Type-III seesaw mechanism at CERN LHC

Type-III seesaw mechanism at CERN LHC

Roberto Franceschini,1 Thomas Hambye,2 and Alessandro Strumia3

1Scuola Normale Superiore and INFN, Pisa, Italy2Service de Physique Theorique, Universite Libre de Bruxelles, Bruxelles, Belgium

3Dipartimento di Fisica dell’Universita di Pisa and INFN, Pisa, Italy(Received 4 June 2008; published 6 August 2008)

Neutrino masses can be generated by fermion triplets with TeV-scale mass, that would manifest at LHC

as production of two leptons together with two heavy standard model (SM) vectors or Higgs, giving rise to

final states such as 2‘þ 4j (that can violate lepton number and/or lepton flavor) or ‘þ 4jþ E6 T . We

devise cuts to suppress the SM backgrounds to these signatures. Furthermore, for most of the mass range

suggested by neutrino data, triplet decays are detectably displaced from the production point, allowing to

infer the neutrino mass parameters. We compare with LHC signals of type-I and type-II seesaw.

DOI: 10.1103/PhysRevD.78.033002 PACS numbers: 13.15.+g, 13.35.Hb, 14.60.Pq, 14.60.St

I. INTRODUCTION

The smallness of the observed neutrino masses [1] sug-gests that they are more likely generated at an energy scalemany orders of magnitude above the TeV scale that isgoing to be explored by the LHC pp collider.Nevertheless nothing prevents that the particles that medi-ate neutrino masses have TeV-scale masses, and it is worthto see what would be their manifestations, given that find-ing a signal of new physics among the backgrounds presentat LHC is easier if one knows what to search for. Tree levelexchange of three different types of new particles withmasses M can generate neutrino masses:

(i) Type-I seesaw employs at least two neutral fermions,the ‘‘right-handed neutrinos’’ with Yukawa cou-plings �: in view of m� ¼ �2v2=M, for M� TeVthe Yukawa coupling � directly related to neutrinomasses are so small that right-handed neutrinos arenegligibly produced at LHC [2].

(ii) Type-II seesaw employs a SUð2ÞL scalar triplet, thatwould be produced at LHC via its gauge interactionsleading to the signals explored in [3,4] if M & TeV,however such a small M is not technically natural.

(iii) Type-III seesaw [5] employs at least two SUð2ÞLfermion triplets, and here we explore their LHCphenomenology. A TeV-scale M is technically natu-ral, although unmotivated.

Combinations of these neutrino mass sources are alsopossible, as, for example, in left-right models which con-tains both type-I and type-II, or as with the adjoint repre-sentation of SU(5) which contains both type-I and type-III[6–9].

Section II describes the triplet fermion Lagrangian.Section III studies triplet production at LHC. Section IVstudies triplet decays. Section V combines the previousresults to derive signatures at LHC. In Sec. VI we presentour conclusions.

II. THE LAGRANGIAN

Generic neutrino masses can be mediated by at leastthree fermion SUð2ÞL triplets Na with zero hypercharge:the Lagrangian keeps the same structure as in the singletcase, but with different contractions of the SUð2ÞL indicesthat we explicitly show

L ¼ LSM þ �Nii 6DNi þ��ijNa

i ðLj � " � �a �HÞ

þMij

2Na

i Naj þ H:c:

�: (1)

The SUð2ÞL gauge index a runs over f1; 2; 3g, �a are thePauli matrices, and " is the permutation tensor ("12 ¼ þ1);i, j are flavor indices. Gauge covariant derivatives aredefined as D ¼ @þ igAATA; the lepton doublets L ¼ð�; eLÞ and the Higgs doublet H ¼ ðhþ; h0Þ have hyper-charge Y ¼ �1=2 and Y ¼ 1=2, respectively, and trans-form as a two under SUð2ÞL. Taking into account thebreaking of SUð2ÞL, we choose the usual unitary gauge

where hþ ¼ 0 and h0 ¼ vþ h=ffiffiffi2

pwith v ¼ 174 GeV.

