Proton Decay and Grand Unification

Home , Proton decay

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[7] his Furry majorana and in on [6] Majorana [5] by paper 1937 was classic in violation already number discussed lepton seriously sacred, becoming was ber hyetbihdalmto 10 of limit a established They con- a exists there that surmised been often has ”It ic hr sntigsce bu lblsymmetries global about sacred nothing is there Since § ae ntepeaytlsa h UY9adPASCOS09 and SUSY09 the at talks plenary the on Based hoywt eeti nrisbetween energies in impl of, desert necessarily search a would the with discovery theory h better Their or a leptons. from h limits, charged predictions and experimental model related of accepted some improvement th universally and the that decay no demonstrate proton Since of I mi analysis and experiment. the physics, realist with only LHC minimal accord interesting discuss the how to I show lead de I unification. can proton supersymmetric. grand and of on ordinary status only, both experimental not and but theoretical mostly, the review I 26 rtndcyadgadunification grand and decay Proton rltro.Adwietebro num- baryon the while And on. later yr nentoa etefrTertclPyis 40 Tries 34100 Physics, Theoretical for Centre International h nygo global good only the 21 r hc hywould they which yr, 18 M er.I was, It years. W h sym- The . and oa SenjanovićGoran M Abstract GUT . 1 o nrypyissnete rcial aihi any in vanish practically they since physics energy low a y hnGog,QinadWibr 1]cmue the lifetime computed proton predicted [10] and Weinberg scale [9]. and unification Glashow Quinn and Georgi Georgi, of When theory perfectly SU(5) exemplified minimal is the unifi- and on the leptons on of and [8] quarks Salam unification of and Pati cation grand of grew ideas It pioneering behind: of interactions. out theory electro-magnetic to and a point weak asked is The strong, is there conferences. one major that at that is it fact on talks the plenary com- by give changed illustrated has as atmosphere pletely, the today decay, proton gravity). with competition nesyuacp orsodn ag opigt be to coupling small: gauge corresponding ridiculously a accept Further- you unless one. experimentalists. exact for useless fully is a zero as a useful more and protected as h inccanlaltewyt bu 10 about to way the all pushed channel recently that pionic SK the with culminating limits, decay Europe. to US experiments to of Japan list to a India is Here from all world, [11], the underground over rushed experimentalists many yr, r iiso oepoo ea channels. decay proton some on limits are a hoyadeprmn.Rgrigter,Ifocus I theory, Regarding experiment. and theory cay hl odae ta a ojsiytersac for search their justify to had al et Goldhaber While n aynnme snta xc ag symmetry gauge exact an not is number baryon And h erhrsle ngetipoeet nproton on improvements great in resulted search The • • detector Cherenkov • • • • detector Calorimeter g cl neligter.Asrn aei aefor made is case strong A theory. underlying scale igh iia uesmercS()ter si perfect in is theory SU(5) supersymmetric minimal e aikne-Mzm ie(ia Japan) (Hida, lations mine Mozumi Super-Kamiokande - Kamiokande US) (Ohio, mine salt Morton - IMB (Minnesota, US) mine underground Soudan SOUDAN- France) (Alps, tunnel Frejus - FREJUS France) (Alps, Blanc Mont - NUSEX India) (Kamataka, district Kolar - Field Gold Kolar so e mre,Idsusteeetv operator effective the discuss I emerged, yet of as w oynurndcymdsit hre kaons charged into modes decay neutron body two cetnin fteoiia eri-Gahwmodel Glashow - Georgi original the of extensions ic ia,wl salse U5 n O1)models, SO(10) and SU(5) established well nimal, g B e Italy te, ≤ → (10 topei etiooscil- neutrino atmospheric − 20 − 10 § − 19 arepulsive (a ) 34 τ r Here yr. p ≃ 10 → 30 33 Channel τp(10 years) for realistic neutrino Dirac Yukawa couplings It pre- dicts a light fermion triplet (1C , 3W ), with a mass + 0 p → e π 8.2 below TeV so that the running of the SU(2) gauge + 0 p → π 6.6 coupling is slowed down and meets U(1) above + 0 p → K 1.3 1015 GeV. It’s phenomenology is quite interesting + 0 p → e K 1.0 for it leads to lepton number violation at colliders + p → νK 2.3 in the form of same sign di - leptons as suggested + − n → e K 0.02 originally in seesaw a long time ago [19]. For the − + n → e K 0.03 relevant studies in the context of the type III seesaw see [20]. The last two channels are important since they are an indication of low scale as discussed in sections 3 and 5. The two theories have in common a ‘fast’ proton de- 35 In what follows I discuss the