Probing the seesaw mechanism at CERN LHC

Borut Bajc,1 Miha Nemevsek,1 and Goran Senjanovic2

1J. Stefan Institute, 1001 Ljubljana, Slovenia2International Centre for Theoretical Physics, Trieste, Italy

(Received 1 June 2007; published 24 September 2007)

We have recently proposed a simple SU(5) theory with an adjoint fermionic multiplet on top of theusual minimal spectrum. This leads to the hybrid scenario of both type I and type III seesaw and it predictsthe existence of the fermionic SU(2) triplet between 100 GeV and 1 TeV for a conventional grand unifiedtheory scale of about 1016 GeV, with main decays into W (Z) and leptons, correlated through DiracYukawa couplings, and lifetimes shorter than about 10�12 sec. These decays are lepton number violatingand they offer an exciting signature of �L � 2 dilepton events together with 4 jets at future pp (p �p)colliders. Increasing the triplet mass endangers the proton stability and so the seesaw mechanism could bedirectly testable at LHC.

DOI: 10.1103/PhysRevD.76.055011 PACS numbers: 12.10.�g, 14.60.Hi, 14.60.Pq, 14.60.St

I. INTRODUCTION

The seesaw mechanism [1] has been recognized as themost natural scenario for understanding the smallness ofneutrino mass. It implies the existence of heavy particles,which after being integrated out, lead to the gauge invariantoperator [2]

L eff � yeffLLHHM

; (1)

withM� MW usually assumed. As shown in [3], there arethree different types of heavy particles that can induce (1):

(I) Standard model (SM) fermionic singlets, coupled toleptons through Dirac Yukawa couplings and usuallycalled right-handed neutrinos (type I seesaw) [1];

(II) SU(2) bosonic triplet (Y � 2) coupled to leptonsthrough Majorana type couplings (type II seesaw)[4];

(III) SU(2) fermionic triplet (Y � 0) coupled to leptonsthrough Dirac Yukawas, just like the singlet ones in(I) (type III seesaw) [5].

Whatever one chooses, one needs a predictive theoryabove the SM in order to shed some light on neutrinomasses; otherwise, one can as well stick to the effectiveoperator in (1). The best bet for such a theory is grandunification since it can predict new mass scale(s). It turnsout that both type I and type II seesaw find their natural rolein SO(10) theory due to the automatically present left-rightsymmetry [6–9]. Although SO(10) is sufficient by itself todetermine all the parameters in the (I) and (II) cases, andeven the 1–3 mixing angle [10], the check of the seesaw isonly indirect: one can at best relate neutrino properties toproton decay. The main point is that both right-handedneutrinos and the SU(2) scalar triplet are predicted to bevery heavy, close to the grand unified theory (GUT) scale.

What about the type III seesaw? It is clearly custom fitfor the SU(5) theory, as suggested recently [11], since itonly requires adding the adjoint fermions 24F to the exist-ing minimal model with three generations of quarks and

leptons, and 24H and 5H Higgs fields. This automaticallyleads to the hybrid scenario of both type I and type IIIseesaw, since 24F has also a SM singlet fermion, i.e. theright-handed neutrino. One ends up with a realistic spec-trum of two massive and one massless light neutrino. Themassless one can of course pick up a tiny mass due to sayPlanck scale effects [12] or running effects [13], too smallto play any direct phenomenological role.

The main prediction of this theory is the lightness of thefermionic triplet (for a recent alternative scenario with lighttriplets see [14]). For a conventional value of MGUT �1016 GeV, the unification constraints strongly suggest itsmass below TeV, relevant for the future colliders such asLHC. The triplet fermion decay predominantly into W (orZ) and leptons, with lifetimes shorter that about 10�12 sec.

Equally important, the decays of the triplet are dictatedby the same Yukawa couplings that lead to neutrino massesand thus one has an example of predicted low-energy see-saw directly testable at colliders and likely already at LHC.

In this expanded version of the original work, we sys-tematically study the spectrum and the couplings of thetheory. In the next section we focus on the unificationconstraints on the particle spectrum. We perform a numeri-cal study using two-loop renormalization group equationstaking into account various mass scales of the theory. Wediscuss b� � unification and the predictions of the fermi-onic triplet mass depending on the GUT scale. We find amaximal value of the GUT scale: MGUT � 1016 GeV,which offers a great hope of observing proton decay in anot so distant future. The color octets turn out not to belight enough for direct observation.