The three components of the Weyl fermion Na are N0 �N3 with charge zero and N� � ðN1 � iN2Þ= ffiffiffi

2p

withcharge�1. With this convention all kinetic and mass termshave conventional normalization. Defining a Dirac spinor�C ¼ ðN�; �NþÞ and aMajorana spinor�N ¼ ðN0; �N0Þ thevector couplings become all of vectorial type [10]

L ¼ �g2ð ��NW6 þ�C þ ��CW6 ��NÞ þ e ��CA6 �C

þ g2cW ��CZ6 �C þ � � � : (2)

N0 has the same Yukawa interaction and mass term as theright-handed neutrino of type-I seesaw: so one has theusual seesaw formula for light Majorana neutrino massesm� ¼ �ðv�ÞT �M�1 � ðv�Þ. We work in the basis of Ni

PHYSICAL REVIEW D 78, 033002 (2008)

1550-7998=2008=78(3)=033002(9) 033002-1 � 2008 The American Physical Society

http://dx.doi.org/10.1103/PhysRevD.78.033002

mass eigenstates, whereMij ¼ diagðM1;M2;M3Þwith 0<M1 � M2 � M3. The light neutrino masses are 0 � m1 �m2 � m3. We define the parameters ~mi � jPj�

2ijv

2=Mijthat tell how fast Ni decays: �i ¼ ~miM

2i =ð8�v2Þ. The ~mi

are unknown, but must satisfy the following neutrino massconstraints

~m i � m1;Xi

~mi �X3i¼1

mi: (3)

The first bound is known [11] and only holds with threetriplets. The second bound can be derived applying theSchwarz inequality to the trace of the neutrino mass ma-trix. The parameter ~m1 is unknown: it can be comparable tothe observed solar and atmospheric mass splitting, or itcould be much smaller (or much larger if cancellationsbetween large Yukawa couplings occur in the neutrinomasses).

One or more Ni could be light enough to be probed byLHC.

It would be especially interesting to measure the prop-erties of the lightest triplet, N1, that could play an impor-tant role in cosmology: its decays source a leptonasymmetry, dominantly at temperatures T �M1=20,somewhat depending on the precise interplay betweenthe annihilation rate, the decay rate, and the expansionrate [12]. According to the standard model (SM), in cos-mology a nonzero Higgs vacuum expectation value startsto appear via a second-order phase transition below acritical temperature comparable to the Higgs mass mh,suppressing the sphaleron rate [13]. As a consequencethermal baryogenesis via leptogenesis is suppressed ifM1 & 10mh, leading to some absolute boundary on M1

even in the most favorable case of a large CP asymmetry inN1 decays. Along the lines of [14] one can invent argu-ments that allow one to argue that values ofM1 around thisanthropic boundary are motivated by multiverse consider-ations. The CP asymmetry in N decays (i.e., from vertexloop diagrams) is negligibly small, while CP violation inN2=N1 mixing can be large enough to allow successfulresonant leptogenesis if M2 �M1 � �, and the decaywidth � can be large enough (see below) that N1 $ N2

oscillations could be observable at LHC.We focus on the lightest heavy triplet N1, we denote as ‘

the unknown combination of e, �, � coupled to N1, andfrom now on we drop the index 1 on M and N. Thecoupling to the Higgs generates a mass-mixing term be-tween N0, N�, and �‘, ‘L respectively

�‘ N0

�‘

N0

0 ��v��v M

� �;

‘L N�‘RNþ

�‘v 0� ffiffiffi

2p

�v M

� �:

(4)

The resulting N0=�‘ and N�=‘L mixings are of order

�v=M ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi~m1=M

p � 10�6 and can be neglected (the Z

couplings of ‘L has been measured at LEP with precisionof about 10�3) and the N0, N� couplings to the Higgs hremain unchanged. The resulting mass splitting betweenthe charged and the neutral components of theNa multipletis of order ~m1 and can be neglected with respect to the masssplitting generated by one-loop corrections: in the limitM MZ one has �M � M� �M0 ¼ 166 MeV [15].The only relevant effect of the mixings is to generate

SUð2ÞL-breaking couplings between the Na, the SM lep-tons, and the heavy Z,W� vectors that ‘‘eat’’ the Goldstonecomponents of the Higgs. This is how the �NLH couplingsinvolving the Goldstones reappear in the Lagrangian.Indeed, the unitary field redefinitions that define the masseigenstates at first order in �v=M 1

�‘ ! �‘ � �v

MN0; N0 ! N0 þ �v

M�‘;

‘L ! ‘L � ffiffiffi2

p �v

MN�; N� ! N� þ ffiffiffi

2p �v

M‘L

(5)

generate the following couplings [8,10]

L � g22cW

�v

MZ�ð �N0��þ ffiffiffi

2p

�N � ��eL þ H:c:Þ

þ g22

�v

MWþ

� ð2 �N þ �� ffiffiffi2

p�N0��eLÞ þ H:c: (6)

relevant forN0,N� decays. Such interactions are typical ofmodels where heavy states have a SUð2ÞL-breaking mixingwith leptons. Type-III interactions induce mixing effectsnot only for the (unobservable) neutrinos like type-I mod-els but also for charged leptons which leads to a richphenomenology.Precision electroweak data are affected via a small

correction to the W parameter of [16]: W ¼þ�2M

2W=15�M

2.

