LHC and the Origin of Neutrino Mass§

LHC and the origin of neutrino mass§

Goran Senjanovi´c International Centre for Theoretical Physics, 34100 Trieste, Italy

Abstract

It is often said that neutrino mass is a window to a new physics beyond the standard model (SM). This is certainly true if neutrinos are Majorana particles since the SM with Majorana neutrino mass is not a complete theory. The classical text-book test of neutrino Majorana mass, the neutrino-less double beta decay depends on the completion, and thus cannot probe neutrino mass. As pointed out already more than twenty five years ago, the colliders such as Tevatron or LHC offer a hope of probing directly the origin of neutrino Majorana mass through lepton number violating production of like sign lepton pairs. I discuss this in the context of all three types of seesaw mechanism. I then discuss in detail the situation in L − R symmetric theories, which led originally to the seesaw and which incorporate naturally both type I and type II. A WR gauge boson with a mass in a few TeV region could easily dominate neutrino-less double beta decay, and its discovery at LHC would have spectacular signatures of parity restoration and lepton number violation. At the end I give an example of a predictive SU(5) grand unified theory that results in a hybrid type I and III seesaw with a light fermion triplet below TeV scale.

1 Introduction If M is huge, there is no hope of direct observation of new physics. It is often said that large M is more We know that neutrinos are massive but light [1]. If natural, for then Yukawas do not have to be small. For we wish to account for tiny neutrino masses with only example, M = 1013GeV − 1014GeV corresponds to Y the Standard Model (SM) degrees of freedom, we need of order one. However, small Yukawas are natural in a Weinberg’s [2] d = 5 effective operator sense of being protected by chiral symmetries and any- way most of the SM Yukawas are small. Furthermore, LiHHLj L = Yij , large ratios of mass scales need fine-tuning, so there is M nothing more natural about large M. I adopt the strat- egy here of keeping M free and looking for theoretical where Li stands for left-handed leptonic doublets and H for the usual Higgs doublet (with a vev v). This in turn predictions, in particular through grand unification. produces neutrino Majorana mass matrix In order to get a window to new physics, we need a renormalizable theory of the above effective operator. In v2 the minimal scenario of adding just one new type of par- M = Y . ν M ticles, there are only three different ways of producing it through the exchange of heavy The non-renormalizable nature of the above operator I) fermion singlet (1C , 1W , Y = 0), called right- signals the appearence of new physics through the mass handed neutrino; type I seesaw [5], scale M. The main consequence is the ∆L = 2 violation II) bosonic weak triplet (1C , 3W , Y = 2); the type of lepton number through II seesaw [6], • neutrino-less double beta decay ββ0ν [3] III) fermion weak triplet (1C , 3W , Y = 0); called type III seesaw [9] • same sign charged lepton pairs in colliders. where C stands for color and W for SU(2) weak quantum numbers. While the neutrino-less double beta decay is a text- It is easy to see that all three types of seesaw lead to book probe of Majorana neutrino mass, the like sign arXiv:0911.0029v2 [hep-ph] 24 Mar 2010 one and the same d = 5 operator above. lepton pair production, although suggested already long By itself, seesaw is not more useful than just Wein- time ago [4], has only recently received wide attention. berg’s operator unless we can reach the scale M or have In what follows I argue that this process may be our best a theory of these singlets and/or triplets. This is remi- bet in probing directly the origin of neutrino mass. Due niscent of the Fermi effective theory of low energy weak to the lack of space I can cover only the essential points interactions: saying that the four fermion interactions and I cannot do justice to the fast growing literature in can be described by the exchange of a W boson is ap- the field. I have tried to be complete in citations, but I propriate either at the scale MW or if you have a theory am sure I failed, although not on purpose. I apologize in of a W boson. This is precisely what the SM gauge the- advance for the omission of papers that merit quotation. ory had achieved by correlating a plethora of low energy This is a short review, not at all a comprehensive study (E MW ) weak interaction processes. of these interesting issues. It is often said that neutrino mass is a window to new §Based on plenary talks at Neutrino 08, Christchurch, New physics . This is definitely true if it is Majorana for the Zealand and Physics at LHC - 2008, Split, Croatia. SM with Majorana neutrino mass is not complete, as

