Volume 188, number 1 PHYSICS LETTERS B 2 April 1987

LIMITS ON NEUTRINO OSCILLATION PARAMETERS FROM THE C H L O R I N E SOLAR-NEUTRINO EXPERIMENT

M. CRIBIER, J. RICH, M. SPIRO, D. VIGNAUD DPhPE, CEN Saclay, F-91191 Gif sur Yvette. France

W. HAMPEL Max Planck Institut J~r Kernphysik, D-6900 Heidelberg 1, Fed. Reg. Germany

and

B.T. CLEVELAND Los Alarnos National Laboratory, Los Alamos, NM87545, USA

Received 23 January 1987

MSW regeneration of solar v~ in the earth can lead to a seasonal variation in the capture rate in the chlorine solar-neutrino experiment. The absence of such an effect in the data allows us to set a limit on the neutrino oscillation parameters for Am 2 near 3 X 10 -6 eV 2. The limit thus obtained is only weakly dependent on solar-model inputs.

The recently discovered MSW effect [ 1,2] pro- vides an elegant explanation [2-5] for the low counting rate of the chlorine solar-neutrino experi- ment [ 6 ]. In the simple case of mixing between v~ and v , but negligible mixing with v~, we have Ve=VlCOS0+VEsin0 and v~= --visin0+VECOS0. I f the electron couples dominantly to the lighter neutrino, i.e., m~ < m2 (0 <45 ° ), the effects of coherent-for- ward scattering of the neutrinos in the solar medium of slowly falling density can lead to an adiabatic transformation of ve produced near the center of the sun into the neutrino mass eigenstate weakly coupled to electrons (VE). Roughly speaking, this happens for Ve with momenta between Pmin and Pmax determined by the standard neutrino parameters, Am 2 ( .~- m 2 __

m~) and sinE20 [4]:

Prnin = 0.075 M e V / c

×cos 20 ( - -AmZ/10-6 eV 2) , (1)

Pmax = 200 MeV/c

×sin220 cos 20 ( - - A m E / 1 0 - 6 e V E) . (2)

Between these limits, the solar neutrinos leave the sun as rE, equivalent to a suppression of the ve content by a factor sinE0. Because Vz is a mass eigenstate, there are no oscillations between the sun and earth, but, as the neutrinos pass through the earth to the neutrino detector, there will be VE-Vt oscillations since VE is not an eigenstate at non-zero density. This regener- ates ave flux since vl couples strongly to electrons. The v t - r E oscillations have a large amplitude for neutrino momenta near the momentum satisfying the MSW resonance condition [ 4 ]

Pros ~ 2 MeV/c ( - - A m E / 1 0 - 6 e V E ) . (3)

The regeneration is only important at night since the oscillation length is comparable to the earth's radius. Hence, the solar ve flux is higher at night than at day- time, and, therefore, higher in the winter than in the summer [4,7]. The radiochemical chlorine experi- ment is sensitive to such an effect since, for the last 16 years, it has measured the v~ flux, integrated over periods of between one and three months.

Fig. 1 shows the band in parameter space (delim- ited by the dashed lines) [4] where the time aver-

168 0370-2693/87/$03.50 © Elsevier Science Publishers BN. (North-Holland Physics Publishing Division)

Volume 188, number 1 PHYSICS LETTERS B 2 April 1987

10 -:~ . . . . . . . . I . . . . . . . . I . . . . . . . . I ' ' ~ < '~"

<~ I

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Fig. I. The parameter space defined by - A m 2 and sin220. For parameters between the two dashed contours, the initial solar ve flux determined by the standard solar model combined with the time averaged MSW suppression yields the observed counting rate of the chlorine experiment. For parameters inside the solid line, the ratio between the December and June counting rates is greater than 1.5. The solid curve is calculated for the spectrum of the standard solar model.

aged MSW suppression makes the measured neutrino capture rate (2.1_+0.3 SNU, 1 S N U = 10 -36 captu- res/atom/s) consistent with the capture rate (5.8 SNU) calculated in the standard solar model [ 8 ]. We have divided the space into three regions, A, B, and C, according to whether the point is to the exterior of the band, inside the band, or to the interior of the band.

In the standard solar model, the ve's to which the chlorine experiment is sensitive come primarily from the beta decay of 8B (4.3 SNU) with small amounts coming from the electron capture of 7Be (l SNU) and other sources (0.5 SNU). I f the neutrino oscil- lation parameters lie in region A, the solar model must be modified to lower the flux of these neutri- nos. I f the parameters lie in region C, the flux must be increased. In a large class of non-standard solar models [ 9 ], the flux can be increased by increasing, via some mechanism, the central temperature of the sun. This results in an even greater dominance by the 8B neutrinos.