III. PRODUCTION AT LHC

Production at LHC is dominated by gauge couplings: thedominant partonic process that leads to pair production oftriplets in pp collisions is q �q0 ! W�, Z. The partonicproduction cross sections, summed over initial state colorsand over final-state polarizations, and averaged over initialstate polarizations, are

d�

dt¼ V2

L þ V2R

16�s2Ncð2M4 þ s2 � 4M2tþ 2s tþ2t2Þ; (7a)

� ¼ ð3� 2Þ48�

NcsðV2L þ V2

RÞ (7b)

where Nc ¼ 3, � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 4M2=s

pis the N velocity (0 �

� 1), and


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VA ¼ 0 for q �q ! N0N0

VA ¼ Qqe2

sþ gqAg

22

s�M2Z

for q �q ! NþN�

VA ¼ g22s�M2

W

ALffiffiffi2

p for u �d ! NþN0

(8)

where gqA ¼ T3 � s2WQq is the Z coupling of quark q for

A ¼ fL; Rg. This result does not agree with Eq. (10) of[17]. SUð2ÞL invariance is restored in the limit M2 M2

Z,

and the result 2�u �u ¼ 2�d �d ¼ �u �d ¼ �d �u agrees with[15]. The cross section e�eþ ! NþN�, relevant for apossible future collider, is found by replacing q ! e inEq. (8).

Figure 1(a) shows �ðpp ! N0N�Þ and �ðpp !NþN�Þ as a function of M at LHC, i.e., at

ffiffiffis

p ¼ 14 TeV.We integrated the parton distribution functions of [18], andwe checked that the result numerically agrees with the oneobtained implementing the triplet model in MADGRAPH

[19]. This would lead to about 3� 103 (10) pairs createdat LHC for M ¼ 250 GeV (M ¼ 1 TeV) for an integratedluminosity of 3=fb which should be collected at LHC inless than one year. These numbers have to be multiplied byabout 2 orders of magnitude after five years of data taking.Therefore LHC should be able to produce at least a fewtens of events up to masses ofM� 1 TeV, or even 1.5 TeVin the long term. Figure 1(b) shows the distribution in thetransverse momentum pT , as computed by ourMonte Carlo for three representative values of M: it ispeaked at pT �M=2.

Testing the production cross section would allow one toidentify the quantum numbers of the particle and to testthat/if the theory correctly predicts the gauge interactionsof a fermionic SUð2ÞL triplet [e.g., for a scalar replaceð3� 2Þ ! 3=2 in Eq. (7b)] but not to study its con-nection with neutrinos. This is encoded in N0, N� decays,that also define the signatures at LHC.

IV. DECAYS

The N0 decay widths agree with the results of [8]

�ðN0 ! �‘hÞ ¼ �ðN0 ! ��‘hÞ ¼ 1

8

�2M

8�

�1� m2

h

M2

�2;

(9a)

�ðN0 ! Z�‘Þ ¼ �ðN0 ! Z ��‘Þ ¼ 1

8

�2M

8�

�1�M2

Z

M2

�2

��1þ 2

M2Z

M2

�; (9b)

�ðN0 ! Wþ‘�Þ ¼ �ðN0 ! W�‘þÞ ¼ 1

4

�2M

8�

�1�M2

W

M2

�2

��1þ 2

M2W

M2

�: (9c)

The Higgs contribution is only possible if mh <M and forM mh it equals 1=8 of the SUð2ÞL invariant width,�ðN0Þ ¼ �ðN�Þ ¼ �2M=8�. The remaining terms arisebecause of lepton mixing, Eq. (5), and the fact that in theunitary gauge the W�, Z vectors became massive eatingcompletely the Goldstones in the Higgs doublet. The pos-sibility that M<MW such that all two-body decays arekinematically forbidden is already excluded by LEP2.The N� decay widths are given by [8]

�ðN� ! ‘�hÞ ¼ 1

4

�2M

8�

�1�m2

h

M2

�2; (10a)

�ðN� ! ‘�ZÞ ¼ 1

4

�2M

8�

�1�M2

Z

M2

�2�1þ 2

M2Z

M2

�; (10b)

�ðN� ! �ð�Þ

‘W�Þ ¼ 1

2

�2M

8�

�1�M2

W

M2

�2�1þ 2

M2W

M2

�: (10c)

The charged/neutral mass small splitting �M 166 MeVis bigger than m� in all the allowed range of M and givesrise to the following extra decay channels [15]

FIG. 1 (color online). Left plot: total production cross section at LHC. Right plot: pT distribution.

