A brief review of the status of neutrino masses and mixings is presented, with emphasis on Italian contributions to this field of research

Lisi, E.

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DOI 10.1393/ncc/i2009-10421-9Colloquia: IFAE 2009IL NUOVO CIMENTO Vol. 32 C, N. 3-4 Maggio-Agosto 2009Neutrino physicsE. LisiINFN, Sezione di Bari - Via Orabona 4, 70126 Bari, Italy(ricevuto il 19 Settembre 2009; pubblicato online il 9 Ottobre 2009)Summary. — A brief review of the status of neutrino masses and mixings ispresented, with emphasis on Italian contributions to this field of research.PACS 14.60.Lm – Ordinary neutrinos (νe, νμ, ντ ).PACS 14.60.Pq – Neutrino mass and mixing.PACS 13.15.+g – Neutrino interactions.1. – IntroductionNeutrino physics has witnessed a dramatic revolution in the last decade, after thediscovery of atmospheric νμ oscillations in 1998. Such a breakthrough, as well as furtherdecisive results on ν masses and mixings, have greatly raised the level interest in thisfield, with O(103) “neutrino” preprints released per year, as shown in fig. 1.The rapid pace experienced in the last few years should not make us forget thatneutrino physics is, in general, an exercise in patience. As a matter of fact, the threemost basic neutrino questions have been formulated long ago in the past century:– How small is the neutrino mass?(W. Pauli, E. Fermi, ’30s);– Can a neutrino turn into its own antiparticle?(E. Majorana, ’30s);– Do different ν flavor change (“oscillate”) into one another?(B. Pontecorvo; Maki, Nakagawa and Sakata, ’60s).However, only the last question has been positively solved, while hard work is still goingon to answer the others. In this talk, I shall briefly review the current status of the field(as of 2009), by using the above questions as a template, and emphasizing recent Italiancontributions. For more extensive and detailed overviews, the reader is referred to [1-5],as well as to the book [6] and to the website [7].c© Societa` Italiana di Fisica 3940 E. LISIFig. 1. – Yearly distribution of preprints with “neutrino(s)” in the title, from the SPIRESdatabase. Relevant peaks of interest are also indicated.2. – Pontecorvo’s question: Do different ν flavors oscillate into one another?The short answer is: Yes. We have learned, from the results of beautiful experiments,that the neutrino flavor states (να) mix with neutrino mass states (νi),(νe, νμ, ντ )T = U(ν1, ν2, ν3)T ,(1)via a unitary matrix U , parametrized in terms of mixing angles θij and a CP phase δ asU =⎛⎝ 1 0 00 c23 s230 −s23 c23⎞⎠⎛⎝ c13 0 s13e−iδ0 1 0−s13eiδ 0 c13⎞⎠⎛⎝ c12 s12 0−s12 c12 00 0 1⎞⎠ ,(2)where cij = cos θij and sij = sin θij .In general, the oscillation amplitudes are governed by the θij ’s, while the oscillationphases are determined by the squared mass differences δm2 and Δm2  δm2, defined as(m22, m22, m23) =m21 + m222+(−δm22, +δm22, ±Δm2),(3)where the case +Δm2 refers to the “normal” (quark-like) hierarchy with m3 > m1,2,while the case −Δm2 refers to the “inverted” hierarchy with m3 < m1,2.Assuming standard interactions, the mass-mixing parameters (δm2, ±Δm2, θij , δ)completely define the ν flavor evolution, even in complicated cases involving forwardNEUTRINO PHYSICS 41Fig. 2. – Global 3ν oscillation analysis, from [10]: bounds on the mass-mixing oscillation pa-rameters, in terms of standard deviations from the best fit. Note the slight preference forsin2 θ13 > 0.scattering on fermion backgrounds (provided that their density profile is known). Ingeneral, the Hamiltonian H of ν flavor evolution is then the sum of three terms,H = Hvacuum + Hmatter + Hνν ,(4)where the first one (Hvacuum) is kinematical, while the second one (Hmatter) embedseffects of neutrino interactions in matter (e.g., in the Earth or in the Sun), and thethird one (Hνν) describes neutrino-neutrino interactions (only relevant in high-densityconditions such as core-collapse supernovae [8]).A more detailed answer to Pontecorvo’s question is then: We know several of the oscil-lation parameters governing H, but not all of them. Indeed, there are robust upper andlower limits on the squared mass differences δm2 and Δm2, as well as on the two anglesθ12 and θ23; however, nothing is known about the mass spectrum hierarchy [sign (Δm2)]or the CP phase (δ). Equation (2) makes it clear that, in order to access leptonic CPviolation, the