Type II neutrino seesaw mechanism at the LHC: The roadmap

Alejandra Melfo,1,2 Miha Nemevsek,2,3 Fabrizio Nesti,2 Goran Senjanovic,2 and Yue Zhang2

1Universidad de Los Andes, Merida, Venezuela2International Center for Theoretical Physics, Trieste, Italy

3J. Stefan Institute, Ljubljana, Slovenia(Received 7 October 2011; published 23 March 2012)

In this article, we revisit the Type II seesaw mechanism based on the addition of a weak triplet scalar to

the standard model. We perform a comprehensive study of its phenomenology at the LHC energies,

complete with the electroweak precision constraints. We pay special attention to the doubly-charged

component, object of collider searches for a long time, and show how the experimental bound on its mass

depends crucially on the particle spectrum of the theory. Our study can be used as a roadmap for future

complete LHC studies.

DOI: 10.1103/PhysRevD.85.055018 PACS numbers: 14.80.Fd, 12.15.Lk, 14.60.Pq, 14.80.Ec

I. INTRODUCTION

The modern-day understanding of the origin and thesmallness of neutrino mass is based on the seesaw mecha-nism [1]. The most natural source for this mechanism isprovided by the left-right symmetric theories [2], whichrequire the existence of the SUð2ÞL (and SUð2ÞR) tripletswith hypercharge Y ¼ 2. Left-right symmetry can be real-ized either at low scale, or embedded in a grand unifiedtheory such as SOð10Þ. It turns out that once the seesawmechanism is turned on, the SUð2ÞL triplet gets a smallvacuum expectation value, even if it is very heavy. One caneven contemplate the possibility that this triplet is the onlylow-energy remnant of the new physics beyond the stan-dard model (SM),1 in which case one talks of the Type IIseesaw mechanism [6].

An appealing feature of what could otherwise be seen asan ad hoc hypothesis is the minimality and the predictivityof this scenario, namely, the fact that the Yukawa couplingsdetermine the neutrino mass matrix. This would becomeparticularly important if the triplet were to lie in the TeVregion, for then its decays could directly probe the neutrinomasses and mixings.

The doubly-charged component of the triplet has beenthe focus of attention due to its possibly spectacularsignatures at colliders [7]: if Yukawa couplings are suffi-ciently large, it will decay predominantly into same-sign-charged leptons, which is a clear signature of leptonnumber violation. The same-sign leptons at colliders are ageneric high-energy analog of the neutrinoless doublebeta decay as a probe of lepton number violation, envi-sioned in [8].

Both CDF and D0 performed a search of the doubly-charged component [9]. However, only the pair production

of the doubly-charged components was considered. Thelatest search at CMS [10] takes into account the associatedproduction with the singly-charged component but as-sumes the triplet spectrum to be degenerate. None ofthem have taken into account the full complexity of itsproduction and decay modes. An attempt in this directionwas made in [11]. Here we provide a global view of thephenomenological implications of the Type II seesaw sce-nario at hadron colliders, in particular, at the LHC.We perform the first electroweak high-precision study

and demonstrate the strong dependence of the above CMSlimit on the spectrum of the scalar triplet. In particular wefind that the quoted limit on the order of 250–300 GeV cango down all the way to 100 GeV for the mass split around20–30 GeV. In what follows we discuss and quantify ourresults.

II. THE MODEL

Let us start by summarizing the salient features of theType II seesaw mechanism. Besides the usual SM particlecontent, the model requires the existence of a Y ¼ 2SUð2ÞL triplet �. When its neutral component �0 acquiresa vacuum expectation value (VEV) v�, it generates aMajorana mass for the neutrinos through the Yukawa term

Mij�

v�

LTi Ci�2�Lj þ H:c:; (1)

where Li is a left-handed lepton doublet, C the chargeconjugation operator and

M� ¼ U�m�Uy (2)

is the neutrino mass matrix in the basis where the chargedlepton masses are diagonal. Herem� stands for the neutrinomasses and U is the Pontecorvo-Maki-Nakagawa-Sakataleptonic mixing matrix. The complete potential for thescalars, including the Higgs doublet H, is

1For instance, in the case of left-right symmetry, it is knownthat the scale must beMWR

* 2:5 TeV [3] on theoretical groundsand 1.7 TeV [4,5] on experimental grounds.

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V ¼ �m2HH

yH þm2�Tr�

y�þ ð�HTi�2��H þ H:c:Þ

þ �1ðHyHÞ2 þ �2ðTr�y�Þ2 þ �3Trð�y�Þ2þþ�HyHTr�y�þ �Hy��yH; (3)

and the triplet VEV is v� ¼ �v2=ffiffiffi

2p

m2�, where v is the

SM Higgs VEV. Thus a small v� is technically natural, asits size is controlled by the� parameter which is only self-renormalized. A nonvanishing v� spoils the � parameter,which requires v� smaller than a few GeV.

