Determination of Solar Neutrino Oscillation
Parameters using 1496 Days of Super-Kamiokande-I
Data
S. Fukuda , Y. Fukuda , M. Ishitsuka , Y. Itow , T. Kajita ,J. Kameda , K. Kaneyuki , K. Kobayashi , Y. Koshio ,M. Miura , S. Moriyama , M. Nakahata , S. Nakayama ,T. Namba , A. Okada , N. Sakurai , M. Shiozawa , Y. Suzuki ,H. Takeuchi , Y. Takeuchi , Y. Totsuka , S. Yamada , S. Desai  ,M. Earl  , E. Kearns  , M.D. Messier  £ , J.L. Stone  , L.R. Sulak  ,C.W. Walter  , M. Goldhaber  , T. Barszczak  , D. Casper  ,W. Gajewski  , W.R. Kropp  , S. Mine  , D.W. Liu  , M.B. Smy  ,H.W. Sobel  , M.R. Vagins  , A. Gago  , K.S. Ganezer  , W.E. Keig  ,R.W. Ellsworth  , S. Tasaka  , A. Kibayashi  , J.G. Learned  ,S. Matsuno  , D. Takemori  , Y. Hayato  , T. Ishii  , T. Kobayashi  ,T. Maruyama  Ý , K. Nakamura  , Y. Obayashi  , Y. Oyama  ,M. Sakuda  , M. Yoshida  , M. Kohama Þ , T. Iwashita ,A.T. Suzuki , A. Ichikawa  , T. Inagaki Þ , I. Kato , T. Nakaya
K. Nishikawa , T.J. Haines  , S. Dazeley , S. Hatakeyama ,R. Svoboda , E. Blaufuss , M.L. Chen , J.A. Goodman ,G. Guillian , G.W. Sullivan , D. Turčan , K. Scholberg ,A. Habig  , M. Ackermann  , J. Hill  , C.K. Jung  , M. Malek  ,K. Martens  Ü , C. Mauger  , C. McGrew  , E. Sharkey  , B. Viren   ,C. Yanagisawa  , T. Toshito  , C. Mitsuda  , K. Miyano  , C. Saji  ,T. Shibata  , Y. Kajiyama  , Y. Nagashima  , K. Nitta  , M. Takita  ,H.I. Kim  , S.B. Kim  , J. Yoo  , H. Okazawa  T. Ishizuka  ,M. Etoh  , Y. Gando  , T. Hasegawa  , K. Inoue  , K. Ishihara  ,J. Shirai  , A. Suzuki  , M. Koshiba  , Y. Hatakeyama  ,Y. Ichikawa  , M. Koike  , K. Nishijima  , H. Ishino , M. Morii ,R. Nishimura , Y. Watanabe , D. Kielczewska   , H.G. Berns ,
S.C. Boyd  , A.L. Stachyra  , R.J. Wilkes Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582,
Japan

Preprint submitted to Elsevier Preprint

30 July 2002 Department of Physics, Boston University, Boston, MA 02215, USA Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA Department of Physics and Astronomy, University of California, Irvine, Irvine, CA

92697-4575, USA Department of Physics, California State University, Dominguez Hills, Carson, CA 90747,

USA Department of Physics, George Mason University, Fairfax, VA 22030, USA Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA Institute of Particle and Nuclear Studies, High Energy Accelerator Research

Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
Department of Physics, Kyoto University, Kyoto 606-8502, Japan
Physics Division, P-23, Los Alamos National Laboratory, Los Alamos, NM 87544, USA
Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA
70803, USA
Department of Physics, University of Maryland, College Park, MD 20742, USA
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139,
USA Department of Physics, University of Minnesota, Duluth, MN 55812-2496, USA Department of Physics and Astronomy, State University of New York, Stony Brook, NY

