126 1 1960 ! R.Davis P3Q 30 (' [1]) * + ,.- / 0 1.2 "3#54! P Q 6 7 8 :9.; /?A@B !:C 7 8 D...

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1

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1996 � 4 � 1 ������� ��!#"%$�&�')(#*#+ 5 ��,�-/.102$ 1260

�3�346587�9�:�;�</= �>��? �A@�BC0�D�EF9�GH�I�J ��K�L 1260 � L����? �3M��3N�OP�Q D�E�93GK�LR���������� ������L3S�T/U�V8�CW�X�Y </=Z�3[�E]\ Q 9 ����?�^ \_$ 8BU�V8�

W#X3YL�`�a1Wcb �Ad�ef0�g/h L3SFT%^ \ L νe i�j�k al�>LRm%nloqp 0ADΦ(νe)/ΦBP98(

8B) ≤ 1.75%(90%CL)

≤ 1.77%(95%CL)

��r�gsGH�I/J L�t�u�� $R&�'6(s* LRv��wW�XR� k W $

Φ(νe)/ΦBP98(8B) < 3.5%(95%CL) [10]

�yx%zF7Z9�{ o *�|>9�GK#L�t�u�� $ U�V�}W8X�Y�~��)� j��R��� *�|������>� ������W ���>�s����$νe → (RSFP ) → νµ → (Oscilation) → νe

p E��Rg3�%� ~���� \ Q 9�� UFV/�CWlX3YL���� �A� 9 m *����Z*�|�9#G(sg3$��Z�3� µ ���l9���  L�¡%¢£ ��¤/¥�¦ ^ \¨§©>7F9Aª%« � M ¢ $ spallation prod-

ucts ���R9l¬ v]� W ��$#­�®�¯3°/± �A[FED#²�B�³l�8g pKl´ $ �����Z�Z�y >��A��Lµ�¶�· bF¸�� ¬ v�� Wº¹ { MeV »¼Z* � $�½ k a/¾ j�¿ �]À¨L + 80% Á m%~)K�L�Â�à ��s9>³ L *�|�9 p EÅÄ_Æ ~#Ç�^ �Rg#GK8L ½ k a�¾ j�¿ ��À ��Èq03ÉfʨÆ6�F���#Dl$ SFT%^ \ L νe

L�m�n8o �s��E%D P \3�Ë 0�EΦ(νe)/ΦBP98(

8B) ≤ 0.95%(90%CL)

p E�Ä t%u �Ar)g#G

1

�1 � � 6

1.1 ��� SFT � �/b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2U�V� W�X�Y��

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.1 � � �� . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.2 MSW � u . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 Resonant Spin Flavor Precession . . . . . . . . . . . . . . . . . . . . . . . 12

1.4U�V� W�X�Y ���F� ���>�]W L/m�n8o . . . . . . . . . . . . . . . . . . . . . 13

1.5SFT%^ \ L νe i�j�k a8�>LRm�n8o . . . . . . . . . . . . . . . . . . . . . . . 14

1.6 Resonant Spin Flavor Precession ��[FE%g S�T�U>V/�qW�X�Y����ZL���� . . 14

1.7 H���� L�� ¯ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

�2 � ��� �!�#"%$�&�' 15

2.1U�V� W�X�Y)(+*

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2�>�8�Z� �� ����� ,%-#.

. . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 /0 �1+2�3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4���>?#4�576s�98:

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4.1¶<; a1W>=#U�al�

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4.2 � j ¬ �?6s��8�: . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 @���A�B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

�3 � CDFE#G�H���IKJ�L 21

3.1 PMT M�N X#O ; ��6FPl� . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.1 Q%¬ � M�N X�O ; ��67Pl� . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.2? ¬ �%�¾ M�N X#O ; ��6FP�� . . . . . . . . . . . . . . . . . . . . 22

3.2 � LSR�Â9T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.1 U8¬ ; �WV�� ���9WX�Y�Z�e . . . . . . . . . . . . . . . . . . . . . 24

3.2.2 ���#� µ �F�9#Z/e . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 LINAC¶�· b�¸/� M�N X[O ; ��67Pl� . . . . . . . . . . . . . . . . . . . . 26

3.4 Ni-Cf¶�· bF¸�� MN X#O ; ��6FP8� . . . . . . . . . . . . . . . . . . . . . 29

3.5 DT¶�· b�¸/� M�N X[O ; ��67Pl� . . . . . . . . . . . . . . . . . . . . . . 29

3.6 �)�#� µL�\9] 0 � ��[�E�g ¶�· b�¸R� M�N X�O ; ��6^Pl� . . . . . . . . 31

3.7 Trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2

�4 � ��������� 35

4.1 ¬ v]��W�� ; a 67Pl� . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1.1 ½ ��8 k a���L N/O . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1.2 � � L N/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1.3X��8b ? ¬ : ¬ v�� W�� ; a�67Pl� . . . . . . . . . . . . . . . . . . 36

4.1.4 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.1.5 Spallation cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.6 Second Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1.7 Final Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1.8 Reduction summary . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 ��� ����?��Å���#b�L ¶�· b�¸/�R�/`)afW b . . . . . . . . . . . . . . . . . 45

4.3 Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.3.1 B8UFVs� WlX3Y i�jZk a�� . . . . . . . . . . . . . . . . . . . . . 45

4.3.2 νe + p → e+ + n crossection and cos θ distribution . . . . . . . . . 46

4.3.3 Expected�/`�a1W b

. . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.4SFT%^ \ L?( 0 � U�V�}W8X�Y i�j�k a8��L/m�n8o . . . . . . . . . . . . . 48

4.5 ­�®�¯ ��� ; �67Pl� ¬ v]��W L ²%Bw� . . . . . . . . . . . . . . . . . . . 52

4.6   � ����� ¬ v6�]W ��[>E�gl½ k a%¾ j>¿ �]À����L� "!8� . . . . . . . . 60

�5 � #%$ 64

& � J�' 65

3

� �

1.1 pp-chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 solar neutrino spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Production point distribution as a function of the solar radius . . . . . . . 9

1.4 CNO-cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1�>�8�Z� �� ����� ,%-#.

. . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 PMT ���%�F7�9 �+8]� ; � N���� . . . . . . . . . . . . . . . . . . . . . . 17

2.3 20 ¬ ��� ( X 50cm)PMT . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4���>?#4�576s�98:

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5 @���A�B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1 /��^M�N X#O ; ��6FP8��L � k W � k � . . . . . . . . . . . . . . . . . . . 21

3.2 /�� L �>~ � . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 /�� L �>~ � L h�,���� . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4 TQ� k � . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.5 20 ¬ ��� PMTL h�, Ç < ! . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.6 � LSR�Â9T Z%e L � k W � k � . . . . . . . . . . . . . . . . . . . . . . . . 24