mixing angle θ13 must be nonzero. At present, this angle is bounded fromabove by the celebrated CHOOZ reactor neutrino data [9] (plus additional, subdominantdata from a variety of different experiments [1]), and the possibility that θ13 = 0 is stillopen, although perhaps slightly disfavored (see below).Figure 2 shows updated results on the mass-mixing parameters, as derived from aglobal analysis of world neutrino oscillation data [10]. The results are shown in terms ofstandard deviations nσ from the best fit (where nσ =√Δχ2 after χ2 marginalization).Table I summarizes the same results in numerical form.The parameters (δm2, θ12), which govern oscillations in the (ν1, ν2) sector, are con-strained by solar and (long-baseline) reactor neutrino experiments in the νe disappearancechannel. In this sector, the Borexino solar neutrino experiment at Gran Sasso can alsoaddress additional issues [11]: 1) test of Hmatter in the Sun (already observed); 2) testof radiogenic Earth models via detection of geoneutrinos (in progress); 3) test of thestandard solar model via CNO-cycle neutrino detection (under study). The latter testmay benefit from accurate cross-section data of astrophysical interest, as measured bythe LUNA facility at Gran Sasso [12]. In general, probing the Sun and the Earth interiorwith neutrinos is an important and interdisciplinary science goal.42 E. LISITable I. – Global 3ν oscillation analysis, from [10]: best-fit values and allowed nσ ranges forconstrained mass-mixing oscillation parameters. The parameters δ and sign (Δm2) are uncon-strained by current data.Parameter δm2/10−5 eV2 sin2 θ12 sin2 θ13 sin2 θ23 Δm2/10−3 eV2Best fit 7.67 0.312 0.016 0.466 2.391σ range 7.48–7.83 0.294–0.331 0.006–0.026 0.408–0.539 2.31–2.502σ range 7.31–8.01 0.278–0.352 < 0.036 0.366–0.602 2.19–2.663σ range 7.14–8.19 0.263–0.375 < 0.046 0.331–0.644 2.06–2.81The parameters (Δm2, θ23), which drive oscillations in the (ν2, ν3) sector, are con-strained by atmospheric and (long-baseline) accelerator neutrino experiments in the νμdisappearance channel. The expected νμ → ντ appearance signal is currently being testedby the OPERA experiment at Gran Sasso [13]. In this sector, significantly more accuratedeterminations of the oscillation parameters are expected in the T2K accelerator experi-ment in Japan, which has just started beam operations (with an Italian participation tothe near detector) [14].In general, better constraints on the ν oscillation parameters are important to dis-criminate among various theoretical models for the ν mass matrix, see [15] and referencestherein. For instance, some approximate numerical relations have been noted, includingthe so-called “tri-bimaximal mixing pattern,” (sin2 θ12, sin2 θ23, sin2 θ13)  (1/3, 1/2, 0),and the “quark-lepton complementarity,” θq12 + θν12  π/4. Do such relations representaccidental facts, or signals of underlying symmetries [15]? More accurate data will helpto probe and disentangle different theoretical options, and possibly suggest new ones.It is worth recalling that, from T2K onward, better or novel determinations of theoscillation parameters may face the problem of “degeneracies” or “clones,” namely, ofmultiple solutions in the oscillation parameter space (δm2, ±Δm2, θij , δ). The strategiesneeded to select the “true” solution (via measurements at different neutrino energies,pathlengths, and oscillation channels) are actively being investigated, in order to optimizethe choice of future neutrino facilities and their synergies [16].The selection of the true hierarchy [sign (Δm2)] via oscillations might be particularlydifficult. In general, one needs to observe an “interference” between oscillation effectsinduced by ±Δm2 and by another quantity Q entering—with a known sign—the Hamil-tonian H of eq. (4). Barring new neutrino states or interactions, there are then onlythree possibilities: i) Q = δm2; ii) Q = matter density; or iii) Q = neutrino density. Thefirst option might be explored, in principle, with very accurate reactor experiments [17],but, in practice, the required sensitivity seems too demanding. The second option mightoccur via peculiar collective effects on observable supernova neutrino spectra [18], pro-vided that a galactic core-collapse event is detected with high statistics in high-resolutionexperiments. The third option seems