Neutrino-2008: Where are we? Where are we going?
aa r X i v : . [ h e p - ph ] O c t Neutrino-2008: Where are we? Where are we going?
Alexei Yu. Smirnov International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy,Institute for Nuclear Research, RAS, Moscow, RussiaE-mail: [email protected]
Abstract.
Our present knowledge of neutrinos can be summarized in terms of the “standardneutrino scenario”. Phenomenology of this scenario as well as attempts to uncover physicsbehind neutrino mass and mixing are described. Goals of future studies include completereconstruction of the neutrino mass and flavor spectrum, further test of the standard scenarioand search for new physics beyond it. Developments of new experimental techniques may lead toconstruction of new neutrino detectors from table-top to multi-Megaton scales which will opennew horizons in the field. With detection of neutrino bursts from the Galactic supernova andhigh energy cosmic neutrinos neutrino astrophysics will enter qualitatively new phase. Neutrinosand LHC (and future colliders), neutrino astronomy, neutrino structure of the Universe, andprobably, neutrino technologies will be among leading topics of research.
1. Introduction “Where are we?” is a beloved question of neutrino physicists, which may be explained by theelusive character of the subject of research. According to the HEP Spires from 52 papers withsuch a title, 13 are on neutrinos. John Bahcall keeps the record: 6 papers (all on solar neutrinos;in the field where real progress has been achieved). Of course, not only neutrino physicists arelost, however the number of papers in other fields is substantially smaller: “where we are” inparticle physics, in heavy ion collisions, in non-baryonic dark matter, in high energy physicshave been asked 2 times each. String theory? - 1 time ...Encouraging: Glashow, Lederman and Weinberg were among those who asked. Variationson the theme: “How it started and where we are?” “Where we are and where do we stand?”“Where should we go?” “Where are we coming from?” and even more profound: “Who weare?” (J. Ellis, with reference to P. Gauguin).Let us elaborate further: Where are we in time? By the way, the New Zealand time wasintroduced in 1868 - 40 years before the year of the Rutherford’s Nobel prize award - our startingpoint. Then1928 - Dirac equation.1938 - Majorana, his disappearance.1948 - Gardner and Lattes: artificial production of pions.1958 - Goldhaber, Grodzins, Sunyar: Helicity of neutrino (50th anniversary!).1968 - Davis: the first solar neutrino result - the birth of the solar neutrino problem. Invited talk at the XXIII International Conference on Neutrino Physics and Astrophysics, Christchurch NewZealand, May 25 - 31, 2008 The author does not take responsibility for the title of his talk. Still, he will do his best to make sense out of it.
978 - Wolfenstein: “Neutrino oscillations in matter”.1988 - Kamiokande-II: the birth of the atmospheric neutrino problem .1998 - Discovery of oscillations in atmospheric neutrinos.2008 - Discovery of New Zealand by the neutrino community; the start of LHC.Where are we in space? - about 5000 km (baseline) from IceCube in 3D, somewhere in theelectroweak brane, in extra D...Where are we in the field of neutrino physics? The answer includes: “conquest territory” -the standard neutrino scenario (sec. 2); understanding neutrino masses and mixing (sec. 3);beyond the standard scenario (sec 4); a future which we know (sec. 5); a future which we canonly imagine (sec. 6).