3.7 ��� 420nm ������9���� p /�� L�� { . . . . . . . . . . . . . . . . . . . . 25

3.8 ����� L ��� ��! Ç#" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.9 � LSR�Â9T L h%, � � . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.10 LINACL%$ � &('*) Q,+lQ L.- /�� 0 � L%0 «�1��3210�D�E�9 . . . . . . 27

3.11 LINACL

endcap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.12 LINACL ½ � 8 k a%4sÇ�" . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.13 LINAC energy scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.14 LINAC position dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.15 Ni-Cf M�N X[O ; �67Pl�#L � k W�� k � . . . . . . . . . . . . . . . . . . 30

3.16 DT generator data taking . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.17 5�66¯87 DT M�N X�O ; ��6FP8�8L�4�`�a1Wcb . . . . . . . . . . . . . . . 31

3.18 DT M�N X�O ; ��6FP8�3^ \ L ¶�· b�¸/��4�9>�lb�L%: B ��! � . . . . . . 32

3.19 DT M�N X�O ; ��6FP8�3^ \ L ¶�· b�¸/��4�9>�lb�L%; < ��! � . . . . . . 32

3.20 LE triggerL

efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.21 SLEWlX>=%�

-260mV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.22 SLEWlX>=%�

-250mV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.23 SLEWlX>=%�

-222mV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4

3.24 SLEWlX>=%�

-212mV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.1 goodnessÇ "

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2 Qres

L6 � L »%¼�������9 DL

Ç#". . . . . . . . . . . . . . . . . . . . . 39

4.3 The distribution of the likelyhood for DL . . . . . . . . . . . . . . . . . . 40

4.4 The distribution of the likelyhood for DT . . . . . . . . . . . . . . . . . . 40

4.5 Distribution of Qres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.6 Qres

Llikelyhood function . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.7 SK 1260days cos θsun distribution . . . . . . . . . . . . . . . . . . . . . . . 43

4.8 ��� ����?��Å���#b�L ¶�· b�¸/� 4/`)afW b . . . . . . . . . . . . . . . . . 45

4.9 8BU�V�CWlX�Y i%jZk a%4�L ��� o . . . . . . . . . . . . . . . . . . . . . 46

4.10 crossection & cos θÇ#"

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.11 0th order output positron energy . . . . . . . . . . . . . . . . . . . . . . . 47

4.12 1st order output positron energy . . . . . . . . . . . . . . . . . . . . . . . 47

4.13 �Z P3Q 9��Z 4/`)afW b . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.14 Expected4�`�a1Wcb

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.15SFT%^ \ L νe i�j�k a�4>LRm�n8o . . . . . . . . . . . . . . . . . . . . . . . 50

4.16 Fitting for final sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.17 Fitting for MC sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.18 �1³ Ë 0�E m%n#o�L ¶�· bZ¸���� . . . . . . . . . . . . . . . . . . . . . . 52

4.19µ�¶�· bF¸�� ¬ v]��W3p ���8� µ

p3L h�,�È Ç�" . . . . . . . . . . . . . . 54

4.204�� ; ��6FP8� ¬ v��]W_L�� � p ¶�· bZ¸�%L 4 � . . . . . . . . . . . . . 55

4.21 ��� ����?��Å���#b   L 4 � ; �67Pl� ¬ v]��W L�� � (DT≤100sec) . . . 55

4.22 DL �� n ��� � 7�E8��� L µ�¶%· b�¸�� ¬ v���W3p ���8� µp3L h�,�ÈÇ#"

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.23 SK?��lalL��Z^ \ 5m Á� L ¬ v ��W �A[>E�g µ�¶%· b�¸R� ¬ v � W�p �

�8� µp3L h%,�È Ç�" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.24 SK?��lalL  �� ^ \ ��^ \ 5m (#* L ¬ v6�]W ��[�E�g µ>¶%· bF¸R� ¬ v��W3p ���8� µ

p3L h%,�È Ç�" . . . . . . . . . . . . . . . . . . . . . . . . 57

4.25µ�¶�· bF¸�� ¬ v]��W3p ¬ v��]W_L È . . . . . . . . . . . . . . . . . . . . . 58

4.26 � run �R��E%D L ���3� µL h�,#È Ç�" . . . . . . . . . . . . . . . . . . . 58

4.27¶�· b�¸R��L�� E����R9����8� µ

p µ>¶�· b�¸R� ¬ v�� W L h�,�È Ç�" 1 . 59

4.28¶�· b�¸R��L�� E����R9����8� µ

p µ>¶�· b�¸R� ¬ v�� W L h�,�È Ç�" 2 . 59

4.29¶�· b�¸R��L�� E����R9����8� µ

p µ>¶�· b�¸R� ¬ v�� W L h�,�È Ç�" 3 . 59

4.30 ��� ����?��Å���#b   L 4 � ; �67Pl� ¬ v]��W L�� � (DT≤50sec) . . . 60

4.31 2.2MeVγL � �#8�Rb�=�6��sV ; ��6FP8��L�Ç#" . . . . . . . . . . . . . . 62

4.32WRX�=>��6)�lV ; � 67Pl� ��� 08g�� L 2.2MeVγ

L � �[8F/b =�6)�lV; ��6FP��8L�Ç ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5

� �

1.1 ������������ �������� . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.1 Summary of spallation products . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Reduction summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

