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University of Wisconsin - Madison

arXiv:hep-ph/9207257v1 20 Jul 1992University of Wisconsin - MadisonMAD/PH/708ISJ-4700July 1991LONG-WAVELENGTH OSCILLATIONS ANDTHE GALLEX SOLAR NEUTRINO SIGNALV. Barger1, R. J. N. Phillips2 and K. Whisnant31Physics Department, University of Wisconsin, Madison, WI 53706, USA2Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, England3Physics Department and Ames Laboratory, Iowa State University, Ames, IA 50011, USAABSTRACTThe recently reported solar neutrino signal in the 71Ga GALLEX detec-tor adds a new dimension to the solar neutrino puzzle, complementing thepreviously known signals in 37Cl and water-Cherenkov detectors.

Possible ex-planations for this new signal in terms of matter-enhanced neutrino oscillations(MSW effect) are already awaiting in the literature. We point out here thatlong-wavelength vacuum oscillations can furnish an alternative explanation ofall three signals simultaneously; such solutions give neutrino spectra with dis-tinctive energy dependence and seasonal time dependence.

The recent observation of a solar neutrino signal in the 71Ga detector of the GALLEX group [1]has added an important new constraint in the solar neutrino puzzle. Going beyond early upperlimits and recent more positive indications from the SAGE group [2], that uses a different techniquebased on metallic gallium, GALLEX reports a definite signal of 83 ± 19 ± 5 SNU to be comparedwith predictions of about 132 SNU in the standard solar model (SSM) [3,4] with conventionalneutrino propagation.

This indicates a suppression ratioRGa = (observed Ga rate)/(SSM Ga rate) = 0.63 ± 0.16(1)relative to the latest Bahcall-Pinsonneault calculation [4], that differs from the corresponding sup-pression ratiosRCl = 0.26 ± 0.05 ,RKam II = 0.47 ± 0.09 ,(2)in the classic 37Cl Homestake detector [5] and in the water Cherenkov (ν-e scattering) Kamiokande IIdetector [6], that have higher neutrino energy thresholds. Both experimental and theoretical errorsare included here.

The new solar neutrino puzzle is to explain these three different observationssimultaneously.A first discussion, presented by the GALLEX group itself [7] and amplified by others [8,9],argues that an explanation in terms of non-standard solar models is still at least conceivable,although not particularly promising. They also show that explanations in terms of matter-enhancedneutrino oscillations (the MSW effect [10]) are possible, for two distinct regions in the (sin2 2θ, δm2)parameter plane.

Indeed, several authors have previously studied MSW fits to the Homestake andKamiokande II data simultaneously via mixing with active [11,12] or sterile [13] neutrino species;their solutions broadly agree, their range of predictions for the gallium experiment exist in theliterature and already indicate where the new GALLEX result can be accommodated in a MSWscenario [11–13].In the present Letter we point out an alternative explanation in terms of long-wavelength vacuumneutrino oscillations [14–19]; solutions of this kind [17–19], previously fitted to the Homestake andKamiokande data, predict 71Ga capture rates quite consistent with the new GALLEX result above.2

With such oscillations, having wavelengths comparable to the Earth-Sun distance, it is naturalfor some sections of the solar neutrino spectrum to be greatly suppressed while others suffer lesssuppression.In the following we shall first present updated long-wavelength oscillation (LWO)fits to the Homestake plus Kamiokande data, using the most recent version of the SSM [4] andincorporating the first 220 days preliminary results from the upgraded Kamiokande III detector [20],that giveRKam III = 0.60+0.15−0.13 . (3)Superposing these solutions on an iso-SNU plot of the corresponding predictions of a 71Ga detectorexhibits visually the range of GALLEX predictions that is allowed for this kind of solution and theneutrino mass and mixing parameters that are required.

Finally, we shall present LWO fits to theHomestake plus Kamiokande plus GALLEX data simultaneously and discuss their predictions forfuture observations.We have first re-fitted the LWO hypothesis to the latest suppression ratios from Homestakeand Kamiokande III (above), together with the Kamiokande II ratios separated into 14 bins ofrecoil electron energy Te (their weighted mean appears in Eq. (2) ), in order to input the maximalpre-GALLEX spectral information.

The initial solar neutrino spectrum is taken from the recentBahcall-Pinsonneault [4] update of the SSM, that includes He diffusion and other improvementson previous calculations [3]. We assume two-flavor mixing of the electron-neutrino νe, either withan active neutrino species να (α = µ or τ) or with a sterile neutrino νX; these two scenariosare indistinguishable in 37Cl or 71Ga detectors, but give different results in detectors (includingKamiokande) that are sensitive to neutral-current scattering of να.

Figure 1 shows our resultingregions of fit in the (sin2 2θ, δm2) plane, where θ is the usual mixing angle and δm2 is the differenceof mass-squared eigenvalues. There are 16 data points (Cl rate, 14 Te bins from Kam II, Kam IIIrate) and two free parameters; the best fit was for νe-να oscillations with δm2 = 6.4×10−11 eV2 andsin2 2θ = 0.83, yielding χ2min = 12.5.

