NEUTRINO MASS AND THE LHC

M. NEMEVSEK1,2

1ICTP, Trieste, Italy, Email: miha@ictp.it2Jozef Stefan Institute, Ljubljana, Slovenia

Received January 10, 2012

We discuss the feasibility of probing the physics of neutrino mass generation atthe LHC and its connection to low energy phenomena. Motivation for existence of a lowscale of the neutrino mass operator might be provided by an observation of a signal inneutrinoless beta decay searches, which may run in tension with cosmology, if neutrinomass is its only source. An example of a theory which resolves this tension, and atthe same time may be probed at the LHC, is provided by the minimal left-right (LR)symmetric model with Majorana neutrinos. We show how colliders can probe leptonnumber and flavor violating couplings and how these are connected to other low energyprocesses. Moreover, we exemplify the impact of the low luminosity data from the 7TeV LHC run on the parameter space of the theory, both for the heavy right-handedneutrinos and for doubly charged scalars.

Key words: Neutrino masses, lepton number, Large Hadron Collider, neutrino-less double beta, seesaw mechanism.

PACS: 12.60.Cn, 13.85.Rm, 14.60.St, 14.70.Pw, 23.40.Bw.

1. NEUTRINO MASS AND LEPTON NUMBER

Neutrino mass is an experimentally established fact for physics beyond theStandard Model. Measurements of neutrino oscillations require at least two of thethree light neutrino states to be massive and furthermore two mixing angles shouldbe large with hints of the third parameter to be non-zero. The overall mass scale,hierarchy and any of the complex phases are still unknown. However, the most fun-damental unanswered question is the nature of the neutrino mass, which is directlytied to the breaking of the lepton number. In other words, we do not know, whetherneutrino is a Dirac or a Majorana particle.

Microscopic tests of this symmetry are currently going on and I will argue thatlepton number can be probed not only by precision measurements at low energiesbut also in high energy colliders, like the LHC. We may have a chance to probe thephysics responsible for neutrino mass at colliders, which would connect the collidermeasurements to low energy phenomena, as envisioned in [1].

2. NEUTRINOLESS DOUBLE BETA AND NEW PHYSICS

Almost immediately after Majorana wrote his famous work to point out thatneutral particles can be described with a real field, phenomenological implications

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2 Neutrino mass and the LHC 925

lightest neutrino mass in eV

normal

inverted

|mee ν

|in

eV

10−4 0.001 0.01 0.1 110−4

10−3

0.01

0.1

1.0

10�4 0.001 0.01 0.1 110�4

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lightest mN in GeV

lightest neutrino mass in eV

normalinverted

MWR = 3.5 TeV

largest mN = 0.5 TeV

|mee ν

+N|i

neV

1 10 100 400 500

10−4 0.001 0.01 0.1 110−3

0.01

0.1

1.0

10�4 0.001 0.01 0.1 10.001

0.0050.01

0.050.1

0.51.

1

Fig. 1 – Contribution to 0ν2β decay due to the standard neutrino mass mechanism (left) and due to theexchange of a heavy right-handed neutrino via WR (right), taken from [1].

followed. Racah and Furry pointed out that, if this mass is large, neutrinoless doublebeta decay should take place with an appreciable rate. Already in 1959, Goldhaberand Feinberg realized that 0ν2β can have other sources, beside the usual Majoranamass term of the neutrino. Symbolically, the amplitudes are

Aν ∝G2F

meeν

p2, ANP ∝G2

F

m4W

Λ5, (1)

where meeν is the effective Majorana mass and Λ is the scale of new physics. On

dimensional grounds alone, this scale has to be around TeV to give a contributioncomparable to the neutrino mass.

There exist a number of searches for 0ν2β with different nuclei and there haseven been a claim of observation by the Heidelberg-Moscow collaboration. A newgeneration of experiments is on the way, which are planning to improve on the exist-ing limit and check the alleged claim. A large rate measured rate could have profoundimplications, beyond solely measuring the effective Majorana mass. Specifically, ifthe HM claim is confirmed, a tension with cosmology may disfavor the standardmechanism due to light neutrino exchange. The point is that a fairly large mee

ν & 0.1eV requires a degenerate spectrum with mmin

ν & 0.1 eV, which is disfavored by con-straints on the sum of neutrino masses, coming from cosmology as seen on Fig. 1,left. If so, new physics at TeV in the ballpark of the LHC, is a must.