6

�1 �

1960 ������� R.Davis ��� �������������������� ��! P3Q ��"$#&% 30 �(' [1] )�*+�,.- �/��0�1.2�"3#54�! P�Q�6 �7�8������� �:9.;�<8=�>�/?A@B��! P�Q:C �7�8������ ��D��7EF#G"�IHKJ�L �MLONP�:�����8��� �I�AQSRKT�U.V P�Q ��L�J�L W(X �IYZ�[]\6�C�^ )8_$` a �:��0�1�2 �S��b�)�c(dM�A��!�e 6 �7���f����� �S��b�"$#&g(hSJ�i j��J P�Q �Fk C WldM"ldB)8ghAJ��:��0�1�2K[�m:L��K@�X ��QSR �SU�V�T�n(o�p�".J�": C W` C )�qsr��t��A A� u/v P�Q�C �����f�S��� �wLlNyx�� ��z.{|@G}(�~O`��:�.L 6 W ,- ����0�1�2K7�w�/��)��.x�� � ;�� �I��DT�����d�) z�� �8�7�8������� T����[t� C� )�����0��7�:�$�M@ �.����� ��@B��� ��dwJ�L8WdI"ld8XI�3#ITI���FI�3��L �7a7� 6� ��.� ��dI��� 0 ���.L��@P�� |d�J�L ��a:�� ���).¡8zO 0 a:� 6 �MLsN5¢�£�n�¤�T¥ #G�:��L.J�L�W¦A§ ) 1998 � The Super-Kamiokande Collaboration 7�� I�A)8¨��/�7�A�©�S�I�.9.;�<=�>���ª�«��.¬�­.®/"$# νµ �����A�©���I�]¯�°O[M±sX�dM�.L 6 )8²�`F?³H�J|´ � @ 1 ² ����A�3�S�I�AA²�L8���������Sµ/¶���a�� 6G· [2] ��¸�¹$�t�A)t�.�/I¨$k�J�º|»A[]¼ ^�C�.TS½�¾(�¿�dtL�WS�:�����8�����I��8²�L��F@�À�gF�) ���7Á ��Â�Ã��/"l#y¸.Ä7e 6 νe�A���[t�$ÅI)�c��8�/���f�����]¯:°(��� �� νe � νx �Æ�Ç�e 6 � I��!3�t� 6 ���8��S��� �S�7�8�$��L � @�i.Èl#B� 6 � ) É�@I�����©� �I� �S���70:���:�$�B[w� ���LC�Ê �.).�:��ËSa:T Ì:L�� Ê � 4.Ís�I� 6 �:Î�Ï � νeL � Ð Ï � νeR �Æ�Ç©dP)���!OÑtÒJ.L �ILlN]0.1.2@�i�Ès#P� 6 WÓ�Ô�Õ a�T�)��.���©���I���S���70��.�:�O�Ö[M�7² Ê �Kt)w�:��"l#³×.Ò.e 6 � ��Ø����A��S��� � Ù������������������Æ�Ç7e 6tÚ�Û ®$[t\Ü?Ý)/>�� q���ÞFßtà�Þ(��1 1260 á �1:�7â �Bã�ä�e 6M· /�(?³Ù����K�7���f� �I� �:9�;�<8=A>��.ª�¶A�K�²:L.��i j/e 6 W1.1 åçæéèëêçìîíðï_©á�)��/���8Â�Ù�ñ(/� �� ò.ó('�ô�¨/J�õ�ö 2K÷��:[t¸�Ä|�wø7�.L 6I· TSùú´üûú#P���L 6 W�ý7þ�ÿ��l���dPò7ó �����$[���².���/T8)���)��� F��7�$[����©dt�:õ�ö�2÷.��[I¸7e 6���� ��3? )Fc � 98.5% `8a:T pp-chain(proton-proton chain) ���:�8� 6Ù.ñF��� ���õ:öA2(÷���[M¸�e 6 WX � pp-chain �Iz��FT���« �K�:NtJ��Ka��|��� 6 W

4p → α + 2e+ + 2νe

X:X�a 2e+ T���Z�� � �G¬� "!�d���% 1MeV ��õ�ö�2÷:��[�¸�Ä©��ø�)�z�� ��d���%27MeV �8õ:ö�2(÷���[$#�².W ¦8§ )3X �SÂ.à ��Ù�ñ$��� �� 2 ² ���������A��� � ¸�Äe 6 ��)&% 1.1 ('/e$�:N�S)�¨F` "� pp-I,pp-II,pp-III � 3 â*) � (+/".� 6 W

�1 � � 7

(1)p+p → D+e++νe

99.75%

(2)p+e-+p → D+νe

0.25%

(3)D+p → 3He+γ

(4)3He+3He →4He+2p

86%(5)3He+4He →

7Be+γ

13.8%(6) 3He+p →

4He+e++νe

∼ 0.00002%

(7) 7Be+e- →7Li+νe+(+γ)

13.78%

(8) 7Be+p →8B+γ

0.02%

(9) 7Li+p →4He+4He (10)

8B → 8Be*+e++νe4He+4He

4 He + 2νpppp-I

4 He + νpp + νBe

pp-II

4 He + νpp + νB

pp-III

4 He + νpp + νhep

% 1.1: pp-chain

�1 � � 8

` C )sX � pp-chain ������ÿ�"s#�¸�Ä d C ��"�/�. S� )�������� ��� ��õ:ö�2K÷.���:« ���7NwJ��/L [3] �:� 6 Wp + p →2 H + e+ + νe : Eνe < 0.423MeV

p + e− + p →2 H + νe : Eνe = 1.445MeV

7Be + e− →7 Li + νe : Eνe = 0.863MeV (89.7%)

: Eνe = 0.386MeV (10.3%)

8B →8 Be ∗ +e+ + νe : Eνe <∼ 16.5MeV

3He + p →4 He + e+ + νe : Eνe < 18.78MeV

X � pp-chain "s#�¸.Äfd C ����� �A���A��)����O��fd C�Ê ��4�Í3��� 6 > �F=�ü2F[ 'fd C �8� % 1.2 a7� 6 W.>7��qK��ÞFßMà7Þ���1 ( ��« SK) ��õ�öA2(÷����A�l[�i� ���� 6 �P)���! Ú/Û J���T 8B �/���f�S��� � hep �������A���Aa7� 6 W

% 1.2: solar neutrino spectrum

` C )��7�8���A�I� �S¸�Ä�D��P�:� �I�������� ��[$'fd C �8��% 1.3 a�� 6 W�(?��L��.�(T���?����7a�)(cFdM���KL����(T��(?MÁ��F��/L! "�a8Ù�ñ$[M±|X�e · �*+�" 6 W¦�§ )�õ:ö�2K÷.��Ä�# �%$Ü? 1.5% T CNO cycle (carbon-nitrogen-oxygen cycle) ���� � 6 Ù�ñK�J: ���L 6 W(X ��Ù�ñO[ ' d C �8� % 1.4 a7� 6 W(X ��%�[I¹7�*+7" 6 �:N ) C,N,O � ¦�& e 6$��� ��Á a p [� �' d�)/�/���©� ����[M¸�Ä3��ø 6I· ��+/" 6 WX �SÙ�ñ(/�. S�A¸.Ä/e 6 �/���©� ��� �8õ:ö82(÷���T*��« �%(Ü? [3] a�� 6 W13N + p →13 C + e+ + νe : Eνe < 1.198MeV

15O + p →15 N + e+ + νe : Eνe < 1.732MeV

17F →17 O + e+ + νe : Eνe < 1.736MeV

�1 � � 9

% 1.3: Production point distribution as a function of the solar radius

p+12C→13N+γ

13N→13C+e++νe

p+13C→14N+γ

p+14N→15O+γ

15O→15N+e++νe

p+15N→12C+α p+15N→16O+γ

p+16O→17F+γ

17F→17O+e++νe

p+17O→14N+α

∼4×10-4

�1.4: CNO-cycle

�1 � � 10

dw"$dG)$X � CNO �"):=�2K7�� �� ¸�Äfd C �/���©� �I��TS):>��AqK��Þßwà�ÞF�w1 �õ�ö82(÷��!�8�|�/?A@�«�a�� 6 � I��!7e 6M· ��Ñ�Ò�J�L�W1.2 � ���

����� �

1998 ��) The Super-Kamiokande collaboration ��¨��7���A�©���I�M�.!K7� I� νµ →ντ (νx) ¯�°�)��(oA)��7���f� �I� ��µ�¶S���7�8¸�¹3�t� C W�ÀSg νe, νµ @M���l[]��² �i�Èl#]��)Kc�� Ê � νe ↔ νµ(ντ ) ) νe ↔ νµ(ντ ) ¯�°/� ±$k 6 W1.2.1 ������X�X�a �.� ����µ����l[ ν1,ν2 �I��´ �&)����FÁ�a �79��t� �K� ����� ��T��:« ���/N���e$X �M��Ñ�Ò 6 W