In Sec. III we focus on the phenomenological implica-tions of the theory for LHC. We discuss carefully the decaymodes of the triplets and their connection with neutrinomasses and mixings. Whereas for generic values ofYukawa couplings it is not easy to make clear predictions,for the case of vanishing �13 or large Yukawa couplings(possibly related to large flavor violating processes) one

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can constrain the relevant branching ratios and thus di-rectly test the seesaw mechanism at colliders.

Next, in Sec. IV we turn our attention to cosmology anddiscuss leptogenesis. We find that it can work only in theresonant regime which implies the same mass of the fer-mionic triplet and singlet and further constrains the pa-rameter space of the theory. The nice feature of a highdegree of predictivity of this theory has also a negativeimplication: we show that there is no stable particle can-didate for the dark matter of the universe. We conclude ourwork with Sec. V, where we also discuss the relevance ofour work for supersymmetry.

II. UNIFICATION CONSTRAINTS AND THE MASSSCALES OF THE THEORY

The minimal implementation of the type III seesaw innonsupersymmetric SU(5) requires a fermionic adjoint 24Fin addition to the usual field content 24H, 5H and threegenerations of fermionic 10F and �5F. The consistency ofthe charged fermion masses requires higher dimensionaloperators in the usual Yukawa sector [15]. One must addthe new Yukawa interactions:

L Y� � yi0 �5iF24F5H �1

��5iF�y

i124F24H � y

i224H24F

� yi3 Tr24F24H�5H � H:c: (2)

After the SU(5) breaking

h24Hi �MGUT������

30p diag�2; 2; 2;�3;�3�; (3)

one obtains the following physical relevant Yukawa inter-actions for neutrino with the triplet �F3 ~�F3 ~� (type III)and singlet �F0 (type I) fermions:

L Y� � Li�yiT�F3 � y

iS�

F0 �H � H:c:; (4)

where yiT , yiS are two different linear combinations of yi0and yiaMGUT=� (a � 1, 2, 3). It is clear from the aboveformula that, besides the new appearance of the tripletfermion, the singlet fermion in 24F acts precisely as theright-handed neutrino; it should not come out as a surprise,as it has the right SM quantum numbers.

Even before we discuss the physical consequences indetail, one important prediction emerges: only two lightneutrinos get mass, while the third one remains massless.

In order to discuss the masses of the new fermions, weneed the new Yukawa couplings between 24F and 24H,

LF � mF Tr242F � �F Tr242

F24H

�1

��a1 Tr242

F Tr242H � a2�Tr24F24H�

2

� a3 Tr242F242

H � a4 Tr24F24H24F24H�; (5)

where we include the higher dimensional terms for the sakeof consistency. The masses of the new fermions are

mF0 � mF �

�FMGUT������30p �

M2GUT

�

�a1 � a2 �

7

30�a3 � a4�

�;

(6)

mF3 � mF �

3�FMGUT������30p �

M2GUT

�

�a1 �

3

10�a3 � a4�

�;

(7)

mF8 � mF �

2�FMGUT������30p �

M2GUT

�

�a1 �

2

15�a3 � a4�

�;

(8)

mF�3;2� � mF �

�FMGUT

2������30p �

M2GUT

�

�a1 �

�13a3 � 12a4�

60

�:

(9)

Next we turn to the bosonic sector of the theory. We willneed the potential for the heavy field 24H,

V24H � m224 Tr242

H ��24 Tr243H � �

�1�24 Tr244

H

� ��2�24 �Tr242H�

2; (10)

and its interaction with the light fields,

V5H � m2H5yH5H � �H�5

yH5H�

2 ��H5yH24H5H

� �5yH5H Tr242H � �5yH242

H5H: (11)

It is a straightforward exercise to show that the masses ofthe bosonic triplet and octet are arbitrary and that one canperform the doublet-triplet splitting through the usual fine-tuning. However, splitting its mass from the triplet and theoctet fermion masses requires the inclusion of higher di-mensional terms, which in turn gives an upper bound to themass of the leptoquark,

mF�3;2� &

M2GUT

�; (12)

where � is the cutoff of the theory. One could take naively� on the order of the Planck scale, since the theory isasymptotically free. However, without higher dimensionaloperators one predicts mb � m� at the GUT scale [16],which fails badly, as much as in the standard model, andthus one must take a lower cutoff (for further details see[17]). To see this we did a one-loop Yukawa running, with atwo-loop gauge running. The result y� � 0:01 and the ratioyb=y� & 0:65 are valid for any physically allowed value ofMGUT.