2. Standard neutrino scenario “Standard neutrino scenario” can be formulated in the following way: • Neutrino interactions are described by the standard electroweak model. • There are only 3 types of light neutrinos (three flavor and three mass states). • Neutrinos are massive. Neutrino masses are in the sub-eV range - much smaller than massesof charged leptons and quarks. • Neutrinos mix. There are two large mixing angles and one small or zero angle. The patternof lepton mixing strongly differs from that of quarks. • The observed masses and mixing have pure vacuum origin; they are generated at theelectroweak, and probably, higher energy scales. These are “hard” masses.The standard scenario is a result of work of several generations of neutrino physicists,the collective effort of experimentalists and theoreticians [1]. This scenario is our “conquestterritory”, basis and starting point for further advance, summary of results of the first phase ofstudies of neutrino mass and mixing. The following comments are in order.1). Interactions: The gauge interactions of neutrinos are well known and well checked. Incontrast, there is no information about the Yukawa couplings with the Higgs boson (if the RHneutrinos exist); these couplings can be relevant for leptogenesis. Neutrino interactions withcomplex systems: nucleons and nuclei are not completely understood and open questions arerelated to the physics of strong interactions. As a probe, neutrinos are unique, being sourcesof the axial vector currents. The open questions include the value of axial mass in the quasi-elastic scatterings [2], the coherence in a single pion forward production [3], the role of theaxial vector anomaly in interactions of Z , γ , ω in explanation of the low energy excess observedin the MiniBooNE experiment [4]. Significant progress has been achieved in nuclear physicsfor ββ -decays [5]. Rare neutrino processes and processes at extreme conditions relevant forastrophysics, e.g., ν ¯ ν − pair production in nucleon collisions, are under consideration.2). Propagation: There are still some discussions about the theory of neutrino oscillationseven in vacuum. “Eternal questions” include the equality of momenta or energies in considerationof interference, validity and applications of the stationary source approximation, relevance of thewave packets, coherence, role of recoil of accompanying particles, etc. . Some of these issues havejust an academic interest in normal situation, but become important for oscillations at extremeconditions, e.g. , oscillations of “Moessbauer neutrinos” [6], where the uncertainty in energy ismuch smaller than the oscillation frequency: ∆ E ≪ ∆ m / E [7].Concerning propagation in a medium, the forefront of studies has shifted to extremeconditions - high densities, temperatures, magnetic fields, propagation in neutrino gases, etc .. L. Sulak has informed me on some earlier indications of the anomaly in the IMB results. ollective non-linear effects induced by the νν − scattering are in explorative phase and seriousprogress has been achieved since 1993 [8] - [11].3). Mass and mixing. The main line of thinking is that the right handed componentsof neutrinos exist, neutrinos are the Majorana particles, seesaw is realized and the smallnessof mass is due the existence of some high mass scales (large masses of RH neutrinos). Thedifference of the quark and lepton mass spectra and mixing patterns is related somehow to thesmallness of the neutrino mass. In general, m ν = m hard + m soft ( E, n ) , (1)where m soft ( E, n ) is the medium-dependent soft component which can be substantial forneutrinos but not for other particles. An important phenomenological and experimental problemis to put model independent limits on (or discover?) m soft . To a large extend phenomenology of the standard scenario has been elaborated, in some cases- in great details. Still some areas exist (cosmic, supernova neutrinos) where active researchcontinues now. Few spots have not been covered yet.1). Solar neutrinos. A complete description of physics of conversion has been elaborated andvery precise analytic results have been obtained. From experimental side some points are stillmissing. These include detection of- the Earth matter effect: day-night asymmetry, zenith angle dependence of the signal;- upturn of the energy spectrum of boron neutrinos at low energies (see, however, the recentBOREXINO result [12]) ;- neutrinos in the so called “vacuum-to-matter” transition region (N, O, pep);- the pp-neutrinos, and - on the other side - the hep-neutrinos.These measurements will provide further tests of the LMA solution and matter effects ingeneral, they will open additional possibilities to search for new physics. The measurementsmay shed some light on various astrophysical issues, e.g., the role of CNO cycle, abundance ofthe heavy elements at the surface of the Sun and initial conditions for solar evolution [13], etc. .2). Atmospheric neutrinos. Comprehensive description of neutrino propagation through theEarth is given in terms of neutrino oscillograms of the Earth - lines of equal probabilities in theneutrino energy - nadir angle, E − Θ ν , plane, fig. 1. The oscillograms give a global view onthe oscillation phenomena inside the Earth being relevant also for the accelerator and cosmicneutrinos[14]. The oscillograms are the neutrino images of the Earth. The Earth is unique andthe structures of oscillograms seen in fig. 1 are unique and well defined. They are defined bythe generalized amplitude and phase conditions. The former is reduced to the MSW resonancecondition for one layer (mantle) and to the parametric resonance condition for 3 layers (mantlecrossing trajectories).The CP-violation properties of the oscillograms have the domain structure (see fig. 2for the ν µ → ν e channel). The δ -dependence appears via the interference term: P intµe ∼| A A A S | cos( φ − δ ), where A A and A S are (in the first approximation) the “atmospheric” and“solar” 2 ν − amplitudes correspondingly and φ ≡ arg ( A ∗ S A A ) is the interference phase. To assessthe δ -dependent terms, one can consider the difference of the oscillation probabilities for twodifferent values of the CP-phase: ∆ P CPµe ( δ ) ≡ P µe ( δ ) − P µe ( δ ). The equality ∆ P CPµe = 0 holds,if at least one of the following three conditions is fulfilled A S ( E ν , Θ ν ) = 0 , A A ( E ν , Θ ν ) = 0 , φ ( E ν , Θ ν ) = ( δ + δ ) / πl . (2)These equalities determine the solar and atmospheric “magic” lines and the interference phaseslines [14] in fig. 2 along which the CP-violation effects are zero. These lines give the borders of igure 1. Neutrino oscillogramsin the 3 ν -mixing case. Shown arethe contours of constant probability1 − P ee (upper panels) and 1 − P ¯ e ¯ e (lower panels) for ∆ m = 8 × − eV , tan θ = 0 .
