Phenomenology of light sterile neutrinos

Home Search Collections Journals About Contact us My IOPscience Phenomenology of Light Sterile Neutrinos This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Conf. Ser. 631 012052 (http://iopscience.iop.org/1742-6596/631/1/012052) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 147.162.110.100 This content was downloaded on 03/08/2015 at 13:04 Please note that terms and conditions apply. 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014) IOP Publishing Journal of Physics: Conference Series 631 (2015) 012052 doi:10.1088/1742-6596/631/1/012052 Phenomenology of Light Sterile Neutrinos Marco Laveder Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, and INFN, Sezione di Padova, Via F. Marzolo 8, I–35131 Padova, Italy E-mail: laveder@pd.infn.it Carlo Giunti INFN, Sezione di Torino, Via P. Giuria 1, I–10125 Torino, Italy E-mail: giunti@to.infn.it Abstract. After a short review of the current status of standard three-neutrino mixing, we consider its extension with the addition of one or two light sterile neutrinos which can explain the anomalies found in short-baseline neutrino oscillation experiments. We review the results of the global analyses of short-baseline neutrino oscillation data in 3+1, 3+2 and 3+1+1 neutrino mixing schemes. 1. Introduction Neutrino oscillations have been measured with high accuracy in solar, atmospheric and longbaseline neutrino oscillation experiments. Hence, we know without doubt that neutrinos are massive and mixed particles (see Ref. [1]) and that the Standard Model must be extended in order to take into account these neutrino properties. In this short review we present the status of standard three-neutrino mixing in Section 2 and we discuss the indications in favor of the existence of additional sterile neutrinos given by anomalies found in short-baseline neutrino oscillation experiments in Section 3. 2. Three-Neutrino Mixing Solar neutrino experiments (Homestake [2], GALLEX/GNO [3], SAGE [4], Super-Kamiokande [5], SNO [6], Borexino [7]) measured νe → νµ , ντ oscillations generated by the solar squaredmass difference ∆m2SOL ≃ 7 × 10−5 eV2 and a mixing angle sin2 ϑSOL ≃ 0.3. The KamLAND experiment [8] confirmed these oscillations by observing the disappearance of reactor ν̄e with average energy hEi ≃ 4 MeV at the average distance hLi ≃ 180 km. Atmospheric neutrino experiments (Kamiokande [9], IMB [10], Super-Kamiokande [11], Soudan-2 [12], MACRO [13], MINOS [14]) measured νµ and ν̄µ disappearance through oscillations generated by the atmospheric squared-mass difference ∆m2ATM ≃ 2.3 × 10−3 eV2 and a mixing angle sin2 ϑATM ≃ 0.5. The K2K [15] and MINOS [16] long-baseline experiments confirmed these oscillations by observing the disappearance of accelerator νµ with hEi ≃ 1.3 GeV and 3 GeV at distances L ≃ 250 km and 730 km, respectively. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014) IOP Publishing Journal of Physics: Conference Series 631 (2015) 012052 doi:10.1088/1742-6596/631/1/012052 (−) The Super-Kamiokande atmospheric neutrino data indicate that the disappearance of νµ is (−) (−) likely due to νµ → ντ transitions with a statistical significance of 3.8σ [17]. This oscillation channel is confirmed at 4.2σ by the observation of four νµ → ντ events in the OPERA longbaseline accelerator experiment [18] in which the detector was exposed to the CNGS (CERN– Gran Sasso) beam with hEi ≃ 13 GeV at L ≃ 730 km. The two independent solar and atmospheric ∆m2 ’s are nicely accommodated in the standard framework of three-neutrino mixing in which the left-handed components of the three active flavor neutrino fields νe , νµ , ντ are superpositions