minimal SU(5) and cay, with τp ≤ 10 yr, to keep in mind in what follows. SO(10) theories, both ordinary and supersymmetric. Due to the lack of space, many important references are likely to be omitted. For a review and more complete 3 Minimal supersymmetric SU(5) references on the subject, see [12]. The underground rush continued, or better to say, got boosted with the success of the minimal supersymmetric 2 Minimal realistic SU(5) SU(5). Low energy supersymmetry, suggested in order to stabilize the Higgs mass hierarchy, predicted correctly It was the minimal SU(5) that caused the underground 2 sin θW =0.23 in 1981 [21] [22] [23] [24] ten years before rush, for it predicted proton lifetime on the order of 30 its confirmation at LEP. It actually did even better: the τp ≃ 10 yr. And on top, it also predicted the nucleon 2 prediction of sin θW = 0.23 was tied to the prediction decay branching ratios as shown by Mohapatra [13]; un- of the heavy top quark, with mt ≃ 200 GeV. Namely, fortunately these predictions resulted from the wrong 2 in 1981 the low indirect measurements gave sin θW = mass relations: me = md, wrong for all three genera- 0.21, with the assumed value ρ = 1. In order to make tions. These relations can be corrected easily by simply a case for low energy supersymmetry, Marciano and I adding higher dimensional operators [31] (at least for the [24] had to say that ρ was bigger, which required loops, first two generations) , but then the theory stops being which required at least one large coupling, and a natural predictive. SM candidate was the top quark, with yt ≃ 1. It is In any case this is only history now, for the theory is 2 remarkable that both the sin θW =0.23 and the heavy not even consistent: top would turn out to be true. It should be stressed that heavy top quark played also a crucial role in the • gauge couplings do not unify since α2 and α3 meet 16 radiative Higgs mechanism [25] [26]. Thus heavy top is at 10 GeV (as in SM), but α1 meets α2 too early 13 an integral part of low energy supersymmetry. at ≈ 10 GeV ; 16 The GUT scale was predicted: MGUT ≃ 10 GeV 35±1 • neutrinos are massless as in the SM. and in turn τp(d = 6) ≃ 10 yr, which would have rendered proton decay out of experimental reach. Possible higher dimensional operators are not enough: However, supersymmetry leads to a new contribution: neutrino mass comes out too small (. 10−4eV ) and the d = 5 operators [27] through the exchange of heavy color ¯ threshold effects do not cure the lack of unification. triplet Higgsino (T and T ). A rough estimate gives It is important to know then what the minimal con- α mgaugino − sistent realistic extensions are. There are two. You can G ≃ y y ≃ 10−30 GeV 2 T 4π u d M m2 T f˜

• add a symmetric complex scalar field (and higher −4 which for yu ≃ yd ≃ 10 , mgaugino ≃ 100 GeV, dimensional operators for charged fermion masses) 16 m ˜ ≃TeV and MT ≃ 10 GeV gives τp(d = 5) ≃ [14] 15H = (1C, 3W ) + (6C, 1W ) + [(3C, 2W ) = f 1030−31 yr. It would seem that today this theory is leptoquarks], with (1C, 3W ) being the usual Higgs triplet behind the type II seesaw [15]. The lepto- ruled out. It was actually proclaimed dead in 2001 quarks (3 , 2 ) may remain light (but not neces- when the triplet mass was carefully computed to give C W 0 15 sarily), and a rather interesting prediction is a fast MT = 3 × 10 GeV [28] (for the superscript 0 explana- proton decay, on the edge of experimental limits. tion, see below). Caution must be raised however for two important reasons: i) the uncertainty in sfermion • add an adjoint fermion field 24F = (8C , 1W ) + masses and mixings [29] and ii) uncertainty in MT [30] (1C , 3W )+(1C, 1W )+(3C, 2W )+(3¯, 2W ). The fields due to necessity of higher dimensional operators [31] to (1C , 1W )+(1C , 3W ) are responsible for type I [17] correct bad fermion mass relations md = mℓ [32]. The + III [18] hybrid seesaw. The model requires higher d = 4 operators, besides correcting these relations also dimensional operators both for charged femions and split the masses m3 and m8 of weak triplet and color