45 and threedifferent values of θ . Here P ee is the ν e − ν e survival probability.Normal mass hierarchy is assumed.Up to small interference effectthe inverted mass hierarchy wouldcorrespond to interchange of theupper and lower panels. From ref.[14].the CP-violation domains, the CP-violation has different sign in the neighboring domains andstrong CP-violation is in their central parts.3). Long baseline experiments. The physics is well understood (see the oscillograms). Anumber of analytic and semianalytic results have been obtained and approximate expressionsfor probabilities were derived which use various expansions (perturbation theories) in specificranges of energies and baselines [15]. We can speak about the LBL industry: numerical codeshave been developed which allow one to determine sensitivities of experiments to unknownparameters: e.g. θ or phase δ using characteristics of experiment (neutrino energy, baseline,experimental uncertainties, etc.) as input parameters [16].4). Supernova neutrinos. The νν − scattering leads to the flavor exchange and variety ofcollective (non-linear) effects [8] - [11]. One of them uncovered recently is the spectral split[9, 10] or swap according to terminology in [11]. An example of the split in a system of neutrinosand antineutrinos is shown in figs. 3, 4. In fig. 4 from [10] the evolutions of the B –components(or projection on the mass axis) of the polarization vectors are shown as functions of strengthof the νν − interactions µ ≡ √ G F n ν , where “up” (+1 projection) corresponds approximatelyto the e –flavor and “down” ( − x –flavor. According to the figure, all modes withfrequencies below the split frequency: ω ≡ ∆ m / E < ω split , change flavor, whereas the oneswith ω > ω split first evolve in flavor space but then return to their original flavor. The split maylead to observable consequences. The relevance of these effects for real supernovas still shouldbe clarified.4). Cosmic neutrinos. This is the field of active studies which moves now to qualitativelynew level. A number of developments is related to recent results in the γ − astronomy ( ν − γ connection, implications of the EM radiation data). The developments were also triggered by igure 2. Oscillograms for the dif-ference of probabilities ∆ P CPµe ( δ ) = P µe ( δ ) − P µe ( δ ) with δ = 0 ◦ .Shown are the solar (black), at-mospheric (white) and interferencephase condition (cyan) lines. Thelines form the borders of the CP-domains. Non-coincidence of thelines and contours of ∆ P CPµe ( δ ) =0 from numerical computations ismainly due to the level crossingphenomenon. The normal mass hi-erarchy and sin θ = 0 .
05 are as-sumed. From ref. [14].
Figure 3.
Neutrino spectra foran initial box spectrum with 70%antineutrinos and initial mixingangle sin 2 θ eff = 0 .
05. Neg-ative frequencies correspond toantineutrinos. Thin line: ini-tial. Thick dotted: final adia-batic. Thick solid: numerical ex-ample.forthcoming large scale experiments (IceCube, ANTARES). Among possible sources of neutrinosare AGN, GRB, core collapse supernovae, SN remnants, microquasars, blasars [17]. Detailedcomputations of the neutrino yield have been performed for different conditions in the sources.Various effects of neutrino propagation are under consideration: vacuum oscillations, conversionin matter of the source, effects of non-standard interactions. For maximal 2-3 mixing theoriginal flavor ratio equals F e , F µ , F τ ≈ π → µν µ → e ν µ ν e . Oscillations “equilibrate” flavors and the ratio becomes 1 : 1 : 1.Measurements of the ratio and searches for deviations from equilibration will be one of the maingoals of neutrino astronomy [18]. The deviation can be due to matter effects in the source, variousnon-standard interactions, deviation of 2-3 mixing from the maximal one, contributions fromother possible mechanisms of neutrino production. One of interesting possibilities is neutrinofrom thick sources: Protons are accelerated in the relativistic jets by the inner shocks andneutrinos are produced in the pp − and pγ − collisions. Flavor conversion occurs in the He- andH- envelopes [19]. It leads to breaking of flavor democracy. There are new recent developments igure 4. P ωB ( µ ) for individ-ual modes for the case of neutri-nos plus antineutrinos. Left:
Nu-merical solution; for sin 2 θ eff =0 . Right:
Adiabatic solutionfor sin 2 θ eff = 0. In each caseneutrinos with 51 modes (top)and antineutrinos with 6 modes(bottom). From ref.[10].related to establishing the GZK cut-off and evidences that AGN are the sources of the cosmicrays. Perspectives to see the cosmogenic neutrinos will be further clarified.