TYPE-III SEESAW MECHANISM AT CERN LHC PHYSICAL REVIEW D 78, 033002 (2008)

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�ðN� ! N0��Þ ¼ 2G2FV

2ud�M

3f2��

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� m2

�

�M2

s; (10d)

�ðN� ! N0e��ð�Þ

eÞ ¼ 2G2F�M

5

15�3; (10e)

�ðN� ! N0��ð�Þ

�Þ ¼ 0:12�ðN� ! N0e��ð�Þ

eÞ (10f)

which do not depend on any free parameter. Figure 2 showsthe various decay rates as a function of M for fixed ~m1 ¼meV; we recall that �2M ¼ ~m1M

2=v2.Notice that, while pp ! N0N0 does not arise at tree

level, this production channel is effectively produced bythe N� ! N0�� decay because the �� are too soft to beobserved. The decay mode into pions is dominant for ~m &3� 10�4 eV � ð100 GeV=MÞ2, so that the effective pro-duction rate pp ! N0N0 is given by the sum of all crosssections in Fig. 1(a).

V. SIGNALS AT LHC AND DISPLACED VERTICES

Production of N0N� and N�N� and their decays giverise to a variety of possible final states. We focus on thoseinvolving jets, that have higher rates than purely leptonicfinal states, and need a discussion of standard model back-grounds and how they can be suppressed. In Sec. VA westudy the signal with the higher rate; lepton-flavor violationis studied in Sec. VB, and lepton-number violation inSec. VC. For simplicity in what follows we often leaveimplicit that events with each particle replaced by itsantiparticle are also possible: signal and background ratesare similar but not equal.

A. The signal with the higher rate

In view of the small fb-scale cross sections for N0, N�production, we first discuss the channel with the relativelyhigher rate (for ~m1 * 10�4 eV)

pp ! NþN0 ! ��WþW�‘�

! 4 jetsþmissing energy

þ a charged lepton, all hard: (11)

In the following discussions we will consider the followingset of cuts, needed to make the leptons and jets identifiable:

pT;j > 20 GeV; pT;‘ > 10 GeV;

�R‘‘;jj;j‘ > 0:4; �j;‘ < 5;(12)

where pT is the momentum orthogonal to the beam axis, �

is the pseudorapidity, and �R ¼ ð��2T þ ��2Þ1=2, with

��T being the angular separation in the plane transverseto the beam. In order to suppress the SM backgrounds wewill also implement the extra cut of Eq. (13): about 24%(36%) of the signal events pass all cut requirements forM ¼ 250ð750Þ GeV. With an integrated luminosity of3=fb, this would lead to about 100 events for M ¼250 GeV.Disregarding misdetections and particles escaping be-

cause of the geometrical acceptance of the detectors weidentify as possible SM backgrounds:(i) pp ! ðV ! 2jÞðV ! 2jÞðW� ! ‘ ��Þ with V either

a W or Z; its total cross section is about 37 fb [19].pp ! 4jðW� ! ‘ ��Þ where j means a light jet or-iginated by QCD interactions has a larger crosssection, about 4500 fb [20], after imposing the cutsof Eq. (12).pp ! ðt ! bðW� ! ‘ ��ÞÞð�t ! �bjjÞ has an evenlarger cross section, about 160 pb.

All above background cross sections have been computedsumming over lepton flavors and can be reduced to zeroexploiting the fact that type-III seesaw produces uncorre-

lated ‘ ��ð �‘�Þ pairs, while the above SM processes producepairs correlated through W decays. In practice, this can bedone by requiring that the measurable transverse mass mT

of the ‘, �� system does exceed theW mass, such that theseparticles cannot come from W decays

m2T � 2E‘

TE6 Tð1� cos�Te�Þ>M2

W (13)

FIG. 2 (color online). Triplet decay widths as function of the triplet mass for ~m1 ¼ meV and mh ¼ 115 GeV.