1 n p the right-handed neutrino mass mN in the 100 GeV - TeV region, this contribution can easily dominate over the left-handed one. Neutrino mass can even go to zero W e (vanishing Dirac Yukawa) while keeping the WR contribution ﬁnite. x m n p e

WR W e n

p x mN

Figure 1: Neutrino-less double beta decay through the neutrino Majorana mass. WR n e p manifest from the d = 5 operator. In the Dirac case, the theory is complete so that the new physics is not Figure 2: Neutrino-less double beta decay induced by mandatory. Flavor violation in charged lepton decays is the right-handed gauge boson and right-handed neu- 2 2 GIM suppressed by ∆mν /MW and is is too tiny to be trino. observed. Of course, the new physics may emerge from a model of these masses, but it is not mandatory by itself. Majorana case, on the other hand, necessarily con- • Colliders: produce W through Drell-Yan as in Fig. nects m to new physics, such as desperately searched R ν 3. for ββ0ν, in Fig.1. This probes neutrino Majorana mass in the range 0.1 - 1 eV. j However, in general mν is not directly connected to ββ0ν decay. While it does produce it, the inverse is not j true. ββ0ν decay does not imply the measure of neu- WR trino mass, since it depends on the completion of the SM needed for the d = 5 neutrino mass. An example N d is provided by the L − R symmetric theory discussed in the next section. This is the theory that led originally WR l to the seesaw mechanism, and as such deserves atten- u− tion. As we will see, if the scale of parity restoration is in the few TeV region, the theory oﬀers a rich LHC phenomenology and a plethora of lepton ﬂavor violating l (LFV) processes.

Figure 3: The production of WR and the subsequent decay into same sign leptons and two jets through the 2 Left-right symmetry and the Majorana character of the right-handed neutrino. origin of neutrino mass

L−R symmetric theories [10] are based on the SU(2)L × Once the right-handed gauge boson is produced, it will SU(2)R × U(1) gauge group augmented by parity or decay into a right-handed neutrino and a charged lepton. charge conjugation. Then: The right-handed neutrino, being a Majorana particle, decays equally often into charged leptons or anti-leptons • WL implies WR, and jets. This often confuses people for naively one ar- gues that the production of a wrong sign lepton must • ν implies ν , with m of order M through the L R νR R be suppressed by the mass of the right handed neutrino. breaking of L − R symmetry, True, but so does the production of the right sign lepton • Type I seesaw: connects neutrino mass to the scale in its decay; this is the usual time dilation. It is enough of parity restoration. that N is heavy enough as to decay into a lepton and two jets, and then the above claim must be true. In These facts lead immediately to the new contribu- turn one has exciting events of same sign lepton pairs tion to the neutrino-less double beta decay mentioned and two jets, as a clear signature of lepton number vio- above, see Fig. 2. With WR in the TeV region and lation. This is a collider analog of neutrino-less double

