Neutrinos: Key to New Physics

Home , Andrew Strominger

arXiv:hep-ph/0411009v1 31 Oct 2004 a .Ramond Physics P. New to Key Neutrinos: fEeg ne rn DE-FG02-97ER41029. grant under Energy of ∗ ntdStates United ciigi ndti emrl oesm fits of some note merely we features: de- detail startling than in Rather it scribing millifermis. to down teractions LEGACIES MODEL STANDARD 2. the begin tapestry. we a Below, such of time. weaving its theoreti- of great speculations the cal of of context presentation the bread-brush in a it couching without complete be distances, Grand-Unification. short so-called very the one at of partners proposal structure equal more mathematical are Salam’s[5] leptons been and and quarks has that Pati None than and dominating puzzles, questions. new many generated successfull, elicited has how incomplete, matter is no it Nature, Like of models Gravity. all all except for paradigm Interactions the Fundamental as Model Standard the estab- lished distances[4] shorter at Strong Electromagnetic weaken the Interactions that and realization the Weak and com- Interations[3], of a massive description of of emergence mon of renormalizability the Stan- The theories[2], afterglow Yang-Mills the by the Model. generated dard in turmoil intellectual born the was Mechanism[1] INTRODUCTION 1. specul endearing most p near-Planck the to with properties flavor. Model. fits neutrino Standard static and of the old, measurement by century prompted quarter ideas a theoretical new using hsRsac sspotdi atb h SDepartment US the by part in supported is Research This nttt o udmna hoy hsc eatet Univer Department, Physics Theory, Fundamental for Institute h eswmcaimpeitdtn etiomse ypost by masses neutrino tiny predicted mechanism Seesaw The h tnadMdldsrbsfnaetlin- fundamental describes Model Standard The would mechanism Seesaw the of celebration No Seesaw the ago, years five Twenty a ∗ 1 yis tmyee rv e osligterdlsof riddles the solving to key prove even may it hysics, e:tesotrtedsac,the distance, bro- the spontaneously shorter the are and symmetries ken: quarks gauge neutrino. The of massless – families a chiral with each three leptons, are There – quan- leptons. and for between quarks cancel needed anomalies are gauge leptons consistency: tum and quarks Both – U ncte rmams ordcdso experi- of the decades of Measurements practically four ments. emerged almost has from Model unscathed Standard The – agMlstere ae on three based from theories Yang-Mills stem neutrinos Interactions experiments: – by rest Model masses. to have Standard put the been of has prediction Higgs One be elusive the to of particle. mass remains the have experiment, parameter by leptons One fixed and quarks discovered. its been of all pre- and of radiative structure, decade its vindicated a have neutrinos, measurements active cision three of limit a tpeit Pvoaini h toginterac- Strong the in fea- CP-violation unsavory predicts some It predictions: – puzzle, wrong some new and one tures, side with dark a it, is to there expectations, beyond cessfull PUZZLES OLD & NEW 3. the particle, scalar fundamental boson. a Higgs predicts It – metry. (1). lhuhteSadr oe a ensuc- been has Model Standard the Although toso liaeuicto.B eaigthe relating By unification. ultimate of ations tad rdnet hoeia it htis that vista theoretical a to credence adds It ltn e ag cl npril physics, particle in scale large new a ulating iyo lrd,Gievle L32611, FL Gainesville, Florida, of sity Z SU bsnwdhputs width -boson (3), ekycoupled weakly more SU h sym- the 2 and (2) 2 tion, albeit with unknown strength. new scale of physics, close to the Planck mass: the – It requires Yukawa interactions but does not quantum number patterns did not quite match offer any organizing principle. the dynamical information. This near unification – It fails to explain the values of the masses and introduced Planck scale physics into the realm of mixing patterns of quarks and charged leptons. particle physics. – It contains too many parameters. A by-product of this Grand Unification is the – It is not a complete description of Nature since violation of baryon number. Hitherto unob- it does not address gravitational interactions. It served, proton decay remains one of the most only describes only the matter side of Einstein’s important consequences from these ideas. In a equation, sans cosmological constant. serendipitous twist, proton decay detectors now – It fails to account for neutrino masses. serve as the telescopes of neutrino astronomy! For these and other reasons, it is obvious that Other global symmetries also bite the dust: the the Standard Model is an unfinished picture that relative lepton numbers are violated in SU(5) and needs to be put in a more general framework SO(10) violated the total lepton number as well, where these shortcomings are addressed. It ap- and the extraordinary limits on these processes pears to be like the shards of a once beautifull are consistent with the grand-unified scale. pottery, shattered in the course of cosmological evolution. 5. GRAND-UNIFIED LEGACIES