033002-4

where �Te� is the angle between the missing transverse

momentum p6 T and the transverse component of the leptonmomentum, p‘

T . Having used this cut, it will be of utmostimportance to understand the instrumental sources of iso-lated leptons uncorrelated to the missing energy: we do notfully address this detector issue.

iv pp ! 4jðZ ! � ��ÞðW� ! ‘ ��Þ has a cross section ofabout 200 fb [21] (summed over lepton flavors; only thecuts on jets are imposed). This background cannot be sup-pressed using Eq. (13) and is not yet implemented in anyavailable code; therefore we can only study it in a semi-quantitative way. We estimate that it can be reduced downto �10 fb by requiring that the 4j system reconstructs aWW pair, having assumed that two jets j1 ad j2 reconstructa vector V if their invariant mass mðj1j2Þ satisfies

jmðj1j2Þ �MV j< 10 GeV: (14)

Furthermore, taking into account that larger M implies asmaller signal but also harder leptons and jets, we canimpose, e.g.,

p‘T * 0:25M: (15)

This cut on the lepton pT only mildly reduces the signal.Observing the process in Eq. (11) allows one to deter-

mine the parameter M. Indeed M is equal to the invariantmass of the system made out of the charged lepton and thetwo jets produced in theN0 decay. To determine which twojets come from N0 decay one can divide the four jets inpairs, each with invariant mass close to MW , and assumethat the right jets pair is the one with the smallest �R withrespect to the charged lepton.

After the discovery of the signal Eq. (11) other signa-tures with lower rate but similar final states can be used tocheck the model. Once the properties of the Higgs bosonwill be assessed by the LHC, Eqs. (9) and (10) predict theratio of any possible decay chain without pions over therate of the discovery signal. This prediction is independentof the value of � and weakly sensitive to M (for M at leastfew hundreds of GeV), providing an early check on thecoupling structure of the theory we are studying.

B. Lepton-flavor violating signatures

Lepton-flavor violation manifests in processes like

pp ! ‘1 �‘2ZWþ and pp ! ‘1 �‘2ZZ; where ‘1 and ‘2 de-

note any two lepton flavors present in ‘, whose branchingratios depend on the flavor of ‘. The decays Z ! �þ�� orZ ! eþe� would give the cleanest signature. We herestudy the less clean signature with largest event rate,obtained when all weak vectors decay hadronically, giving

pp ! ‘1 �‘24j (16)

without missing transverse energy ET . The SM back-grounds that can fake this signal are processes wherelepton flavor is carried away by neutrinos, that escapecarrying away a missing ET below the energy resolution

of the detector. One needs to consider at least the followingprocesses (we quote background cross sections for any

given pair of lepton flavors ‘1 and �‘2)

(i) pp ! ðW� ! ‘1 ��‘1ÞðWþ ! �‘2�‘2ÞðVV ! 4jÞ has

a small cross section, about 0.04 fb [19] after impos-ing the cuts of Eq. (12), and can be reduced down to anegligible level by requiring a below treshold E6 T .

(ii) pp ! ðW� ! ‘1 ��‘1ÞðWþ ! �‘2�‘2Þ4j is analogousto the previous process, but with the jets producedfrom QCD rather than electroweak processes. Thecross section is 50 fb [21] (only the cuts on jets areimposed), below the background (iii), and can bereduced in a way similar to the one we now discuss.

(iii) pp ! ð�t ! �b‘1 ��‘1Þðt ! b �‘2�‘2Þ2jwith the jets pro-duced by QCD. After imposing the cuts of Eq. (12)the cross section is 7200 fb [19]: we need to suppressit with appropriate cuts, taking into account thepeculiarities of the signal. First, the requirementthat the 2jb �b system reconstructs a VV pair [impos-ing the criterion of Eq. (14)] lessen this backgroundto 250 fb. Second, we can require that leptons have alarge enough pT , Eq. (15).Let us consider, for example, the case M ¼250 GeV: imposing p‘

T > 70 GeV reduces the back-ground to 36 fb, to be compared with a signal crosssection of

240 fb� BRðNþN0 ! ZWþ‘1 �‘2Þ & 8 fb:

We have not optimized the cuts in p‘T and p

jT , and not

used cuts on E6 T . For larger values of M, one has towait for a larger integrated luminosity for a discov-ery which would also imply a better understanding ofthe detector, allowing to reliably impose a cut on theabsence of missing transverse energy E6 T . A largerMimplies a more central production of N: for example,we assume M ¼ 750 GeV, we impose �‘;j < 2:5,

and fix Eq. (15) to p‘T > 140 GeV yielding a back-

ground cross section of about 1.7 fb. Imposing E6 T <50 GeV (that seems a reasonable estimate for theresolution of a well understood detector) the back-ground gets reduced to about 0.25 fb. Under the samecuts and the same branching ratio (BR) as above themaximal signal cross section is 0.08 fb.