to be accessible in future accelerator beams travers-ing long paths in the Earth crust (e.g., a T2K upgrade [14] with a far detector in Korea),provided that θ13 is not too small.A measurement of (or better limits on) θ13 is crucial to determine not only the masshierarchy but also future directions in neutrino oscillation physics and in leptonic CPviolation searches. For this reason, there is great interest in improving θ13 constraints.Recently, it has been observed that atmospheric ν data, as well as solar plus long-baselinereactor data, may provide two weak hints in favor of θ13 > 0; their global combinationNEUTRINO PHYSICS 43amounts to a 90% CL preference (1.6σ) for θ13 > 0 [19], as displayed in the central panelof fig. 2. Shortly before this Workshop, another possible hint in favor of θ13 > 0 hasbeen provided (at a roughly similar confidence level) by preliminary νμ → νe appearanceresults in the MINOS accelerator experiment [20]; combining together all such “hints,”we get the following best estimate of sin2 θ13 [21]:sin2 θ13  0.02± 0.01 (All ν data, 2009).(5)If correct, the above 2σ indication in favor of nonzero θ13 may be upgraded to the∼ 3σ level by further results from existing experiments [21]. However, the first decisive,direct measurement (or limit) for θ13 in the above range is expected in next-generationreactor experiments such as Double-CHOOZ [22], which will exploit a near-far detectorcombination to improve the sensitivity down to sin2 θ13  0.01. (It is an unfortunatecircumstance, in my opinion, that the Italian engagement in reactor ν oscillation searchesdid not proceed after the CHOOZ experience [9].)3. – How small is the neutrino mass? (Fermi). Is ν ≡ ν? (Majorana)These two basic—and still unsolved—questions are somewhat entangled. In fact, theonly realistic probe of the spinorial nature of massive neutrinos (either Dirac, ν = ν; orMajorana, ν = ν) is the process of neutrinoless double-beta decay (0νββ), which takesplace only for Majorana neutrinos and is also sensitive to their masses [23].In general, absolute neutrino masses can be probed by three main observables. Thefirst, classical one is the spectral endpoint in β decay, sensitive to the so-called “effectiveelectron neutrino mass” mβ ,mβ =[∑i|Uei|2m2i]1/2=[c213c212m21 + c213s212m22 + s213m23]1/2.(6)The second observable is the effective “Majorana neutrino mass” mββ in 0νββ decay,mββ =∣∣∣∣∣∑iU2eimi∣∣∣∣∣ = ∣∣c213c212m1 + c213s212m2eiφ2 + s213m3eiφ3 ∣∣ ,(7)where φ2,3 are additional unknown parameters (Majorana phases). The third observableis the sum of neutrino masses, which affects the formation of large-scale structures instandard cosmology:Σ = m1 + m2 + m3.(8)At present, there are only safe upper bounds on these absolute mass parameters, at theeV level for mβ , and in the sub-eV range for mββ and Σ, see [10] for a recent review.Various Italian groups are at the forefront of absolute ν mass searches, with impor-tant contributions to: i) construction of highly sensitive 0νββ decay experiments at GranSasso, namely, CUORE [23] and GERDA [24]; ii) leading roles in the recently startedPLANCK satellite mission [25], which will measure cosmic wave background anisotropies44 E. LISIFig. 3. – (Colour on-line) In each panel, representing a projection of the (mβ , mββ , Σ) parameterspace, the slanted bands show the regions allowed by current oscillation data at 2σ in normalhierarchy (blue) and inverted hierarchy (red). The crosses represent hypothetical future dataaccording to eq. (9). See [10] and references therein for a discussion of this kind of plots.and infer cosmological parameters (including Σ) with unprecedented accuracy; and iii) in-tense R&D activity to reach the deep sub-eV range for mβ with calorimetric techniquesin the MARE Project [26].For small neutrino masses, the observables (mβ , mββ , Σ) have, in principle, some sen-sitivity to the hierarchy, which vanishes in the degenerate mass limit (when all the massesare much larger than their splittings). In the next decade, there are good chances to ex-plore the degenerate and (part of) inverted hierarchy cases, while the normal hierarchycase entails the smallest values of (mβ , mββ , Σ) and is, thus, much more challenging.Let us entertain a very optimistic possibility, namely, that the ν masses are degenerateand just below current limits, e.g., m1  m2  m3  0.2 eV. In this hypothetical case,absolute neutrino mass signals would then be “around the corner,” and next-generationexperiments could measure, e.g., (with 1σ fractional errors):mβ  0.2 (1± 0.5) eV, mββ  0.2 (1± 0.3) eV, Σ  0.2 (1± 0.5) eV.