Neutrino Mass Physics at LHC

Available online at www.sciencedirect.com

Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 393–399 www.elsevier.com/locate/npbps

Neutrino Mass Physics at LHC R. N. Mohapatra Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD-20742,USA

Abstract I discuss the possibility of probing neutrino mass physics at the CERN Large Hadron Collider. Keywords: Seesaw, Left-right models, supersymmetry

1. Introduction The discovery of neutrino masses and mixings during the past decade has provided the first conclusive evidence for new physics beyond the standard model(SM). The absence of the right handed neutrino as well as conservation of B-L symmetry in SM are the two main factors responsible for neutrino masses being zero. To understand nonzero neutrino mass therefore, one must go beyond it by either extending SM to include three right handed neutrinos or include fields to break B-L quantum number or both. In the approach that adds RH neutrinos (denoted by N) but keeps B-L symmetry, observed small neutrino masses require that the new Yukawa couplings ¯ involving the N’s i.e. hν LHN must be extremely tiny (i.e. hν ∼≤ 10−12 ). One must then understand why this coupling is so small e.g there may be other new symmetries or there must be other physical phenomena that require such small couplings (for all three flavors). In the absence of any obvious compelling arguments for tiny hν , most attention in the field has been focussed on taking the alternative path of breaking B − L in SM extensions. We will restrict ourselves to this case in this review. The simplest way to parameterize the B-L breaking effects in the SM extension is to have the operator λ(LH)2 /M added to the SM Lagrangian [1], which after symmetry breaking leads to neutrino mass of the v2 form mν = λ Mwk . M is the scale of new physics that induces this operator. Small neutrino masses require that the scale Mλ ≥ 1014 GeV. The exact magnitude of the 0920-5632/$ – see front matter, Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2012.09.062

new energy scale therefore depends on how small λ is and hence on model details. If λ is such that M ∼ TeV’s, then this new physics can be probed at the LHC. This is what I focus on in this talk. There are two classes of models: the seesaw approach where after heavy masses associated with new physics are integrated the effective operator takes the BL violating form given above. An alternative class is where loop corrections that involve new particles generate small masses. The examples of the first class are seesaw models[2] whereas the second class are loop models[3]. Both can have new particles at the TeV scale and therefore can be probed at LHC. Here I focus on the first class. 2. Seesaw Paradigm In generic seesaw models, the effective B-L violating operator arises from an UV completion of SM above scale M. The simplest possible UV theory where this can happen is the extension with SM+N but with a large Majorana mass for N i.e. new terms of the form ¯ hν LHN + MNN + h.c. added to the SM Lagrangian. They lead after electro-weak symmetry breaking to a formula for light neutrino masses of the form mν  v2wk hTν M −1 hν where hν and M are 3 × 3 matrices. This is only one of several different types of seesaw mechanisms. A second way to generate the Weinberg type operator is to look at the effective dim five operators of the following form LT τL · H T τH/M. This can be

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 with implemented by adjoining a scalar Higgs triplet Δ Y = 2 to the standard model. The effective parameter M2 M in this case is given by M = μΔ where MΔ is the mass of the Higgs triplet and μ is the coupling strength defined by μH 2 Δ[4]. The above two types of seesaws were called type I and II by this author many years ago. If in type I seesaw, instead of considering a Majorana SM singlet, we consider a Dirac SM singlet fermion, the resulting seesaw is called inverse seesaw[5]. The seesaw lagrangian in this case is given by ¯ LY = hν LHN + MNS + μS S

(1)

The (ν, N, S ) mass matrix in this case has the form: ⎞ ⎛ ⎜⎜⎜ 0 mD 0 ⎟⎟⎟ ⎟ ⎜ (2) M = ⎜⎜⎜⎜ mTD 0 M ⎟⎟⎟⎟ ⎠ ⎝ 0 M μ The resulting seesaw formula for neutrino masses is given by: mν = mTD M −1 μM −1 mD

(3)