Thus the analysis requires a cutoff at most 2 orders ofmagnitude above the GUT scale. In what follows we take� � 100MGUT to ensure the correct mass relations andmaximize perturbativity (for a lower cutoff see [17]).

We are now fully armed to study the constraints on theparticle spectrum by performing the renormalization groupanalysis. For the sake of illustration, we present first the

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one-loop analysis. From [11], one has

exp30���11 � �

�12 ��MZ�� �

�MGUT

MZ

�84��mF

3 �4mB

3

M5Z

�5

�

�MGUT

mF�3;2�

�20�MGUT

mT

�; (13)

exp20���11 � �

�13 ��MZ�� �

�MGUT

MZ

�86��mF

8 �4mB

8

M5Z

�5

�

�MGUT

mF�3;2�

�20�MGUT

mT

��1;

(14)

where mF;B3 , mF;B

8 , mF�3;2�, and mT are the masses of weak

triplets, color octets, (only fermionic) leptoquarks, and(only bosonic) color triplets, respectively.

From the well-known problem in the standard model ofthe low meeting scale of �1 and �2, it is clear that theSU(2) triplet should be as light as possible and the colortriplet as heavy as possible. In order to illustrate the point,take mF

3 � mB3 � MZ and mT � MGUT. This gives

[��11 �MZ� � 59, ��1

2 �MZ� � 29:57, ��13 �MZ� � 8:55]

MGUT � 1015:5 GeV. Increasing the triplet masses mF;B3

reduces MGUT dangerously, making proton decay too fast.For more reliable results one needs a two-loop analysis.

We focused on the following regions in parameter space:(1) mF;B

8 > 105 GeV to comply with cosmologicalbounds coming from nucleosynthesis. This limit isanalogous to the limit on the sfermion masses insplit supersymmetry [18,19] coming from gluinolifetime [20]. At the time of nucleosynthesis allcolor octets should have already decayed into aright-handed quark and an off-shell color tripletthrough the Yukawa interactions (2);

(2) mT > 1012 GeV from proton decay;(3) MGUT > 1015:5 GeV again from proton decay;(4) mF

�3;2� <M2GUT=� � MGUT=100 from (12) and the

above discussion on the choice of the cutoff.

The two-loop analysis maintains an approximate depen-dence on the combinations m3 ��mF

3 �4mB

3 �1=5 and m8

��mF8 �

4mB8 �

1=5 as at 1-loop order (13) and (14). This isuseful in the numerical analysis, since one can first useas varying parameters just these combinations, and thenextrapolate the result for the case of different fermionic andbosonic masses.

We have seen that at 1-loop order the mass of thefermionic triplet is predicted to lie below TeV. This boundgets somewhat relaxed at 2-loop order, as can be seen fromFig. 1.

The fermionic triplet can be even higher at the price oflowering the bosonic triplet. It must be stressed although,that these maximal values are not typical: one must stretchthe parameters, i.e. go to some corner in parameter space toevade the 1-loop bounds. In other words, in most of theparameter space the bound mF

3 & TeV still persists.It has been noticed in [17] that the constraint (4) for

mF�3;2� can actually be evaded. In fact, there are solutions, in

which mF�3;2� � mF

8 =2 that can be of order MGUT. We havebeen however unable to find any solution withMGUT biggerthan 1015 GeV, which makes them less realistic due tolikely problems in large proton decay widths.

Finally, one can ask, where must the octets be. TakingMGUT � 1015:5 GeV, one can find the possible region inthe m3 �m8 plane, that leads to unification (differentsolutions for m8 for the same m3 correspond to differentchoices of mF

�3;2�). This region is shown in Fig. 2.

III. PHENOMENOLOGICAL IMPLICATIONS:TESTING SEESAW AT LHC?

In the previous section we learned that the triplets arequite light, even likely to be found at LHC. How wouldthey be identified?

The Yukawa couplings of the triplet and singlet fermionare parametrized by (we choose the basis in which theDirac Yukawa matrix between ec and L is diagonal andreal, while yiT are real)

FIG. 1. The maximum value of the effective triplet mass m3 asa function of the unification scale MGUT from the two-loopanalysis.

FIG. 2 (color online). The region that gives unification atMGUT � 1015:5 GeV.

