aa r X i v : . [ h e p - ph ] N ov Sterile Neutrino Status
Carlo Giunti
INFN, Sezione di Torino, Via P. Giuria 1, I–10125 Torino, ItalyE-mail: [email protected]
Abstract.
We review the results of global analyses of short-baseline neutrino oscillation datain 3+1, 3+2 and 3+1+1 neutrino mixing schemes.
Talk presented at NuFact 2013, 15th International Workshop on Neutrino Factories,Super Beams and Beta Beams, 19-24 August 2013, IHEP, Beijing, China.
1. Introduction
Neutrino oscillations have been measured with high accuracy in solar, atmospheric and long-baseline neutrino oscillation experiments (see [1–3]). Hence, we know that neutrinos are massiveand mixed particles (see [4,5]) and there are two independent squared-mass differences: the solar∆ m ≃ . × − eV and the atmospheric ∆ m ≃ . × − eV . This is in agreementwith the standard three-neutrino mixing paradigm, in which the three active neutrinos ν e , ν µ , ν τ are superpositions of three massive neutrinos ν , ν , ν with respective masses m , m , m . The two measured squared-mass differences can be interpreted as ∆ m = ∆ m and∆ m = | ∆ m | ≃ | ∆ m | , with ∆ m kj = m k − m j .The completeness of the three-neutrino mixing paradigm has been challenged by the followingindications in favor of short-baseline neutrino oscillations, which require the existence of at leastone additional squared-mass difference, ∆ m , which is much larger than ∆ m and ∆ m :1. The LSND experiment, in which a signal of short-baseline ¯ ν µ → ¯ ν e oscillations has beenobserved with a statistical significance of about 3 . σ [6, 7].2. The reactor antineutrino anomaly [8], which is a deficit of the rate of ¯ ν e observed in severalshort-baseline reactor neutrino experiments in comparison with that expected from a newcalculation of the reactor neutrino fluxes [9, 10]. The statistical significance is about 2 . σ .3. The Gallium neutrino anomaly [11–15], consisting in a short-baseline disappearance of ν e measured in the Gallium radioactive source experiments GALLEX [16] and SAGE [17] witha statistical significance of about 2 . σ .In this review, we consider 3+1 [18–21], 3+2 [22–25] and 3+1+1 [26–29] neutrino mixingschemes in which there are one or two additional massive neutrinos at the eV scale and the massesof the three standard massive neutrinos are much smaller. Since from the LEP measurement ofthe invisible width of the Z boson we know that there are only three active neutrinos (see [4]),in the flavor basis the additional massive neutrinos correspond to sterile neutrinos [30], whichdo not have standard weak interactions.The possible existence of sterile neutrinos is very interesting, because they are new particleswhich could give us precious information on the physics beyond the Standard Model (see [31,32]).he existence of light sterile neutrinos is also very important for astrophysics (see [33]) andcosmology (see [34, 35]).In the 3+1 scheme, the effective probability of ( − ) ν α → ( − ) ν β transitions in short-baselineexperiments has the two-neutrino-like form P ( − ) ν α → ( − ) ν β = δ αβ − | U α | (cid:0) δ αβ − | U β | (cid:1) sin (cid:18) ∆ m L E (cid:19) , (1)where U is the mixing matrix, L is the source-detector distance, E is the neutrino energyand ∆ m = m − m = ∆ m ∼ . The electron and muon neutrino andantineutrino appearance and disappearance in short-baseline experiments depend on | U e | and | U µ | , which determine the amplitude sin ϑ eµ = 4 | U e | | U µ | of ( − ) ν µ → ( − ) ν e transitions, theamplitude sin ϑ ee = 4 | U e | (cid:0) − | U e | (cid:1) of ( − ) ν e disappearance, and the amplitude sin ϑ µµ =4 | U µ | (cid:0) − | U µ | (cid:1) of ( − ) ν µ disappearance.Since the oscillation probabilities of neutrinos and antineutrinos are related by a complexconjugation of the elements of the mixing matrix (see [4]), the effective probabilities of short-baseline ν µ → ν e and ¯ ν µ → ¯ ν e transitions are equal. Hence, the 3+1 scheme cannot explaina possible CP-violating difference of ν µ → ν e and ¯ ν µ → ¯ ν e transitions in short-baselineexperiments. In order to allow this possibility, one must consider a 3+2 scheme, in which, thereare four additional effective mixing parameters in short-baseline experiments: ∆ m , which isconventionally assumed ≥ ∆ m , | U e | , | U µ | and η = arg (cid:2) U ∗ e U µ U e U ∗ µ (cid:3) . Since this complexphase appears with different signs in the effective 3+2 probabilities of short-baseline ν µ → ν e and ¯ ν µ → ¯ ν e transitions, it can generate measurable CP violations.A puzzling feature of the 3+2 scheme is that it needs the existence of two sterile neutrinoswith masses at the eV scale. We think that it may be considered as more plausible that sterileneutrinos have a hierarchy of masses. Hence, it is interesting to consider also the 3+1+1scheme [26–29], in which m is much heavier than 1 eV and the oscillations due to ∆ m are averaged. Hence, in the analysis of short-baseline data in the 3+1+1 scheme there is oneeffective parameter less than in the 3+2 scheme (∆ m ), but CP violations generated by η areobservable.