The triplet components then follow the sum rules

m2�þ �m2

�þþ ’ m2�0 �m2

�þ ’ �v2=4; (4)

mS ’ mA ¼ m�0 ; (5)

where mS and mA are the masses of the scalar (S) andpseudoscalar (A) components of �0. The triplet compo-nents are separated by equal mass square difference, andthere is an upper limit on the splitting from the perturba-tivity of �. These rules are valid up to tiny Oðv2

�=v2Þ

corrections.We first focus on smaller values v� & 10�3 GeV, rele-

vant for probing the connection with neutrino masses atLHC and later on comment on larger v� and quantify itsupper bound.

A. Probing the flavor structure

The doubly-charged scalar �þþ plays a central role inthe physics of this model. In particular, its decays intosame-sign-charged leptons probe the neutrino masses andmixings. This is clear from (1), and is made explicit in thedecay rate

��þþ!‘i‘j¼ m�þþ

8�ð1þ ijÞ�

�

�

�

�

�

�

�

ðU�m�UyÞij

v�

�

�

�

�

�

�

�

�

2

: (6)

This connection between the collider physics and the low-energy processes has been studied extensively [12,13]. Ifthis were the only mode, one could probe the Yukawaflavor structure through branching ratios to different flavormodes. In addition, the decay of the singly-charged com-ponent �þ ! ‘i� may also serve as a possible channel todetermine the Yukawa structure.

B. Probing the neutrino mass scale

By probing the flavor structure as above one also mea-sures the ratio of neutrino masses, so that by using neutrinooscillation data one might infer the absolute neutrino massscale. There is also a chance of directly measuring theabsolute mass scale at LHC. In fact, the other decay mode,

��þþ!WþWþ ¼ g4v2�

8�m�þþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1� 4M2W

m2�þþ

v

u

u

t

�

2þ�

m2�þþ

2M2W

� 1

�

2�

;

(7)

opens up for a nonvanishing v�. Higgs triplet withgauge boson fusion production and decay at the LHChas been studied in [14]. If large enough this channelwould thus enable the determination of v�. The criticalvalue is obtained for ��þþ!‘i‘j

¼ ��þþ!WþWþ which gives

v� ¼ 10�4 � 10�3 GeV, see Fig. 1.

III. THE DECAY PHASE DIAGRAM

The triplet mass sum rules in Eqs. (4) and (5) allow foronly two scenarios,

Case A : m�0 � m�þ � m�þþ (8)

Case B : m�þþ >m�þ >m�0 : (9)

When the triplet components are not degenerate, thecascade channels �0 ! �þW�� ! �þþW��W�� (forcase A) and �þþ ! �þWþ� ! �0Wþ�Wþ� (for case B)are open [11,13]. These processes have been overlookedin previous experimental studies due to the assumption ofthe degeneracy.In Fig. 1 we provide a phase diagram separating the

regions where different decay modes play a dominant role.We take as an example scenario B with m�þþ ¼ 150 GeV,and consider the �þþ decays. It shows that for moderatemass splits, the cascade channels become important andone basically loses the same-sign dilepton channel. Oncethe mass difference is large enough, cascade decaysquickly dominate. Similar decaying phase diagrams hold

Cascade Decay

Leptonic Decay

Gauge

Boson Decay

10 10 10 8 10 6 10 4 0.01 1

0.5

1.0

5.0

10.0

50.0

100.0

v GeV

MG

eV

FIG. 1 (color online). Generic decay phase diagram for �decays in the Type II seesaw model, exemplified for case Bdefined in the text, with m�þþ ¼ 150 GeV. Dashed, thin solid,and thick solid contours correspond to 99, 90 and 50% of thebranching ratios. Here �M ¼ m�þþ �m�þ .

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also for �þ decay in case B and �0, �þ in case A. On theother hand, for the lightest triplet component there are onlytwo possibilities: it decays either into leptons or gaugebosons. The mass splits have thus a dramatic impact onthe direct search limits on the doubly-charged scalarmasses, as we show below.