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LY � �yiEHyeci Li � y

iTH

Ti�2�aTaLi � yiSHTi�2SLi

� H:c:

� �v� h���

2p yiEe

ci ei � y

iT�

���2pT�ei � T0�i�

� yiSS�i� � H:c:; (15)

where T , T0 are the three states from the fermionic triplet,while S is the fermionic singlet. We have changed thecumbersome notation from the previous section (where itwas necessary), since this whole section is devoted only tothe fermionic triplet and singlet.

The Majorana masses for the triplet and singlet (withproperly defined Tk and S the masses mT and mS can bemade real and positive) are

L m � �mT

2�2T�T� � T0T0� �

mS

2SS� H:c: (16)

To the leading order in the neutrino Dirac Yukawacouplings, the following transformations define the physi-cal states:

�j ! �j � jTT

0 � jSS; (17)

T0 ! T0 � kT�k; (18)

S! S� kS�k; (19)

ej ! ej ����2pjTT

�; (20)

T� ! T� ����2pkTek; (21)

T� ! T�; ec ! ec; (22)

where

iX yiXv���2pmX

: (23)

In the above equation recall that T� is a different statefrom T�, just like ec is a different state from e.

The light neutrino mass matrix is then given by

m�ij � �

v2

2

�yiTy

jT

mT�yiSy

jS

mS

�(24)

in the basis in which the charged Yukawas and the cou-plings with W are diagonal.

A. T ! W�Z� � light lepton

These are the predominant decay modes of the triplets,whose strength is dictated by the neutral Dirac Yukawacouplings:

��T� ! Ze�k � �mT

32jykT j

2

�1�

m2Z

m2T

�2�1� 2

m2Z

m2T

�; (25)

Xk

��T� ! W��k� �mT

16

�Xk

jykT j2

��1�

m2W

m2T

�2

�

�1� 2

m2W

m2T

�; (26)

��T0!W�e�k � � ��T0!W�e�k �

�mT

32jykT j

2

�1�

m2W

m2T

�2�1� 2

m2W

m2T

�; (27)

Xk

��T0 ! Z�k� �mT

32

�Xk

jykT j2

��1�

m2Z

m2T

�2�1� 2

m2Z

m2T

�;

(28)

where we averaged over initial polarizations and summedover final ones. From (27) one sees that the decays of T0,just as those of right-handed neutrinos, violate leptonnumber. In a machine such as LHC, one would typicallyproduce a pair T�T0 (or T�T0), whose decays then allowfor interesting �L � 2 signatures of same sign dileptonsand 4 jets. This fairly SM background free signature ischaracteristic of any theory with right-handed neutrinos asdiscussed in [21]. The main point here is that these tripletsare really predicted to be light, unlike in the case of right-handed neutrinos. The detailed analyses of the LHC sig-natures including the production, the decays, and the back-ground is now in progress [22].

The decay rates above are rather sensitive to the Yukawacouplings which, on the other hand, can vary a lot. First ofall, they are not directly related to the neutrino properties,and they are of course rather flavor dependent. The domi-nant rate goes through the largest Yukawa coupling whichhas an approximate lower limit of � 5� 10�7 from theatmospheric neutrino oscillations. This translates into thefollowing upper limit for the lifetime of the dominant two-body triplet decay, for say mT � 300 GeV:

�T & 10�1 mm: (29)

Measuring the above decays means in some sensechecking the seesaw parameters. Let us see in more detailthis correspondence. The situation with the singlet andtriplet making the light neutrino massive through the see-saw mechanism is analogous to the situation with tworight-handed neutrinos (for a recent review of this situationsee [23]). Thus we can use the known relations [24] (in thecase of hierarchical case, i.e. m�

1 � 0)

vyi�T���2p � i

�������mTp

�Ui2

�������m�

2

pcosz Ui3

�������m�

3

psinz�; (30)

vyi�S���2p � �i

�������mSp

�Ui2

�������m�

2

psinz�Ui3

�������m�

3

pcosz�; (31)

or (in the case of inverse hierarchy, i.e. m�3 � 0)

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vyi�T���2p � i

�������mTp

�Ui1

�������m�

1

pcosz Ui2

�������m�

2

psinz�; (32)

vyi�S���2p � �i

�������mSp

�Ui1

�������m�

1

psinz�Ui2

�������m�

2

pcosz�; (33)

valid in a different basis than used before, since here yiT arenot necessarily real. To compare with the previous results,one needs just to compute the absolute value jyiT j in (30)and (32).