2. Global Fits
Global fits of short-baseline neutrino oscillation data have been presented recently in Refs. [36,37]. These analyses take into account the final results of the MiniBooNE experiment, whichwas 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 neutrinooscillations depend. Unfortunately, the results of the MiniBooNE experiment are ambiguous,because the LSND signal was not seen in neutrino mode [38] and the signal observed in 2010 [39]with the first half of the antineutrino data was not observed in the second half of the data [40].Moreover, the MiniBooNE data in both neutrino and antineutrino modes show an excess in thelow-energy bins which is widely considered to be anomalous because it is at odds with neutrinooscillations [41, 42] .In the following we summarize the results of the analysis of short-baseline data presented inRef. [37] of the following three groups of experiments:(A) The ( − ) ν µ → ( − ) ν e appearance data of the LSND [7], MiniBooNE [40], BNL-E776 [45], KARMEN[46], NOMAD [47], ICARUS [48] and OPERA [49] experiments. The interesting possibility of reconciling the low–energy anomalous data with neutrino oscillations throughenergy reconstruction effects proposed in Refs. [43, 44] still needs a detailed study. +1 3+1 3+1 3+1 3+2 3+2 3+1+1 3+1+1LOW HIG noMB noLSND LOW HIG LOW HIG χ χ ) APP χ ) DIS χ PG PG χ . . . . . . . . NO nσ NO . σ . σ . σ . σ . σ . σ . σ . σ Table 1.
Results of the fit of short-baseline data [37] 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 χ ( χ ), the number ofdegrees of freedom (NDF) and the goodness-of-fit (GoF). The following five lines give the quantities relevant for theappearance-disappearance (APP-DIS) parameter goodness-of-fit (PG) [57]. The last three lines give the differencebetween the χ without short-baseline oscillations and χ (∆ χ ), the corresponding difference of number ofdegrees of freedom (NDF NO ) and the resulting number of σ ’s ( nσ NO ) for which the absence of oscillations isdisfavored. (B) The ( − ) ν e disappearance data described in Ref. [15], which take into account the reactor [8–10]and Gallium [11–14, 50] anomalies.(C) The constraints on ( − ) ν µ disappearance obtained from the data of the CDHSW experiment [51],from the analysis [24] of the data of atmospheric neutrino oscillation experiments , fromthe analysis [41] of the MINOS neutral-current data [54] and from the analysis of theSciBooNE-MiniBooNE neutrino [55] and antineutrino [56] data.Table 1 summarizes the statistical results obtained in Ref. [37] from global fits of the dataabove in the 3+1, 3+2 and 3+1+1 schemes. In the LOW fits all the MiniBooNE data areconsidered, including the anomalous low-energy bins, which are omitted in the HIG fits. Thereis also a 3+1-noMB fit without MiniBooNE data and a 3+1-noLSND fit without LSND data.From Tab. 1, one can see that in all fits which include the LSND data the absence of short-baseline oscillations is disfavored by about 6 σ , because the improvement of the χ with short-baseline 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 issignificantly worse than that in the HIG analysis and the appearance-disappearance parametergoodness-of-fit is much worse. This result confirms the fact that the MiniBooNE low-energyanomaly is incompatible with neutrino oscillations, because it would require a small value of∆ m and a large value of sin ϑ eµ [41,42], which are excluded by the data of other experiments(see Ref. [37] for further details) . Note that the appearance-disappearance tension in the 3+2-LOW fit is even worse than that in the 3+1-LOW fit, since the ∆ χ is so much larger that itcannot be compensated by the additional degrees of freedom (this behavior has been explained The IceCube data, which could give a marginal contribution [52, 53], have not been considered because theanalysis is too complicated and subject to large uncertainties. One could fit the three anomalous MiniBooNE low-energy bins in a 3+2 scheme [58] by considering theappearance data without the ICARUS [48] and OPERA [49] constraints, but the corresponding relatively largetransition probabilities are excluded by the disappearance data. in J e m D m [ e V ] - - - - - + - - - - - + sn e DIS n m DISDISAPP sin J ee D m [ e V ] - - - + n e DIS sin J mm - + n m DIS
Figure 1.