Notice the double suppression by the Dirac mass of the heavy singlet neutrinos in the formula and also the direct proportionality of mν to the lepton number violating parameter μ (i.e. the Majorana mass of the singlet field S). This feature is very different from the type I case and allows the scale M to be low while keeping the Yukawa couplings in the generic range for charged leptons. Yet another way to write the Weinberg operator is (LT τH)2 /M. This can be implemented by adjoining Y=0 fermion triplets Σ with a Majorana mass to the standard model. This is known as type III seesaw[6]. This is very similar to the type I case with the difference that the new triplet fermions couple directly to W-boson and that makes it easier to search for them in colliders if their masses are in the TeV range. Seesaw paradigm raises a number of questions: • What is the seesaw scale M and in particular is it accessible at the LHC ? • What new physics is associated with M i.e. are there new gauge symmetries whose breaking scale is M ? If so, does the new physics provide any clue to the value of M and how does it help in the search for the seesaw scale. 2.1. Minimal Seesaws at TeV scale and their LHC accessibility As noted already, the seesaw scale will be accessible at the LHC provided the new particles associated with

seesaw have masses in the TeV range or below and their couplings with SM particles are of reasonable strength. The new particles in question are: N, (Δ++ , Δ+ , Δ0 ) and Σ. Let us discuss this for the various seesaw scenarios discussed above. We will first discuss this within the minimal seesaw models by which we mean SM gauge group with addition of the new particles required for implementing the seesaw mechanism. Since the seesaw formula for neutrino masses involve parameters other than the masses of the seesaw particles, one cannot produce the seesaw scale without additional information or assumption. One class of models where the scale is actually predicted are the grand unified theories such as SO(10) that embed the type I seesaw mechanism. In this case, the seesaw scale is predicted to be near the GUT scale of 1016 GeV pushing it beyond the collider regime. Within the minimal schemes however, we could simply assume the Dirac masses (in type I or type III cases) to be in the 30 keV range in which case, the seesaw scale can be a TeV. Similar assumptions also work for type II as well as inverse seesaw models which have the free parameter μ (having different meaning in the two models) so that in principle the seesaw scale in all these cases falls within the LHC energy range. Since at LHC, the partons inside the proton beams can only produce states that couple to u, d, u¯ , d¯ and gluons etc, first we have to find ways by which we can produce the seesaw states. This depends on the particular scenarios and we outline them below. 2.2. Type I case In type I case, the seesaw states are the singlet RH neutrinos, N. Being SM singlets, they can only be produced via ν − N mixing θν−N after virtual W’s produced in parton collision decay to  + ν. In seesaw models, mν −6 this mixing is given by θν−N ∼ MN ≤ 10 . Once produced, the N’s decay to both charged leptons and anti-leptons giving like sign di-leptons in the final states which is a unique signal. The problem however is that the small θν−N suppresses the production of N’s. Analysis of such models have shown that unless θν−N ≥ 10−2 , minimal type I seesaw will not be testable at LHC despite the scale being in the TeV range[7]. Since we do not know the mass of the right handed neutrinos, it is important to check if there are any constraints on θν−N as a function of mass from low energy as well as accelerator experiments. This has been carried out in a recent paper [8] for masses below MN = 100 GeV. The result of this analysis is that above about 10 GeV, θν−N ∼ 10−2 or less is allowed. These bounds become considerably weaker above 100 GeV mass for

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right handed neutrinos. Therefore, it is phenomenologically safe to assume θν−N to be larger for higher mass right handed neutrinos in exploring LHC signals.

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2.4. Type II case

quite distinct. An advantage of type II case compared to type I or III is that the production cross section is directly proportional to the neutrino masses. One would therefore expect a reflection of the underlying mass matrix pattern in the cross section e.g. in the case of normal hierarchy, third generation lepton pairs would be dominant over the ee or μμ production. In this case doubly charged Higgs bosons with masses upto a TeV can be easily explored at LHC. Type III case has also been studied in great detail[14]. The seesaw particles in this case are part of a fermion triplet with Y=0 and can be written as (Σ+ , Σ0 , Σ− ) Again like type II case, their SM non-singlet nature makes production via W and Z modes possible giving enhanced cross section. The decay of these particles are as follows: Σ0 → W − + and Σ+ → Z + + . These multilepton final states make it possible to explore the seesaw scales till 700 GeV Σ masses.

The addition to the SM Lagrangian in the type II case is given by:

3. Left-right seesaw at LHC

2.3. Inverse seesaw This situation improves in the case of inverse seesaw as far as the production is concerned since the θν−N in this case is not related to the neutrino mass directly and could therefore easily be above 0.01. However the signal in this case will not be like sign dileptons since the N’s are mostly Dirac particles and will therefore conserve lepton number with high accuracy. Instead the signal will be ± ∓ ± ν, one lepton coming from the Wdecay as before and two charged leptons and a neutrino coming from N decay. In this case, it will be hard to probe N mass beyond about 300 GeV[9] or so.