In the formulas above z is a complex number, while U isthe lepton mixing matrix, which diagonalizes the neutrinomass matrix (24) (for the experimental values and limitssee [25]):

m� � U�m�

1 0 00 m�

2 00 0 m�

3

0@

1AUy: (34)

Suppose we could measure from T decays the Yukawacouplings yiT . Then, in the above formulas we have thefollowing unknowns: one complex number z and two CPphases, assuming that the 1–3 mixing will be measuredsoon (keep in mind that there is one CP phase less in thecase of one massless neutrino). In general, it is not possibleto give much constraints or to make some nontrivialchecks, since one has 3 real measurements (the absolutevalues of yiT), but 4 parameters available to describe them.In some special cases however the above relations simplifyand some nontrivial constraints appear.

As an example consider the inverse hierarchical casewith a vanishing �13. One gets

��������

� tan2�atm (35)

independent on the phases. This can serve as a direct test ofthe theory if the inverse hierarchy and a small enough �13

are to be established in the future.Another interesting case is jIm�z�j � 1, which is

equivalent to the large Dirac Yukawa limit. Here the com-plex parameter z disappears from the branching ratios,which then depend only on the in principle measurableparameters of the lepton mixing matrix.

B. T ! T0 decays

For a nonvanishing and positive mass split �mT mT� �mT0 , the charged triplet fermion can decay into aneutral one and an (off-shell) W.

One gets for �mT at the one-loop level,

�mT ��2

2m2W

mT

�f�mT

mZ

�� f

�mT

mW

��; (36)

where

f�y� �1

4y2 logy2 �

�1�

1

2y2

� ����������������4y2 � 1

qarctan

����������������4y2 � 1

q;

(37)

which gives �mT � 160 MeV with 10% accuracy in thewhole range mZ � mT � 1. Notice that there is also apossible direct tree-level contribution from (5) through anonvanishing vev of the bosonic triplet

�mtreeT � yhTBi: (38)

However, hTBi & 1 GeV for the W and Z masses andy & 10�2 since suppressed by MGUT=�, so �mtree

T &

10 MeV, a negligible addition.The fastest decay mode through the above mass differ-

ence is clearly T ! T0 , estimated to be O�10�10� sec[26], negligible in comparison with the W � or Zl decaychannels considered in the previous subsection.

In short, the triplet mass difference can be safelyignored.

C. T ! H� light lepton

If the fermionic triplet is heavier than the SM Higgs, itcan decay unsuppressed also to the Higgs and a lightlepton. The decay widths can be calculated from (15) togive

��T� ! he�k � �mT

32jykT j

2

�1�

m2h

m2T

�2; (39)

Xk

��T0 ! h�k� �mT

32

�Xk

jykTj2

��1�

m2h

m2T

�2: (40)

These results can now explain the apparent ‘‘puzzle’’from the results (25)–(28). In fact, these decays come outto be nonzero also in the SU(2) preserving limit (v! 0).However, in this limit there is no mixing between thetriplets and the light leptons, so apparently no decays.The results (39) and (40) explain the discrepancy: in thislimit there are 4 degrees of freedom from the Higgs doubletand the final states in (25)–(28) should be interpreted as Zbeing the imaginary partner of the standard Higgs, and Wbeing the complex partner in the doublet (the upper com-ponent). It is easy to check that the exact SU(2) gaugesymmetry connects the results (25)–(28) with (39) and (40)in the limiting case v, mh ! 0.

IV. COSMOLOGICAL IMPLICATIONS

A. Dark matter

As usual, in order to have a viable dark matter candidate,it must be stable for at least the age of the universe, whichcan be translated into an extremely small decay width:

� & 10�42 GeV: (41)

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Let us systematically consider various possible candi-dates:

(1) The most obvious is the fermionic neutral triplet T0:obviously this cannot work, see (29).

(2) Next consider the bosonic triplet from 24H, with amass of at least mB

T � 100 GeV from collider con-straints. Now, the following operator,

�5 F24H�

10F5yH; (42)

is needed to correct the b� � unification, as dis-cussed in the previous section. So the bosonic tripletcan decay into a fermion antifermion pair with adecay width of

� ��mW

�

�2mBT (43)

much too fast ( � 10�32 GeV) even in the unreal-istic case of � � MPl.

(3) What about the bosonic singlet in 24H? This singletis nothing else than the field that breaks SU(5), sothe validity of the whole approach requires its massto be larger than the electroweak scale. Then every-thing of the previous case applies also here, and thusthe same negative conclusion.