Allowed regions in the sin ϑ eµ –∆ m , sin ϑ ee –∆ m and sin ϑ µµ –∆ m planes obtainedin the global (GLO) 3+1-HIG fit [37] of short-baseline neutrino oscillation data compared with the 3 σ allowedregions obtained from ( − ) ν µ → ( − ) ν e short-baseline appearance data (APP) and the 3 σ constraints obtained from ( − ) ν e short-baseline disappearance data ( ν e DIS), ( − ) ν µ short-baseline disappearance data ( ν µ DIS) and the combinedshort-baseline disappearance data (DIS). The best-fit points of the GLO and APP fits are indicated by crosses. in Ref. [59]). Therefore, we think that it is very likely that the MiniBooNE low-energy anomalyhas an explanation which is different from neutrino oscillations and the HIG fits are more reliablethan the LOW fits.The 3+2 mixing scheme, was considered to be interesting in 2010 when the MiniBooNEneutrino [38] and antineutrino [39] data showed a CP-violating tension. Unfortunately, thistension reduced considerably in the final MiniBooNE data [40] and from Tab. 1 one can seethat there is little improvement of the 3+2-HIG fit with respect to the 3+1-HIG fit, in spite ofthe four additional parameters and the additional possibility of CP violation. Moreover, sincethe p-value obtained by restricting the 3+2 scheme to 3+1 disfavors the 3+1 scheme only at1 . σ [37], we think that considering the larger complexity of the 3+2 scheme is not justified bythe data .The results of the 3+1+1-HIG fit presented in Tab. 1 show that the appearance-disappearanceparameter goodness-of-fit is remarkably good, with a ∆ χ that is smaller than those in the3+1-HIG and 3+2-HIG fits. However, the χ in the 3+1+1-HIG is only slightly smaller thanthat in the 3+1-HIG fit and the p-value obtained by restricting the 3+1+1 scheme to 3+1disfavors the 3+1 scheme only at 0 . σ [37]. Therefore, there is no compelling reason to preferthe more complex 3+1+1 to the simpler 3+1 scheme.Figure 1 shows the allowed regions in the sin ϑ eµ –∆ m , sin ϑ ee –∆ m and sin ϑ µµ –∆ m planes obtained in the 3+1-HIG fit of Ref. [37]. These regions are relevant, respectively,for ( − ) ν µ → ( − ) ν e appearance, ( − ) ν e disappearance and ( − ) ν µ disappearance searches. The correspondingmarginal allowed intervals of the oscillation parameters are given in Tab. 2. Figure 1 showsalso the region allowed by ( − ) ν µ → ( − ) ν e appearance data and the constraints from ( − ) ν e disappearanceand ( − ) ν µ disappearance data. One can see that the combined disappearance constraint in the See however the somewhat different conclusions reached in Ref. [36].
L ∆ m [eV ] sin ϑ eµ sin ϑ ee sin ϑ µµ . − .
72 0 . − . . − .
15 0 . − . . − .
91 0 . − . . − .
17 0 . − . . − .
97 0 . − . . − .
18 0 . − . . − .
97 0 . − . . − .
18 0 . − . . − .
09 0 . − .
003 0 . − . . − . . − .
19 0 . − . . − .
22 0 . − . Table 2.
Marginal allowed intervals of the oscillation parameters obtained in the global 3+1-HIG fit ofshort-baseline neutrino oscillation data [37]. sin ϑ eµ –∆ m plane excludes a large part of the region allowed by ( − ) ν µ → ( − ) ν e appearance data,leading to the well-known appearance-disappearance tension [36, 41, 42, 58–62] quantified by theparameter goodness-of-fit in Tab. 1.It is interesting to investigate what is the impact of the MiniBooNE experiment on the globalanalysis of short-baseline neutrino oscillation data. With this aim, the authors of Ref. [37]performed two additional 3+1 fits: a 3+1-noMB fit without MiniBooNE data and a 3+1-noLSND fit without LSND data. From Tab. 1 one can see that the results of the 3+1-noMB fitare similar to those of the 3+1-HIG fit and the exclusion of the case of no-oscillations remains atthe level of 6 σ . On the other hand, in the 3+1-noLSND fit, without LSND data, the exclusionof the case of no-oscillations drops dramatically to 2 . σ . In fact, in this case the main indicationin favor of short-baseline oscillations is given by the reactor and Gallium anomalies which have asimilar statistical significance (see Section 1). Therefore, it is clear that the LSND experiment isstill crucial for the indication in favor of short-baseline ¯ ν µ → ¯ ν e transitions and the MiniBooNEexperiment has been rather inconclusive.
3. Conclusions
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