4. GRAND UNIFICATION Although Grand Unification by itself does not yet have any direct experimental vindication, it The quantum numbers within each of the three has proven to be an incubator of ideas that, to families of quarks and leptons strongly suggest a this day, drive speculations on the Physics of more unified picture. It is remarkable that Pati extra-short distances. and Salam’s original idea is realized by unifying – It showed how the large grand-unified scale the three gauge groups of the Standard Model could be used to generate tiny neutrino masses[1]. into one simple gauge group. In the simplest[6], – It suggested some links between quark and SU(5), each family appears in two representa- charged lepton masses, with some success for the tions. In SO(10)[7], they are grouped in the two heaviest families. Still, the flavor riddles of fundamental spinor representation, by adding a the Standard Model remain largely unexplained right-handed neutrino for each family. At the by Grand Unification. next level of complication, we find E6[8] where – It created the “gauge hierarchy” problem, why each family contains several right-handed neutri- quantum corrections leave the ratio of the Higgs nos as well as vector-like matter. Organizing the mass to the Grand-Unified scale unscathed. elementary particles into these beautiful struc- Moreover, two of its predictions have linked tures particle physics to pre-Nucleosynthesis Cosmol- – Unifies three gauge groups into one. ogy: – Relates quarks and Leptons. – It predicted the existence of monopoles in our – Explains anomaly cancellations. universe. This led to the idea of Inflationary There are indications that this idea “wants Cosmology[9], which solves many long standing to work”. When last seen, the three coupling puzzles and whose prediction of a flat universe constants of the Standard Model are perturba- has been recently verified experimentally. tive. Using the renormalization group equations – It predicted proton decay, and offered a frame- to continue them deep into the ultraviolet, they work for understand the baryon asymmetry[10] of get closer to one another, but fail to meet at the Universe. one scale. Originally, the Weinberg angle was Today, only one of these predictions, tiny neu- not measured with sufficient accuracy, and it was trino masses, has been borne out by experiment. thought that they met at one point, suggesting a Like the Standard Model, it clearly is not a com- 3 plete theory of Nature, since it does not address 7. SUPERSYMMETRY Gravity (space-time is either flat or a fixed background ), nor the origin of the three chiral families Supersymmetry is clearly an attractive theo- and the associated flavor puzzles. retical concept; it is required by the unification of gravity and gauge interactions, and links fermions and bosons. Also, the mass of the spinless su- perpartner of a Weyl fermion, inherits quantum- naturality [12] through the chiral symmetry of its 6. SUPERSTRINGS partner. Morever, when applied to the Standard Model, At the 1973 London conference, David Olive in it yields quantitative predictions that fit remark- his rapporteur talk, declared Superstring Theo- ries to be “Theories of Everything”. As he stated, ably well with Gauge Unification. – The Gauge hierarchy problem is managed: the Superstring theories reproduce Einstein’s gravity mass of the Higgs is stabilized even in the pres- at large distances with no ultraviolet divergences, ence of a large (grand-unification) scale and can also contain (some) gauge theories. This – The three gauge couplings of the Standard view has since gained much credence and notori- Model run to a single value in the deep ultravio- ety. The matter content has gotten much closer to let with the addition of superpartners in the TeV reality[11], although this unification of the grav- range. Thus naturally emerges a new scale using itational and gauge forces takes place in a some- what unsettling background: the renormalization group, a scale that matches the quantum number patterns of the elementary – Fermions and Bosons are related by a new type particles. of symmetry: supersymmetry! – With supersymmetry the renormalization group – Ultimate Unification takes place in more than displays an infrared fixed point that predicts[13] three space dimensions! a heavy the top quark, in agrrement with exper- Nature at the millifermis displays neither su- iment. persymmetry nor extra space dimensions. Yet, – Under a large class of ultraviolet initial con- the lesson of the Standard Model of more sym- ditions, the same renormalization group shows metries at shorter distances provide an argument that the breaking of supersymmetry triggers elec- for these to be fabrics of the Ultimate Theory; troweak breaking[14]. they are shattered by cosmological evolution. To Supersymmetry at low energy is the leading compare the highly symmetric superstring theo- theory for physics beyond the Standard Model, ries to Nature, a dynamical understanding of the although many puzzles remain unanswered and breakdown of these symmetries is required, an un- new ones are created as well. derstanding that still eludes us. Firstly, there are almost as many theories of su- To make contact with experiments, it is neces- persymmetry breaking as there are theorists, and sary to know the energy at which these symme- none, theories and theorists alike, are convincing. tries manifest themsemselves. Both types could It is an experimental question. be just around the energy corner, but I would like Secondly it adds little to the flavor prob- to argue that circumstantial evidence lends more lem; rather it makes it worse by predicting new credence to low- energy supersymmetry than to scalar particles which generically produce flavor- low-energy extra dimensions. For some reason, changing neutral processes. Even if the breaking the collapse of the extra space dimensions oc- mechanism is flavor-blind (tasteless), non-trivial curs first, while Supersymmetry hangs on to later effects are expected: supersymmetry-breaking is times (lower energies). It is a challenge to the- already highly constrained by the existing data ory to find a dynamical reason which triggers the set. breakdown of higher-dimensional space (perhaps All will be forgotten when superpartners are through brane formation), while leave supersym- discovered at the LHC. May the supersymmetry- metry nearly intact. 4 breaking mechanism parameters prove to be bizarre enough to allow intellectually-challenged sin2 2θ > 0.85 , 0.30 < tan2 θ < 0.65 , theorists to infer its origin from the LHC data ⊕ ⊙ alone! while there is a only a limit[22] on the third angle 8. TINY NEUTRINO MASSES ǫ 2 < 0.05 . | | The only solid experimental evidence to date Spectacular as they are, these results generate for physics beyond the Standard Model is the ob- new questions for experimenters: servation of oscillation among neutrino species. – Are the neutrino masses Majorana-like (i.e. lep- Experiments on solar neutrinos [15,16,17] yield ton number violating)? – What is their absolute values? Can one measure 2 2 2 2 5 2 the sign of ∆m ? ∆m = mν1 mν2 7. 10− eV , ⊙ | − | ∼ × – Is CP-violation in the lepton sector observable? with corroborating evidence on antineutrinos[18]. They also generate new theoretical questions Neutrinos born in Cosmic ray collisions[19], and – Are there right-handed neutrinos? on earth[20] give – If so, how many, how heavy, with what hierarchy? – Where do they live? Brane or bulk? 2 2 2 3 2 – Do they cause leptogenesis? ∆m = mν2 mν3 3. 10− eV . ⊕ | − | ∼ × The best bound to their absolute value of the 9. Standard Model Analysis masses comes from WMAP[21] Masses and mixings of the quarks are deter- mined from the diagonalization of Yukawa matri- mνi < .71 eV . 1 ces generated by the ∆IW = breaking of elec- Xi 2 troweak symmetry, for charge 2/3 These experimental findings are not sufficient to determine fully the mass patterns. One oscillates mu 0 0 between three patterns, hierarchy,  0 m 0  † , U2/3 c V2/3 0 0 mt m < m m ,   | ν1 | | ν2 | ≪ | ν3 | and charge 1/3 inverse hierarchy − md 0 0 † mν1 mν2 mν3 , 1/3  0 ms 0  1/3 , | | ≃ | | ≫ | | U− 0 0 m V− or even hyperfine  b  resulting in the observable CKM matrix m m m . | ν1 | ≃ | ν2 | ≃ | ν3 | CKM 2†/3 1/3 . The mixing patterns provide some surprises, since U ≡ U U− it contains one small angle and two large angles. Up to Cabibbo-size effects, it is equal to the unit In terms of the MNS mixing matrix, matrix, implying that mixing is similar for up-like and down-like quarks. Their masses are of course highly hierarchical. cos θ sin θ ǫ The charged lepton Yukawa matrix  cos θ ⊙sin θ cos θ cos⊙ θ sin θ  , − ⊕ ⊙ ⊕ ⊙ ⊕ sin θ sin θ sin θ cos θ cos θ me 0 0  ⊕ ⊙ − ⊕ ⊙ ⊕  1  0 mµ 0  † 1 the various experiments yield U− 0 0 m V−  τ  5