In [1], we have shown that LR symmetry is a natural candidate for such newphysics and may alleviate the tension with cosmological bounds, as seen on Fig. 1,right. Moreover, with WR in the TeV region, LHC searches can be employed topredict the rates for 0ν2β and lepton flavor violating (LFV) transitions, as discussedbelow.

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926 M. Nemevsek 3

3. LEFT-RIGHT SYMMETRY AND COLLIDERS

LR symmetric theories offer an understanding of parity violation at low ener-gies by taking a symmetric theory at high energies and breaking it spontaneously. Inthis way, the gauge bosons and right-handed neutrinos obtain a mass proportional tothe scale of symmetry breaking.

The minimal model is highly constrained by precision measurements of lightmesons, in particular by the kaon mixing. This issue has recently been re-examinedin [2] and a lower bound of 2.5 TeV established when charge conjugation is taken forLR parity. In this case, the CKM matrices for left and right-handed quark currentsare equal. Therefore, the interactions of WR are fixed completely and the productionat colliders depends only on its mass.

3.1. LEPTON NUMBER AT THE LHC

One can choose among several different channels to look for WR, howeverphysically most compelling is the final state with two lepton and two jets, proposedin [3]. This is the high-energy analog of the neutrinoless double beta decay withneutrons replaced by incoming protons and jets. If the right-handed neutrinos areheavy, they will decay into a charged lepton and two jets via off-shell WR, as seenin Fig. 2. The Majorana nature of the neutrino can now be seen directly. OnceN is produced, it decays half of the time into a particle and the other half into anantiparticle. The same-sign final state is a proof of lepton number violation and itcan be used to predict the rate of 0ν2β due to new physics. In order to do that, themasses of WR and N should be measured. This can be done by considering theinvariant mass of the final states. The entire final state (``jj) give theWR mass peak,while the (usually 2nd in pT ) `jj invariant provides information on the N masses.Since there is no missing energy in the process, the information is fairly complete.

3.2. LEPTON FLAVOR VIOLATION

Note also, that the diagram in Fig. 2 gives a clean relation between collidersand low energy experiments. The flavor of the leptons in the final state can be taggedand by considering all the six final states with e,µ and τ , the right-handed analogof the PMNS matrix, VR can be reconstructed. This allows one to predict the LFVrates due to WR exchange, like e.g.: `→ `′γ, `→ 3` and µ− e conversion. Due toabsence of a signal from the LHC, we have illustrated this connection [1] in a portionof parameter space, where neutrino mass is dominated by the type II contribution.In such case, the right-handed mixing angles turn out to be the same as those in thePMNS matrix, which in turn are determined by neutrino oscillations. Although allof the processes mentioned above are loop suppressed, the mixings in the neutrino

RJP 57(Nos. 5-6), 924–930 (2012) (c) 2012-2012

4 Neutrino mass and the LHC 927

p

p

WR

ℓi

Nα

ℓj

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j

j

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VRjα

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e + jet�EM activity

ΤN~1 mm

ΤN~5 m

0Ν2ΒHHML

D0

:d

ij

et

s

L=33.2pb-1

Fig. 2 – Feynman diagram for the production ofWR at colliders with a subsequent decay to two leptonsand two jets (left) and a combined bound in the WR−N plane (right), taken from [5].

sector are rather large, therefore the precision measurements force N to be lighterthan WR, precisely in the region of interest in Fig. 2.