11794-3800, USA Department of Physics, Nagoya University, Nagoya, Aichi 464-8602, Japan Department of Physics, Niigata University, Niigata, Niigata 950-2181, Japan Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan Department of Physics, Seoul National University, Seoul 151-742, Korea
 International and Cultural Studies, Shizuoka Seika College, Yaizu, Shizuoka, 425-8611,

Japan Department of Systems Engineering, Shizuoka University, Hamamatsu, Shizuoka

432-8561, Japan
 Research Center for Neutrino Science, Tohoku University, Sendai, Miyagi 980-8578,

Japan The University of Tokyo, Tokyo 113-0033, Japan Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan

Department of Physics, Tokyo Institute for Technology, Meguro, Tokyo 152-8551, Japan
 Institute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland Department of Physics, University of Washington, Seattle, WA 98195-1560, USA2

Abstract
A number of different fits to solar neutrino mixing and mass square difference were performed using 1496 days of Super-Kamiokande-I’s solar neutrino data. These data selecttwo allowed areas at large neutrino mixing when combined with either the solar  B flux
prediction of the standard solar model or the SNO interaction rate measurements. A global
fit combining SK data with the solar neutrino interaction rates measured by Homestake,
SNO, Gallex/GNO and SAGE prefers a single allowed area, the Large Mixing Angle so between the twolution, at the 98.9% confidence level. The mass square differenceeV , while the mixing angle is in themass eigenstates ranges from about to0.25–0.65.
range of  

 

Keywords: neutrino, solar neutrino, Super-Kamiokande

1 Solar Neutrino Oscillations

While a number of previous solar neutrino experiments [1–4] have measured a smaller neutrino interaction rate than that predicted by the Standard Solar Model (SSM) [5], in 1996 Super-Kamiokande(SK) began collecting data of unprecedented precision and quantity. In addition to a reduced interaction rate of solar  B neutrinos (originating from  decay of  B nuclei) with electrons in the detector,
SK measured with high precision the spectrum of the recoiling electrons as well as time variations of
this reduced rate [6].
Neutrino flavor oscillations are able to explain all observed solar neutrino interaction rates, including
the rate difference between SK and SNO [7]. The large neutrino flavor mixing between the second
and third generation inferred from atmospheric neutrino data [8] in conjunction with the absence ofan oscillation signal in the CHOOZ reactor neutrino experiment [9] (which is sensitive to oscillations
in a similar region of mass square difference) requires a small component of one of the three mass
eigenstates to the electron flavor eigenstate. Solar neutrino oscillations can therefore be approximatedby a two-neutrino description with the parameters  (mixing angle) and  (difference in masssquare). The mass eigenstate  ( ) is chosen to have the smaller (bigger) mass  . Therefore,   is always positive and the mixing angle ranges between 0 and  . For  betweeneV andeV , matter densities in the sun and the earth can strongly affect the oscillation
 isprobability. Consequently, the symmetry of the vacuum oscillation probability around 
broken. For    , resonant enhancement of the oscillations (MSW effect [10]) can occur in thesun, while for    , an anti-resonance can suppress the oscillations. Since matter-dominatedsolutions usually don’t occur for    , we have not shown this “dark side” of the parameter spaceeV , the oscillation probability is more affected by the oscillationin previous reports. Belowphase than by matter effects. A logarithmic scale of the variable illustrates the mirror symmetryeV ) at the maximal mixing line. Figure 1 (a) shows theof the vacuum region (below  experimentally allowed areas using various measurements.