1 also stems from ∆IW = 2 electroweak break- which we can rewrite as ing. To generate neutrino masses, add one right- (0) T handed neutrino for each family, producing its Seesaw = 0 0 , own Yukawa matrix M U C U in terms of the central matrix[23] m 0 0 1 1  0 m 0  † . † 0 2 0 = 0 0 (0) 0∗ 0 . U 0 0 m V C D V V D  3  MMajorana In order to proceed, the nature of the right- It is diagonalized by the unitary matrix handed neutrino’s masses needs to be specified. F They are of the Majorana type. Since the right- = ν T , handed neutrinos have no gauge quantum num- C F D F bers, their masses necessarily violate total lepton where the mass eigenstates produced in β-decay number. are (unimaginatively labelled as “1”, “2”, “3”) In the spirit of effective field theories, one there- fore expects their masses to be of the order of mν1 0 0 lepton number breaking. Total lepton number- ν =  0 mν2 0  . D 0 0 m violating processes have never been seen result-  ν3  ing in a bound from neutrinoless double β de- The effect of the seesaw is to add the unitary cay experiments. So either they are very large or matrix to the MNS lepton matrix F zero. If they are zero, the analysis is like that in the quark sector, and the observable MNS lepton MNS = † 1 0 . mixing matrix is just U U− U F This framework enables us to recast our theoreti-