Actually, there exist another source of both, LNV and LFV in this model due tothe extended Higgs sector. In order to break the LR symmetry and give a Majoranamass to right-handed neutrinos, a pair of (LR symmetric) scalar triplets with Y = 2is used. They too can mediate 0ν2β and LFV decays, depending on their massscale. For example, the doubly charged components ∆++

L,R couple to two same-chargeleptons and two WL,R, giving a tree-level amplitude for 0ν2β. Their contributionsare proportional to mν,N/m

2∆L,R

, therefore ∆L contribution is insignificant. The∆R contribution, on the other hand, could play an additional role, depending on theflavor structure of its couplings. The point is that ∆R also mediates LFV processesand in the case of type II discussed above, they are calculable and are rather large.Contrary to the WR exchange, there are a few enhancements in the case of the scalarexchange. First of all, the `→ 3` decays now proceed at the tree level and the µ− econversion is enhanced by a large log term logm2

µ/m2∆. When all the flavor channels

are taken into account, a bound on mN/m∆Rcan be set, depending on the lightest

neutrino mass and on the values of the neutrino mixing angles (see [1] for details).The bottom line is that LFV forces mN . 0.1m∆R

, and since the 0ν2β amplitudeof ∆R is suppressed by m2

N/m2∆R

compared to WR, its contribution is genericallysubdominant.

Recently, the issue of an upper limit on the scale of LR symmetry which wouldbe needed to explain a large 0ν2β signal in the absence of fine-tuning has been takenup in [4]. It shown that LHC will be able to cover a sizable portion of the parameterspace if heavy N is the culprit. In case ∆R is the dominant source (possible onlywhen VR is diagonal and therefore type II is subdominant), the relevant parameterspace is entirely within the reach of the LHC.

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928 M. Nemevsek 5

3.3. COLLIDER SEARCHES FOR HEAVY NEUTRINOS

The LHC is now running and data can be used to put experimental limits. Toillustrate that even very early data can be useful, an estimate of the limit has beenperformed in [5]. A recent search on pair-produced leptoquarks has provided ex-perimental data and the background on the ``jj final state. Using a Monte-Carlogenerator for the LR model and passing it through PYTHIA and PGS, a naive theo-rist’s limit can be obtained.

The Drell-Yan production is enhanced for an on-shell of WR, therefore thecross-section is rather large (σ ' O(100)pb for MWR

' TeV), therefore a ratherlarge number of events is expected and a bound can be set. As seen in the rightpanel of Fig. 2, a significant portion of the parameter space in the WR−N plain canbe excluded, even with 33 fb−1 of data for an intermediate mass of the right-handedneutrino. This estimate has already been superseded by experimental searches, whichalready push the limit to 1.6 TeV with 240 fb−1 of data. The large mass regionis inaccessible due to jets overtaking the branching ratio, while the lower part isinsensitive due to an isolation cut on the lepton. When N becomes light, the chargedlepton, resulting from its decay, gets collimated with the two jets. In order to excludethis region, a dedicated search for a single isolated charged lepton and a jet containinganother one would be required. For further light N masses, an interesting possibilitywith a displaced vertex arises and finally, the right-handed neutrino becomes long-lived enough to escape detection and can be constrained by the generic searches ofW ′ → `ν [7]. With one inverse femtobarn of data, these searches already excludeMWR

> 2.2 TeV for a very light right-handed neutrino.

3.4. SEARCHES FOR THE DOUBLY CHARGED SCALARS

A popular mechanism for neutrino mass generation is the so-called type II see-saw, where instead of the exchange of a heavy neutrino, the left-handed scalar tripletobtains a vacuum expectation value v∆. In such case, neutrino masses are directlyproportional to the Yukawa coupling matrix and one can hope to probe the neutrinomass matrix directly by studying the decays of the doubly charged component of thescalar triplet. This mechanism arises naturally in LR theories, where the right-handedtriplet gives mass to the right-handed neutrinos. Due to LR symmetry, its left-handedcounterpart has to be present as well, with a vev suppressed by the scale of paritybreaking.

