Type II Seesaw at LHC: the Roadmap
Alejandra Melfo, Miha Nemevsek, Fabrizio Nesti, Goran Senjanovic, Yue Zhang
TType II Seesaw at LHC: the Roadmap
Alejandra Melfo,
1, 2
Miha Nemevˇsek,
2, 3
Fabrizio Nesti, Goran Senjanovi´c, and Yue Zhang Universidad de Los Andes, M´erida, Venezuela International Center for Theoretical Physics, Trieste, Italy J. Stefan Institute, Ljubljana, Slovenia (Dated: December 27, 2012)In this Letter we revisit the type-II seesaw mechanism based on the addition of a weak triplet scalar tothe 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-chargedcomponent, object of collider searches for a long time, and show how the experimental bound on itsmass depends crucially on the particle spectrum of the theory. Our study can be used as a roadmapfor future complete LHC studies.
Introduction.
The modern day understanding of the ori-gin and the smallness of neutrino mass is based on thesee-saw mechanism [1]. The most natural source for thismechanism is provided by the Left-Right symmetric the-ories [2], which require the existence of the SU (2) L (and SU (2) R ) triplets with hypercharge Y = 2. Left-Rightsymmetry can be realized either at low scale, or em-bedded in a grand unified theory such as SO (10). Itturns out that once the see-saw mechanism is turnedon, the SU (2) L triplet gets a small vacuum expectationvalue, even if it is very heavy. One can even contemplatethe possibility that this triplet is the only low-energyremnant of the new physics beyond the standard model(SM), in which case one talks of the Type II see-sawmechanism [6].An appealing feature of what could otherwise be seenas an ad-hoc hypothesis is the minimality and the predic-tivity of this scenario, namely, the fact that the Yukawacouplings determine the neutrino mass matrix. Thiswould become particularly important if the triplet wereto lie in the TeV region, for then its decays could directlyprobe the neutrino masses and mixings.The doubly charged component of the triplet has beenthe focus of attention due to its possibly spectacular sig-natures at colliders [7]: if Yukawa couplings are suffi-ciently large, it will decay predominantly into same-signcharged leptons which is a clear signature of Lepton Num-ber Violation (LNV). The same sign leptons at collidersare a generic high energy analogue of the neutrinolessdouble beta decay as a probe of LNV, envisioned in [8].Both, CDF and D0 performed a search of the doublycharged component [9]. However, only the pair produc-tion of the doubly charged components was considered.The latest search at CMS [10] takes into account the as-sociated production with the singly charged componentbut assumes the triplet spectrum to be degenerate. Noneof them have taken into account the full complexity of itsproduction and decay modes. An attempt in this direc- For instance, in the case of left-right symmetry, it is known thatthe scale must be M W R (cid:38) . tion was made in [11]. Here we provide a global view ofthe phenomenological implications of the Type II seesawscenario at hadron colliders, in particular at the LHC.We perform the first electroweak high precision studyand demonstrate the strong dependence of the aboveCMS limit on the spectrum of the scalar triplet. Inparticular we find that the quoted limit on the order of250 −
300 GeV can go down all the way to 100 GeV for themass split around 20 −
30 GeV. In what follows we discussand quantify our results.
The model.
Let us start by summarizing the salientfeatures of the Type II see-saw mechanism. Besides theusual SM particle content, the model requires the exis-tence of a Y = 2 SU (2) L triplet ∆. When its neutralcomponent ∆ acquires a vev v ∆ , it generates a Majo-rana mass for the neutrinos through the Yukawa term M ijν v ∆ L Ti Ciσ ∆ L j + h.c. , (1)where L i is a left-handed lepton doublet, C the chargeconjugation operator and M ν = U ∗ m ν U † , (2)is the neutrino mass matrix in the basis where thecharged lepton masses are diagonal. Here m ν stands forthe neutrino masses and U is the PMNS leptonic mixingmatrix. The complete potential for the scalars, includingthe Higgs doublet H , is V = − m H H † H + m Tr∆ † ∆ + ( µH T iσ ∆ ∗ H + h.c.) ++ λ ( H † H ) + λ (Tr∆ † ∆) + λ Tr(∆ † ∆) ++ α H † H Tr∆ † ∆ + β H † ∆∆ † H , (3)and the triplet vev is v ∆ = µ v / √ m , where v is theSM Higgs vev. Thus a small v ∆ is technically natural,as its size is controlled by the µ parameter which is onlyself-renormalized. A non-vanishing v ∆ spoils the ρ pa-rameter, which requires v ∆ smaller than a few GeV.The triplet components then follow the sum rules m + − m ++ (cid:39) m − m + (cid:39) β v / , (4) m S (cid:39) m A = m ∆ , (5) a r X i v : . [ h e p - ph ] D ec where m S and m A are the masses of the scalar (S) andpseudoscalar (A) components of ∆ . The triplet compo-nents are separated by equal mass square difference, andthere is an upper limit on the splitting from the pertur-bativity of β . These rules are valid up to tiny O ( v /v )corrections.We first focus on smaller values v ∆ (cid:46) − GeV, rele-vant for probing the connection with neutrino masses atLHC and later on comment on larger v ∆ and quantify itsupper bound. Probing the flavor structure.