MNS † 1 0 . cal questions in terms of . So we can ask where U ≡ U− U the large angles reside: itF is convenient to catalog It would be generated solely from the isospinor the models in terms of the number of large angles breaking of electroweak symmetry, just like the contained in , none, one or two? quarks’, even though the mixing patterns are so F different. In the belief that global symmetries are an en- 10. A Modicum of Grand Unification dangered species (black holes eat them up), we To relate the CKM and MNS matrices and the expect their masses to set the scale of the Stan- quark and lepton masses, the natural framework dard model’s cut-off, since they are unprotected is of course grand unification. There, the ∆IW = by gauge symmetries. This yields the Seesaw 1 2 quark and lepton Yukawa matrices are related, where large right-handed neutrino masses engen- using the simplest Higgs contents. der tiny neutrino masses, the latter being sup- At the level of SU(5), the charge 1/3 and presses over that of the charged particles by the charge 1 Yukawa matrices are family-transposes− ratio of the two scales of one another.− 1 ∆IW = 2 ( 1/3) ( 1) T . − − . ∆IW =0 M ∼ M This introduces a large electroweak-singlet scale In SO(10), it is the charge 2/3 Yukawa matrix in the Standard Model. The neutrino mass ma- that is related to the Dirac charge 0 matrix trix is then (2/3) (0) . M ∼ MDirac 1 (0) = (0) (0) T , These result in naive expectations for the unitary MSeesaw MDirac (0) MDirac matrices that yield observable mixings MMajorana 6

which is hardly family symmetric. In the limit of

1/3 ∗ 1 ; 2/3 0 . no Cabibbo mixing, U− ∼ V− U ∼ U Assuming these, we can relate the CKM and MNS 0 0 0 ( 1/3) matrices −  0 0 0  + (λ) , M ≈ 0 a b O   and MNS = † 1 0 U U− U F † 1 1/3 CKM† ∼ U− U− U F T 1 0 0 1/3 1/3 CKM† ∼ V− U− U F MNS =  0 cos θ sin θ  , U 0 sin θ⊕ cos θ⊕ F Hence two wide classes of models:  − ⊕ ⊕ 