The regions of fit have summed χ2 < χ2min + 6.1 correspondingto 95% CL. As in previous fits [11,17,19], we see that sterile-neutrino mixing solutions are morerestricted but not excluded.

We note that νe-νX oscillations with maximal mixing are an essential3

feature of a recent custom-designed model [21] for the controversial 17 keV neutrino; in such modelsLWO are then preferable to MSW solutions as an explanation for the solar neutrino puzzle.Figure 1 also shows time-averaged iso-SNU contours for the 71Ga capture rate. We see that theLWO regions of fit to Homestake and Kamiokande data fall almost entirely between the 60 SNUand 80 SNU contours, predicting 71Ga capture rates compatible both with the GALLEX signalof 83 ± 19 ± 5 SNU [1] and with the published SAGE upper limit of 79 SNU [2] at 90% CL(compatibility with SAGE data alone was previously discussed in Ref.

[19]). This figure shows thatthe LWO hypothesis accommodates the present gallium data quite naturally.

It also shows how afuture more precisely determined 71Ga rate can fit in.Finally we have fitted the LWO hypothesis to all Homestake plus Kamiokande plus GALLEXresults combined (17 data points with two free parameters); the best fit parameters are nearlyidentical to those in the fit without the GALLEX result, and give χ2min = 13.7. Figure 2 shows thecorresponding regions of fit at 95% CL in the (sin2 2θ, δm2) plane.

These regions summarize theLWO picture for present data.The LWO predictions for future experiments are particularly sensitive to line sources in the solarneutrino spectrum, such as the 862 keV 7Be line (that generates most of the wiggles in the 71Gacontours in Fig. 1).

Observations of ν-e scattering at the planned BOREXINO detector [22], in theelectron recoil energy band 0.26 < Te < 0.66 MeV, will be very sensitive to this 7Be line contribution.Figure 2 shows contours of the time-averaged suppression factor R(Borexino) for this energy band;a range of possible values 0.3 <∼R <∼0.9 is allowed for νe-να active neutrino oscillations, or a range0.1 <∼R <∼0.4 for νe-νX sterile neutrino oscillations. These are quite wide bands, that fully overlapthe range 0.21–0.65 expected for MSW solutions [8,11]; unless the BOREXINO results lie outsidethe MSW band, or future data make the bands much narrower, this time-averaged measurementalone will not discriminate sharply between MSW and LWO solutions.

One may also look at higherTe values, which contain contributions from pep, 13N and 15O neutrinos, but there the number ofevents is smaller by an order of magnitude and the statistical uncertainties correspondingly greater.A distinctive feature of LWO scenarios, however, is that they contain clean and potentiallyresolvable oscillations in the νe survival probability P(νe →νe) = 1−sin2 2θ sin2(δm2L/4E), where4

L is the distance from source to detector; this feature is absent in MSW scenarios with larger δm2values where the corresponding oscillatory factors are averaged due to the size of the solar source.An immediate consequence is a time dependence of the contributions from line sources, due tothe seasonal changes in the Earth-Sun distance [14–19]; here we fix E and find L dependence inP(νe →νe). Eventually, it should be possible to discriminate between LWO and other explanationson this basis alone, but at present there is little evidence on this score.

The 37Cl capture rate hasa 7Be component and could exhibit some time dependence; it is intriguing to find that our bestfit with LWO to the seasonal 37Cl data (using results cited in Ref. [23]) is actually better (lowerχ2) than a fit to constant RCl with no time dependence.

At present this is just an interesting hint,not a statistically significant result. The 71Ga and BOREXINO signals, however, contain largercomponents from the 7Be line and could provide better evidence.

Typical LWO solutions with δm2of order 5 × 10−11, 1 × 10−10 and 2.5 × 10−10 eV2 have differences between maximal and minimalsix-month 71Ga count rate of up to 8, 17 and 29 SNU, respectively, due to the variation in theEarth-Sun distance. Ultimately, the statistical uncertainty in a six-month gallium measurementmay be reduced to 7 SNU, so these variations may be detectable in 71Ga for solutions with largerδm2.

In the BOREXINO experiment the count rate is much higher; the statistical uncertainty inthe monthly measurement of R may be as low as 0.04. The ranges of differences between maximaland minimal monthly measurements of R in BOREXINO are 0.02–0.24, 0.09–0.45 and 0.39–0.66,respectively, for LWO solutions in the three aforementioned δm2 regions.