 









 



Alternatively, it is possible to call the mass eigenstate  (  ) which has the larger coupling to electrons
 might be negative. The oscillation probability
and(muons). In that case, ranges between 0 and

¼
¼
 .
remains invariant under the transformation  and









3

In addition to the suppression of the  rates, neutrino oscillations also produce other neutrino flavors.
Furthermore, they can induce distortions of the neutrino spectrum and time variations of the solar
neutrino fluxes. In the MSW region, the time variations arise from matter effects inside the earth(daily variations). In the vacuum regions, the time variations are the consequence of the change of theoscillation phase due to the yearly variation of the oscillation baseline – the distance between the sun
and the earth.
In this paper we report on the new SK data set of 1496 days, which represents the completion of theanalysis of all the data from Super-Kamiokande-I. Previous SK energy spectrum and time-variation
measurements ruled out large regions of the oscillation parameter space allowed by other experiments [11]. In particular, all the allowed parameter space for oscillations into a purely sterile neutrino
was strongly disfavored. When combined with the SSM, these measurements also restricted tobe bigger than about 0.2. Our final data set confirms our previous measurements and further constrains
the range of possible oscillation parameters.

Even stronger constraints can be obtained by combining SK results with the rate measurements ofother experiments. In particular, the combination of SNO’s measurement of the solar  B  interaction
rate [12] with the SK rate yields additional information [7,13] about  B flavor conversion, since SK
also has sensitivity to other active neutrino flavors. If the  survival probability is moderately small
for  B neutrinos (less than about 50%) then SK can observe a significant excess due to the presence ofother active species in its precise measurement of the elastic scattering rate. A similar signature canbe observed in the combination of SK and the Homestake rate. In this case, however, the lower energy
threshold of Homestake and its resulting sensitivity to other than  B neutrinos lead to an ambiguity
between spectral distortion and appearance signatures and therefore to a larger uncertainty in theobserved excess.

2 Parameter Estimation for Two-Neutrino Oscillations
Without SK data, the strongest constraint of the parameters is a  fit to the charged-current neutrino
rates from Gallex/GNO, SAGE (combined into a single “Gallium” rate), Homestake (“Chlorine”)
and SNO experiments []. The light gray areas of Figure 1 (b) use only these three rates and theirSSM-based predictions. The regions can be understood as the “overlap” of the three allowed regionsof Figure 1 (a). Above  eV near(maximal mixing) all three regions meetand form the large mixing angle (LMA) solution. The small mixing angle solution (SMA) is the!
“crossing point” of the Gallium region and the Chlorine region and lies between  
eV



and
eV at. The LOW solution is the large  part of the extensive region(s)"eV andeV , while the lower part of this region is called the quasi-vacuum
between (quasi-VAC) solution. Finally, the vacuum solutions (VAC) are found below eV . All regions).
have similar  (though the LOW fits are slightly worse with   min









  










SK data breaks the degeneracy in  of these regions by analyzing the shape of the “zenith angle spectrum” [11] which combines spectrum and daily variation analyses. Here we utilize the zenith angle
spectrum from the entire SK-I data set collected between May 31st, 1996 and July 15th, 2001 (1496
live days). The numerical results are listed in Tables 1 and 2. There is no indication of spectral distortion, the  to an undistorted spectrum is 4.6 for 7 degrees of freedom (71% C.L.). No significant daily4  

Day-Night
variation is found, the day/night rate asymmetry is DN 0.5(Day+Night)
0.020(stat)  (syst).
The gray excluded regions of Figure 2 (a) are the result of the zenith angle spectrum fit. The SMA andVAC regions are excluded since they require a distorted  B neutrino spectrum. The lower part of the
LMA and the upper part of the LOW solution predict daily variations and are therefore disfavored.
The excluded areas are independent of the SSM neutrino fluxes. While the SK zenith angle spectrum
shape is best described by quasi-VAC solutions, LMA fits have similar  .

Since there is no indication of a distortion of the SK zenith spectrum, an analysis of the zenith spectrum shape alone can only yield excluded regions. However, if the  B flux is known, the SK rate can bepredicted. Then, the zenith spectrum shape can be combined with the SK rate into a single measurement. Figure 2(b) shows the allowed regions using SK rate and zenith angle spectrum in combination
with the  B flux prediction and uncertainty of the SSM. Unlike other experiments, whose allowed
areas are shown in Figure 1 (a), SK allows only large mixing at 95% C.L, and there are two allowed
regions: the LMA and quasi-VAC solution.