IV. ELECTROWEAK PRECISION TESTS:A LESSON ON SPECTRA

Let us take this model seriously as an effective theory atthe LHC, so that any other new physics is effectivelydecoupled. Then, high-precision electroweak study is amust. We apply the general formulas in [15] to the caseof the triplet. The dominant constraint comes from theoblique parameter T which is governed by the mass dif-ferences. The essential role in this analysis is thus playedby the sum rules in (4) and (5), which eliminate twoarbitrary mass scales. The first message from electroweakprecision tests (EWPTs) is that the mass split may be large.In particular, for very light SM Higgs the mass differencecan range from zero to roughly 50 GeV. Actually, many ofthe studies assumed the degeneracy (or tiny mass differ-ence) among the members of the triplet. Although this ispossible for a light SM Higgs, it is strongly disfavored forlarger masses, beyond 200 GeV. For instance, a very heavyHiggs of 400 GeV requires the mass difference to be biggerthan �40 GeV. The reason for this is that the heavy SMHiggs contribution to the T parameter has to be compen-sated by a splitting of the triplet components. There is alsoan upper limit on the mass separation due to the sum ruleand the coupling perturbativity, as noted above. This im-plies the triplet mass is bounded from above if the SMHiggs boson is heavy. The above remarks are visible inFig. 2 where the constraints from EWPT and sum rules are

brought together with the collider phenomenology, thesubject of the next section.

A. v�: how large?

Before moving on, let us comment on the impact of v�

on the EWPT. It simply gives a negative tree-level contri-bution to the T parameter: �T ¼ �4v2

�=�emv2, where

�em is the fine-structure constant, and plays a similar roleas a heavy Higgs boson (but with �S ¼ 0). The effect of alarge v� can be canceled by a large mass split, and wefind its upper limit from perturbativity (� & 3) to bev� & 7 GeV, for mh ¼ 120 GeV.

B. v�: how small?

A complete study on lepton flavor violation constraintshas been carried out in [16]. The bottom line is the com-bined limit on the VEV times the mass of the doubly-charged component of the triplet

v�m�þþ * 100 eVGeV: (10)

These constraints further ensure that the triplet Yukawacouplings are small enough so that the above EWPTanaly-sis based on oblique parameters is self-consistent.

V. CURRENT LHC LIMITS

The CMS collaboration has published the latest data onfour-lepton final states, with a luminosity of 980 pb�1 atffiffiffi

sp ¼ 7 TeV, in [10]. No excess over the SM prediction isobserved and an updated lower limit on the mass of thedoubly-charged Higgs is set. The analysis is performedassuming degeneracy of the triplet components. In the

Direct searchLHC 980 pb 1

v 10 6GeV

Sum Rule

Sum Rule &Z width

LEP EWPTmh 130GeV

0 100 200 300 400 500 600 700

100

50

0

50

100

m GeV

mm

GeV

Direct searchLHC 980 pb 1

v 10 6GeV

Sum Rule

Sum Rule &Z width

LEP

EWPTmh 300GeV

0 100 200 300 400 500 600 700

100

50

0

50

100

m GeV

mm

GeV

FIG. 2 (color online). Summary of all the experimental and theoretical constraints in the m�þþ �m�þ parameter space, fordegenerate light neutrino masses. The LHC 2� exclusion is shown by the region to the left of the red solid curve, relative tov� ¼ 10�6 GeV. The analogous curve for v� ¼ 10�9 GeV is red dashed. The purple (dotted) contour excluded by EWPT at95% confidence level is shown for SM Higgs mass 130 GeV (left panel) and 300 GeV (right panel). The (green) region excluded by theZ-width bound and the mass sum rule in Eq. (4) is shown for the triplet-SM Higgs coupling � ¼ 3.

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following, we perform an estimate of the limit in the fullparameter space. We generate the events for the pair andassociated production of all the �’s using MADGRAPH 4.4.57

[17], decay them with BRIDGE 2.23 [18] and then do theshowering and detector simulation with PYTHIA-PGS 2.1.8

[19,20]. We adopt the K-factor from [21] to account fornext-to-leading order correction to the production. Wefocus on the four-lepton final states and implement thesame cuts as in [10]. These cuts may be further optimizedfor different event topologies of cascade decays, howeverwe would expect only a minor increase of the bound, dueto the rather small triplet splitting. For illustration pur-poses we take the triplet VEV v� ¼ 10�6 GeV and nearlydegenerate light neutrino masses (corresponding to thesample point BP3 in [10]).

We summarize in Fig. 2 the limits on the masses ofthe charged components, along with the theoretical con-straints, i.e., the regions favored by electroweak precisiontests at 95% confidence level, for SM Higgs mass of130 GeV and 300 GeV. The updated lower limit on m�þþ

for relatively large v�, is independent of the SM Higgsboson mass.

In case A, we find a lower limit of 240 GeV onthe doubly-charged Higgs mass for the degenerate case.This is to be contrasted with the CMS limit of 258 GeVusing four-lepton final states only, probably due to the useof different statistics. For moderately large mass splits thislimit can be increased by as much as 50 GeV, compared tothe degenerate case. We note the analysis can be furtherimproved by combining both the three- and four-leptonfinal states, as done by the CMS collaboration, seealso [22].