(iv) pp ! ð�t ! �b‘1 ��‘1Þðt ! b �‘2�‘2ÞðV ! 2jÞ has a to-tal cross section of about 13 fb [19]. The process (iii)has a larger rate even after the requirements on thefour jets. As such, (iii) is always dominant and thisprocess can safely be neglected.

C. Lepton-number violating signatures

Lepton-number violation can be discovered in the chan-nels


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pp ! ðNþ ! ‘þ1 ZÞðN0 ! ‘þ2 W�Þ ¼ ‘þ1 ‘

þ2 ZW

�

pp ! ðN� ! ‘�1 ZÞðN0 ! ‘�2 WþÞ ¼ ‘�1 ‘�2 ZWþ:(17)

All the N ! SM decays in Eqs. (9) and (10) are expectedto have comparable sizable branching ratios and measuringthe flavors of ‘i would allow to identify the flavor of thelepton doublet coupled to the triplet N. If N� ! N0��also happen to have a detectably large branching, extraL-violating channels where a soft �� is present arise

pp ! ‘1‘2�þZWþ; ‘1‘2�

�WþWþ;

‘1‘2�þ��WþWþ:

(18)

Even if the �� are too soft to be detected, BRðN� !N0��Þ can still be measured from the relative rate of‘1‘2W

þWþ vs ‘1‘2ZWþ events (using decay channels

that allow to discriminate a Z from a W�; Z ! b �b orinto leptons allow an event-by-event discrimination) allow-ing to infer the value of ~m1: both type of decays have a

detectably large BR if ~m1 � 10�ð3�4Þ eV � ð100 GeV=MÞ2.Neglecting the soft ��, all the final-state particles ofEqs. (17) and (18) can be seen, allowing for a precisemeasurement of M.

Let us now discuss the backgrounds

(i) The physical background to (17) is pp !VVðW� ! ‘�1 �

ð�ÞÞðW� ! ‘�1 �ð�ÞÞ where V are heavy

SM vectors and the (anti-)neutrinos happen to carryso little missing transverse energy that their presenceis not detected. Using MADGRAPH [19] we find, atLHC �ðpp ! VVWþWþÞ 0:8 fb and �ðpp !VVW�W�Þ 1 fb.

As in the previous section, hadronic decays of the W�, Zgive the signal with the higher rate

pp ! ‘1‘24j (19)

without missing transverse energy ET . The cross section ofthe already discussed processes (i) pp ! ðW� ! ‘1 ��‘1Þ�ðW� ! ‘2 ��‘2ÞðVV ! 4jÞ is about 0.05 fb, which is al-

ready negligible before imposing the cuts of Eqs. (12)and (15), etc. The other background to (19) is(ii) pp ! ðW� ! ‘1 ��‘1ÞðW� ! ‘2 ��‘2Þ4j where the jets

are produced from QCD. The cross section is 20 fb [21](summed over lepton flavors; only cuts on jets are im-posed), and can be significantly reduced in a way similarto background (iii) in Sec. VB. Notice that the lepton-number violating signature also allows one to see lepton-flavor violation and, compared to the lepton-flavor violat-ing and lepton-number conserving signal of Sec. VB, has acomparable rate and a much less background, because itcannot be faked by t�t production (same-sign leptons pro-duced by hadronization and by t ! b ! c decays are in-side jets, and are therefore strongly suppressed by theisolation cut). An integrated luminosity of 10=fb shouldallow one to see the lepton-number violation signal forM & 0:8 TeV. While the lepton-flavor violation signal ofSec. VB should not be used for a discovery search, its laterdetection would clarify the physics, e.g., it is produced bytype-III seesaw and not by type-II seesaw.Of course the observation of a L-violating same-sign

dilepton channel would be a striking signature [22] for theMajorana character of the neutrino (as well a N) masses.