Hence, there is a stronglikelihood that the time dependence could be observed in BOREXINO in a LWO scenario.The Sudbury Neutrino Observatory (SNO) experiment [24] cannot detect 7Be neutrinos and willtherefore have little time dependence, but will be able to test a second distinctive property of LWO,namely an oscillatory modulation of the 8B neutrino spectrum. This property follows immediatelyfrom the expression for P(νe →νe), that oscillates versus Eν when measured at (approximately)constant L. SNO will obtain a determination of the high-energy 8B neutrino spectrum throughits measurement of charged-current νed →ppe−scattering.Here the neutrino energy will bemeasured directly, not averaged (as in 37Cl capture) nor smeared by the recoil electron distribution(as in ν-e scattering).P(νe →νe) is given by the ratio of the observed 8B spectrum to the5

calculated spectrum; the normalization of the latter may be affected by the solar model but theshape is not. Figure 3 illustrates the dependence of P(νe →νe) on Eν for our best-fit LWO solution(including an average over the varying Earth-Sun distance); we see that a clear oscillation minimumis predicted in the energy range above 5 MeV, the practical threshold for SNO.

This behavior isdistinguishable from that of two MSW solutions, also shown. If this 8B spectrum modulation orthe 7Be time dependence were detected, they would provide the first case(s) in which a resolvedneutrino oscillation had been seen.SNO will also detect neutral-current ναd →ναpn scattering, which will help determine if os-cillations are occurring to sterile neutrinos.

For example, in a sterile neutrino oscillation scenarioboth the CC and NC ranges would be suppressed (to perhaps R ≈0.4), while for νe-να oscillationsonly the CC rate would be suppressed.We conclude the following:(a) The LWO hypothesis with two-neutrino mixing can comfortably account for the present 37Cl,Kamiokande and 71Ga data. There are discrete regions of fit as shown, for either active or sterileneutrino mixing.

(b) Time-averaged BOREXINO measurements may not cleanly discriminate between LWO andMSW solutions, since their predictions overlap considerably. (c) A very distinctive signature of LWO solutions, however, is the seasonal time-dependence ofthe 7Be line.

There is at present no more than an intriguing hint in the 37Cl data, but futureBOREXINO measurements would probably be able to detect this seasonal dependence. (d) Another distinctive LWO signature is the oscillatory modulation of the 8B spectrum shape,which should be tested at SNO.

More precise data of all kinds should also restrict the options inthe future. (e) Measurements of NC scattering in SNO may possibly discriminate between active-neutrino andsterile-neutrino mixing options.Up until now we have discussed oscillations between two neutrino species, but oscillationsamong three neutrino flavors are another possibility.

Although the maximal three-neutrino mix-ing case (which predicts RKam = 0.43 and a 71Ga rate of 44 SNU) is clearly disfavored by the6

new Kamiokande III and GALLEX data, many other scenarios with mass-squared difference scalesin the δm2 ∼10−10 eV2 range can comfortably account for these results [11,17,18]. The allowedrange of BOREXINO predictions is larger, and the three-neutrino solutions have the characteristicseasonal variations and oscillatory modulation of two-neutrino LWO.7

ACKNOWLEDGMENTSOne of us (VB) thanks the Aspen Center for Physics for hospitality during the completion ofthis work. This research was supported in part by the U.S. Department of Energy under contractNo.

DE-AC02-76ER00881 and contract No. W-7405-Eng-82, Office of Energy Research (KA-01-01),Division of High Energy and Nuclear Physics, and in part by the University of Wisconsin ResearchCommittee with funds granted by the Wisconsin Alumni Research Foundation.8

REFERENCES[1] GALLEX collaboration: P. Anselmann et al., “Solar neutrinos observed by GALLEX at GranSasso,” report GX1-1992, submitted to Physics Letters B. [2] SAGE collaboration: A. I. Abazov et al., Phys.

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[8] J. M. Gelb, W. Kwong and S. P. Rosen, University of Texas report UTAPHY-HEP-2. [9] S. A. Bludman, N. Hata, D. C. Kennedy and P. G. Langacker, University of Pennsylvaniareport UPR-0516T.

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FIGURESFIG. 1.LWO solutions to Homestake plus Kamiokande data are shown as shaded regions inthe (sin2 2θ, δm2) plane, for (a) νe-να active neutrino mixing (α = µ or τ) and (b) νe-νX sterileneutrino mixing.

Solid curves denote iso-SNU contours of the predicted 71Ga capture rate in eachcase.FIG. 2.LWO solutions to Homestake plus Kamiokande plus GALLEX data are shown asshaded regions in the (sin2 2θ, δm2) plane, for (a) νe-να mixing (α = µ or τ) and (b) νe-νX mixing.Solid curves are contours of the suppression ratio R for the time-averaged ν-e scattering signal inthe BOREXINO detector, in the band 0.25 < Te < 0.66 keV.FIG.

3.Electron-neutrino survival probability P(νe →νe) is shown versus neutrino energyEν for the best-fit νe −να LWO solution (δm2 = 6.4 × 10−11 eV2 and sin2 2θ = 0.83, solid curve)and solutions typifying the two MSW regions of fit: δm2 = 5.0 × 10−6 eV2, sin2 2θ = 0.008 (dashedcurve) and δm2 = 1.0 × 10−5 eV2, sin2 2θ = 0.8 (dotted curve).11

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