 + M 2 Δ† Δ + h.c. (4) A much more fruitful way to probe type I seesaw  + μH T τH · Δ LI = fαβ LαT τLβ · Δ Δ scale at LHC emerges within frameworks that try to explain the type I seesaw scale as a result of gauge symmeThe triplet field Δ consists of three components: ++ + 0 try breaking. A simple possibility is to embed seesaw (Δ , Δ , Δ ). Minimization of the potential in the case within the left-right models based on the gauge group induces a vev for the neutral member of this triplet a vev μv2wk S U(2)L ×S U(2)R ×U(1)B−L symmetry[15]. These modvT = M 2 . els have many other attractive features e.g. making parThe presence of doubly charged as well as singly ity a short distance symmetry of the theory. They procharged Δ particles lead to interesting low energy efvide a natural explanation of the seesaw scale as confects that have been searched for experimentally. An nected to the scale of S U(2)R × U(1)B−L breaking (or interesting one is the muonium to anti-muonium oscilparity breaking) since the right handed neutrino mass lation μ+ e− → μ− e+ which appears with an amplitude arises from the coupling f LR LR ΔR where LR is the right f f ∼ 4Mee 2μμ [10]. Current experimental upper limits on this handed doublet of leptons that contains the N’s and Δ Δ++

process[11] at the level of 2 × G F × 10−3 depends on the coupling constants but for reasonable values of the coupling parameters (e.g. fee,μμ ∼ 0.1), MΔ++ near 200 GeV or higher is allowed. Such mass values are within the range of LHC. The Δ’s being SM non-singlets they couple to W, γ and Z. They can therefore be directly produced via γ and W-exchange and can be directly probed if their masses are in sub-TeV to TeV range[12]. For instance, the Δ++ member of the triplet Higgs couples to like sign lepton pairs (e− e− , μ− μ− , τ− τ− ). Thus the LHC signal will be pp → μ− μ− μ+ μ+ + X and both the like sign muon pairs will exhibit an invariant mass peak at the same mass. This should be spectacular signal. This has been studied by many authors[12, 13]. One can also have final states of type Δ++ Δ− arising from virtual W + exchange in parton collisions. In this case, there will be a missing energy piece. Nonetheless, these signals are

R

is a right handed triplet with B − L = +2 that makes the above coupling gauge invariant. Once we give a vev < ΔR > = vR , it breaks parity as well as B-L and gives mass to the RH neutrinos N’s that come into the seesaw formula. This also has the interesting property that smallness of neutrino mass is connected to the extent to which is the right handed current are suppressed at low energies. The minimal version of this theory is a well defined theory of neutrino masses and can be used to study its possible LHC accessibility. There are bounds on the left-right models from a variety of low energy flavor changing processes e.g. KL − KS mass difference, CP violating observables K and K , Bs − B¯ s mixing etc. These have been extensively studied in recent papers[16] which update the old results. The current limits on WR depend on how CP violation is introduced into the theory and the best limit on WR for the case where the left and right CKM angles are equal is

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L = hD LφLc + f Lc χc S + μS S

(5)

Here φ(2, 2, 0) is the bi-doublet of the left-right model. On giving vevs to χc and φ the inverse seesaw Lagrangian emerges. It is also important to point out that without the left-right gauge symmetry, there will be other terms in superpotential e.g. NN, MHS etc destabilizing the inverse seesaw neutrino mass matrix. Thus in some sense, the left-right gauge symmetry is essential to have inverse seesaw mass matrix to be natural. An interesting question of great theoretical interest is whether a TeV scale seesaw is compatible with coupling unification. In this case one could imagine the low scale left-right theory being part of a grand unifying group like SO(10) raising the hope that it could lead to predictions that can be tested experimentally. This issue has been investigated for both type I[19] and inverse seesaw[20]. The conclusion that emerges in type I case, is that TeV scale seesaw does not lead to coupling unification in supersymmetric models due to the presence of B-L=2 S U(2)R triplet Higgs fields that adversely affect the running of B-L as well as the S U(2)R gauge couplings. On the other hand, in the case of inverse seesaw one invokes only B − L = 1 S U(2)R doublet Higgs fields whose effect on coupling running is very mild and coupling unification occurs with TeV mass WR and Z  . However since slope of α−1 running becomes steeper for S U(2)L as well as other weak gauge couplings, for unification to occur, the slope of α−1 c must be lowered over its MSSM value. This is easily done by introducing one pair of vectorlike up quarks which are S U(2)L,R singlets. They are present in SO(10) multiplets like 45dim. representations. This would appear to make the case for searching for TeV mass WR and Z  at LHC much stronger.