3 Combination of Super-Kamiokande Data with Other Experiments
A comparison between the SK rate and SNO’s charged-current rate [12] yields another  B flux constraint which is independent of the SSM, so a combination of the SK rate and zenith angle spectrumwith the SNO charged-current rate need not rely on any neutrino flux prediction [13]. The SK rate of    
  SSM (see Table 1) exceeds the SNO charged-current rate [12] of  SSM, by. If this is interpreted as an appearance signal of other active neutrino flavors, these flavors
aboutelastic scattering cross section
contribute about 25% to the SK rate and 70% to the  B flux (the for the other flavors is six to seven times smaller than for  ). As a consequence of this appearance signal, the two allowed regions (dashed-dotted lines) of Figure 3 (a) result from a combined fit: a LMA
and a quasi-VAC solution. If the SNO neutral-current rate is used as well, the quasi-VAC solutions
are disfavored as seen in Figure 3 (a) (gray shaded areas).



 



To constrain the quasi-VAC region below the LOW solution, it is necessary to add the Gallium [3,4]

  #
(
 SNU or SSM) SNU or  SSM) and Chlorine rates [1] (to the fit. Such a global fit is still not influenced by the B and hep neutrino (arising from  He p# He+e + )flux predictions of the SSM, which suffer from the largest uncertainties. However, it relies on the other
SSM neutrino fluxes, in particular the " Be flux (10% uncertainty) and the neutrino fluxes of the CNO
uncertainty). Those fluxes contribute [5] about 15% (" Be) and 6% (CNO) to the Chlocycle (rine rate and 27% (" Be) and 7% (CNO) to the Gallium rate in the SSM. The allowed areas of thisglobal fit shown in Figure 3 (b) looks quite different when compared with the fit without SK data
displayed in Figure 1 (b): only the upper part of the LMA survives.

 

 





   Table 3 compares the four smallest local minima of the  describing the global fit. The best fit islocated in the upper LMA area. The  B flux resulting from this fit is somewhat higher than expected !
by the SSM (cm s) but well within the uncertainty. The hep flux is considerably  cms); however, the uncertainty of this prediction ishigher than expected by the SSM (thought to be very large. The fit agrees with the SK zenith angle spectrum moderately well and easily
accommodates the Gallium, SK and SNO rates, though the predicted Chlorine rate is abouttoo
high. This worsens the otherwise very good best fit  .









5

The quasi-VAC solution describes the SK zenith angle spectrum slightly better than the LMA does,
short of the SSM prediction.
however, the rates do not fit well. The resulting best fit  B flux falls
The surviving (at 99% C.L.) LOW solution fits the rates about as poorly as the quasi-VAC solution.
The SK zenith angle spectrum fits LOW worse than it does either LMA or quasi-VAC. The lack of"zenith angle variation in the SK data reduces the  (usually aroundeV ) and worsens the
LOW best fit which is already under pressure from the rates.

level a small mixing angle solution appears. The mixing angle is about a factor
At around theof four smaller than the usual SMA. For any given  B flux, such a small mixing angle region can be
defined by the crossing of the Gallium and the Chlorine allowed areas; those two rates therefore automatically fit very well. In case of the classic SMA, the SK spectral data lack the predicted distortion.
As a consequence, the region gets shifted towards smaller mixing, and even then the SK zenith angle
spectrum considerably (about 3.5 ) disfavors this fit. Due to the reduced mixing angle, the predictedabove the measurement. Consequently, small mixing is
SNO charged-current rate is more than
excluded at thelevel.