(

νe

νµ

)

=

(

cosθ sinθ

−sinθ cosθ

)(

ν1

ν2

)

≡ U

(

νe

νµ

)

X.X�a�) θ T!���Á8a � ��� �a:� 6 W` C ) νe,νµ T!���FÁ�[ ��Z�x�� ��dI�#"�$:e 6 � )���� ����µ����KTS)(

ν1(t)

ν2(t)

)

=

(

e−iE1t 0

0 e−iE2t

)(

ν1(0)

ν2(0)

)

Xt�|#w"s#&) νe → νµ % ��¯:° �!&�'KTA)P (νe → νµ) = sin22θ · sin2

(

1.27∆m2L

E

)

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�:Þ;���(� ) � Z0( ÁM®�Þ;���K� ) [=<?>sd���� ��@ �A�I�3�t�w�BA?CF[�±OX]e���G¬sdÖ) νµ(τ )T Z0 �?D�[E<F>�e 6 � �)E2.�(ÁAa-GIH 6-J+K �-L?MG2�N* (Ve =√

2GF Ne, GF : 9!Ow2ßPn��� .D , Ne : ��� ��D ��� ) ��� 6 "3#Ma7� 6 WlXw��#P2��Á��RQ�¤$[ �7� C "�$ §� �FTA)���« �K�:N��J 6 Wid

dt

(

νe

νµ

)

= H

(

νe

νµ

)

X.X�a#SsßG2 � �8T��AT H ' E + 12E (M2 + 2EV ) a7� 6 W�` C ) J�K � L+M�2 V TS)A¬

�# + �-5�(�Us[V*fd-W.L��V =

(

Ve 0

0 0

)

�1 � � 11

M2 TS)M2 = U

(

m21 0

0 m22

)

U−1

� �:eKX �B�:ÑMÒ 6 W���#] A = 2EVe = 2√

2GF NeE �=4�L � ) H "$# E [ *�d Wl´ �y)2EH =

1

2(M2

1 + M22 + A)

(

1 0

0 1

)

+1

2

(

A − ∆m2cos2θ ∆m2sin2θ

∆m2sin2θ −A + ∆m2cos2θ

)

�wJ 6 W$Xt�|#w"$# "�$ § � �FT���« ���/Nt ��� Ç$��� 6 Wid

dt

(

νe

νµ

)

= 2π

(

1Le

− cos2θLv

sin2θ2Lv

sin2θ2Lv

0

)(

νe

νµ

)

Lv :4πE

∆m2

Le :4πE

A=

√2π

GF Ne(t)

X.X�a�2��FÁ � � � ����� ¦ � Ê � (A = �D ) ) νe → νµ �I¯:°�&�'KTP (νe → νµ) = sin2(2θm)sin2(

πL

Lm)

�wJ 6 W$X.X�a�)Lm = Lv

[

sin2(2θ) +

(

Lv

Le− cos2θ

)2]

−1

2

sin2(2θm) = sin2(2θ)

[

sin2(2θ) +

(

Lv

Le− cos2θ

)2]

−1

5 7����(T Lv = Le cos 2θ � Ê �F�¸.Ä©dB)���¨ ��¯:°O[w±3X�eSW�.ª���?ü)�¯�° �t¨$k�� θm T�� � �ID�� � (Ne) ����O[� �w)(� 1.1 ���:NtIÆ.Ç�e 6 W

N resonancee =

∆m2

2√

2GF Ecos(2θ)

Ne 0 � N resonancee � ∞

θm θ � π/4 � π/2

� 1.1: ��������� ��� �� ��� �

X � Q.¤�TIu/vd C 3 � ����� ��� Õ�� "l# MSW (Mikheyev-Smirnov-Wolfenstein) Q¤ [4] � �:��� 6 W

�1 � � 12

1.3 Resonant Spin Flavor Precession

@:dM���8�f�S������>��.��[MÙ � �wø 6 �/N]JA�.�70:������B[w�7² Ê ��)S� Ê ������� m(/�� S���7���f� �I� ��� � L K�� � Î�Ï kS"$#�Ð Ï k��Æl��� ¥ 6 Wid

dt

(

νL

νR

)

=

(

0 µB

µB 0

)(

νL

νR

)

X ��T�)�1 � T.T Cisneros [5] �� ��Au�l����) Okun,Voloshin, Vysotskii [6] �� ���������A�|�A�I� Q�R(I¬�e 6 U���dM�Au�l�t� C W�` C ) νL �:Át®/Þ � ��&7� 6!J�K� L�Mw2 ��� �O[� � 6 ���¬|dw�A) νR T� ��J�L�W�c � � )!2��(ÁAa7T�� ��d C MSW

Q�¤����/Nt�������������� � 6!J�K ��LFMI2��R*(��/?Ý)#5 7 9�IÐ Ï ��������������Æ�Ç7e 6 WlX�� νe � � 6�J�K �#L M�27T*�7«�����N���l��� 6 )Hνe = H(νee → νee)Ne + H(νep → νep)Np + H(νen → νen)Nn

=G√2(1 + 4sin2θ)Ne +

G√2(1 − 4sin2θ)Np − G√

2Nn

=G√2(2Ne− Nn)

À�gFS)Hνµ = − G√

2Nn

X.X�a Nx T!2��Á��D���l[ �fdB) Ne=Np [tm�L C W` C )��7�8��� �I�A��1 � ;�<S=Ix���"�����;���x��(J���"�a8)8Ð Ï ������������� �6 J�K ��LFM�2K �(L��7� 6 W(@7d]1 � ;/<S=A���8�f� �I��� Ê��� Ð Ï�� �"!�#%$ &(') 2��+* � ����,.- /10 ��2 JFK43 LFM�5 ) � /076�8 � � � (9AÆ�Ç ) : ��;�<>= �?(@�A>�id

dt

(

νeL

νR

)

=

(

G√

2(2Ne − Nn) µB

µB 0

)(

νeL

νR

)

µ :�B!�#C$ &�' ��DFE"G #�H 3 $

G : I8O(5.J �KB : D�L

Ne : MF���>K��F�Nn : N>O��P��K��1�

Q7R ����S�� �T!�#C$U&>' ��L �� νR = νL 2"V A�WYX 2Z+*\[ �F��,4]_^�`"- �Fa�bP3cFd 5 )�e�f ��;�<>= / A 6

Hνe = − G√2(2Ne− Nn)

Hνµ =G√2Nn

�1 � � 13

` ��� � ���7S � �B!�#%$�&�' ���9�� ) e"f ��� �id

dt

(

νeL

νµ

)

=

G√

2(2Ne − Nn) µB

µB G√

2Nn

(

νeL

νµ

)