D. Displaced vertices

Moreover all the channels above can have an extrasignature: we observe that the lifetimes �Na ¼1=P

f�ðNa ! fÞ can be so large that N0, N�-decay verti-

ces can be detectably displaced from the primary produc-tion vertex. Indeed in the SU(2)-invariant limit M MZ

one has

�N0¼ �N� ¼ 8�v2

~m1M2¼ 1:5 cm

meV

~m1

�100 GeV

M

�2: (20)

Figure 3 shows the total lifetimes � of N0 and of N� asfunction of M and ~m1. We see that there are two possiblecases.

FIG. 3 (color online). Contour plot of triplet lifetimes for mh ¼ 115 GeV.


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(1) For larger ~m1, one has smaller �N0 �N� , e.g.,

�N0 �N� 0:3 mm � ðM=100 GeVÞ2 for ~m1 ð�m2

atmÞ1=2 ’ 0:05 eV.(2) For smaller ~m1 one has �N0 �N� � 5 cm; N�

decays predominantly to N0�� leading to multipledisplaced vertices. Unfortunately the �� producedin the N� decay are too soft to be detected and thetypical track produced by N� is too short to be wellmeasured. It can be tagged by the N0 decay, if ittakes place close enough.

Figures 4(a) and 4(b) show the distribution in the second-ary vertex displacement � for triplets produced at LHC,after taking into account the time-dilatation effect. We seethat the average displacement perpendicular to the beamaxis is h�?i 0:9�, with a minor dependence onM. In thedirection parallel to the beam axis one has h�ki 2:4� at

M 250 GeV and h�ki � at M ¼ 1 TeV. Both distri-

butions are very roughly exponentials, dN=d� e��=h�i.Capabilities of LHC detectors (we focus on ATLAS and

CMS, although LHCb can also be relevant) strongly de-pend on the unknown flavor composition of the leptoncoupled to N and on the displacement �, because decayswould happen in different parts of the apparatus. Forsmaller �, LHC detectors should allow one to reconstructthe position of the secondary vertex with an uncertainty ofabout 0.5 mm and 0.1 mm, in the directions parallel andorthogonal to the beam axis, respectively. For larger �, theN0 displacement can be �? > 50 cm: in such a case LHCdetectors could see the muons but not electrons and tauswhich need almost the full length of the inner detector to beproperly observed; although no dedicated studies exist, adisplaced vertex could be identified if N0 ! ��W� hap-pens around the first layers of the muon detector, and theWdecays hadronically. Finally, if � * 10 m, all the produc-tion channels result in the effective production of N0N0

plus undetectable pions. The decayed N� have a too shorttrack to be tagged or well measured, thus they are of nohelp. The produced N0s escape the detector and thereforethe event has no trigger and no signature. For this reasonthe detection of events with such a large � seems verychallenging.

This opens a plethora of scenarios. In view of the firstinequality in Eq. (3) (that holds with three triplets), any

observed triplet lifetime larger than 0:3 mm �ð100 GeV=MÞ2 would imply a small m1 < ð�m2

atmÞ1=2,i.e., nondegenerate neutrino spectrum. In the most opti-mistic cases where all triplets (N � N1 and N2, N3) havesub-TeV masses, one could infer informations on the neu-trino masses and mixings and test the consistency of thescenario via the bounds of Eq. (3). E.g., the second inequal-ity in Eq. (3) impliesmaxð ~m1; ~m2; ~m3Þ �

Pimi=3 or equiv-

alently

�min � minð�1; �2; �3Þ� 1 mm � ð0:05 eV=

Xi

miÞð100 GeV=MÞ2: (21)

Measuring �min & 1 mm and M 100 GeV would, e.g.,point to neutrinos with normal mass hierarchy (

Pmi

0:05 eV) since inverted mass hierarchy (P

mi 0:1 eV)or a quasidegenerate spectrum (

Pmi > 0:15 eV) lead to a

stronger upper limit on �min. Therefore the type-III seesawallows one to measure the couplings directly related toneutrino mass physics from displaced vertices.