The doubly charged scalar∆ ++ plays a central role in the physics of this model.In particular, its decays into same-sign charged leptonsprobe the neutrino masses and mixings. This is clearfrom (1), and is made explicit in the decay rateΓ ∆ ++ → (cid:96) i (cid:96) j = m ∆ ++ π (1 + δ ij ) (cid:12)(cid:12)(cid:12)(cid:12) ( U ∗ m ν U † ) ij v ∆ (cid:12)(cid:12)(cid:12)(cid:12) . (6)This connection between the collider physics and the lowenergy processes has been studied extensively [12, 13]. Ifthis were the only mode, one could probe the Yukawa fla-vor structure though branching ratios to different flavormodes. In addition, the decay of the singly-charged com-ponent ∆ + → (cid:96) i ν may also serve as a possible channelto determine the Yukawa structure. Probing the neutrino mass scale.
By probing the flavourstructure as above one also measures the ratio of neutrinomasses, so that by using neutrino oscillation data onemight infer the absolute neutrino mass scale. There isalso a chance of directly measuring the absolute massscale at LHC. In fact, the other decay mode,Γ ∆ ++ → W + W + = g v πm ∆ ++ (cid:115) − M W m ++ (cid:34) (cid:18) m ++ M W − (cid:19) (cid:35) (7)opens up for a non-vanishing 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 Γ ∆ ++ → (cid:96) i (cid:96) j = Γ ∆ ++ → W + W + whichgives v ∆ = 10 − ÷ − GeV, see Fig. 1.
The decay phase diagram.
The triplet mass sum rulesin Eqs. (4) and (5) allow for only two scenarios,Case A : m ∆ ≥ m ∆ + ≥ m ∆ ++ (8)Case B : m ∆ ++ > m ∆ + > m ∆ . (9)When the triplet components are not degenerate, the cas-cade channels ∆ → ∆ + W −∗ → ∆ ++ W −∗ W −∗ (for caseA) and ∆ ++ → ∆ + W + ∗ → ∆ W + ∗ W + ∗ (for case B) areopen [11, 13]. These processes have been overlooked inprevious experimental studies due to the assumption ofthe degeneracy. Cascade DecayLeptonic Decay GaugeBoson Decay10 (cid:45) (cid:45) (cid:45) (cid:45) v (cid:68) (cid:72) GeV (cid:76) (cid:68) M (cid:72) G e V (cid:76) (cid:29) FIG. 1. Generic decay phase diagram for ∆ decays in thetype-II seesaw model, exemplified for case B defined in thetext, with m ∆ ++ = 150 GeV. Dashed, thin solid and thicksolid contours correspond to 99, 90 and 50% of the branchingratios. Here ∆ M = m ∆ ++ − m ∆ + . In Fig. 1 we provide a phase diagram separating theregions where different decay modes play a dominantrole. We take as an example scenario B with m ∆ ++ =150 GeV, and consider the ∆ ++ decays. It shows thatfor moderate mass splits, the cascade channels becomeimportant and one basically looses the same-sign dilep-ton channel. Once the mass difference is large enough,cascade decays quickly dominate. Similar decaying phasediagrams hold also for ∆ + decay in case B and ∆ , ∆ + in case A. On the other hand, for the lightest tripletcomponent there are only two possibilities: it decays ei-ther into leptons or gauge bosons. The mass splits havethus a dramatic impact on the direct search limits on thedoubly-charged scalar masses, as we show below. Electroweak precision tests: a lesson on spectra.