3. Where are we in understanding the neutrino mass and mixing?
In recent years there was an enormous theoretical activity in attempt to understand originsof neutrino mass and mixing, to explain the smallness of neutrino mass and peculiar mixingpattern. The simplest possibilities have been explored. A number of approaches and scenariosof physics beyond the standard model were proposed. Clearly, with only one theoretical talk[20] the program of the conference does not reflect this activity. Reason? Nothing is reallyaccomplished? No progress? Recall, we measure all these θ , δ , etc. , to uncover eventuallythe underlying physics, to make on this basis new testable predictions. Another aspect ofthe measurements is neutrino applications. The whole excitement was that neutrino mass andmixing are manifestations of physics beyond the standard model. Dramatically, after many yearsof studies and many trials the underlying physics has not been identified. We should explorehow the progress can be achieved. There are three lines of studies in the bottom-up approach with different implications forfundamental physics and different connections between leptons and quarks.1). Tri-bimaximal mixing (TBM). Immediate implication: flavor symmetry. The majorityof models proposed so far are based on the discrete symmetry group A . Other possibilitiesexplored in this connection include the groups T ′ , D , S , S , ∆(3 n ). Extension of thesesymmetries to quarks is, however, problematic, it requires further complication of models. TBMmay indicate that quarks and leptons are fundamentally different. Mixing and masses are notrelated at least in a straightforward way.2). Quark-Lepton Complementarity (QLC) is based on observations that θ l + θ q ≈ π/ θ l + θ q ≈ π/
4. A general scheme is “the lepton mixing = bi-maximal mixing - CKM”. Twoextreme realizations of the complementarity,
QLC ν and QLC l , are determined by the order ofthe bi-maximal and CKM rotations: U P MNS = U bm U † CKM ( QLC l ) , U P MNS = U † CKM U bm , ( QLC ν ) . (3)mplications: Quark-lepton symmetry, or grand unification (GUT), plus the existence ofstructure which produces the bi-maximal mixing. The latter may require some symmetry. Againthere is no straightforward connection between mixing and masses.3). Quark-lepton universality. This approach does not rely on any specific symmetry in thelepton sector. The mass (Yukawa coupling) matrices of quarks and leptons have no fundamentaldistinction. The whole difference is related to the seesaw mechanism itself which explainssimultaneously the smallness of neutrino mass and large lepton mixing. The mass matricesof quarks and leptons are constructed on the basis of the same principles (e.g. Froggatt-Nielsenmechanism, U (1) − flavor symmetry), and furthermore, masses and mixing are related with eachother. Large lepton mixing can be associated to the weak mass hierarchy of neutrinos.TBM and two versions of QLC differ by predictions of the mixing angles ( θ , θ ): QLC ν : (35 . ◦ , ◦ ) , T BM : (35 . ◦ , , QLC l : (32 . ◦ , . ◦ ) . (4)Notice that θ ( QLC l ) = π/ − θ C and θ ( QLC ν ) ≈ θ ( T BM ). All three possibilities (subjectto RGE corrections) agree with the present data within 1 σ . Clearly, a combination of futureprecise measurements of these angles will disentangle the schemes. In specific models, someadditional corrections appear due to violation of the underlying symmetry. Small deviationsfrom the predictions do not exclude the context. Exact confirmation would be very demandingand restrictive.There is no reason to consider TBM but ignore the Koide relations which are, in contrast toTBM, the pure mass relations [21]. Furthermore, it may happen that some connection betweenthe Koide relation and TBM exists. Recall, the equality m e + m µ + m τ ( √ m e + √ m µ + √ m τ ) = 23 (5)is satisfied with accuracy 10 − on the mass shell and with 10 − - at M z . The equality (5) hasbeen obtained in attempts to explain relation between the Cabibbo angle and lepton masses.Both relations can be reproduced if m i = m ( z i + z ) , X i z i = 0 , z = sX i z i / , (6)where z i are some numbers. Brannen [22] has generalized the relation to neutrinos: m + m + m ( −√ m + √ m + √ m ) = 23 , (7)where the minus sign in front of the first term in denominator is crucial. According to (7)neutrinos have a hierarchical spectrum with m = 3 . · − eV. Non-abelian flavor symmetryand specific VEV alignment can be behind the relations. Flavor features of various symmetry groups have been explored: Discrete groups A (subgroup of SO ) and T - Frobenius group (subgroup of SU ) [23] look rather promising. It was argued thatthe minimal group which leads to TBM mixing is S [24]. The “successful” models imply tuningof symmetries and patterns of their breaking. The following aspects are of special interest.1). Fundamental versus effective. The required symmetry may appear only at the effective level after decoupling of heavy degrees of freedom. No flavor symmetry or some other symmetryexist at the fundamental level. In the case of decoupling of the RH neutrinos the emergingymmetry can be called the “see-saw symmetry” [25]. This idea is along with the line of Ref.