2 beta decay, and it allows for the determination of WR 3 Minimal non supersymmetric mass as shown in the Fig. 4. SU(5) This offers The minimal SU(5) theory consists of: 24 + 5 Higgs a) direct test of parity restoration through a discov- H H multiplets, where 24H is used to break the original sym- ery of WR, metry to the SM one, and 5H completes the symmetry breaking; and the three generation of quarks and leptons b) direct test of lepton number violation through a 3(10F + 5F ). The theory fails for two reasons: Majorana nature of νR, • gauge couplings do not unify c) determination of WR and N masses. 16 α2 and α3 meet at about 10 GeV (similar as in A detailed study [11] concludes an easy probe of W up 13 R the MSSM), but α1 meets α2 too early, at ≈ 10 to 3.5 TeV and νR in 100 - 1000 GeV for integrated lumi- GeV nosity of 30 fb−1. It needs a study of flavor dependence, i.e. connection with LFV. There have been recent claims • neutrinos remains massless as in the SM. of MR & 4 TeV [12] (or even MR & 10 TeV [13]) in the minimal theory, but these limits depend on the defini- The d = 5 Weinberg operator for neutrino mass we tion of L − R symmetry and its manifestness. Namely, started with is not enough: neutrino mass comes out −4 this limit stems from CP violation which depends on the too small (. 10 eV ) since the cut-off scale M must be definition of L − R symmetry. at least as large as MGUT due to SU(5) symmetry. In Recall that L−R symmetry can be P as in the original any case, one must first make sure that the theory is works or C as it happens in SO(10). The authors of consistent and the gauge couplings unify. [12, 13] use P, but it can be shown that in the case of C, A simple extension cures both problems: add just one the freedom in CP phases leaves only the CP conserving extra fermionic 24F [25]. This requires higher dimen- limit MR & 2.4 TeV [12]. This allows for both WR and sional operators just as in the minimal theory, but can the accompanying neutral gauge boson ZR to see seen be made renormalizable as usual by adding extra 45H at LHC. scalar [26]. It is worth noting that the same signatures can be Under SU(3)C × SU(2)W × U(1)Y the adjoint is de- studied in the SM with νR [14], but it requires mirac- composed as: 24F = (1, 1)0+(1, 3)0+(8, 1)0+(3, 2)−5/6+ ulous cancellations of large Dirac Yukawa couplings in (3¯, 2)5/6. The unification works as follows: triplet order to keep neutrino masses small. When a protec- fermion (like wino in MSSM) slows down α2 coupling tion symmetry is called for, one ends up effectively with without affecting α1. In order that they meet above lepton number conservation and the phenomenon disap- 1015 GeV for the sake of proton’s stability, the triplet pears [15]. must be light, with a mass below TeV. Then in turn α3 The L − R theory possesses naturally also type II see- must be slowed down, which is achieved with an inter- 7 saw [7]. The type II offers another potentially interesting mediate scale mass for the color octet in 24F around 10 signature: pair production of doubly charged Higgses GeV or so. which decay into same sign lepton (anti lepton) pairs For a practitioner of supersymmetry, the theory be- [16]. This can serve as a determination of the neutrino haves effectively as the MSSM with a light wino, gluino mass matrix in the case when type I is not present or heavy (107GeV), no Higgsino, no sfermions (they are ir- very small [17]. It is worth commenting that the minimal relevant for unification being complete representations). supersymmetric left-right symmetric model [18] predicts This shows how splitting supersymmetry [27] opens a doubly charged scalars at the collider energies [18] [19] Pandora’s box of possibilities for unification. The great [20] even for large scale of left-right symmetry breaking. success of low energy supersymmetry was precisely the This is all very nice, but the question is whether a low prediction of gauge coupling unification [28] [29] [30] L−R scale is expected or not. It is perfectly allowed, but [31], ten years before the LEP confirmation of its pre- 2 not predicted. This theory can be embedded in SO(10) diction sin θW = .23. In 1981 when it was thought 2 grand unified theory, where L − R symmetry becomes that sin θW = .21, this required asking for a heavy top charge conjugation and is a finite gauge transformation. quark, with mt ' 200 GeV [31]. Unlike the case of su- The scale of L − R breaking ends up being high though, persymmetry, where the scale was fixed by a desire for either close to MGUT in the supersymmetric version [21] the naturalness of the Higgs mass, and then unification [22], or around 1010 GeV or so in the ordinary version predicted, in this case the SU(5) structure demands uni- [23]. fication which in turn fixes the masses of the new parti- We are faced then with a question: is there a simple cles in 24F . The price is the fine-tuning of these masses, predictive grand unified theory with seesaw at LHC? but a great virtue is the tightness of the theory: the The answer is yes, a minimal extension of the original low mass of the fermion triplet (and other masses) is a Georgi-Glashow theory [24] , with an addition of an ad- true phenomenological prediction not tied to a nice but joint fermion representation [25]. imprecise notion of naturalness.

3 l! l! jj or l" l" jj: ll"jj invariant mass 20

17.5

12.5

7.5

2.5

500 1000 1500 2000 2500 3000 3500

−1 Figure 4: The number of events as a function of energy (GeV) for L = 8fb (courtesy of F. Nesti) where MR (TeV) is taken to be: 1.8; 2, 0; 2.4; 2.6; 3, 0; 3.4.

With the notation singlet S = (1, 1)0, triplet T = With proper cuts SM backgrounds appear under con- −1 (1, 3)0, it is evident that we have mixed Type I and trol [33]. With integrated luminosity of 10 fb one Type III seesaw could ﬁnd the fermionic triplet T for MT up to about 400 GeV. i j i j ! ij 2 yT yT ySyS The light triplet fermion also plays an important role (Mν ) = v + mT mS in lepton ﬂavor violation, especially in µ → e conversion in nuclei, which is induced at the tree level and could be An immediate consequence is one massless neutrino. observed even for a triplet out of LHC reach [34]. Thus one cannot have four generations in this theory, for Before concluding, it should be mentioned that one then all four neutrinos would be light which the Z decay can also add a 15-dimensional scalar as an alternative of width does not allow. Since the triplet may be out of curing the minimal SU(5) theory. This leads instead to LHC reach, seeing the fourth generation would serve an the type II seesaw with possibly light lepto-quarks and important test of a theory; it would simply rule it out. its own interesting phenomenology [36].