of three massive neutrino fields ν1 , ν2 , ν3 with masses m1 , m2 , m3 : 3 X ναL = Uαk νkL (α = e, µ, τ ) . (1) k=1 The unitary mixing matrix can be written in the standard parameterization in terms of three mixing angles ϑ12 , ϑ23 , ϑ13 and a CP-violating phase1 δ:   c12 c13 s12 c13 s13 e−iδ U = −s12 c23 − c12 s23 s13 eiδ c12 c23 − s12 s23 s13 eiδ s23 c13  , (2) iδ iδ s12 s23 − c12 c23 s13 e −c12 s23 − s12 c23 s13 e c23 c13 where cab ≡ cos ϑab and sab ≡ sin ϑab . It is convenient to choose the numbering of the massive neutrinos in order to have ∆m2SOL = ∆m221 ≪ ∆m2ATM = 1 ∆m231 + ∆m232 , 2 (3) with ∆m2kj = m2k − m2j . Then, there are two possible orderings for the neutrino masses: the normal ordering (NO) with m1 < m2 < m3 and the inverted ordering (IO) with m3 < m1 < m2 . With the conventions in Eqs. (2) and (3), we have ϑSOL = ϑ12 and ϑATM = ϑ23 . Moreover, (−) (−) (−) the mixing angle ϑ13 generates νe disappearance and νµ → νe transitions driven by ∆m2ATM , which can be observed in long-baseline neutrino oscillation experiments. In 2011 the T2K experiment reported the first indication of long-baseline νµ → νe transitions [19], followed by the MINOS experiment [20]. More recently, the T2K Collaboration reported a convincing 7.5σ observation of νµ → νe transitions through the measurement of 28 νe events with an expected background of 4.92 ± 0.55 events [21]. The most precise measurement of the value of ϑ13 comes from the measurement of ν̄e disappearance in the Daya Bay reactor experiment [22], which has been confirmed by the data of the RENO [23] and Double Chooz [24] reactor experiments: sin2 2ϑ13 = 0.090+0.008 −0.009 [25] . (4) Hence, we have a robust evidence of a nonzero value of ϑ13 . This is very important, because the measured value of ϑ13 opens promising perspectives for the observation of CP violation in the lepton sector and matter effects in long-baseline oscillation experiments, which could allow to distinguish the normal and inverted neutrino mass orderings (see Ref. [26]). The three-neutrino mixing parameters have been determined with good precision with global fits of the neutrino oscillation data. In Tab. 1 we report the results of the global fit presented in Ref. [27], which agree, within the uncertainties, with the NuFIT-v1.2 [28] update of the global analysis presented in Ref. [29]. One can see that all the oscillation parameters are determined 1 For simplicity, we do not consider the two Majorana CP-violating phases which contribute to neutrino mixing if massive neutrinos are Majorana particles, because they do not affect neutrino oscillations (see Ref. [1]). 2 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014) IOP Publishing Journal of Physics: Conference Series 631 (2015) 012052 doi:10.1088/1742-6596/631/1/012052 parameter mass order ∆m2S /10−5 eV2 sin2 ϑ12 /10−1 ∆m2A /10−3 eV2 sin2 ϑ23 /10−1 sin2 ϑ13 /10−2 NO IO NO IO NO IO best fit 7.54 3.08 2.43 2.38 4.37 4.55 2.34 2.40 1σ range 7.32 2.91 2.37 2.32 4.14 4.24 2.15 2.18 – – – – – – – – 7.80 3.25 2.49 2.44 4.70 5.94 2.54 2.59 2σ range 7.15 2.75 2.30 2.25 3.93 4.00 1.95 1.98 – – – – – – – – 8.00 3.42 2.55 2.50 5.52 6.20 2.74 2.79 3σ range 6.99 2.59 2.23 2.19 3.74 3.80 1.76 1.78 – – – – – – – – 8.18 3.59 2.61 2.56 6.26 6.41 2.95 2.98 relative uncertainty 3% 5% 3% 3% 10% 10% 8% 8% Table 1. Best fit values of the neutrino mixing parameters obtained in the global analysis of neutrino oscillation data presented in Ref. [27] in the framework of three-neutrino mixing with normal ordering (NO) and inverted ordering (IO). The relative uncertainty has been obtained from the 3σ range divided by 6. with precisions between about 3% and 10%. The largest