(4) Finally, consider the fermionic singlet S in 24F. Atfirst sight, this could not work for the same reason asfor the fermionic triplet T. However, here there areno such tight constraints on its mass from colliders,so in principle it could weigh around keV. In thiscase its decay rate gets suppressed strongly by theWpropagator, giving

� � �yiSGF�2m5

S; (44)

which is slow enough in the keV region as soon asyiS & 0:1, needed anyway for unitarity. Unfor-tunately, in order to have the right amount of darkmatter, such a small mass cannot give a sizablecontribution to the neutrino masses (see [27] fordetails).

B. Leptogenesis

This issue has been discussed at length in a fairlycomplete paper devoted to the phenomenology and cos-mology of the type I seesaw mechanism with only tworight-handed neutrinos [23]. The assumption (two �R) inthat case is a prediction of our model (T and S). The bottomline now is that, as opposed to the generic situation withthree right-handed neutrinos,1 there is a true physical lowerlimit on the scale of leptogenesis of the order 1010 GeV.This can be seen from a straightforward derivation of thefollowing expression for the maximal CP asymmetry (as-

suming a hierarchy mT � mS):

max �1

16mT�m�

3 �m�2�

v2 : (45)

It is evident that for mT � TeV the CP asymmetry ishopelessly small. The only possibility for leptogenesis inthis theory is the resonant [31–33] one. It is not difficult toshow that one can get realistic value for the baryon asym-metry. Following [29], the triplet asymmetry (and similarlythe singlet one) can be rewritten as

T � �Im� ~yT ~y�S�

2

2j ~yT j2j ~ySj

2 �2�m2

S �m2T�mT�S

�m2S �m

2T�

2 �m2T�2

S

; (46)

where �S is the total decay width of the singlet fermion.The last term in the above product can take its maximalvalue 1 for properly chosen singlet mass, i.e. for m2

S �m2T �mT�S. The first term depends on the value of the

unknown complex parameter z and the parameters(masses, mixing angles, and phases) of the light neutrinosector. This term can be numerically even of order one,showing that a very large asymmetry can be obtained. Ithas to be stressed however that successful resonant lepto-genesis does not allow all values of z. For example, if Re�z�or Im�z� is zero, the final result vanishes. It is interestingthat the asymmetry generically decreases with large Im�z�values, restricting the allowed region. A more detaileddescription with the calculation of the efficiency factorand the inclusion of flavor effects [34,35] is beyond thescope of this paper and is in progress [36]. Preliminaryestimates seem to show that these constraints are morerestrictive than the ones coming from flavor changingneutral processes.

The requirement of successful leptogenesis thus putsvarious constraints on the yet unknown model parameters.Although the degeneracy between the singlet and the trip-let mass is not of direct meaning for LHC searches [it maybe relevant however for processes under study [36] like�! 3e (at tree order) or �! e�], because the singletswill not be easily produced, the constraints on the Yukawascould be tested measuring the different branching ratios intriplet decays.

V. SUMMARY AND OUTLOOK

We have recently [11] constructed what can be consid-ered a possible minimal realistic SU(5) grand unified the-ory. Instead of changing the Higgs sector as conventionallydone, we have simply added to the minimal model anadjoint fermion representation which gives a hybrid seesawscenario, a mixture of type I and type III. The fact that thetheory is in accord with experiment may not be so surpris-ing; after all, one has enlarged its particle sector. What isremarkable is a prediction of a light fermionic SU(2)triplet, with a mass below TeV, and for a large portion ofthe parameter space in the LHC reach of below 500 GeV.

1For a way out of the well-known Davidson-Ibarra limit [28],see [29,30].

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One has a badly needed predictive theory of seesaw mecha-nism that can be tested at the collider energies.

Whereas it is always possible to imagine a low-energyseesaw, predictive theories such as GUTs normally preferlarge seesaw scale, close to MGUT. Even when you assumethis scale to be low as is often done in the type I case, theproduction of right-handed neutrinos is suppressed by thesmall (compared to the gauge couplings) Yukawa cou-plings (for a recent work see [37]). The type II could ofcourse be tested for a low scale, but again that is not whatcomes out. In a way, the type III seesaw, up to now almostnot studied at all, may provide a unique possibility ofseesaw tested at LHC.