[26], where it was argued that symmetries at the effective level may follow from certain hierarchiesof masses at the fundamental level.2). Real versus accidental? Are the observed flavor features, such as maximal 2-3 mixing,tri-bimaximal mixing, small (zero) 1-3 mixing, Koide relations accidental? Some value of mixingangle is accidental if it is a combination of two or more independent contributions. If some valueor relation appears as immediate “one-step” consequence of symmetry (the group structure),we conclude that they are not accidental, that is, a real. The decisive criteria are new testablepredictions from symmetries. Discovery of the degenerate mass spectrum would be convincingevidence of a real symmetry.3). Flavors and GUT. The scale of RH neutrino masses favors of GUT. In fact, the value ofmass of the heaviest RH neutrino can coincide with the GUT scale M R ≈ M GUT ∼ GeV,which can be achieved in the presence of mixing of three generations. Alternatively, the scale ofRH neutrino masses can be related to M GUT via the Planck scale M P l : M R ≈ M GUT /M P l ∼ GeV (the latter is realized, e.g., in the double seesaw scenario). Another indication of GUT isQLC. The generic problem of unification of quarks and leptons is the difference of their mixingpatterns. To explain data with flavor symmetries, the quarks and leptons, the RH componentsof charged leptons and neutrinos should have different flavor properties This prevents theirunification, or the original flavor symmetry should be broken differently in quark and leptonsectors, for up and down components of multiplets.The data on masses and mixing show both order (regularities) and some degree of randomness,and no simple parametrization is found. Therefore no simple “one-step” explanation is expected.Furthermore, different pieces of data testify for different underlying physics. This may indicatethat several unrelated contributions to the neutrino mass matrix exist (zero order structure plussmall corrections?). Keeping this in mind one can develop the following approach: (i) refrainfrom attempts to explain all the data at once; (ii) take the most symmetric and minimal context“GUT plus flavor symmetry”, (iii) explore how far one can go in explanation of the data. Onepossibility is SO (10), without Higgses but with non-renormalizable operators, with flavonsand singlet fermions. Flavons and singlet fermions (their number can be bigger than three) cancompose a hidden sector of theory with certain symmetries and dynamics. In this context onecan disentangle the hierarchies of quark and neutrino masses and, e.g., relate the geometricalhierarchy of the up quark masses and nearly maximal 2-3 leptonic mixing [27].4). Energy scales of new physics. In the “seesaw approach” the smallness of neutrino massis in general related to the existence of some new large scale, Λ. In the simplest version Λ isjust the bare mass of the RH neutrino. In general, there is some particle sector and dynamicsbehind. Various realizations have been proposed with Λ equal M P l (which requires many RHneutrinos), or M GUT , or √ M P l M EW , or M EW . In νM SM scenario [28] Λ < . − . f ew eV, is not excluded [29]. All this means that “Physicsbehind the neutrino mass” is not yet identified.
4. Beyond the standard scenario
There are two aspects of further experimental and phenomenological studies: tests of thestandard scenario and searches for new physics. The ways new physics appears in ourconsiderations can be classified as follows: 1). Neutrino anomalies. Recall that neutrinoanomalies were the driving force of the developments for more than 40 years. 2). Newphysics related to explanation of the neutrino masses. 3). New physics motivated by otherfields. This includes various extensions of the standard model: Left-Right symmetric models,supersymmetry, GUT, extra dimensions. 4). Unmotivated (explicitly) speculations. .1. Neutrino anomalies
Neutrino anomalies can be considered as potential seeds of new developments. The anomaliesup to date are summarized in the Table 1.
Table 1.