(9)These mock nonoscillation data, combined with real oscillation data (see fig. 3) wouldallow: i) a 25% accurate determination of the absolute ν mass scale at 0.2 eV; and ii) firsthints on the Majorana phase φ2 in eq. (7), with a preference for φ2  0 over φ2  π forthis specific dataset. Therefore, at least in principle, next-generation experiments mightprovide important clues about both the absolute mass scale and the Majorana nature ofneutrinos. Needless to say, progress will be harder for smaller ν masses.NEUTRINO PHYSICS 45From the theoretical viewpoint, further work is needed to reduce the 0νββ nuclearmatrix uncertainties at the safe level of < 30% assumed in eq. (9). Concerning Σ, oneshould not forget that it comes from a data fit to the standard cosmological model, whosemain components (dark energy and dark matter) are still of unknown origin; therefore,the robustness of future Σ constraints should be tested in detail upon model variations.4. – Conclusions and prospectsIn the slow process of solving basic questions, ν physics has recently reached impor-tant goals which raised peaks of interest (fig. 1). Future “peaks” may include: furtheroscillation probes (e.g., ντ and νe appearance); measurements of the unknown θ13, δ,sign(Δm2), mβ , mββ , Σ; theoretical understanding of underlying structures. In addi-tion, one should not forget possible surprises (new ν states or interactions) and detectionof new astrophysical ν sources [27, 28]—not discussed herein for brevity. The qualifiedItalian contribution to ν physics will make such progress most interesting.∗ ∗ ∗This work is supported in part by the Italian INFN (Astroparticle Physics FA51initiative) and MIUR (Astroparticle Physics PRIN). EL thanks G. L. Fogli, A. Mar-rone, A. Melchiorri, A. Mirizzi, A. Palazzo, A. M. Rotunno, P. Serra, andI. Tamborra for collaboration on recent neutrino mass-mixing analyses.REFERENCES[1] Fogli G. L., Lisi E., Marrone A. and Palazzo A., Prog. Part. Nucl. Phys., 57 (2006)742 [arXiv:hep-ph/0506083].[2] Camilleri L., Lisi E. and Wilkerson J. F., Annu. Rev. Nucl. Part. Sci., 58 (2008) 343.[3] Strumia A. and Vissani F., arXiv:hep-ph/0606054.[4] Dore U. and Orestano D., Rep. Prog. Phys., 71 (2008) 106201 [arXiv:0811.1194 [hep-ex]].[5] Gonzalez-Garcia M. C. and Maltoni M., Phys. Rep., 460 (2008) 1 [arXiv:0704.1800[hep-ph]].[6] Giunti C. and Kim C. W., Fundamentals of Neutrino Physics and Astrophysics (OxfordUniversity Press, UK) 2007, p. 710.[7] Neutrino Unbound website (maintained by Giunti C. and Laveder M.): www.nu.to.infn.it.[8] Vissani F., these proceedings.[9] Apollonio M. et al. (CHOOZ Collaboration), Eur. Phys. J. C, 27 (2003) 331[arXiv:hep-ex/0301017].[10] Fogli G. L., Lisi E., Marrone A., Melchiorri A., Palazzo A., Serra P., Silk J.,and Slosar A., Phys. Rev. D, 78 (2008) 033010 [arXiv:0805.2517 [hep-ph]].[11] Franco D., these proceedings.[12] LUNA website: npgroup.pd.infn.it/luna.[13] Pastore A., these proceedings.[14] Mezzetto M., these proceedings.[15] Merlo L., these proceedings.[16] Bonesini M., these proceedings.[17] Petcov S. T. and Piai M., Phys. Lett. B, 533 (2002) 94 [arXiv:hep-ph/0112074].[18] Fogli G. L., Lisi E., Marrone A., Mirizzi A. and Tamborra I., Phys. Rev. D, 78(2008) 097301 [arXiv:0808.0807 [hep-ph]].46 E. LISI[19] Fogli G. L., Lisi E., Marrone A., Palazzo A. and Rotunno A. M., Phys. Rev. Lett.,101 (2008) 141801 [arXiv:0806.2649 [hep-ph]].[20] MINOS website: www-numi.fnal.gov.[21] Fogli G. L., Lisi E., Marrone A., Palazzo A. and Rotunno A. M., Neutrinooscillations, global analysis and theta(13), in Proceedings of the 13th InternationalWorkshop on Neutrino Telescopes (Venice, Italy, 2009), edited by Baldo Ceolin M.(University of Padua, Padua, Italy) 2009, p. 81.[22] Double-CHOOZ Website: doublechooz.in2p3.fr.[23] CUORE website: crio.mib.infn.it.[24] GERDA website: gerda.lngs.infn.it[25] PLANCK website: www.asi.it/en/activity/cosmology/planck.[26] MARE, dedicated Workshop website: http://www.ge.infn.it/~numass/.[27] Anghinolfi M., these proceedings.[28] M. Spurio, these proceedings.

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