=T; ����� ?>@�A 6Y`` 2 νe 2 /�� νµ

/�� ) �CPT ��� =�;���� νe → νe * 0 <��������� ?U@�A � � transition(flavor-off-diagonal) magnetic moment

�� �! � A�W.X 2"VA[7]6

` @ X � "�# =";%$ ��a�bY3 c�d 5 ��& =B;���� �F!1#%$�&>' �(' & c b*) # ��+-, ��.� �_/ $0/ A * 0 <21 � Lim * Marciano [8],Akhmedov [9] =�;-����3 ? @54 6 ` @ )Resonant Spin Flavor Precession(RSFP) *768 @�A 6

1.4 9 :�; <>=@?BADC ED;GFIH < JIKML�NOQP+- 4Resonant Spin Flavor Precessin

) � D�L�=B;��R�S%T 3 �R+-,�] ^�`7U ;�</ D�E"G #FH 3 $ ]V!XW L � = YZ$0[ \B2FV A 6�8� � � D�EBG #FH 3 $ = W�0 � "�] A� )�^_�`Qa�b 2FV A 6cdfe 2 �hg�i�j k =�; A DFE�GXl H 3 $ �Qm Y�npoRq e�f � ;�< =Vr%s X @ ��t A�uS�l�vwl xPJzywx|{~} 825 � ��� � }�l�� ]7� =hq�D1EBG�l H { $ ]z!|W L�� �7��w������ S��%� $�� ��� � W X qµνe < 1.5 × 10−10µB(90%CL) [11]

u� ��� W.X �

νe

��� � W X qµνe < 1.8 × 10−10µB(90%CL) [12]

ue−e+ → νµνµ

W.X qµνµ < 7.4 × 10−10µB .(90%CL) [13]

uντ e− → ντ e−

W�Xµντ < 5.4 × 10−7µB .(90%CL) [14]

u` @ X g�i j k ="; A j�k � o���=�q(�-���p��=X�7�X�Ql $���� � DFE"GXl H { $ ��m Yn � r*s X @ ��t A [15]

u ` @ o�q ' ����� 3   WYX¢¡-£ ��=";Q�R� 12C]¥¤ A � tY< c{�¦ ��§�¨�© =B;��R��ª ]¥«¬ ?~­ ��t A ¨�© =�V A q�®�¯B°²± WYX´³(µB¶V·*4 � � ¸ V¹ u �Xº7���Ql $��7� � D�ETG�l H { $ ]z! �R��t 4 L���q�»�¼*½�� ¾º 4 ���(l $��7�½|¿�����ª �QÀ@Á ¶R· ¹ �½FN�à ��Ä�Å � f � $ (cooling) qwÆ · ½%¿Q���-Ç�È �QÉ � §¹ u `��("�# W X D�ETG�l H { $ ��m Y�n ] r%s ¹ 1 � a|Ê ¸ q(�-���p� § _�Ë WYX � D

ETG�l H { $ ��m Y�n%o�qµν < 3 × 10−12µB(Majorana)

µν < 2 × 10−12µB(Dirac)� § ����t ¹ u

�1 � � 14

1.5 ����� � J νe ����� � J K L Ne m������ ¨�© ½���t��q*�*� l $��R� �• SpT�{ ]7+�, ¶~­ ¹ ¿�� §������ l��w{ $ ]V!*W• � ��N � � L ��!#".%$ t• Z�& ]z!(' q*)�+ ] ^ `~U• ,.-�S�/�0 �� t1�3254 ]76 4 U L��5½ νe → (RSFP ) → νµ → (Oscilation) → νe ½w¿ ���8��� W X

νe

�:95; º7��t ¹ � t<� a*Ê O � "�] Xz· ¹ u νe o � � � .<$ § ���*�(� � ]~! �R��t¹ 1 W X q=��� W X � νe

]?>5@wU ¹ 1Âo-�|� l $��R� � ����� l��*{ $ ]BA�C ¹ � ½�DE W u` · e ¸ �=� WYX � νe F S=G���S �-m Y�n � / X²· ���B$�q S�l�v5l-xIHzy�x5{~} 825 �� }Xlw� ]7� ½

Φ(νe)/ΦBP98(8B) < 3.5%(95%CL) [10]� § ����t ¹ u

1.6 Resonant Spin Flavor Precession JLK M:NL�O� 9 :�; <=@?�PRQ JTSOUcXd q��I��|� l $Q����V�W ��X � º7��Y¾�z[�Z § � o MSW \ k ½*¿ ¹ �w�-l $��� )#+ ]\[ t ¹ � } � ¸ V $ q RSFP

]\[ t 4 X5] ½ W t�Xo�V e $_^a` ¶R· ��t § t uº W º q RSFP ½*¿ ¹ X*] � ^#b º-�dc*e ¶h·�4gf ¸ o § � [16] q Joao Pulido�

E.Kh.

Akhmedov ½|¿ · 8 [17] q µν = 10−11µB , ��� �ih�j5k%�ilp� ��m � 3 × 105G [18] V ·8 !5" ½i�=�����(l $��7�gViW ½ W t� ��X � º¥�gn $ E W � º¥��t ¹ u e 4 qÂ��º `����� ��m ½ 2,3 o ��p t � V · 8�q ��� �@�V/ X ·X4 �5��� l=��{ $ ��m Y5� 6 4 º q�����*� l $��R��V\W ��X � º7��t e8q ½R[\ ¸ V ¹ u

1.7 rtsvu J wyxO�z e ¸X�-"�# ½|¿5$ q��=�5{%| νe

�89�; U ¹ a|Ê�} �5~ ¹ u ��º²q�����{%| � νe F� G(��S � 0¸ oi�wt m �p½ o-��� l $���� ½ ����� l=�X{ $ � � d U ¹���� � § $�q .$ § ��� ���#�5½?� � ¹ � "�] | · ¹ u8��� F � G���S ��m Y�n � r e ¹ m ��q5,I- � /�w�-l $���� ½ hwU ¹ ����� l��*{ $ � m Y�n(�Vr5s ¹ � � § $�q|Æ · ½*¿%$ Resonant

Spin Flavor Precession ½*¿ ¹ ����|� l $����gViW �iX�] ½��5Y��?� ] ¹ 1f½ § ¹ u��� � ¸ o�q ` · | �i�*� � �1� ½|¿*$�� �5{(| � νe F � G(��SX½ W t� X�� �B��� u

15

�2 � � � � � � � � �

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Detection Experiment)¸ ~ ¹ u SXl�v|lxIHVyXx5{7} � Á�� o������� �!�"$#&%$' ��()+*

( ,�- 36.43Å

, .�/ 137.32Å

))�021

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ν + e− → ν + e−

νe + p → e+ + n

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\ X�8�X ò�ó 20inch(50cm)

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LINAC room

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water system

control room

electronics hut

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A

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0

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113 Li 0.0085 β− 20.77 ( 31 % )

β− n ∼ 16 ( 61 % )114 Be 13.8 β− 11.48 ( 61 % )

9.32 + 2.1 ( γ ) ( 29 % )124 Be 0.0114 β− 11.66125 B 0.0204 β− 13.37127 N 0.0110 β− 16.38135 B 0.0173 β− 13.42138 O 0.0090 β− 8 ∼ 14145 B 0.0161 β− 14.07 + 6.09 ( γ )156 C 2.449 β− 9.82 ( 32 % )

4.51 + 5.30 ( γ )166 C 0.7478 β− ∼ 4167 N 7.134 β− 10.44 ( 26 % )

4.27 + 6.13 ( γ ) ( 68 % )

- 4.1: Summary of spallation products.