Neutrino anomaliesName: Feature possible interpretationsLSND excess of e + events ( exotics ) , see textMiniBooNE excess of events at E <
400 MeV see textNuTeV value of sin θ W structure functions,new heavy leptonsHomestake low rate, tension with other data mixing with very lightsterile neutrino;unparticle physicsGallium deficit of observed signal cross-section;in calibration experiments small scale oscillationsUnnamed time variations of solar neutrino signals neutrino magnetic moment,periodicity of the energy releaseSN1987A angular, time distribution, LSD signal astrophysics? Z -width N effν < exotics ) : e.g., sterile neutrinos andextra dimensions [32], sterile neutrinos with energy dependent masses, [33], CPT- violation andsterile neutrinos [34], 3 sterile neutrinos and light vector boson [35], soft decoherence [36]. In thelast case both “decoherence” and “soft” are exotic. Do we deal here with something unusual, notconnected to known physics processes? An interesting task is to reconstruct from the data L − and E − dependence of the underlying effect in model independent way and check the consistencywith the other data. Broadly it can be classified as (i) non-standard interactions (NSI); (ii) new neutrino states, (iii)new dynamics.(i) Possible existence of non-standard neutrino interactions is related to extensions of SM atthe EW scale and terascale as well as to new particles motivated by astrophysics. NSI haverich phenomenology influencing both propagation and detections of neutrinos. In particular,they can modify the refraction phenomena, especially at high energies where usual mixing issuppressed, see fig. 5 from [37],(ii) New neutrino states or sterile neutrinos. If light, these states can have direct observableconsequences: be produced in various neutrino processes, participate in oscillations, and decays, etc. . Mixing of new states with usual neutrinos leads to indirect effects: modifications of themass matrix of active neutrinos (induced mass: m ind ≈ m S sin θ S ), breaking of universality,ppearance of FCNC. Light sterile neutrinos both participate in low energy phenomenology andmodify the mass matrix of active neutrinos. The heavy ones produce indirect effects only.For m S < ∼
200 MeV the strong bounds on the mixing of sterile neutrinos from astrophysicsand cosmology exclude significant influence on the mass and mixing of active neutrinos. Incontrast, for m S > ∼ g increases with the decrease of energy andat the energies below certain scale Λ U approaches the infrared fixed point, g → g ∗ . If g ∗ ≫ ∼ Λ QCD .The particles of HS couple to the SM particles via the exchange of messenger fields with mass M ≫ Λ U . At energies below M the interaction of SM particles with HS particles are describedby the effective interactions M k O SM O UV , where O SM and O UV are the operators which dependon the SM and HS fields correspondingly. In analogy with QCD one can consider, e.g., that O SM is leptonic operator, whereas O UV is the quark operator. Below Λ U the operator O UV transforms into operator of composite (confined) states O U (e.g., “pion”): O UV → O U and theinteraction becomes C Λ d UV − d U U M k O SM O U , (8)where d UV and d U are dimensions of operators O UV and O U correspondingly. The key differencefrom the hadron case is that here due to scale invariance (no energy gap) the confined states Figure 5.
Neutrino oscillogramsof the Earth in the presence ofNSI. The electron neutrino sur-vival probability, P ee , as functionof zenith angle α and energy. Dif-ferent panels correspond to differ-ent strength of NSI, sin 2 β ≈ − ǫ eτ , θ = 8 ◦ . Panel with β = 0 corre-sponds to the the standard interac-tions only. Strong transitions are inwhite regions. For β = − π/ β = − π/
16 these regions extendto high energies. From ref. [37].aa
Figure 6.
Possible shape of the leptonicunitarity triangle now.
Figure 7.
The unitarity triangle in future(see text).have continuous mass spectrum [39, 40]. As a result, individual mass modes have infinitesimaleffect. Finite rates of production and exchange of unparticles appears as a consequence ofintegration over mass spectrum of composite states.As far as applications to neutrinos are concerned, several processes have been considered:the neutrino decays ν i → ν j + U [41] [42], scattering on electrons ν α e → ν β e [42], and neutrinoannihilation νν → γγ , νν → f f [43] via an unparticle exchange. The exchange of unparticlesinfluences refraction: it modifies the matter potential (in the case of vector operators) andeffective neutrino mass (in the case of scalar operators). This, in turn, modifies conversionprobabilities in matter [44]. The present data give various bounds on unparticle properties.
5. Future which we know
Clear phenomenological and experimental goal is to accomplish reconstruction of the neutrinomass and mixing spectrum. It includes measurements of θ , the deviation of 2-3 mixing fromthe maximal one, δ , absolute scale of mass, searches for the ββ ν decay and determination ofnature of neutrinos, measurements of m ee and Majorana phases. The program has emerged morethat 10 years ago. It is well motivated and elaborated. On the basis of these measurements onecan reconstruct the neutrino mass matrix (in the flavor basis), at least partially.The situation can be presented using the leptonic unitarity triangle. In fig. 6 we showthe possible form of the triangle as it follows from the existing data [45]. Three eµ -trianglescorrespond to sin θ = 0 .