3.1 T at LHC 4 Summary and Outlook We saw that unification predicts the mass of the fermion triplet below TeV, and thus it becomes accessible to the I discussed here an experimental probe of Majorana neu- colliders such as Tevatron and LHC. It can be produced trino mass origin, both at colliders through the produc- through gauge interactions (Drell-Yan) tion of the same sign dileptons, and a neutrino-less double beta decay. A classical example is provided by the pp → W ± + X → T ±T 0 + X L − R symmetric theory that predicts the existence of pp → (Z or γ) + X → T +T − + X right-handed neutrinos and leads to the seesaw mechanism. A TeV scale L − R symmetry, as discussed here, with the cross section for the T pair production in Fig. would have spectacular signatures at LHC, with a pos- 5. sible discovery of WR and νR. This offers a possibility The best channel is like-sign dileptons + jets of observing parity restoration and the Majorana nature of neutrinos. It is important to search for an underlying 1 |yi |2|yj |2 theory that predicts it naturally. For a recent attempt, BR(T ±T 0 → l±l± + 4jets) ≈ × T T i j P k 2 2 see [37]. 20 ( k |yT | ) I have provided next an explicit example of a predic- i Same couplings yT contribute to ν mass matrix and tive grand unified theory: ordinary minimal SU(5) with T decays, so that T decays can serve to probe the neu- extra fermionic adjoint. A weak fermionic triplet is pre- trino mass matrix [32] and the nature of the hierarchy dicted in the TeV range (type III seesaw) whose decay is of neutrino masses. connected with neutrino mass. This offers good chances

4 pp -> T+- T0 + X at LHC 101

0 10 T+ T0 T- T0

10-1

10-2 cross section (pb)

10-3

10-4 100 200 300 400 500 600 700 800 900 1000

mT (GeV)

Figure 5: Cross section for the T pair production at LHC.

for discovery at LHC with integrated luminosity of 10 rizio Nesti, Ivica Puljak, Andrija Raˇsin(Andrija, vrati −1 fb for MT up to about 400 GeV. se, sve ti je oprosteno), Francesco Vissani and especially One can also simply study the minimalist scheme of Borut Bajc. I acknowledge with great pleasure my col- pure seesaw in the connection with the colliders. The laboration with Wai-Yee Keung on the issue of lepton type II and III are naturally rather exciting from the ex- number violation at colliders. I am grateful to Enkhbat perimental point of view, for the new states can be easily Tsedenbaljir for numerous useful discussions. Thanks produced through the gauge couplings. In the case of the are also due to Alejandra Melfo and Vladimir Tello for type I it becomes a long shot, since the Dirac Yukawas their help with this manuscript, and Borut Bajc, Miha must be large and the smallness of neutrino mass is then Nemevˇsekand Enkhbat Tsedenbaljir for careful reading attributed to the cancellations. Strictly speaking that of the manuscript. This work was partially supported should not be called the seesaw whose name was meant by the EU FP6 Marie Curie Research and Training Net- to indicate a natural smallness of neutrino mass after work ”UniverseNet” (MRTN-CT-2006-035863). the heavy states are integrated out. In summary, I argued here that in spite the smallness of neutrino masses, the hope of probing their origin at References LHC is not just wishful thinking. Small Yukawa couplings are as natural as the large ones, and the low scale [1] For a review and references on neutrino masses and seesaw is perfectly realistic, and even likely in the con- mixings, see A. Strumia and F. Vissani, arXiv:hep- text of the SU(5) grand uniﬁed theory. There are other ph/0606054. possible ways of having TeV scale seesaw, as e.g. with R. N. Mohapatra and A. Y. Smirnov, Ann. mirror leptons [38] and in the case of dynamical symme- Rev. Nucl. Part. Sci. 56, 569 (2006) [arXiv:hep- try breaking [39]. ph/0603118].

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