓ ^± ℓ ^∓ X

^{; (b) two like-sign dileptons}

ℓ ^± ℓ ^± X

^{, where}

X

^denotes

possible additional jets and the leptons an have dierent avour. Final states with

two opposite-sign leptons or only one lepton are unobservable for these small ross

se tions.

4.1 Final state

ℓ ^± ℓ ^± ℓ ^∓

Trileptonsignalsare produ edin thetwo harged urrent de ay hannelsof the heavy

neutrino, with subsequent leptoni de ay of the

W

^{boson, e.g.}

ℓ ⁺ N → ℓ ⁺ ℓ ⁻ W ⁺ → ℓ ⁺ ℓ ⁻ ℓ ⁺ ν , ¯

ℓ ⁺ N → ℓ ⁺ ℓ ⁺ W ⁻ → ℓ ⁺ ℓ ⁺ ℓ ⁻ ν ,

⁽⁵¹⁾

(and small additional ontributions from

τ

^{leptoni de ays). This nal state is very}

lean on e that

W Znj

^{produ tion an be almost eliminated with a simple ut onthe}

invariantmass of opposite harge leptons.

For event pre-sele tion we require the presen e of two like-sign harged leptons

ℓ 1

and

ℓ 2

^{(orderedbyde reasing}

p _T

^{)with transverse momentum largerthan30GeV,and}

an additionallepton of opposite harge. The hoi e of the

p _T

^{ut for like-sign leptons}

is motivated by the need to redu e ba kgrounds where soft leptons are produ ed in

b

de ays, forexample

t¯ tnj

^{inthe dilepton hannel. Foreventsele tion, inarst step we}

only require that neitherof the two opposite-signlepton pairs have an invariantmass

loser to

M _Z

^{than 10 GeV. These} pre-sele tion and sele tion riteria are the same as those appliedin the analysis of s alar and fermion tripletsignals in the next se tions,

but in this subse tion we split the sample in two disjoint sets: nal states with at

least twoele trons (labelled as

2e

^{)and with atleast two muons (}

2µ

^{). Thenumber}