��� � <Å% spallation products e�X���� ������Â��,² X �=­�������?� ��� spallation

products� L��4+ - 4.1 �=B��C@�A-� 0.001 Á��8: 10 �IÁ ������ ��!#"{% � MeV $

20MeV�

β % γ �/­��% ( F�U¾¼-�DV@W*)?¹Tº�)�� ) & � ]E\��(' � h�iTjBk�)+*�,�+FEG2H�q�).-*(�� ��/�0#1+2 D :��34*�,�1E\8Y´%�5<��7+C E�½�6 ��7 �'eL7By�z D �8a�'�9;:<'L�¾: spallation event =4?>�[ 1 :EJIK � 3 � �A@ �CB )���)�:

DL : S�U{V µ��DFE e � h6iTj�k;),¹4º 7 - � C�)4s@E�½�F �+G�H

DT : S�U{V µ��I�JLK �;M�Nbe � h6iTj�k�),¹4º 7 -M]�­�� K ��M�N ��O

Qres : Qtotal − p(t)L

= 2�P z likelyhood function =4QcYR:�S F�U�¼T):V W 7 ¹*º 7 -+U K �LVW= XB��Y8#'�'9 Qtotal Z :(' � ¹4º 7 - � �6² ��[ �F: p(t) Z µ

�ADE#�]\ ��^?�T_�Y 1�/0 �����photo-electron :�a K z L Z µ

�YDFE3� ^��Y9 \�Y`: V ��a )�=T�Fb K �{_2`c]d2� � -

�4 � (�)������ 39

� E*½*]�� v�� =_6` 1��%��� 1� +8" 4.2 Z : Qres

��3P1 � y�z DL ,���� ������� � ��%=.B K �%& � 9����;:<' �" 1 B � � � 1 a������ � Qres

1�� y{z DL� ,�� & ��� K z P � �4,����8 a ��� :

Qres

1 � � likelyhood function�A@ ��B )F�;)%&�a������ 6 � 1 ,��*z 2�� K :('?�

U ��3P1 ��Y K z P +8

4.2: Qres ! 6 " !�#�$&%�'�(*) DL +�,

4.3 - 4.4 .�-�/*02143�576�8:9<;>=@?BADC�EF8FGIHKJ�?�L DL +M,->N O DT +

,QPI-SR�T�U�T ! likelyhood function HWVX=ZYM? )�[\ L�- 4.5 . SK ]M8�^ %@_a`Ib>c>d�e L µ ! Qres +�, (Fcorrerated) d ->f ! �g�hi�j�k�l 3*C�Em8&G !�n 0.1 o�prq ! µ H�J�?�Ls+*,*-�R =@Y>t ! �g�h i�j�k l 3*C�E8 G@P�.>u@v !Kw ?MC�E787GIH@J�?*L�+*, (Funcorrerated) d�xM)K[�y Tz; 2 " ! +*,M{F;|-}*~ G�]�C } ! likelyhood function (LQres(Qres)) .�p�t !r������� -

LQres(Qres) =Fcorrerated(Qres) − Funcorrerated(Qres)

Funcorrerated(Qres)

dK��� ;IT )K[My T�H���=@L ! g* 4.6 !W���dMx�)K[�� ; %�ys! LQres(Qres) HZ� % =ZY��������� 8���=�- Qres %@����) likelyhood function H ����)K[�yK! likelyhood function

HZ��=@Y�? )�! gM 4.6 !��M��d�x�)�[p�f 3 �>� !�� �*� 3�]�3�H�J�?Y*/�0Q�Z3M5F6�8�C�EF87G�.�� `I  {T�Y>? )s[=W{m=�-�¡ ¢ � µ .�£ 2.2Hz d SK ]�8�^ %@¤�e =@Y '¥` -�¦Mo>-�¦ � o !K§r¨�© H4ª�"

�4 � ��)������ 40

�4.3: The distribution of the likelyhood for DL

�4.4: The distribution of the likelyhood for DT

�4 � ��)������ 41

�4.5: Distribution of Qres

�4.6: Qres � likelyhood function

�4 � ��)������ 42

spallation products1�� ���� 7 - 1�� K�� DT

@�� B )��;) 1�� �� �r��P ��� Z :��� 1 5�� � dead time =���� Ks��P���� �� 9�� ��P 8���� � ' � spallation cut 9Z :��� $�!��� � ^ P+�F�� =�!"� spallation products

1�� #�$�%C6 � 7'& �)( >Z cut

K �+* ��P��CP-, ��.�/ �+*%�8%' � ^ P��F�C =�!0��1�2�3�)�465 7 ��� 7 - 1� P�� Z�798 �;: 8

4.1.6 Second Reduction

< U 1)=0>�? Reduction =A@ : , 1���B-� : SK?-CED9F0G�H -)I-JAK�L�9 2�P : final

sample M � : 8• New goodness cutN9O b < *�P�# H�Q $R%R1 ?-S9T"?RUV�XW�Y / ? # H)Q $-%�1�=X�Z� �[: 8�\]* U_^# H)Q $`%R1 W � Pa� goodness =Ab c Kedef�? N�O b < *�P]# H)Q $g%R1 ? goodness

M`h9i �":�j'k K � : ���'l'm W���K�� J��9nE���'lom �ap��)* ��q P�r�s d�ft?goodness u�va*�w Ja��nE���'l6m ?-x�y'z�{6|���}tq�~�W9�"B���q : u����0� ��d\ ?��)daY /�# H�Q $-%�1 ? goodness M ?R� k`� < q MX����w�* :-j \+*�w ?��'�� w daf"? # H�Q $-%�1�M Y /�# H�Q $-%�1 ? goodness

?���� � < q r�s d \+*�w? �Z�6l'm z+���X��� j• Cherencov ring pattern cutN�O�� < *tP direction M d N�O�� < *tP�# H�Q $�%�1 � w HIT ��P�^ PMT �? ��%�m���M ?�� ?-��z+�;� :)j vt� ��d�� l Q0� �� �4"¡ G 3 H 4'5 l � w£¢wg*EP � �6?R¤�¥ � w �;� w�*[P likelyhood function M`h�i�� d s0¦ �9q k ?�z�§���¨� j \R* W�©t� 1�2�3 H 4;5 l)���6l'm«ª d Rn ¬�­ ? 214Bi ® da¯ � ? ringz]° ��± :0k ? u�²�³�´ �g�)µo¶+· :�j

• Clusfit cutN�O�� < *[P�# HZQ $a%�M HIT ��P)^ PMT M ?a¸9¹�º�»)d�¼t½���¾ º6»Ez+�6�:�j;k � d � : PMT?