Figure 4 shows a close up view of the LMA region. The combined fits described above treat the  B
flux as a free parameter, which is only constrained by the solar neutrino experiments. If the SSM
prediction of this flux is used (dashed-dotted line), the quasi-VAC, LOW and small mixing solutions
are further disfavored: the quasi-VAC solution is then excluded at 99.4% C.L., LOW at 99.1% C.L.
and small mixing at 99.96% C.L. If the SNO measurements are removed from the fit (dashed lines),
LMA is still favored. Quasi-VAC solutions appear then at 95% C.L, LOW solutions at 97% C.L. andsmall mixing solutions at 93% C.L. If the radio-chemical measurements (Gallium and Chlorine) are
ignored (dotted lines, or see Figure 3 a), LOW solutions appear at 92% C.L., quasi-VAC at 84% C.L.
and small mixing solutions at 99.99% C.L.

4 Conclusion

The combined fit to the charged-current interaction rates measured by several experiments result inmany allowed regions of neutrino mixing and mass square difference: LMA, SMA, LOW, quasiVAC and VAC solutions. The absence of spectral distortion and daily variations of the SK solar
neutrino interaction rate strongly constrains these regions rejecting SMA, LOW and VAC solutions
at 95% C.L., while leaving only the higher mass square difference LMA and the quasi-VAC region.
When combined with the SK interaction rate and either the SSM prediction of the  B flux or the
SNO rates, large neutrino mixing is selected. When Gallium, Chlorine and SNO data are combinedwith SK data, only the higher mass square difference LMA solutions remain at 98.9% C.L. Thus
the combined results of all solar neutrino experiments can be used to determine a unique region ofoscillation parameters that explains the famous solar neutrino problem.

Acknowledgments

We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. The
Super-Kamiokande detector has been built and operated from funding by the Japanese Ministry of6

Education, Culture, Sports, Science and Technology, the U.S. Department of Energy, and the U.S.
National Science Foundation.

References[] Present address: Harvard University, Cambridge, MA 02138, USA[] Present address: Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA[] Present address: The Institute of Physical and Chemical Reasearch (RIKEN), Wako, Saitama 351-0198,
Japan[] Present address: Department of Physics, University of Utah, Salt Lake City, UT 84112, USA[1] B.T. Cleveland et al., Astrophys. J. 496, 505 (1998).
[2] Y. Fukuda et al., Phys. Rev. Lett. 77, 1683 (1996).
[3] E. Bellotti, Nucl. Phys. B(Proc. Suppl.) 91, 44 (2001);
W. Hampel et al., Phys. Lett. B 388, 364 (1996);
P. Anselmann et al., Phys. Lett. B 342, 440 (1995).
[4] V. Gavrin, Nucl. Phys. B(Proc. Suppl.) 91, 36 (2001);
J.N. Abdurashitov et al., Phys. Lett. B 328, 234 (1994).
[5] J.N. Bahcall, M.H. Pinsonneault, S. Basu, Astrophys. J. 555, 990 (2001).
[6] S. Fukuda et al., Phys. Rev. Lett. 86, 5651 (2001).
[7] Q.R. Ahmad et al. Phys. Rev. Lett. 87, 71301 (2001).
[8] Y. Fukuda et al., Phys. Rev. Lett. 81, 1562 (1998).
[9] M. Apollonio, Phys. Lett. B 466, 415 (1999).
[10] S.P. Mikheyev and A.Y. Smirnov, Sov. Jour. Nucl. Phys. 42, 913 (1985); L. Wolfenstein, Phys. Rev. D 17,2369 (1978).
[11] S. Fukuda et al., Phys. Rev. Lett. 86, 5656 (2001).
[12] Q.R. Ahmad et al. nucl-ex/0204008 (2002).
[13] M. Smy in Neutrino Oscillations in Venice, ed. M. Baldo Ceolin, (Venezia, 2001) 35.
[] A detailed discussion of this uncertainty will be published elsewhere.
[] As we prepared this paper, SNO announced new results on its charged- and neutral-current rates, whichassumes an undistorted  B  spectrum. In particular, the neutral-current rate can be strongly influenced
by such spectral distortions. At present, the SNO measurement of this spectrum cannot be used to extract
neutral-current and charged-current rates for distorted spectra, since the systematic uncertainties have
not yet been given as a function of energy. As a consequence, we do not use the neutral-current rate
in oscillation fits excluding SK data. In combined fits including the SK recoil electron spectrum, thedistortions are small in the regions which are allowed by SK data.