I-) Models with Family-Symmetric 1/3 where M− Yukawa matrices. In these we have a tan θ = , ⊕ b 1/3 = ∗ 1/3 , U− V− is of order one[26]. In these models, need con- F so that tain only one large angle, which is easily accomo- dated, a more generic alternative. Models type I provide a hint as to the size of the MNS = CKM† . U U F CHOOZ angle. With a symmetric charge 1/3 In these models, necessarily contains two large matrix, the MNS matrix reads − angles. In the absenceF of any symmetry acting on , these models appear to be of a type I call F non-generic. In particular they could require a = † UMNS UCKM × non-Abelian structure for . F cos θ sin θ λγ II-) Models with Family-Asymmetric  cos θ ⊙sin θ cos θ cos⊙ θ sin θ  , M 1/3 Yukawa matrices. If we extend− the −sin θ ⊕sin θ ⊙ sin θ⊕ cos θ⊙ cos θ⊕ Wolfenstein[24] expansion of the CKM matrix  ⊕ ⊙ − ⊕ ⊙ ⊕  where we have chosen to fill the zero in the ma- in powers of the Cabibbo angle λ to include F quark mass ratios trix by a Cabibbo efect of unknown order. Then it is easy to see that ms 2 md 4 λ λ , λγ mb ∼ mb ∼ θ13 λ sin θ 1 λ . ∼ √2 we find the charge 1/3 Yukawa matrix ⊕ ∼ − It will be interesting to see if this precise predic- λ4 λ3 λ3 tion of type I models is borne out by experiments. ( 1/3) ? 2 2 Models where the charge 1/3 Yukawa matrix − =  λ λ λ  . − M λ? λ? 1 is not symmetric, no such precise prediction is   possible. If we set If the exponents are related to charges, as in the Froggatt-Nielsen[25] schemes, then the lower di- α β agonal exponents are known, and we get the or- 1 λ λ α ders of magnitude MNS =  λ cos θ sin θ  U λβ sin θ⊕ cos θ⊕ ×  − ⊕ ⊕  λ4 λ3 λ3 cos θ sin θ λγ ( 1/3) 3 2 2 ⊙ ⊙ δ − =  λ λ λ  ,  sin θ cos θ λ  , M λ1 1 1 − λγ ⊙ λδ ⊙ 1     7 we see that the CHOOZ angle can take on any well with grand-unified models such as SO(10) γ α+δ β number of values θ13 λ , λ , or λ , de- and E6, where each right-handed neutrinos is part pending on the relative∼ values of the exponents. of a family. Models of either type suggest a Wolfenstein ex- –A large mixing angle can occur if the diagonal pansion for the MNS matrix, but the problem is elements are much smaller than the diagonal ones, the starting point. Perhaps something like that is , . Then we find C11 C22 ≪ C12 λα m2 0 a cos α sin α 0 . sin α cos α 1 √ M1M2 a 0 MNS  √2 √2 √2  + (λ) , − U ∼ −sin α cos α 1 O  √2 − √2 √2  Hence maximal mixing may infer that some of the π π right-handed neutrinos are Dirac partners of one with α = 4 or 6 ? Finally we mention that in the quark sector, Cabibbo mixing is strongest be- another, leading to conservation in this matrix of tween the first and second families. If this effect some relative lepton number. permeates the leptons, then some Cabibbo flop might be expected, and one should not put too 12. Conclusions much value as to their precise values, especially for 1 2 mixing, so the flop in θ could be as There is still much to be learned from leptons. much− as λ/√2. These issues and⊙ CP-violation With the Seesaw Mechanism, neutrino data can will be discussed elsewhere[27]. provide a glimpse of physics that can never be reached by accelerators. This new era of the 11. Correlations physics centers around right-handed neutrinos. With no electroweak quantum numbers, they may In most models, must contain at least one hold the key to the flavor puzzles. The second F large angle to accomodate the data. This presents large neutrino mixing angle suggests that hierar- a small puzzle since diagonalizes a matrix chy is independent of electroweak breaking, ans F which contains the neutral Dirac Yukawa matrix occurs at grand-unified scales. I conclude this which is presumably hierarchical, coming from talk by noting that Fukugita and Yanagida’s won- the isospinor electroweak breaking. This suggests derful idea of leptogenesis[28] from these neutri- special restrictions put upon the Majorana mass nos is much more credible with such a doubled matrix of the right-handed neutrinos. We can see correlated hierarchy. this by looking at a 2 2 two-families case[23]. I would like to express my thanks to Professors × Let us write K. Nakamura, Y. Totsuka and T. Yanagida for inviting me to such an intellectually stimulating β a λ 0 workshop, and also for the wonderful hospitality 0 = m , D 0 1 they showed me. I am also grateful to the Fu- and define M1 ,M2 to be the eigenvalues of the jihara Foundation, Professor Nishijima and the right-handed neutrino’s Majorana mass matrix. Japan Academy. This matrix can be diagonalized by a large mixing angle in one of two cases: REFERENCES – Its matrix elements have similar orders of magnitude 11 22 12, in which case we find 1. M. Gell-Mann, P. Ramond, and R. Slan- that C ∼ C ∼ C sky in Sanibel Talk, CALT-68-709, Feb 1979, hep-ph/9809459 (retroprint), and in Super- M 1 λ2β , gravity (North Holland, Amsterdam 1979). T. M2 ∼ Yanagida, in Proceedings of the Workshop on suggesting a doubly correlated hierarchy betwen Unified Theory and Baryon Number of the 1 the ∆IW = 0 and ∆IW = 2 Sectors. This agrees Universe, KEK, Japan, Feb 1979. 8

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