Letus take this model seriously as an effective theory at theLHC, so that any other new physics is effectively decou-pled. Then, high precision electroweak study is a must.We apply the general formulae in [15] to the case of thetriplet. The dominant constraint comes from the obliqueparameter T which is governed by the mass differences.The essential role in this analysis is thus played by thesum rules in (4) and (5), which eliminate two arbitrarymass scales. The first message from EWPT is that themass split may be large. In particular, for very light SMHiggs the mass difference can range from zero to roughly50 GeV. Actually, many of the studies assumed the de-generacy (or tiny mass difference) among the membersof the triplet. Although this is possible for a light SMHiggs, it is strongly disfavored for larger masses, beyond200 GeV. For instance, a very heavy Higgs of 400 GeVrequires the mass difference to be bigger than ∼
40 GeV.The reason for this is that the heavy SM Higgs contri-bution to the T parameter has to be compensated bya splitting of the triplet components. There is also an Direct search
LHC 980 pb (cid:45) (cid:72) v (cid:68) (cid:61) (cid:45) GeV (cid:76)
Sum RuleSum Rule &Z width LE P EWPT m h (cid:61) (cid:248) (cid:45) (cid:45) m (cid:68) (cid:43)(cid:43) (cid:64) GeV (cid:68) m (cid:68) (cid:43) (cid:45) m (cid:68) (cid:43)(cid:43) (cid:64) G e V (cid:68) Direct search
LHC 980 pb (cid:45) (cid:72) v (cid:68) (cid:61) (cid:45) GeV (cid:76)
Sum RuleSum Rule &Z width LE P EWPT m h (cid:61) (cid:45) (cid:45) m (cid:68) (cid:43)(cid:43) (cid:64) GeV (cid:68) m (cid:68) (cid:43) (cid:45) m (cid:68) (cid:43)(cid:43) (cid:64) G e V (cid:68) FIG. 2. Summary of all the experimental and theoretical constraints in the m ∆ ++ – m ∆ + parameter space, for degenerate lightneutrino masses. The LHC 2 σ exclusion is shown by the region to the left of the red solid curve, relative to v ∆ = 10 − GeV.The analogous curve for v ∆ = 10 − GeV is red dashed. The purple (dotted) contour excluded by EWPT at 95% C.L. is shownfor SM Higgs mass 130 GeV (left panel) and 300 GeV (right panel). The (green) region excluded by the Z -width bound andthe mass sum rule in Eq. (4) is shown for the triplet-SM Higgs coupling β = 3. upper limit on the mass separation due to the sum ruleand the β coupling perturbativity, as noted above. Thisimplies the triplet mass is bounded from above if SMHiggs boson is heavy. The above remarks are visible inFig. 2 where the constraints from EWPT and sum rulesare brought together with the collider phenomenology,subject of the next section. v ∆ : how large? Before moving on, let us comment onthe impact of v ∆ on the EWPT. It simply gives a neg-ative tree-level contribution to the T parameter: ∆ T = − v /α em v , where α em is the fine structure constant,and plays a similar role as a heavy Higgs boson (but with∆ S = 0). The effect of a large v ∆ can be canceled by alarge mass split, and we find its upper limit from pertur-bativity ( β (cid:46)
3) to be v ∆ (cid:46) m h = 120 GeV. v ∆ : how small? A complete study on LFV 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 ∆ ++ (cid:38)
100 eV GeV . (10)These constraints further ensure that the triplet Yukawacouplings are small enough so that the above EWPTanalysis based on oblique parameters is self-consistent. Current LHC limits.
The CMS collaboration has pub-lished the latest data on four lepton final states, with aluminosity of 980 pb − at √ s = 7 TeV, in [10]. No ex-cess over the SM prediction is observed and an updatedlower limit on the mass of the doubly-charged Higgs isset. The analysis is performed assuming degeneracy ofthe triplet components. In the following, we perform anestimate of the limit in the full parameter space. We gen-erate the events for the pair and associated production of all the ∆’s using MadGraph 4.4.57 [17], decay them with
BRIDGE 2.23 [18] and then do the showering and detectorsimulation with
Pythia-PGS 2.1.8 [19, 20]. We adoptthe K-factor from [21] to account for next-to-leading or-der correction to the production. We focus on the fourlepton final states and implement the same cuts as in [10].These cuts may be further optimized for different eventtopologies of cascade decays, however we would expectonly a minor increase of the bound, due to the rathersmall triplet splitting. For illustration purposes we takethe triplet vev v ∆ = 10 − GeV and nearly degeneratelight neutrino masses (corresponding to the sample pointBP3 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% CL, for SM Higgs mass of 130 GeV and300 GeV. The updated lower limit on m ∆ ++ for relativelylarge v ∆ , is independent of the SM Higgs boson mass.In case A, we find a lower limit of 240 GeV on thedoubly-charged Higgs mass for the degenerate case. Thisis to be contrasted with the CMS limit of 258 GeV us-ing four-lepton final states only, probably due to the useof different statistics. For moderately large mass splitsthis limit can be increased by as much as 50 GeV, com-pared to the degenerate case. We note the analysis canbe further improved by combining both the three- andfour-lepton final states, as done by the CMS collabora-tion, see also [22].For case B on the contrary, the limit goes down allthe way to m ∆ ++ (cid:38)
100 GeV (for v ∆ >
10 eV). In thiscase, all the ∆ states cascade to ∆ and further to neu-trinos. Current missing energy data do not yet possesslarge enough luminosity to set here a relevant limit.We would like to emphasize that: i) the above boundsfrom CMS data are valid only for small enough v ∆ (cid:46) − GeV; ii) the bounds become splitting independentonly for very tiny v ∆ , as shown by the dashed linewith v ∆ = 1 eV. A look from the right perspective.