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(a)

10
10

(b) LMA Solution

SMA
Solution
LOW
Solution
Quasi-VAC Solution

VAC Solutions

-11

-12

10

95%C.L.
νe→νµ/τ
-4

10-3

95%C.L.
Zenith Spectrum νe→νµ/τ
10

-2

10

-1

1

10

10

2

10

-3

10



-2

10

-1

1

10
10
2
tan (θ)2

Fig. 1. (a) Allowed areas from other experiments measuring the solar  flux. The shaded area uses only Homestake data, while the hatched area uses only the SNO charged-current rate. Overlaid (inside dashed lines) is theregion allowed by Gallex/GNO and SAGE. (b) Allowed regions from a combined fit to these charged-current
rates. All contours in this and other figures are 95% C.L.

8

2
2

∆m in eV

10
10
10
10
10
10
10
10
10
10

-3

(a)

(b)

95%C.L.
Zenith Spectrum νe→νµ/τ

95%C.L.
Zenith Spectrum+SK Rate νe→νµ/τ

-4

-5

-6

-7

-8

-9

-10

-11

-12

10

-4

10

-3

10

-2

10

-1

1

10

10

2

10

-3

10

-2

10

-1

1

10
10
2
tan (θ)2

Fig. 2. (a) SSM flux independent excluded areas (gray) using the SK zenith spectrum shape alone overlaid
with the allowed regions of Figure 1 (b) in light gray. The overlap of both is shaded dark gray. (b) Allowed
areas using only SK data and the SSM  B neutrino flux prediction. Both allowed regions indicate large neutrino
mixing.

9

2
2∆m in eV

10

-3

(a)
10
10
10
10
10
10
10
10
10

(b)

-4

-5

-6

-7

-8

-9

-10

-11

-12

all solar ν data
95%C.L.
95%C.L.
8
Zenith Spectrum+SK/SNO Rates νe→νµ/τ νe→νµ/τ ( B, hep free)

10

-4

10

-3

10

-2

10

-1

1

10

10

2

10

-3

10

-2

10

-1

1

10
10
2
tan (θ)2

Fig. 3. Solar neutrino oscillation parameter constraints from combined fits using the SK zenith spectrum andrate and other experimental rates. (a) SK and SNO combined fit. The dashed-dotted lines indicate the allowed
area if the SNO neutral-current rate is removed from the fit. (b) The combined fit to SK data and all rates favor
the LMA solution. The best fit point is indicated by the asterisk. All fits are independent of the SSM  B flux
and hep flux.

10

2

-3

2

∆m in eV

10

10

10

-4

-5

95%C.L.
νe→νµ/τ
o

o

o

o

o

o

o

o

o

o

0 10 20 30 40 50 60 70 80 90
θFig. 4. Magnified view of the LMA solution. Note the linear scale of the x-axis. The 95% C.L. contours are
obtained from the global fit with (dashed, dotted and dashed-dotted lines) and without (gray shaded area) using
the SSM  B flux calculation. The dashed-dotted lines include all experimental information, while the dashed(no SNO rates) and dotted lines (no radio-chemical rate measurements) do not.

11

Tables
Table 1
SK rate and uncertainty for eight energy bins. The rates and statistical and systematic uncertainties (of the spectrum shape) in the third column are presented in units of SSM expectation. These systematic uncertainties are
assumed to be uncorrelated in energy. The uncertainties in the fourth (uncertainty of the  B neutrino spectrum),
fifth (uncertainty of the energy scale of 0.64%) and sixth column (uncertainty of the energy resolution of 2.5%)
are fully correlated in energy (but uncorrelated with each other). The combined uncertainty (last row) is basedon the sum of all bins of the zenith angle spectrum. The combined rate has an additional systematic uncertainty[] (excluding  B shape, energy scale and resolution), which was added to the uncorrelatedof  !
systematic uncertainties of the spectrum shape.