15, and three different values of the CP- phase δ . The scatter-plotgives possible position of the vertex of the triangle. Large number of points along the horizontalaxis corresponds to zero value of the phase (or θ = 0). The fig. 7 shows possible situation afterthe next generation of the experiments (Double CHOOZ, Daya-Bay, J-PARK, NO ν A) assumingcertain set of the results. Here there are no points along the horizontal axis, which means thatnon-zero value of CP-phase can be established, if it is not small. The triangle is not just anillustration, it may provide a method to measure δ and test unitarity.Future experimental programs are mainly based on the long-baseline experiments and theoscillograms give a global view of the situation. Operating and expected accelerator experiments(superbeams, beta beams, muon factories) cover the energy range (0.5 - 30) GeV and severalbaselines at cos Θ ν < .
3, that is, the peripheral regions of oscillograms with poor structure.This is the origin of degeneracies of the oscillation parameters. Interesting new proposal is thelow energy neutrino factory E ∼ f ew GeV [46], which opens a possibility to turn the beam.nother approach could be based on studies of the atmospheric neutrinos which cover hugeranges of energies, E = (0 . − ) GeV and base-lines, (10 − ) km. The problem here islow statistics (especially at high energies) and uncertainties in the original neutrino fluxes. Thepresent large-scale underground and under-ice detectors (AMANDA, IceCube, ANTARES) havehigh energy thresholds, E > (50 − E = (2 −
10) GeV. Both problems can be resolved with multi-Megaton detectors of the TITAND type [47] with energy threshold below (1 - 2) GeV: highstatistics will allow one to measure the oscillograms in a wide E − Θ ν range and determineboth unknown neutrino parameters and the original fluxes (which can be parameterized by fewquantities) simultaneously. In such a detector one may expect about 2000 events in 3 - 5 years,e.g., in the parameter space ∆(cos θ ν ) = 0 - 0.2 and ∆ E = 2 − >
100 km.
The interplay of the results of precise neutrino measurements, data on rare processes like µ → eγ ,cosmological and astrophysical data, as well as results from LHC and other colliders is expectedto be very fruitful. Present bounds will be improved and hopefully signals/signatures of newphysics identified.Neutrinos and LHC. Here expectations range from complete identification of the mechanismof neutrino mass generation to practically nothing. The first case will be realized, if, e.g., theHiggs triplet with a few hundred GeV mass and small VEV generates neutrino mass and mixing.In the second one, the outcome could be that some EW scale mechanisms with certain valuesof parameters are excluded. We will not be able to detect the RH neutrinos responsible for thetype-I seesaw mechanism. If some heavy neutral leptons with terascale mass are observed, theywill not be immediately related to the light neutrino mass generation and in addition some newphysics should be involved. The νM SM − scenario [28] implies yet another scenario of futuredevelopments. Detection of neutrino bursts from galactic supernova may have very strong impact on neutrinophysics, astrophysics and particle physics. It can contribute to the determination of the neutrinoparameters. It may shed some light on nucleosynthesis in SN and on SN explosion mechanismvia the neutrino monitoring of the shock wave propagation. It will be an important test of thetheory of neutrino propagation and flavor conversion. It is rather plausible that we will discoversomething unexpected. There are good chances to measure the relic SN neutrino fluxes.The detection of high energy neutrinos from astrophysical sources will be one of the majordiscoveries of this century. This will trigger more focused theoretical studies, and experimentaldevelopments.