There is a standing line of searches for these particles, all the way from LEP,Tevatron, Hera and recently from the LHC, where a limit of roughly 300 GeV wasreported. The timely issue of the validity of these bounds has recently been revisitedin [8]. We point out that due to a sum-rule among the components

m2∆+−m2

∆++ 'm2∆0−m2

∆+ ' β v2/4 , (2)

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6 Neutrino mass and the LHC 929

Direct searchLHC 980 pb-1

HvD=10-6GeVL

Sum Rule

Sum Rule &Z width

LEP EWPTmh=130GeV

ø

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EWPTmh=300GeV

0 100 200 300 400 500 600 700

-100

-50

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mD

+-

mD

++

@GeV

D

Fig. 3 – Summary of the experimental and theoretical constraints in them∆++–m∆+ parameter space,for degenerate light neutrino masses. The LHC 2σ exclusion is shown by the region to the left of thered solid curve, relative to v∆ = 10−6 GeV. The analogous curve for v∆ = 10−9 GeV is red dashed.The purple (dotted) contour excluded by EWPT at 95% C.L. is shown for SM Higgs mass 130 GeV(left panel) and 300 GeV (right panel). The (green) region excluded by the Z-width bound and themass sum rule in Eq. (4) is shown for the triplet-SM Higgs coupling β = 3, taken from [8].

which is valid up to tinyO(v2∆/v

2) corrections, one can express the relevant parame-ter space, spanning only two mass parameters (e.g. m∆++ and m∆+ −m∆++). Thereason why such a parametrization is crucial, is that the branching ratio for the decaysof the doubly charged component depends significantly on the mass split. Dependingon v∆, the mass split by as little as a few GeV triggers cascade decays into lightercomponents of the triplet. Depending on the sign of the mass split, the experimentalreach may either be enhanced, when the lowest-lying component is doubly-charged,or diminished, if the lightest state is neutral and the final state is more difficult toobserve.

Furthermore, the presence of mass splits is tied directly to the Higgs mass viaelectroweak precision tests. The main contribution of the scalar triplets is due to the Tparameter, which measures the size of the weak isospin breaking. As is well known,a heavy Higgs gives a large negative contribution to T , which can be compensatedby a non-zero split of the triplet components with a positive-definite value of T .

Finally, the data from the LHC search with 980pb−1 has been used to illustratethe above discussion with real data. As seen from Fig. 3, the shape of the exclusionregion changes abruptly as one departs from the degenerate mass point.

4. CONCLUSIONS

The LHC is finally running, taking data and performing searches for BSMphysics. One of the main reasons to go beyond the SM is provided by the discoveryof neutrino mass and the theory which predicted its existence is the LR symmetricmodel with Majorana neutrinos. We argue that a phenomenological rationale for this

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930 M. Nemevsek 7

theory to be at the TeV scale may be provided if a signal in the 0ν2β searches is seen,which would call for new physics.

The high-energy analog of 0ν2β can be used to search for lepton number vio-lation, by a direct production of the heavy Majorana right-handed neutrinos, givingtwo leptons and two jets in the final state. Furthermore, the flavor content of thechannels is directly connected to low energy phenomena and allows one to predictboth, LFV and LNV rates. We have shown that the LHC data can already be usedto put constraints on the LR scale by using precisely this channel. It is interestingto note that the long-standing theoretical limit is finally being overtaken by collidersearches.

Therefore, LHC is not only a Higgs machine, but also looks for new physicsrelated to neutrino mass generation. If the scale of LR symmetry breaking is reallylow, it has a chance to probe lepton number violation at colliders and connect it tolow energy experiments.

REFERENCES

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al., Nucl. Phys. B 802, 247 (2008).3. W.-Y. Keung, G. Senjanovic, Phys. Rev. Lett. 50, 1427 (1983).4. M. Nemevsek, F. Nesti, G. Senjanovic and V. Tello, [arXiv:hep-ph/1112.3061].5. M. Nemevsek, F. Nesti, G. Senjanovic, Y. Zhang, Phys. Rev. D83, 115014 (2011).6. CMS Collab., CMS-PAS-EXO-11-002; ATLAS Collab., ATLAS-CONF-2011-115.7. ATLAS Collab., [arXiv:hep-ex/1108.1316]; CMS Collab., CMS-PAS-EXO-11-024.8. A. Melfo, M. Nemevsek, F. Nesti, G. Senjanovic and Y. Zhang, Phys. Rev. D 85, 055018 (2012)

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