HIT� Ja�Zn����'l6m W0© :�k ? ��� B P-r�s d \]*�w 2

� ?Rº;»�W�� � � .�¿ < * :�k ?�©;�ÁÀ � ���"��°¨Â :�j v ?RÃ�d \�*Äw ? HITz

�§�X��q�� k�ÅgÆ E# H�Q $�%)1 z N�O���± :)j \ ?t© Å W N�O�� < *�P�# H�Q $% 1 �)Ç ²�È�É9Ê (ID

?�Ë � w 2m=�Ì

) �0� B P�r�s d \ ? ���'lom z+�Í�g�Ä� j• Gamma cut}[Î�Ï �[Ð H�Ñ9Ò6W ÓEqZ� u d SK Ô�lZ% ? Ê�Õ d PMT

?�Ö�� 1 ��× � w � : γ Ø® ? #o$-%9Ù ��Ú l & u À � ��Û s zZÜ � :Rj v ?RÃtW-d ��� N9O9� < *EP)# H�Q $% 1�M direction

z h9i�� d SK Ô0lZ% ?�Ì Õ�ÝtÞ W�ß�° �-P9���'l6m � × Å � z+à� ± :�j9á WEÌ Õ�ÝtÞ W�ß�° ��P��Z�'lomâ�0� : r�s d 6.5MeV

=0ã �0� : r�s�u# H�Q $)%�1 ��Ë � w 450cm

="ÌRd6.5MeV

=0> �0� : r�s"u Ë � w 800cm=�Ì�?

r�s W \ ? �Z�6l'm z+���X��� j

�4 � � H Ô+K�L 43

4.1.7 Final Reduction

=E>E?Reduction u d�C[D � w ? νe �Z�ol'm ? K�L W��[q : ÃtW�� � : cut ��� :)j

• Energy cut

7�8 ± :�� b��a1�2�3 H 465�l��Z�ol'm ? K�L ?�� � w d�� 8.0MeV=�>E?ZÎEÏ

�tÐ H�Ñ�Ò�WaÓEq�� u Rn ®� ���� f�;? #�$�%�Ù �0Ú l & ?�Û s ��À � q M]���wg* :�j v ?)Ã�d�������? K�L[�0u 8.0MeV

=0ã�? ����lom z��[q : ,�W ��P j =ã�?��6��W[©;� d N�O�� < *�P Î�Ï �tÐ HZ� 8.0MeV ��� ? ���'l6m z]�Í���¨� j• cos θsun cut

�4.7 u d�� 8 �-P Reduction

z�� ��P�� d 8.0MeV=0ã�?9Î�Ï �;Ð H)ÑZÒ6? �Z�

lom z��[q P cos θsun

¤�¥�z�� � ��q :)jC�D � w ? νe �Z�ol'm£u dtF0G9H m I�J - �!�"�# W"©9B �%$'&�? �! z)(�* ± :Ã�d�F�GaH m�I-J ?�+�, ÝtÞ W.-�q�º6»�� � :Rj v ?)à \ ? νe /10 l6m_u d \ ?�2?43©?�Ñ�Ò�W�5�6 ��7 q :�j�Æ Ý νe /10 l'm£u d � 8 ± : © Å W98: Æ<; W�¤�¥± :)j v ?�Ã�d9C[D � w>= · ± : νe /10 l'm �@?ACB�DFE1G uIH© M9J© G�Ñ�Ò �0�E j � � �LKNM GPO�Q �Eu dRTS � w G νe /10 l'm z]�VUg�¨� Ã�W cos θsun ≤ 0.5G�Ñ�Ò

( H© )z��Eq9W j

SK 1260 days data(E ≥ 8MeV)

0

250

500

750

1000

1250

1500

1750

2000

2250

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1cosθsun

cosθsun < 0.5

① ②

24.7: SK 1260days cos θsun distribution

4.1.8 Reduction summaryX ãGZY)[�\�]'^ l z�� � W � G /.0 l6m z]d.�9���_GPO<Q'`��[q�Eba9c�dfe Ô�gÄl�h�Ci ± E jNj W d1klY�[�\�]m^ l�n1oZp�h�irq 5 � W /104s'tvu `%w�q 7.x 4.1`�� ±%y

�4 � d e Ô O�Q 44

Reduction step numer of events for data numer of events for MC

After real time selection 164771273 1533207

First reduction

Fidutial Volume cut 29528788 1103678

Time different cut 23248492

OD trigger cut 21711646

Electronic noise cut 21636900 1103678

goodness cut 21077368 1088997

Flasher cut 15249791 1085178

Spallation cut

Spallation cut 10797241 21% dead time

Second Reduction

New goodness cut 2910763 10.2% cut

Cherencov ring pattern cut 2183473 12.5% cut

Clusfit cut 1497559 1.8% cut

Gamma cut 267996 9.6% cut

lowenergy final sample(E≥4.5MeV) 267996 591005

Final Reduction

Energy ≥ 8.0MeV 40781 346849

cos θsun ≤ 0.5 25004 258852a9c�dfe Ô)g s h)� 25004 258852

x 4.2:k YP[�\�]4^ s n1omp@h�irq 5 /10's4tvu

�4 � d e Ô O�Q 45

4.2 ��� ������ �� ������������������� ���2

4.7G H© G�Ñ�Ò�� �RTS �"! G

νe /10'smt �%?<ACB�D_E�Ñ9Ò �0� E ii$# `%�'&Í�G n)(+* e]'^ sP/.0ms't � q 5 ��7), E iA��� ! DTERÑZÒ�-/.�E y �106� � q32�74, Ei6587 ! DNE n/(9* ef]'^ s�/�04sCt `%w ,7 � � u4:<;>= G ?4@�?BA # w spallation

products C%DFENiHGI2�7$, E iJ5'7 ! D���K�D ! AJLVUNM"OLG'�1P'Q'`>RTSI-/.9E y/U GÃ)���9�1�<-/� H© G�ÑZÒ'G /10'smt ATV/W 7 ] Ù XZY ��w j UrR�S 0 ! G νe

`8[1E /.0s t i]\/^`_ �<R�S 0 ! G νe aZb p \ n G�ãZc d3Afehg�W y 2 4.8

�i�FK�D ! G�ÑZÒ(a

c d e Ô�g s h Y )G9Î�Ï YtÐ e n$j \ t Y -k. E y

10-3

10-2

10-1

1

10

8 10 12 14 16 18 20MeV

even

ts/d

ay/0

.5M

eV

cosθsun ≤ 0.5

24.8:

acfdfe Ô)g s hiY GZÎEÏ Y"Ð e n>j \ t YlZm �on/p)qCB�DfWvisible

ÎEÏ Y;Ð e : r m � 1 s t WCUu� 0.5MeV.�WZU�G /�0msCt* e t A x V

j W%�FK.G�Ñ9Ò'` Ó8v9E n/(+* e]'^ s�/.0'smt `�w ,7 G 5iw ��x�y)M%z'G1{8| � `w ,�7 � �Z} V_E y