uncertainty is that of ϑ23 , which is known to be close to maximal (π/4), but it is not known if it is smaller or larger than π/4. For the Dirac CP-violating phase δ, there is an indication in favor of δ ≈ 3π/2, which would give maximal CP violation, but at 3σ all the values of δ are allowed, including the CP-conserving values δ = 0, π. 3. Beyond Three-Neutrino Mixing: Sterile Neutrinos The completeness of the three-neutrino mixing paradigm has been challenged by the following indications in favor of short-baseline neutrino oscillations, which require the existence of at least one additional squared-mass difference, ∆m2SBL , which is much larger than ∆m2SOL and ∆m2ATM : 1. The reactor antineutrino anomaly [30], which is a deficit of the rate of ν̄e observed in several short-baseline reactor neutrino experiments in comparison with that expected from a new calculation of the reactor neutrino fluxes [31, 32]. The statistical significance is about 2.8σ. 2. The Gallium neutrino anomaly [33–37], consisting in a short-baseline disappearance of νe measured in the Gallium radioactive source experiments GALLEX [38] and SAGE [39] with a statistical significance of about 2.9σ. 3. The LSND experiment, in which a signal of short-baseline ν̄µ → ν̄e oscillations has been observed with a statistical significance of about 3.8σ [40, 41]. In this review, we consider 3+1 [42–45], 3+2 [46–49] and 3+1+1 [50–53] neutrino mixing schemes in which there are one or two additional massive neutrinos at the eV scale and the masses of the three standard massive neutrinos are much smaller. Since from the LEP measurement of the invisible width of the Z boson we know that there are only three active neutrinos (see Ref. [1]), in the flavor basis the additional massive neutrinos correspond to sterile neutrinos [54], which do not have standard weak interactions. The possible existence of sterile neutrinos is very interesting, because they are new particles which could give us precious information on the physics beyond the Standard Model (see Ref. [55, 56]). The existence of light sterile neutrinos is also very important for astrophysics (see Ref. [57]) and cosmology (see Ref. [58–61]). 3 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014) IOP Publishing Journal of Physics: Conference Series 631 (2015) 012052 doi:10.1088/1742-6596/631/1/012052 (−) (−) In the 3+1 scheme, the effective probability of να → νβ transitions in short-baseline experiments has the two-neutrino-like form [43] P(−) (−) να → νβ  
∆m241 L = δαβ − 4|Uα4 |2 δαβ − |Uβ4 |2 sin2 , 4E (5) where U is the mixing matrix, L is the source-detector distance, E is the neutrino energy and ∆m241 = m24 − m21 = ∆m2SBL ∼ 1 eV2 . The electron and muon neutrino and antineutrino appearance and disappearance in short-baseline experiments depend on |Ue4 |2 and (−) (−) |Uµ4 |2 , which determine the amplitude sin2 2ϑeµ = 4|Ue4 |2 |Uµ4 |2 of νµ → νe transitions, the
(−) amplitude sin2 2ϑee = 4|Ue4 |2 1 − |Ue4 |2 of νe disappearance, and the amplitude sin2 2ϑµµ =
(−) 4|Uµ4 |2 1 − |Uµ4 |2 of νµ disappearance. Since the oscillation probabilities of neutrinos and antineutrinos are related by a complex conjugation of the elements of the mixing matrix (see Ref. [1]), the effective probabilities of short-baseline νµ → νe and ν̄µ → ν̄e transitions are equal. Hence, the 3+1 scheme cannot explain a possible CP-violating difference of νµ → νe and ν̄µ → ν̄e transitions in short-baseline experiments. In order to allow this possibility, one must consider a 3+2 scheme, in which, there are four additional effective mixing parameters in short-baseline experiments: ∆m251 ≥ ∆m241 ,   ∗ U U U∗ |Ue5 |2 , |Uµ5 |2 and η = arg Ue4 µ4 