80 70 60

α-1 B-L

α-1 1Y

MG

50 40 α-1 2R 30 20

α-1 2L

α-1 3c

10 0

α-1 U

MR

MSUSY

2.5 TeV. For the case of non-manifest models where the mixing angles in the right sector are very different, the lower bound on the WR mass is much lower[17]. Another constraint for the manifest left-right symmetry case comes from neutrino-less double beta decay where there is a new contribution involving heavy WR and right handed neutrino Majorana mass[18]. For a one TeV RH neutrino mass, one gets MWR ≥ 1.1 TeV and the lower bound increases like (MN )−1/4 for smaller RH neutrino masses. The gauge embedding of left-right inverse seesaw is different in that it does not require B-L=2 triplet Higgs fields; instead we only need to add B − L = ±1 doublet right handed fields to the model. In fact the Inverse seesaw Yukawa superpotential involving leptons for leftright model is given by:

α-1

396

0

2

4

6

8 10 t [log10(GeV)]

12

14

16

18

Figure 1: Gauge coupling unification with inverse seesaw and TeV WR scale

At LHC, left-right TeV scale seesaw can be tested for both type I and inverse cases via the production of “live” WR and its subsequent decays to right handed neutrinos and the subsequent decays of right handed neutrinos to leptons and jets. In type I case the alternative channel for right handed neutrino via ν − N mixing is suppressed due to small θν−N . The smoking gun signal for type I case is like sign dileptons plus two jets (and no missing energy)[21]. This comes from the following chain: pp → WR + X followed by WR → lR + Nl,R with subsequent decay of right handed neutrino Nl decay to ± +qq¯ being the final signal. The WR → lR +Nl,R occurs roughly 12% of the time whereas N decay is 50% to ± mode each. The like sign decay therefore occurs 6% of the time to any particular lepton flavor. Muons being the easiest to detect, μ− μ− j j mode is the premium final state. There is no missing energy. There are standard model backgrounds coming from WW, tt¯, bb¯ mode etcbut they all have much lower pT than our signal mode. Also, in contrast with the minimal non-gauged seesaw case, the rates for this case are much stronger[22] e.g. WR production times the branching ratio to dilepton mode is 30 fb for MWR = 1 TeV and MN ∼ .9 TeV and 21 fb for MWR = 2 TeV and MN ∼ 1 TeV. The like sign dilepton background from SM is negligible for pT ≥ 80 TeV. Calculations show that the LHC reach for type I case is MWR ≤ 4 TeV. In Fig 1, the invariant mass of two like sign dileptons and two jets plotted along with the SM background. Note the background in red and WR peaks at 2, 2.5, 3 TeVs in blue, green and purple respectively[23] (Figures provided by F. Nesti). The inverse seesaw case has not been as thoroughly explored but what is clear is that as in the minimal seesaw case, the the signal is three leptons plus missing energy and again one can use a pT cut to reduce the SM background and one should have a comparable reach.

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Fig. 2 shows the three lepton missing pT invariant mass for this case. Clearly the peaks are not as sharp- however, the excess events above 1.5 TeV would be a signal for this type of seesaw with 2 TeV WR mass[23].

Figure 2: Invariant mass distributions two like sign dilepton two jets from WR production (blue, magenta, yellow..) along with SM background (in red). The y-axis gives the number of events.

Figure 3: Invariant mass distributions three leptons from WR production(in colors other than red) along with SM background (red)

It is important to point out that a corroborating and independent test for any WR signal at LHC in type I case can come from neutrinoless double beta decay searches. As noted above, the current neutrinoless double beta decay searches using 76Ge lead to a lower bound of only 1.1 TeV. The amplitude scales like inverse 4th power of MWR . So for a 2TeV mass, an amplitude at the level of 16 times lower is expected for MN ∼ 1 TeV. This could however be larger for lower N masses which are perfectly consistent with observations. Neutrino-less double beta decay experiments will therefore throw light on the seesaw scale.