In this longer version of our paper, we have carefullystudied some phenomenological and cosmological issuesin this theory. We have performed a complete two-loopanalysis of unification constraints which confirms the light-ness of the triplets, and at the same time predicts MGUT <1016 GeV, implying the proton lifetime below 1036 years,possibly observable in the next generation of proton decayexperiments. We have discussed the decay of the tripletsinto the charged leptons and neutrinos and shown how theyprobe directly neutrino Dirac Yukawa couplings. TheseDirac Yukawas could be quite large since small neutrinomasses can involve cancellations and in this case lead topossibly observable lepton flavor violating processes. Thisis a rather interesting topic and deserves a careful inves-tigation in a separate note. We also confirmed here anexpected result that only resonant leptogenesis can workdue to the low mass of the fermionic triplet. This wouldalso make a fermionic singlet light; but as in the case ofpure type I seesaw it is not of direct phenomenologicalinterest. Finally, we also showed that the theory lacks adark matter candidate. Of course, one could always add asinglet particle and account for the dark matter if neces-sary, since for a given mass one can choose an appropriatecoupling.

It is interesting to compare this model to the supersym-metric SU(5) theory, or the supersymmetric extension ofthe standard model. After all, the weak triplet fermions

correspond to winos, while the color octet fermions in 24Hcorrespond to gluinos. Now, it is well known that thesfermions do not enter into the renormalization groupconstraints, at least not at the one-loop level; they can beas heavy as we wish. This, split supersymmetry program—light winos, gluinos, and Higgsinos—still allows for theunification of gauge couplings, as much as in the case oflow-energy supersymmetry [38–41]. Our work shows thatthe situation can be more complex if one is willing to splitsupersymmetry: one can have Higgsinos completely de-coupled, and the gluinos in the intermediate region. Butthen, by interpolation, there is clearly a continuum ofsolutions with Higgsino anywhere from the weak to thePlanck scale, and gluinos from the weak to some inter-mediate scale. The work on this is in progress and will bereported elsewhere. It is interesting though that LHC maysee only winos and nothing else if supersymmetry is to besplit, similar to the theory discussed here. The importantdifference in our case is the fact that the fermionic triplet,an analogue of winos, is directly related to neutrino massesand mixings. It should be viewed as a possible alternativeto low-energy supersymmetry; instead of not so well-defined principle of naturalness, it has direct physical andphenomenological motivation.

ACKNOWLEDGMENTS

The work of G. S. was supported in part by the EuropeanCommission under the RTN Contract No. MRTN-CT-2004-503369; the work of B. B. and M. N. was supportedby the Slovenian Research Agency. B. B. and M. N. thankICTP for hospitality during the course of this work. Wethank Paolo Creminelli, Ilja Dorsner, TsedenbaljirEnkhbat, Alejandra Melfo, Fabrizio Nesti, and FrancescoVissani for discussion, and Marco Cirelli, MicheleFrigerio, and Alessandro Strumia for pointing out a signerror in Eq. (36) of the first version of the manuscript, andIlja Dorsner for pointing out to us that the relation among band � Yukawas at the GUT scale needs a cutoff scale lowerthan the Planck mass.

[1] P. Minkowski, Phys. Lett. 67B, 421 (1977); T. Yanagida,Proceedings of the Workshop on Unified Theories andBaryon Number in the Universe, Tsukuba, 1979, editedby A. Sawada and A. Sugamoto (National Lab for HighEnergy Physics, Tsukuba, Japan, 1979), p. 109; S. L.Glashow, The Future of Elementary Particle Physics,NATO Advanced Study Institutes, Ser. B, Vol. 59(Plenum Press, New York, 1979). p. 687; M. Gell-Mann,P. Ramond, and R. Slansky, Proceedings of theSupergravity Stony Brook Workshop, New York, 1979,edited by P. Van Niewenhuizen and D. Freeman (North-

Holland, Amsterdam, 1979); R. Mohapatra and G.Senjanovic, Phys. Rev. Lett. 44, 912 (1980).

[2] S. Weinberg, Phys. Rev. Lett. 43, 1566 (1979).[3] E. Ma, Phys. Rev. Lett. 81, 1171 (1998).[4] M. Magg and C. Wetterich, Phys. Lett. 94B, 61 (1980); G.

Lazarides, Q. Shafi, and C. Wetterich, Nucl. Phys. B181,287 (1981); R. N. Mohapatra and G. Senjanovic, Phys.Rev. D 23, 165 (1981).

[5] R. Foot, H. Lew, X. G. He, and G. C. Joshi, Z. Phys. C 44,441 (1989).