2 octet, respectively, in the adjoint 24H Higgs super mul- The decay is suppressed by the Planck scale [36] tiplet and one gets 3 1 m3/2 2 Γ(3/2 → γν) = 2 Θν gaugino 32π MPl 3 1 m3/2 mν 0 1/2 ≃ 2 0 MGUT 0 16 32π M Mgaugino MGUT = M MGUT ≃ 10 GeV Pl GUT 2m8 −50 26 5 2  / 0 15 ≤ 10 GeV (τ ≥ 10 sec). 0 m3  M =3 × 10 GeV MT = MT m T 8 The lower limit on gravitino lifetime comes from re-   quiring that the flux of produced photons does not ex- ceed the observed diffuse photon background, and it where the superscript 0 denotes the predictions for gives an upper limit on gravitino mass, m3/2 ≤ 1 − m3 = m8 at the tree level with d = 5 operators ne- 10 GeV [36], reasonable for the LSP. If one relaxes the glected. The fact that MGUT goes up with m8 below neutrino-gaugino mixing, gravitino can be heavier; see MGUT was noticed quite some time ago [33]. Imagine e.g. [37]. For a review and references on gravitino dark that d = 4 terms dominate for small cubic Yukawa self matter, see [38]. coupling, in which case one has m3 = 4m8 and thus Once R-parity is not assumed ad hoc, one has a new 0 17 15 MT = 32MT ≃ 10 GeV ≃ MGUT (m8 ≃ 10 GeV). source of proton decay too. Due to allowed couplings c c c c c ˜c In turn a strong suppression of proton decay with τp ≃ in the superpotential λ1 u d d + λ2 q ℓ d + λ3 ℓℓe , d 3 0 33−34 10 τp (d = 5) ≃ 10 yr. In principle the ratio of the mediates d = 6 proton decay, which implies the limit −25 triplet and octet masses can be as large as one wishes, so λ1 λ2 ≤ 10 (=?) for md˜c ≃ T eV . The question mark at first glance the proton lifetime would seem not to be indicates an interesting possibility of these couplings limited from above at all. However, all this makes sense causing proton decay. It can be shown that the param- if the theory remains perturbative and thus predictive. eter space allows for a B+L violating mode n → e + K+ Increasing MGUT would bring it too close to the Planck [39]. As I show below, this decay mode cannot come scale, so it is fair to conclude that the proton lifetime is from a conventional picture of grand unification with a below 1035 yr. This prediction is not hard, though. The desert. d=4 operators not only cure the bad mass relations, but also also split the Yukawa couplings of the SM doublet Higgs and the color triplet. if you allow for cancellation 4 SO(10) between the d=3 and d=4 couplings, one can in prin- Although SU(5) is the minimal theory of grand unifica- ciple make the color triplet couplings as small as one tion and as such deserves maximal attention as a labo- wishes and thus suppress the proton decay. In principle, ratory for studying proton decay, SO(10) has important it is even possible to make a color triplet mass at the merits electro-weak scale [34]. The cancellation of matrices is rather unnatural, so I will not pursue it here. However, • it unifies a fermion family in a spinorial 16F repre- it may emerge in more complex models, such as SO(10) sentation and as such is a minimal unified theory of [35], so this should be kept mind as a serious possibility. matter and interactions In short, the minimal supersymmetric SU(5) is still a • it automatically contains right-handed neutrinos N perfectly viable theory, and the d = 5 proton decay is ex- pected close to the present limit. The theory is crying for • it gives naturally MN ≫ MW and so neutrino has a new generation of proton decay experiments. It would a tiny mass through the see-saw mechanism seem that B-L remains an accidental global symmetry • in supersymmetry R-parity is a gauge symmetry of nucleon decay and one expects the dominant mode [40] + p → K ν¯ characteristic of d = 5 operators. However, this minimal theory must account for neutrino masses • in the renormalizable version R-parity remains ex- and mixings which implies that R-parity is broken. The act [41] and the lightest supersymmetric partner first important implication of not assuming R-parity is (LSP ) is stable, and thus becomes a natural dark that the lightest neutralino cannot be dark matter, for matter candidate. it decays too fast with the collider signature of lepton While ordinary, non supersymmetric SO(10) was number violation. Thus, the only dark matter candidate studied at length over the years, no predictive realistic is an unstable gravitino. It decays into the neutrino and model of fermion masses and mixings ever emerged. the photon through the neutrino-gaugino mixing All the fermion masses and mixings can be accounted for with the 10H and 126H representations, the latter providing a large mass to the right-handed neutrinos. In the Pati- Salam SU(2)L × SU(2)R × SU(4)C language mν Θν gaugino ≃ Mgaugino 10H = (2, 2, 1)+(1, 1, 6)

3 and 5 Eﬀective operator analysis of nucleon decay and the desert ¯ 126H = (2, 2, 15)+ (3, 1, 10)+ (1, 3, 10) + (1, 1, 6) picture