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4. Leptogenesis and seesaw at TeV One of the interesting by products of the seesaw approach to neutrino mass is that the same interactions that goes into understanding the neutrino masses can also be used to understand the origin of matter in the Universe via leptogenesis[24]. This however puts severe constraints on the masses of the right handed neutrinos that participate in leptogenesis. For instance, in high scale seesaw models, the lightest RH neutrino must have a mass which is larger than about 109 GeV[25]. These limits come from a consideration of both satisfying the out of equilibrium condition od Sakharov together with subsequent wash out of lepton asymmetry by lepton number violating interactions. The situation is more complex when there are gauge fields coupling to the right handed neutrinos. There are new channels for lepton number wash out as well as depletion of initial right handed neutrino density. This question has been discussed in the context of two TeV scale left-right models. In left-right models with type I seesaw, it turns out that there is a lower limit on the mass of the WR of about 17 TeV, pushing it out of the range of LHC[26]. This issue was revisited in the context of inverse seesaw in a recent paper[27] and it was found that in contrast with type I seesaw, in the inverse seesaw case the model can generate enough lepton asymmetry even while keeping the WR and Z  masses around a TeV or higher[27]. This is therefore of great interest for LHC searches for WR bosons. Note incidentally that the lower bound on the SM fermions of type III seesaw for successful leptogenesis is 1.6 TeV which pushes it beyond the reach of LHC[28]. 5. LHC tests of SUSY seesaw There are two possible classes of theories: one where the seesaw scale is close to the GUT scale as in many SO(10) theories and a second class where the seesaw scale is near a TeV. If the seesaw scale is very high, there are no LHC signals in the absence of supersymmetry since the effects due to new physics decouples from low energy physics. However, once supersymmetry is included, there are two kinds of signals: (i) the ones coming from renormalization group running in the presence of seesaw scale leading to somewhat different kinds of sparticle spectra at the weak scale compared to nonseesaw models[29, 30]. This is specially visible in the slepton sector[30]; (ii) the second kind of effect of seesaw is in

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the slepton flavor violating effects at LHC[31]. The latter effects are directly caused by the interactions in the seesaw approach that are responsible for neutrino mixing and will provide a more clear test of high scale susy seesaw. They could for example lead to flavor violating slepton decays e.g. τ˜ → e + χ0 , etc. On the other hand when the susy seesaw scale is in the TeV range, in addition to the similar effects as above, there can be new classes of exotic signals. A typical model of this type is the supersymmetric left right model. In minimal versions of these models, it turns out that R-parity breaking is mandatory and occurs via the vacuum expectation value of the right handed slepton fields- < ν˜c > 0. This leads to a mixing between the right handed Wino W˜R+ with ec . The decay profile of the right handed neutrinos then change drastically[32]. For example, if the RH sneutrino which acquires vev is aligned along the the electron flavor direction, then, the right handed muon neutrino Nμ decays to Nμ → μ− + e+ faster than the μ− j j mode. Thus typical new final states that appear are of the form pp → μ− μ− e+ e− j j + X if the smuon is chosen as the NLSP with gravitino being the LSP and the dark matter and has mass lower than the top quark. If its mass is heavier than the top mass and left-right smuon mixing is unsuppressed, another mode pp → e± μ± tb¯ + X appears . Such modes have very low background at high pT and should be observable even in the early runnings at LHC. A unique property of these models is that there is an upper limit on the seesaw scale of a few TeV or so implying that large part of the allowed parameter space can be probed at LHC. 6. Conclusion The basic summary bullet points of the talk are as follows: new physics responsible for neutrino masses and mixings can be at the TeV to sub-TeV scale although it need not. If it does, there are two premium channels for its manifestation: (i) doubly charged Higgs production which will signal a dominant type II seesaw in the neutrino mass generation; and (ii) two like sign jet jet mode which will signal the existence of left-right symmetric gauge group as the origin of neutrino mass; it can then be either type I or type II or both. If the leftright model is supersymmetrized there are new exotic multilepton signals which can probe a large part of the allowed parameter space of the model. The left-right model touches on several other fundamental questions of standard model such as the origin of parity violation, strong CP problem, nature of dark matter etc. and can also receive a cross-check from the search for neutrinoless double beta decay. We there fore urge a serious

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