e5 µ5 (see Refs. [62, 63]). Since this complex phase appears with different signs in the effective 3+2 probabilities of short-baseline νµ → νe and ν̄µ → ν̄e transitions, it can generate measurable CP violations. A puzzling feature of the 3+2 scheme is that it needs the existence of two sterile neutrinos with masses at the eV scale. We think that it may be considered as more plausible that sterile neutrinos have a hierarchy of masses. Hence, it is interesting to consider also the 3+1+1 scheme [50–53], in which m5 is much heavier than 1 eV and the oscillations due to ∆m251 are averaged. Hence, in the analysis of short-baseline data in the 3+1+1 scheme there is one effective parameter less than in the 3+2 scheme (∆m251 ), but CP violations generated by η are observable. Updated global fits of short-baseline neutrino oscillation data have been presented in Refs. [64, 65]. These analyses take into account the final results of the MiniBooNE experiment, which was made in order to check the LSND signal with about one order of magnitude larger distance (L) and energy (E), but the same order of magnitude for the ratio L/E from which neutrino oscillations depend. Unfortunately, the results of the MiniBooNE experiment are ambiguous, because the LSND signal was not seen in neutrino mode (νµ → νe ) [66] and the ν̄µ → ν̄e signal observed in 2010 [67] with the first half of the antineutrino data was not observed in the second half of the antineutrino data [68]. Moreover, the MiniBooNE data in both neutrino and antineutrino modes show an excess in the low-energy bins which is widely considered to be anomalous because it is at odds with neutrino oscillations [69, 70]2 . In the following we summarize the results of the analysis of short-baseline data presented in Ref. [65] of the following three groups of experiments: (−) (−) (A) The νµ → νe appearance data of the LSND [41], MiniBooNE [68], BNL-E776 [73], KARMEN [74], NOMAD [75], ICARUS [76] and OPERA [77] experiments. (−) (B) The νe disappearance data described in Ref. [37], which take into account the reactor [30–32] and Gallium [33–36, 78] anomalies. 2 The interesting possibility of reconciling the low–energy anomalous data with neutrino oscillations through energy reconstruction effects proposed in Ref. [71, 72] still needs a detailed study. 4 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014) IOP Publishing Journal of Physics: Conference Series 631 (2015) 012052 doi:10.1088/1742-6596/631/1/012052 χ2min NDF GoF 2 (χmin )APP (χ2min )DIS ∆χ2PG NDFPG GoFPG ∆χ2NO NDFNO nσNO 3+1 LOW 291.7 256 6% 99.3 180.1 12.7 2 0.2% 47.5 3 6.3σ 3+1 HIG 261.8 250 29% 77.0 180.1 4.8 2 9% 46.2 3 6.2σ 3+1 noMB 236.1 218 19% 50.9 180.1 5.1 2 8% 47.1 3 6.3σ 3+1 noLSND 278.4 252 12% 91.8 180.1 6.4 2 4% 8.3 3 2.1σ 3+2 LOW 284.4 252 8% 87.7 179.1 17.7 4 0.1% 54.8 7 6.0σ 3+2 HIG 256.4 246 31% 69.8 179.1 7.5 4 11% 51.6 7 5.8σ 3+1+1 LOW 289.8 253 6% 94.8 180.1 14.9 3 0.2% 49.4 6 5.8σ 3+1+1 HIG 259.0 247 29% 75.5 180.1 3.4 3 34% 49.1 6 5.8σ Table 2. Results of the fit of short-baseline data [65] taking into account all MiniBooNE data (LOW), only the MiniBooNE data above 475 MeV (HIG), without MiniBooNE data (noMB) and without LSND data (noLSND) in the 3+1, 3+2 and 3+1+1 schemes. The first three lines give the minimum χ2 (χ2min ), the number of degrees of freedom (NDF) and the goodness-of-fit (GoF). The following five lines give the quantities relevant for the appearance-disappearance (APP-DIS) parameter goodness-of-fit (PG) [85]. The last three lines give the difference between the χ2 without short-baseline oscillations and χ2min (∆χ2NO ), the corresponding difference of number of degrees of freedom (NDFNO ) and