Since we do not have the theory of grand unification and one can see that in principle no bad mass relations it is worthwhile to study the generic features of high come out. If 10H is taken to be real, a minimal scenario, scale theories of proton decay. This is done through the predictions turn out to be wrong [43], and making the effective operator expansion [53]. In this program it complex kills the predictions. This is why ordinary one expands the baryon violating operators in MW /MB SO(10) does not do the job. The theory deserves atten- or mp/MB, where MB is the scale responsible for pro- tion for it allows for an intermediate L-R symmetry [44]; ton decay. If MB is very large, one can safely assume for recent attempts to revive ordinary SO(10) see [43], the SM gauge symmetry unbroken at that scale. This [45]. is surely true in conventional grand unification with a This situation improves in supersymmetry: the cou- desert where MB = MGUT . plings being holomorphic simplifies things. Although a There are only four leading d = 6 operators [54] single 10H is necessarily complex, still, analyticity guarantees a single Yukawa, and similarly for 126H. This O1 = (uR dR) (qL ℓL) O2 = (qL qL) (uR eR) minimal supersymmetric version, coined renormalizable, O3 = (qL qL) (qL ℓL) O4 = (uR dR) (uR eR) although suggested already in 1982 [46], and revisited ten years later [47], has been studied at length only in The gauge meson dominance would imply only the recent years [48] [49]. A boost was provided by an obser- first two which can lead to a number of predictions. Even vation that b − τ unification can be naturally tied with in general one has an immediate prediction of an acci- the large atmospheric mixing angled in the type II see- dental B - L symmetry in any theory with a high scale saw [50]. This means that small quark and large lepton MB, which explains why any GUT model was predicting weak mixing angles follow naturally from the common it. Yukawa couplings without any need for flavor symme- There are also a number of immediate isospin relations tries. This is an important result which shows that the + 0 1 + − 1 + much talked about issue of rather different quark and Γ(p → ℓR π )= 2 Γ(n → ℓR π )= 2 Γ(p → νπ¯ )= 0 lepton mixings is not a problem as normally argued. In Γ(n → ν¯ π ) the SO(10) grand unified theory it is simply a prod- + 0 1 + − uct of a broken quark-lepton or Pati-Salam symmetry. Γ(p → ℓL π )= 2 Γ(n → ℓL π ) In other words, although at the GUT scale quarks and Also, it is evident thats ¯ goes out, such as in the al- + leptons are completely equivalent with the same Yukawa lowed decay p → K ν¯ , characteristic of d=5 operators couplings, at the SM energies, their different masses lead in supersymmetry. to different mixing angles. One conclude in turns that there can be no two body neutron decay into kaons and charged leptons After a great initial success, when pinned down, the theory ran into tension between fast proton and neu- n → K+ ℓ n → K− ℓ+ trino masses. It was revisited recently [51] and shown to work with the so called split supersymmetry spectrum This is why the R-parity violating mode n → K+ e of heavy sfermions. It is important to note that the discussed in section 3. is so important: if discovered, it nucleon decay branching ratios are determined. This is would point out immediately towards a low scale source an example for a kind of theory of proton decay we are of proton decay. It results from the operator searching for. It remains to be shown that the solution found is unique. d s d ℓ¯H/m˜ 3 Instead of a large 126H Higgs, one may choose a 16H 2 and then build 126H Higgs effectively as 16H . This in- where the Higgs vev is needed to break the SM sym- duces a proliferation of couplings and one must intro- metry which otherwise guarantees the conservation of duce extra flavor symmetries, and thus go beyond a sim- B - L. The low scalem ˜ of supersymmetry breaking al- ple GUT picture. For a discussion of this approach, see lows for this operator not being suppressed. In GUTm ˜ [52]. In any case, it is clear that no accepted minimal becomes MGUT , implying the suppression MW /MGUT . model has yet emerged. In this sense it is really impor- Furthermore, the necessary presence of s quark for sym- tant to keep in mind that the minimal supersymmetric metry reasons implies the absence of the pionic mode: SU(5) theory is not ruled out. It should be viewed as n → π+ e, which makes the it even more predictive [39]. the laboratory for studying grand unification and related This leads to an important message: the decay modes issues, such as proton decay and magnetic monopoles, n → K+ e and n → K− e+ imply a low energy source of the way the minimal ordinary SU(5) used to be when it proton decay. The limits are roughly 1031 yr and I urge worked. the experimentalists to improve them.