For case B on the contrary, the limit goes down all theway to m�þþ * 100 GeV (for v� > 10 eV). In this case,all the � states cascade to �0 and further to neutrinos.Current missing energy data do not yet possess largeenough luminosity to set here a relevant limit.

We would like to emphasize that: i) the abovebounds from CMS data are valid only for small enoughv� & 10�4 GeV; ii) the bounds become splitting indepen-dent only for very tiny v�, as shown by the dashed line withv� ¼ 1 eV.

A. A look from the right perspective

As said in the introduction this possibility can emergenaturally in the context of left-right symmetric theories.First, the sum rule for �L remains. Second, ��

R gets eatenby W�

R , therefore the cascades do not occur and the limitson �þþ

R mass set by CDF and D0 [9] remain perfectlyvalid.

VI. PROBING THE POTENTIAL

The crucial couplings to probe in the Higgs potential arethose between the Higgs doublet and the triplet. For in-stance, the � parameter is responsible for the splitting of

the triplet masses, while in a certain region of the Higgsmass, the � and � couplings can be probed through theHiggs decays to �’s [23].

VII. IMPLICATIONS FOR THESM HIGGS SEARCH

As is well-known, a heavy SMHiggs is inconsistent withEWPT, unless there is new physics near the electroweakscale. In the context of the Type II seesaw, this implieslarge splits between the components of the triplet. Whenthe Higgs is heavier than twice the triplet mass, theH ! �� channel opens up and may affect the otherbranching ratios appreciably. As shown in Fig. 3, thebranching ratio of SM Higgs decay to WþW� could bereduced for SM Higgs heavier than 200 GeV, and thecurrent limits from the Higgs search at hadron collidersshould be modified. Interestingly, the decay to doubly-charged components can in turn serve as another cleandiscovery channel for the SM Higgs boson. The oppositecase with Higgs decaying into neutral components with theinvisible width controlled by � could easily explain recentevidence for mh � 144 GeV.

VIII. WHAT NEXT?

In this article, we offered a systematic study ofthe collider phenomenology for the Type II seesawmechanism. We showed how the recently set LHC limitchanges dramatically when one moves away from theassumed benchmark points. We believe that our resultswill be a useful roadmap for future experimental analysis.We end with a few suggestions for further exploration.(i) The missing energy channels relevant for case B

require further in-depth study, with more statistics.(ii) One could try to probe the larger values of v� ’

10�4 � 10�2 GeV where the dilepton decay chan-nels give rise to displaced vertices, possibly leadingto simultaneous visibility of both these and WWdecay channels.

500200 3001500.0

0.5

1.0

1.5

Mh GeV

10

100

FIG. 3 (color online). SM Higgs to WW branching ratio form�þþ ¼ 150 GeV and m�þ ¼ 130 GeV (represented by w inFig. 2).

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To close, we believe that our work strengthens further thecase for LHC being also a neutrino machine.

ACKNOWLEDGMENTS

We are grateful to Georges Azuelos, Dilip K. Ghosh,Ivica Puljak, Beate Heinemann, Louise Skinnari andMartina Hurwitz for their interest in our work. We thankthe BIAS institute for the warm hospitality and support.Y. Z. thanks the Aspen Center for Physics for hospitalityduring the final stages of this work.

Note added in proof.—After this work was submitted

for publication, both ATLAS and CMS reported [24]

possible evidence of the Higgs boson, with a mass about

126 GeV, at 2–3� CL. In particular, the H ! branching ratio is found to be roughly twice as large

as the SM prediction. Also, a new paper [25] appeared

discussing the H ! branching ratio in the type-II

seesaw model. It claims the compatibility with the ex-

perimental result for rather large positive values of the

quartic coupling �� 10.We open here a new window for the agreement with

the above LHC results. We find that a moderate value� ’ �0:5 can perfectly do the job, as long as thedoubly-charged scalar is light, m�þþ ’ 100GeV. Thisshows how crucial it is to take cascade decays intoaccount, which is the only way to have such light �þþ,as discussed at length in this paper. We illustrate thispoint in Fig. 4.

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0.05

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0.30.4

0.6

SM

100 110 120 130 140 1501.0

0.5

0.0

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M GeV

Br h Type II seesaw model, with 0.18

FIG. 4 (color online). Contours of BrðH ! Þ in the Type IIseesaw model, for fixed � ¼ �0:18. The horizontal contour with� ’ 0 is approximately equal to the SM prediction BrðH !Þ ¼ 0:2%. We find this branching ratio can be enhanced by afactor of 2, for � ’ �0:5 and m�þþ & 150GeV.

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