the resulting number of σ’s (nσNO ) for which the absence of oscillations is disfavored. (−) (C) The constraints on νµ disappearance obtained from the data of the CDHSW experiment [79], from the analysis [48] of the data of atmospheric neutrino oscillation experiments3 , from the analysis [69] of the MINOS neutral-current data [82] and from the analysis of the SciBooNE-MiniBooNE neutrino [83] and antineutrino [84] data. Table 2 summarizes the statistical results obtained in Ref. [65] from global fits of the data above in the 3+1, 3+2 and 3+1+1 schemes. In the LOW fits all the MiniBooNE data are considered, including the anomalous low-energy bins, which are omitted in the HIG fits. There is also a 3+1-noMB fit without MiniBooNE data and a 3+1-noLSND fit without LSND data. From Tab. 2, one can see that in all fits which include the LSND data the absence of shortbaseline oscillations is disfavored by about 6σ, because the improvement of the χ2 with shortbaseline oscillations is much larger than the number of oscillation parameters. In all the 3+1, 3+2 and 3+1+1 schemes the goodness-of-fit in the LOW analysis is significantly worse than that in the HIG analysis and the appearance-disappearance parameter goodness-of-fit is much worse. This result confirms the fact that the MiniBooNE low-energy anomaly is incompatible with neutrino oscillations, because it would require a small value of ∆m241 and a large value of sin2 2ϑeµ [69,70], which are excluded by the data of other experiments (see Ref. [65] for further details)4 . Note that the appearance-disappearance tension in the 3+2LOW fit is even worse than that in the 3+1-LOW fit, since the ∆χ2PG is so much larger that it cannot be compensated by the additional degrees of freedom (this behavior has been explained in Ref. [86]). Therefore, we think that it is very likely that the MiniBooNE low-energy anomaly has an explanation which is different from neutrino oscillations and the HIG fits are more reliable than the LOW fits. 3 The IceCube data, which could give a marginal contribution [80, 81], have not been considered because the analysis is too complicated and subject to large uncertainties. 4 One could fit the three anomalous MiniBooNE low-energy bins in a 3+2 scheme [63] by considering the appearance data without the ICARUS [76] and OPERA [77] constraints, but the required large transition probability is excluded by the disappearance data. 5 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014) IOP Publishing Journal of Physics: Conference Series 631 (2015) 012052 doi:10.1088/1742-6596/631/1/012052 10 10 3+1 − GLO 3+1 − GLO 68.27% CL 90.00% CL 95.45% CL 99.00% CL 99.73% CL 68.27% CL 90.00% CL 95.45% CL 99.00% CL 99.73% CL 10−1 10−3 10−2 10−1 + 1 νµ DIS νe DIS 3+1 − 3σ νe DIS νµ DIS DIS APP 10−4 + [eV2] + 1 2 ∆m 41 2 ∆m 41 [eV2] + 10−1 1 10−2 2 10−1 10−1 1 si n 2ϑeµ 1 si n 22ϑµµ 2 si n 2ϑee Figure 1. Allowed regions in the sin2 2ϑeµ –∆m241 , sin2 2ϑee –∆m241 and sin2 2ϑµµ –∆m241 planes obtained in the global (GLO) 3+1-HIG fit [65] of short-baseline neutrino oscillation data compared with the 3σ allowed (−) (−) (−) regions obtained from νµ → νe short-baseline appearance data (APP) and the 3σ constraints obtained from νe (−) short-baseline disappearance data (νe DIS), νµ short-baseline disappearance data (νµ DIS) and the combined short-baseline disappearance data (DIS). The best-fit points of the GLO and APP fits are indicated by crosses. The 3+2 mixing scheme was considered to be interesting in 2010 when the MiniBooNE neutrino [66] and antineutrino [67] data showed a CP-violating tension, but this tension almost disappeared in the final MiniBooNE data [68]. In fact, from Tab. 2 