4 6 Proton decay: matrix elements • GLACIER (Giant Liquid Argon Charge Imaging ExpeRiment) Due to the shortage of space, I will be very brief here. Europe - Laguna There have been many attempts of computing the matrix elements using the non-relativistic quark model, the Liquid scintillator - 50 kT: good for the kaon modes bag model, the lattice and the chiral Lagrangian tech- niques. In recent years, the focus has been on the lattice • LENA (Low Energy Neutrino Astronomy) and chiral Langrangians, especially the combination of Europe - Laguna the two. For the work on lattice see e.g. [55]. A lot Hopefully they all will be funded and some will reach of progress was made on the lattice computation of chi- 35 ral Lagrangian coefficients, see e.g. [56]. The trouble is 10 yr in 10-20 years? One cannot overemphasize the that chiral perturbation theory works great for soft pi- importance of trying to reach this scale, generic of grand ons, while the pions from the proton decay would have unification. Without experiment, a beautiful field of the momentum on the order of proton mass. Thus, one proton decay and grand unification is bound to turn into needs to go beyond the leading term of the original clas- metaphysics. sic [57] . 8 Acknowledgements 7 Summary and Outlook I wish to thank Pran Nath and other organizers of SUSY I would conclude with the following messages: 09 for an excellent conference. I also wish to thank Wil- fried Buchmüller and Laura Covi and others at DESY • there is no universally accepted grand unified theory for another great meeting, PASCOS 09. This talk was of nucleon decay ordered by the organizers of both as a review of proton decay and grand unification. I am deeply grateful • most models giveτ ≤ 1035 yr, especially with low p to my collaborators on the topics discussed here Charan energy supersymmetry Aulakh, Borut Bajc, Pavel Fileviez Pérez, Bill Marciano, • minimal SU(5) is ruled out and its minimal exten- Alejandra Melfo, Rabi Mohapatra, Miha Nemevˇsek, An- sion leads to possible LHC physics through the light drija Raˇsin (Andrija, vrati se, sve ti je oproˇsteno) and fermion triplet Francesco Vissani. I am grateful to Ilja Dorˇsner, Gia Dvali, Alejandra • minimal supersymmetric SU(5) still perfectly viable Melfo and Enkhbat Tsedenbaljir for useful discussions. with gravitino being the only possible (unstable) Thanks are also due to Vladimir Tello for his help with dark matter this manuscript. I am deeply grateful to Borut Bajc, • test of GUT desert picture provided by decay modes Svjetlana Fajfer and other members of the theory group n → K+ ℓ and n → K− ℓ+ which would indicate at ”Joˇzef Stefan” Institute in Ljubljana for their warm low energy physics as a source of p decay, such as hospitality during this write up. This work was par- R-parity violating couplings tially supported by the EU FP6 Marie Curie Research and Training Network ”UniverseNet” (MRTN-CT-2006- Thus, a new generation of experiments is badly 035863) and by the Senior Scientist Award from the Min- needed. Here is a list of proposals istry of Science and Technology of Slovenia.

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