6. Future which we can only imagine
Trying to imagine future one can proceed in different ways: (i) “project from the past”, e.g.study programs of previous neutrino conferences; (ii) follow logic of the field; (iii) use somehistorical parallels in neutrino physics and other fields; (iv) imagine new neutrino sources andnew detectors; (v) identify seeds of new developments.1). The breakthrough in the field can be related to developments of new experimentaltechniques: creation of new neutrino sources and detectors. This includes widely discussedbeta-beams and neutrino factories. Experiments with strong sources of low energy neutrinosradioactive nuclei) look very appealing [48]. One can imagine some particular processes atparticular conditions which will open new perspectives. One example along this line (its practicalrealization still should be proved) is neutrino pair emission from metastable atoms [49]. It looksintriguing in view of closeness of the scales of atomic transition energies and neutrino mass.One can expect strong enhancement of the processes - superradiance due to coherence in largevolume. The processes of photon (laser) irradiated neutrino pair emission from metastable atoms γ + A i → ν i ν j + A f and radiative pair emission A i → ν i ν j + γ + A f have been considered [49].The rates are proportional to neutrino masses and to Pauli blocking factor due to the presenceof relic neutrinos. The latter can be used, in principle, to detect relic neutrinos.On the other side, future significant progress can be due to development of large scintillatorobservatories and the multi-Megaton scale water Cherenkov detectors with flavor (may becharge) identification and low energy thresholds. One can imagine new methods of lightcollection, volume detection of event, etc. . Further developments of the balometric techniques,construction of large scale array of calorimeters look very perspective [50]. The use of radioactivenuclei for neutrino detection with zero threshold [51] opens some perspectives to detect relicneutrinos. The neutrino Moessbauer effect can be used to study neutrino oscillations, measurethe 1-3 mixing, determine the mass hierarchy, search for sterile neutrinos, study gravitationalredshift of neutrinos, and even study quantum gravity effects [52]. Coherent neutrino interactionscan be the key feature of future techniques. One can imagine new methods of decrease ofbackground and detection of very weak signals. Array of km-cube size detectors of cosmicneutrinos (with KM3NET as the first step) is not out of discussion.High precision of measurements will open new horizons to discover sub-leading effects andsearch for new physics. This in turn will trigger new phenomenological and theoretical studies.2). Neutrino structure of the Universe. Some work has already been done. One expectsclumping of neutrinos depending on their masses [53]. That can lead to formation of neutrinohalos, and neutrino “stars”. Possible new interactions (e.g., with accelerons) can lead to neutrinocondensates and superfluidity [54]. The issue is important for the direct detection of relicneutrinos.The presence of relic neutrinos has been established indirectly by counting the number ofrelativistic degrees of freedom in the epoch of transition from radiation to matter dominatedUniverse. Future cosmological probes will be able to reconstruct structure of the Universein the earlier epochs, thus resolving various degeneracies and improving bounds on neutrinoparameters. Connections neutrinos - dark energy, neutrinos - dark matter will be further studied.3). With our present advanced knowledge of neutrino properties (interactions, masses andmixing) the aspect “neutrinos as unique probe” of micro and macro worlds becomes againimportant - now at a qualitatively new level. Future experiments with large fluxes andhigh energy neutrinos can be used for further studies of the nucleon structure and precisionmeasurements of the electroweak parameters; NuSoNG proposal [55] is one step in this direction.With large-scale high statistic solar neutrino detectors one can have further advance in studiesof the deep interior of the Sun, and stellar evolution (detection of fluxes of N-, O-, pep-, hep- neutrinos, searches for time variations, correlations with solar flares, etc. ) High statisticssupernova neutrino detection may allow one to monitor the shock wave propagation. Detectionof SN bursts from other remote galaxies may become reality. Direct detection of the relicneutrinos will provide a unique probe of the Early Universe.4). Toward the neutrino technologies. Technology (applied physics) is associated withsomething which can be copied and be of multiple use. Some “technologies” were proposedlong time ago, and now with our accumulated knowledge the proposals become more realistic.Some examples:- monitoring nuclear reactors [56];- oscillation and absorption tomography of the Earth; study of geoneutrinos [57]: creation of the neutrino maps of the Earth;- use of Moessbauer neutrinos for precision measurements;- neutrino communication systems, Galactic communication [58];- creation of the solar scanners to search for oil and minerals [59], etc. .Practical realizations of at least some of these proposals look at present extremely challenging.At this point one can, however, recall the story of neutrinos themselves: in the thirties of thelast century their discovery seemed to be impossible, and another story of establishing non-zeroneutrino mass, when solution came not from the direct kinematic measurements but from thediscovery of long time “exotic” and “non-standard process”- neutrino oscillations.
7. Conclusion
Neutrino physics is in the transition phase. Significant territory is already conquered which canbe described in terms of the standard neutrino scenario. Tests of this scenario and searchesfor physics beyond it are the main objectives for further studies. Precision measurements andexploration of extreme conditions (energies, densities, distances) will open new horizons.And what emerges? - Unclear implications of results for fundamental theory, origins ofneutrino mass and mixing, the existence of flavor symmetries, unification, etc.
The questionwhat should be done to achieve progress in understanding neutrino mass and mixing is already,and will be in future a driving force of developments. LHC and other high energy experimentsmay clarify the situation.In spite of these problems we can start to think seriously about applied neutrino physics andneutrino technologies.
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