one can see that there is little improvement of the 3+2-HIG fit with respect to the 3+1-HIG fit, in spite of the four additional parameters and the additional possibility of CP violation. Moreover, since the p-value obtained by restricting the 3+2 scheme to 3+1 disfavors the 3+1 scheme only at 1.2σ [65], we think that considering the larger complexity of the 3+2 scheme is not justified by the data5 . The results of the 3+1+1-HIG fit presented in Tab. 2 show that the appearance-disappearance parameter goodness-of-fit is remarkably good, with a ∆χ2PG that is smaller than those in the 3+1-HIG and 3+2-HIG fits. However, the χ2min in the 3+1+1-HIG is only slightly smaller than that in the 3+1-HIG fit and the p-value obtained by restricting the 3+1+1 scheme to 3+1 disfavors the 3+1 scheme only at 0.8σ [65]. Therefore, there is no compelling reason to prefer the more complex 3+1+1 to the simpler 3+1 scheme. Figure 1 shows the allowed regions in the sin2 2ϑeµ –∆m241 , sin2 2ϑee –∆m241 and sin2 2ϑµµ – ∆m241 planes obtained in the 3+1-HIG fit of Ref. [65]. These regions are relevant, respectively, (−) (−) (−) (−) for νµ → νe appearance, νe disappearance and νµ disappearance searches. The corresponding marginal allowed intervals of the oscillation parameters are given in Tab. 3. Figure 1 shows (−) (−) (−) also the region allowed by νµ → νe appearance data and the constraints from νe disappearance (−) and νµ disappearance data. One can see that the combined disappearance constraint in the (−) (−) sin2 2ϑeµ –∆m241 plane excludes a large part of the region allowed by νµ → νe appearance data, leading to the well-known appearance-disappearance tension [63, 64, 69, 70, 86–89] quantified by the parameter goodness-of-fit in Tab. 2. 5 See however the somewhat different conclusions reached in Ref. [64]. 6 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014) IOP Publishing Journal of Physics: Conference Series 631 (2015) 012052 doi:10.1088/1742-6596/631/1/012052 CL 68.27% 90.00% 95.00% 95.45% 99.00% 99.73% ∆m241 [eV2 ] 1.55 − 1.72 1.19 − 1.91 1.15 − 1.97 1.14 − 1.97 0.87 − 2.09 0.82 − 2.19 sin2 2ϑeµ 0.0012 − 0.0018 0.001 − 0.0022 0.00093 − 0.0023 0.00091 − 0.0024 0.00078 − 0.003 0.00066 − 0.0034 sin2 2ϑee 0.089 − 0.15 0.072 − 0.17 0.066 − 0.18 0.065 − 0.18 0.054 − 0.2 0.047 − 0.22 sin2 2ϑµµ 0.036 − 0.065 0.03 − 0.085 0.028 − 0.095 0.027 − 0.095 0.022 − 0.12 0.019 − 0.14 Table 3. Marginal allowed intervals of the oscillation parameters obtained in the global 3+1-HIG fit of shortbaseline neutrino oscillation data [65]. It is interesting to investigate what is the impact of the MiniBooNE experiment on the global analysis of short-baseline neutrino oscillation data. With this aim, the authors of Ref. [65] performed two additional 3+1 fits: a 3+1-noMB fit without MiniBooNE data and a 3+1noLSND fit without LSND data. From Tab. 2 one can see that the results of the 3+1-noMB fit are similar to those of the 3+1-HIG fit and the exclusion of the case of no-oscillations remains at the level of 6σ. On the other hand, in the 3+1-noLSND fit, without LSND data, the exclusion of the case of no-oscillations drops dramatically to 2.1σ. In fact, in this case the main indication in favor of short-baseline oscillations is given by the reactor and Gallium anomalies which have a similar statistical significance [37]. Therefore, it is clear that the LSND experiment is still crucial for the indication in favor of short-baseline ν̄µ → ν̄e transitions and the MiniBooNE experiment has been rather inconclusive. In conclusion, the results of the global fit of short-baseline neutrino oscillation data presented in Ref. 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