[6] J. C. Pati and A. Salam, Phys. Rev. D 10, 275 (1974).

PROBING THE SEESAW MECHANISM AT CERN LHC PHYSICAL REVIEW D 76, 055011 (2007)

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[7] R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11, 2558(1975).

[8] G. Senjanovic and R. N. Mohapatra, Phys. Rev. D 12,1502 (1975).

[9] G. Senjanovic, Nucl. Phys. B153, 334 (1979).[10] For a review of the seesaw in the context of SO(10), see

e.g. G. Senjanovic, arXiv:hep-ph/0501244.[11] B. Bajc and G. Senjanovic, arXiv:hep-ph/0612029.[12] E. K. Akhmedov, Z. G. Berezhiani, and G. Senjanovic,

Phys. Rev. Lett. 69, 3013 (1992).[13] S. Davidson, G. Isidori, and A. Strumia, Phys. Lett. B 646,

100 (2007).[14] S. B. Gudnason, T. A. Ryttov, and F. Sannino, Phys. Rev. D

76, 015005 (2007.[15] J. R. Ellis and M. K. Gaillard, Phys. Lett. 88B, 315 (1979).[16] M. S. Chanowitz, J. R. Ellis, and M. K. Gaillard, Nucl.

Phys. B128, 506 (1977).[17] I. Dorsner and P. Fileviez Perez, J. High Energy Phys. 06

(2007) 029.[18] N. Arkani-Hamed and S. Dimopoulos, J. High Energy

Phys. 06 (2005) 073.[19] G. F. Giudice and A. Romanino, Nucl. Phys. B699, 65

(2004); B706, 487(E) (2005).[20] A. Arvanitaki, C. Davis, P. W. Graham, A. Pierce, and J. G.

Wacker, Phys. Rev. D 72, 075011 (2005).[21] W. Y. Keung and G. Senjanovic, Phys. Rev. Lett. 50, 1427

(1983). For a recent work, see, for example, T. Han and B.Zhang, Phys. Rev. Lett. 97, 171804 (2006); F. del Aguila,J. A. Aguilar-Saavedra, and R. Pittau, J. Phys. Conf. Ser.53, 506 (2006).

[22] A. Arhrib, B. Bajc, D. Ghosh, I. Puljak, and G. Senjanovic(work in progress).

[23] W. l. Guo, Z. z. Xing, and S. Zhou, Int. J. Mod. Phys. E 16,1 (2007).

[24] A. Ibarra and G. G. Ross, Phys. Lett. B 591, 285 (2004).[25] A. Strumia and F. Vissani, arXiv:hep-ph/0606054.[26] M. Ibe, T. Moroi, and T. T. Yanagida, Phys. Lett. B 644,

355 (2007).[27] T. Asaka, S. Blanchet, and M. Shaposhnikov, Phys. Lett. B

631, 151 (2005).[28] S. Davidson and A. Ibarra, Phys. Lett. B 535, 25 (2002).[29] T. Hambye, Y. Lin, A. Notari, M. Papucci, and A. Strumia,

Nucl. Phys. B695, 169 (2004).[30] M. Raidal, A. Strumia, and K. Turzynski, Phys. Lett. B

609, 351 (2005); 632, 752(E) (2006).[31] M. Flanz, E. A. Paschos, U. Sarkar, and J. Weiss, Phys.

Lett. B 389, 693 (1996).[32] A. Pilaftsis, Phys. Rev. D 56, 5431 (1997).[33] A. Pilaftsis and T. E. J. Underwood, Nucl. Phys. B692, 303

(2004).[34] S. Pascoli, S. T. Petcov, and A. Riotto, Phys. Rev. D 75,

083511 (2007).[35] S. Pascoli, S. T. Petcov, and A. Riotto, Nucl. Phys. B774, 1

(2007).[36] B. Bajc, M. Nemevsek, and G. Senjanovic (work in

progress).[37] J. Kersten and A. Y. Smirnov, arXiv:0705.3221.[38] S. Dimopoulos, S. Raby, and F. Wilczek, Phys. Rev. D 24,

1681 (1981).[39] L. E. Ibanez and G. G. Ross, Phys. Lett. 105B, 439 (1981).[40] M. B. Einhorn and D. R. T. Jones, Nucl. Phys. B196, 475

(1982).[41] W. J. Marciano and G. Senjanovic, Phys. Rev. D 25, 3092

(1982).

B. BAJC et al. PHYSICAL REVIEW D 76, 055011 (2007)

055011-8