Bin

Range [MeV]1

5.0-5.52

5.5-6.53

6.5-8.04

8.0-9.55

9.5-11.5

6

11.5-13.5

7

13.5-16.0

8

16.0-20.0

Comb. 5.0-20.0

Rate stat syst [SSM]



0.458 0.014 0.473 0.008 
0.460 0.009 
0.463 0.010 
0.462 0.017 
0.567 0.039 
0.555 0.146 
0.465   B Spectrum





0.467 0.040 















E-Scale

E-Resol.







 





 



 








 


 

Table 2
Subdivision of bins 2–7 according to the solar zenith angle  . The range of is given for each bin:
is
‘Day’
and
is
‘Night’(‘Mantle’and‘Core’).
Duetothegeographic
location of SK,
. The rates are given in units of 0.001 SSM. Only statisticalno data can be obtained for
uncertainties are quoted. All systematic uncertainties (see Table 1) are assumed to be fully correlated in zenith
angle.

          

Day

 

MantleCoreBin-0.974–0

0.00–0.16

0.16–0.33

0.33–0.50

0.50–0.67

0.67–0.84

0.84–0.9742

453 20442 53

379 49472 45522 45503 49426 52

3

474 12530 34506 30438 26478 26451 28439 31

4448 13463 36470 33462 29509 29461 32451 355453 15449 40502 38451 32473 32477 35483 406477 25509 67351 55391 49498 53434 56521 647

511 54570 150

831 167

694 131665 127441 118469 1311-8

459.9 6.7

483

476 17451 15496

467 16456 1718

12

15

Table 3 difference (Parameters for the best fit points. The fourth row shows themum (in the LMA-solution: ) between the absolute mini-) and the local minima (Quasi-VAC, LOW and SMA). The probabilitiesof these local minima (given in parentheses) are calculated from this difference. The six rows below show from a fit to the shape of the SK zenith spectrum and the fivethe six independent parts of the fit: the which contains

interaction rates (deviation probabilities are given in units of Gaussian standard deviation

only experimental uncertainties). The last four rows show the values of the minimized fit parameters. The  B
and the hep fluxes are free, while the  B neutrino spectrum shift as well as the SK energy scale and resolution
shifts are constrained within the systematic uncertainties.
Solution

LowAngle (LMA)

(LOW)

 

6.9

 
 (46 dof; (2 dof;


 (



Large Mixing Quasi-Vacuum(Quasi-VAC)

 

6.68

 

7.2

Small Mixing
Angle (SMA)

 !

6.6

0.38

1.5

0.66

0.0012[%])43.5 (57.7)

53.5 (20.9)

52.5 (23.7)

58.9 (9.6)$ [%])

0.0 (100.0)

10.0 (0.7)

9.0 (1.1)

15.4 (0.05)



])

$ [

3.0 (

 )

1.0 (

)

)

15.1 (

)

)

64.4 ()

64.9 ()

78.3 (

  )

)

3.09 (

)

3.03 (

)2.43 ()

45.0 (  )

45.5 ()

45.7 ()

38.9 (

)37.7 (

)40.0 (

)

87 (

)

89 (

)

)

5.6 (

Ga Rate [SNU]

71.7 (Cl Rate [SNU]

2.99 (SK Rate [%SSM]

46.1 (

SNO CC [%SSM]

34.0 (SNO NC [%SSM]

106 (

)

76 (

! cm s)]

5.33 (

)

3.83 (

4.41 (

4.48 (

36

9

23

12









/ /

 [



 cm s)][ B Spectrum ShapeSK E-scale/resol.

/ /  

13

)
)

)
)
  )