E. Comparison with displaced vertices in other seesawmodels

In the type-I seesaw, right-handed neutrinos are negli-gibly produced unless some Yukawa coupling is muchlarger than what was suggested by neutrino masses(thereby loosing a direct connection between LHC andneutrino physics) but such a large Yukawa would notlead to displaced vertices. Alternatively, right-handed neu-trinos might be produced by some extra interaction [suchas gauged Uð1ÞB�L and/or SUð2ÞL extended to SUð3ÞL]1: itmust be stressed that the pp ! N0N0 ! ‘�1 ‘

�2 W

�W� orpp ! N0N0 ! ‘�1 ‘�2 W�W� channels would lead to adisplaced vertex phenomenology similar to the one above,Eqs. (20) and (21). The lepton-number violating N0N0 !‘1‘2W

þWþ channel is of particular interest. This signal isalso generated by the scalar triplet T of type-II seesaw,

FIG. 4 (color online). Distribution of the displacement of the secondary vertex from the interaction point.

1Production from SUð2ÞL extended to SUð2ÞL � SUð2ÞR wouldnot lead to displaced N vertices due to fast N decays mediated bya right-handed gauge boson W�

R , such as N ! ‘RuR �dR.


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together with (19), and together with lepton-number con-

serving ‘1‘2 �‘3 �‘4 and with WþWþW�W� [4].Type-II seesaw can also lead to displaced vertices, but of

limited size: the lifetime �T of the scalar triplet T dependson its unknown relative branching ratios into lepton orHiggs pairs, and is maximal when the two BR are equal

[23]: �T < 8�v2=ðM2T

ffiffiffiffiffiffiffiffiffiffiffiffiPim

2i

qÞ. This leads to �T < 0:3 mm

ðMT=100 GeVÞ2 for normal light neutrino hierarchy, �T <0:15 mm ðMT=100 GeVÞ2 for inverted hierarchy and lessfor degenerate spectrum. Consequently, here too the hier-archy could in principle be distinguished, but only forapproximately equal two branching ratios.

VI. CONCLUSIONS

Although it seems unlikely that neutrino masses aregenerated by the type-III seesaw at energies accessible toLHC, we studied what such an encounter of the third typewould look like, finding very characteristic signals thatallow to reconstruct the Lagrangian.

The unknown parameters are: the massM of the lightestfermion triplet N ¼ fN0; N�g (other triplets might be ac-cessible at LHC); its contribution ~m1 to neutrino masses,and the lepton flavor coupled to N. Triplet gauge couplingsare fully predicted, and they induce a small mass splittingMN� �MN0 166 MeV among the charged N� and neu-tral N0 components of the triplet N. Production of tripletsin pp collisions is dominated by gauge couplings, andFig. 1 shows the predicted cross sections for pp !NþN�, NþN0, N�N0 (N0N0 pairs are not produced) asfunction of the triplet mass M. This mass can be inferredfrom the cross section, from the distribution in transversemomentum, and measured from the invariant mass ofappropriate final-state particles. At an e�eþ collider, thecross section is maximal at s ¼ 1:4� 4M2, and for the

same reason triplets produced by q �q0 partonic collisionsare typically moderately relativistic.Pair production of triplets and their decays gives lepton-

flavor and lepton-number violating signals. There are twokinds of decays:(i) N0, N� into a lepton plus a massive SM vector (or

Higgs, if it is lighter than the triplet), with width ��~m1M

2=v2, that is small enough to lead to detectablydisplaced decay vertices if ~m1 &0:1 eVðM=100 GeVÞ2.

(ii) N� ! N0��, with width �� 1=ðfew cmÞ.In Sec. VA we studied the signal with the higher rate,pp ! 4j‘�E6 T; in Secs. VB and VC we studied themost characteristic final states that violate lepton flavorand lepton number: two charged leptons accompanied bytwo massive vectors or Higgs. In all cases we studied theSM backgrounds and how they can be suppressed allowingfor a discovery. The most promising discovery channelseems pp ! ‘þ1 ‘

þ2 4j, as it has a small background and

its rate is only a factor 2 below the higher rate.The decays (i) can allow one to measure the lepton flavor

coupled to N. Finally, the parameter ~m1 can be inferredfrom either the BR of the decay mode (ii), or from mea-suring how much secondary decay vertices are displacedfrom the production point. These two signals allow one toroughly cover the range 10�7 eV & ~m1 & 0:1 eV, espe-cially if M is as light as possible.

ACKNOWLEDGMENTS

A. S. thanks Milla Baldo Ceolin for having promptedthis paper. T. H. thanks the FRS-FNRS for support. Wethank Fulvio Piccinini for help with 2V4j backgrounds.We thank Pascal Vanlaer, Andrea Perrotta, and RobertoTenchini for discussions about capabilities of LHCdetectors.

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Type-III seesaw mechanism at CERN LHC