As said in the intro-duction this scenario can emerge naturally in the contextof LR symmetric theories. First, the sum rule for ∆ L remains. Second, ∆ ± R gets eaten by W ± R , therefore thecascades do not occur and the limits on ∆ ++ R mass setby CDF and D0 [9] remain perfectly valid.In the LR theory, the neutrino mass situation is morecomplicated since in general there are both contributionsfrom type-I and type-II seesaw. In other words, the de-cay formulae Eq. (6) gets simply modified by the right-handed neutrino masses, mixings and the right-handedtriplet vev. Nonetheless, as long as the competition be-tween the decays into charged leptons and two W bosonsexists, our conclusion on the m ∆ ++ limit obviously holdstrue. Actually, the same conclusion applies in any theorywith such phenomena. Implications for the SM Higgs search.
The crucial cou-plings to probe in the Higgs potential are those betweenthe Higgs doublet and the triplet. For instance the β parameter is responsible for the splitting of the tripletmasses, while in a certain region of the Higgs mass, the α and β couplings can be probed through the Higgs de-cays to ∆’s [23].As is well known, a heavy SM Higgs is inconsistentwith EWPT, unless there is new physics near the elec-troweak scale. In the context of the type II seesaw, thisimplies large splits between the components of the triplet.When the Higgs is heavier than twice the triplet mass,the h → ∆∆ channel opens up and may affect the otherbranching ratios appreciably. As shown in Fig. 3, thebranching ratio of SM Higgs decay to W + W − 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 withthe invisible width controlled by α could easily explainrecent evidence for m h ≈
144 GeV.
What next?
In this letter, we offered a systematicstudy of the collider phenomenology for the type-II see-saw mechanism. We showed how the recently set LHClimit changes dramatically when one moves away fromthe assumed benchmark points. We believe that our re-sults will be a useful roadmap for future experimentalanalysis. We end with a few suggestions for further ex-ploration. • The missing energy channels relevant for case Brequire further in-depth study, with more statistics. M h (cid:72) GeV (cid:76) Α (cid:37) (cid:37) FIG. 3. SM Higgs to
W W branching ratio for m ∆ ++ =150 GeV and m ∆ + = 130 GeV (represented by (cid:70) in Fig. 2). • One could try to probe the larger values of v ∆ (cid:39) − ÷ − GeV where the di-lepton decay chan-nels give rise to displaced vertices, possibly leadingto simultaneous visibility of both these and
W W decay channels.To close, we believe that our work strengthens furtherthe case for LHC being also a neutrino machine.
Acknowledgements.
We are grateful to Georges Azue-los, Dilip K. Ghosh, Ivica Puljak, Beate Heinemann,Louise Skinnari and Martina Hurwitz for their interestin our work. We thank the BIAS institute for the warmhospitality and support. YZ thanks the Aspen Centerfor Physics for hospitality during the final stages of thiswork.
Note added on h → γγ . After this work was submit-ted for publication, both ATLAS and CMS reported [24]a tentative evidence of the Higgs boson, with a massabout 126 GeV, at 2-3 σ CL. In particular, the h → γγ branching ratio is found to be roughly twice as large asthe SM prediction. This feature seems to persist in thecombined 7 and 8 TeV dataset [25]. Also, a new pa-per [26] appeared discussing the h → γγ branching ratioin the type-II seesaw model. It claims the compatibil-ity with the experimental result for rather large positivevalues of the quartic coupling α ∼ O (1 −
2) or larger, de-pending the masses of the charged components, ∆ ± , ±± .A new window in agreement with the above LHC re-sults is opened here. As illustrated in Fig. 4, a moderatevalue α (cid:39) − . m ∆ ++ (cid:39)
100 GeV. This showshow crucial it is to take the cascade decays into account,which is the only way to have such light ∆ ++ , as dis-cussed at length in this paper. (cid:37) (cid:37) (cid:37) (cid:37) (cid:37) (cid:37) (cid:72) SM (cid:76)
100 110 120 130 140 150 (cid:45) (cid:45) M (cid:68) (cid:43)(cid:43) (cid:72) GeV (cid:76) Α Br (cid:72) h (cid:174)ΓΓ (cid:76) Type (cid:45)
II seesaw model , with
Β(cid:61)(cid:45)
FIG. 4. Contours of Br ( h → γγ ) in the Type II seesaw model,for fixed β = − .
18. The horizontal contour with α = 0 isapproximately equal to the SM prediction Br ( H → γγ ) =0.2 %. We find this branching ratio can be enhanced by afactor of 2, for α (cid:39) − . m ∆ ++ (cid:46)
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