It is the purpose of this paper to point out that if the parameters fall in region C, a solar model giving the correct time averaged counting rate would also give, via MSW regeneration, large seasonal varia-

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Fig. 2. The corrected 3TAr production rate in the chlorine exper- iment (atoms/day) as a function of the t ime in the year. The sin- usoidal curve corresponds to the upper limit (95% CL) for the ratio between the December and June counting rates. The straight line shows the average counting rate.

tions in the counting rate. The maximum rate would be at the winter solstice and the minimum at the summer solstice.

Each of the 68 runs of the chlorine experiment (including hitherto unpublished runs made since 1984) yields an average 37Ar production rate [ 6 ]. In order to search for a seasonal variation in this rate, we divided the data into 8 bins of width 1.5 months, with the eighth bin centered on the winter solstice. The known (cosmic ray) background was subtracted from the average rate for each bin. The average rate was then correctedfof~he seasonal variation in the earth-sun distance. The corrected average rate as a function of time-of-the-year is shown in fig. 2.

The data of fig. 2 were fitted to a function of the form A[ 1 +Bcos(2~zt)] with t in years and t = 0 cor- responding to the winter solstice. The ratio between the December and June counting rates is given by R = (1 + B ) / ( I - B ) . The result of the fit is

A=2.1+O.3 SNU, R=0.85_+0.25,

with Z2---6.7 for 6 degrees of freedom. From this we conclude conservatively that R is less than 1.5 (Z2=13.7). This corresponds to a difference in counting rate between December and June of less than 0.8 SNU.

In fig. 1 we show the region (delimited by the solid

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Volume 188, number 1 PHYSICS LETTERS B 2 April 1987

l ine) in which the rat io between the December counting rate and the June counting rate is greater than a factor 1.5 (for the detai ls o f our calculat ional techniques see ref. [4] ) . The m a x i m u m rat io at the center o f the region is about 3. The curve is calcu- lated for the ve spect rum shape o f the s tandard solar model. The region is centered on the Am 2 deter- mined by eq. (3) and the average detected momen- tum in this solar model . Taking a flux that contains only neutr inos f rom SB decay would shift the curve up in - A m a by only ~ 10% (because o f the small increase in average detected neutr ino energy) . Since, f rom the preceding discussion, in region C, a model giving the correct t ime averaged counting rate will have a flux somewhere between the s tandard flux and a pure SB flux, we can exclude the region to the inte- r ior of the solid line with only weak assumpt ions about the solar interior.

In summary, we have used the absence o f a sea- sonal var ia t ion in the da ta of the chlor ine solar-neu- tr ino exper iment to exclude a region of the A m 2 - s i n 2 0 plane a round A m 2 = 3 × 10 -6 eV 2 and sin220 between 0.03 and 0.3. This exclusion zone does not rely on the flux calculat ion of the s tandard solar model but only on the assumpt ion that in order to increase the ini t ia l ve flux over that o f this model , one does not lessen the dominance of solar neutr inos from 8B beta decay. Needless to say, we also assume that the 2,1 SNU measured by the chlorine experi-

ment do, indeed, come from the capture of solar neutrinos.

I t is a pleasure to thank S. Cahen and R. Davis for discussions.

References

[ 1 ] L. Wolfenstein, Phys. Rev. D 17 (1978) 2369 [2] S.P. Mikheyev and A.Yu Smirnov, Nuovo Cimento 9C

(1986) 17; Sov. J. Nucl. Phys. 42 (1985) 913. [3] H.A. Bethe, Phys. Rev. Lett. 56 (1986) 1305;

S.P. Rosen and J.M. Gelb, Phys. Rev. D 34 (1986) 969; V. Barger, R.J.N. Phillips and K. Whisnant, Phys. Rev. D 34 (1986) 980.

[4] J. Bouchez, M. Cribier, W. Hampel, J. Rich, M, Spiro and D. Vignaud Z. Phys. C 32 (1986) 499; M. Cribier, W. Hampel, J. Rich and D. Vignaud, Phys. B 182 (1986) 89.

[5] E.W. Kolb, M.S. Turner and T.P. Walker, Phys. Len. B 175 (1986) 478; S.J. Parke, Phys. Rev. Lett. 57 (1986) 1275; S.J. Parke and T.P. Walker, Phys. Rev. Lett. 57 (1986) 2322.

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[7] A.J. Baltz and J. Weneser, Phys. Rev. D (1987), to be published; A. Dar et al., Technion report PH-86-29.

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