4.3 Detector simulation

4.3.1 B8 ~��/���4��� ���3�k�I��'� RTSZ�d Y ` �Iv�Eo�4�%e t YT� a)b p \ n `@w ,<7 � ;3� Gi�)� d'� n'j \ t YC 5�64VTE C �@�����_` � ,<7 � 1998 � ` J.H.Bahcall,Sarbani Basu,M.H.Pinsonneault`I[ 2@7i�x B�DTW �'� RTS/�1d Y � BP98 [21]A%� , E y K.G BP98

`h[1E 8B�8�<e

t Y%�1G n$j \ t Y A x_ W�G C 2 4.9-/.�E y

�4 � d e���O�Q

46

1

10

10 2

10 3

0 2 4 6 8 10 12 14 16Energy(MeV)

/cm

2 /sec

/keV

24.9: 8B

�<�%e t Y � a/b p \ n GP?�A)dBP98(Bahcall-Pinsonneault ’98)

A1� , W 8B�<�1e t Y ��G n'j \ t Y y l)m �>�h�<e

t Y%����� Y�� e (MeV): r m � a'b p \ n (/cm2/sec/keV )A x V

4.3.2 νe + p → e+ + n crossection and cos θ distribution

n e�fe���� � s d������4-<G νe /.0_s't �6���<$F&.G �! A���e�� p t i$_ W �o�Pet Y%� - !�"# -k��� O � free proton

A��1e�� p t i$_ W X�� G�(��4�νe + p → e++ n

n + p → d + γ(2.2MeV )

[ U � � VTE y KPG�( �<� <!�"<# `�!)W>�"$#FG "<#�%'&�(8C') 100 * (at 10MeV)�+�

$�&<G�, !Ii S ! G�-�. A 5'/ `�0 D 7�#�) 20 *`#21/� B�D_E /104s t C & , y43�5$6-4�P.Vogel i J.F.Beacom

`h[ 2�7 e�g ! D W�798 %:&9( �'x<y ��� S',�;'G�<$=�>@?A1� , E [22]y 2

4.10�i� K@G'A�B C `8[ 2�7 e g ! D�W νep

G�7 8�D &$( i �:0�E _ Wνe iN���9_ W e+ G:F�G�<�>9? (cos θ)

-/. E yKPG�2 0 ! �8�%e t Y �.G��9� Y�� e C u MeV-/� � � � VTE e+

� �<��e t Y1�.G'0E$H�I i ( J'`$��E<G�`�J _ ��K u MeV-/��(4LhVTENM C > 0 E y K�Dk�$�4�%e t Y1� -,$;�798�G�O�P iRQ G E+M 0 ! �RTS 0 ! G νe /104smt i�S�T V_E+M�G@�UZEVXW G�YZ -k. E y

j Wi�"K)KT- ��� V_E e+ G���� Y�� e)�Ee+ = Eν − 1.293 − α

ifG E y K)K - α�i� �

1 [$\�] i e+ G ��� _ W'< ='`8[1E+^4_�->�BKPG αG+`9a+A2b

_ W�c C�d 4.11 i+d 4.12-8.�e yIU�f�g�f �

0 [�\$] (Ee+ = Eν − 1.293)� �

1 [�\$]A1� , W νe i e+c ��� Y�� e9c�h�ikA x _+j/, e y �

0 \9] -/� νe

c��@� Yk� e/� e+

c���� Y�� e9`+J _�j ; l -k.�e C � �1 \$] -4��m C U6ANn w�M C > 0 e y'3@5�6 c]�%� * e�]'^ s -/�i�FK�c �

1 \�] `8[4e e+c��@� Y�� e � cos θ

>�?)�:798 %�&$( A6�, e y

�4 � d e������

47

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14 16 18 20MeVCrossection

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0 2 4 6 8 10 12 14 16 18 20MeVCostheta distribution

d 4.10: crossection & cos θ>�?

� c d � �4� _�� e+ c�<9=FA ( > _+j F�G�� _�� νepc�7 8 %'&�( [10−42cm2]:

� c d �0$E _�� νe ���9_� e+c�F G�<�=$>�?

(< cos θ >)A x V y

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14ν–

e energy(MeV)

e+ ene

rgy(

MeV

)

d 4.11: 0th order output positron energy

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14ν–

e energy(MeV)

e+ ene

rgy(

MeV

)

d 4.12: 1st order output positron energy

�4 � ��� ����� 48

4.3.3 Expected ��� � ���� }_ � 8B�8� � t� ��c� j � t Y �'x y�798 %4&9( AT� , ��� !�� V/W j c 8B�I� ��� � � C νe

��� � _���� .4��� � � 8B�h� ��� � � C V)W j νe

c����SK���� _ ��� .kc�7 8 �kc�,$;)�$xhy"!�,9;�c �)� j#��� Y A%$ _��# c C@d 4.13

-k.�e'&

1

10

10 2

0 2 4 6 8 10 12 14 16visible Energy(MeV)

even

ts/d

ay /M

eV /2

2.5k

ton

νee- → νee

-ν–

ep → e++n

d 4.13: 1)� � f e �)� j �(� YK:c d$C bkVB[�) � � νe *,+�- � � νe *+.- � � !)W��F[ / V W G visible

��� Yk�0�A � V�eNM C > 0 e1&� � � 8B�o� ��� � � C " j νe

�2� � _ �3 c a>b54 � � � }"_ � 7�8 %&4( � cos θ>

?<AJL�/7698�:N�����kc5;��1� *%� ;�< - A2= , �5� !2� �?> Y5� � � %@�A c ReductionA 0 v � ��c4�@� Y��5� j#�B� Y A d 4.14� bkV9&

4.4 CEDGF H�IKJGLNMPO QKR SUTWVNXGY[Z]\_^[IG`baKcd � c � � � � �"e�x�y�;��i� f � ;�< - A%��g � �'� dkc ��� �ZA�h � e/�8� ��� �� � d�� c \)^ e• i"�Wjlk #m -on9p Lrq e�s�)ot i�u � ��v - �7w nyx• z ! j c i"� n K�>�VXW�g• {�|.w nW}�e$O�~ wo�B� q• �#�,���0� ;w ��g ��� . � e z !��W��� U q�e 7�5� � f e p ,�;h�8� ��� � �5� � 4 � 9c �5�� w�� ��� &y��c'��� w b�� � c n d 4.15 k�� e'&

�4 � ��� ����� 49

10-3

10-2

10-1

1

10

10 2

8 10 12 14 16 18 20Energy(MeV)

even

ts/d

ay /0

.5M

eV

cosθsun ≤ 0.5

d 4.14: Expected�� �����

8B�)� �K� � � n q�� j νe

��� �B� � �� � j � -�� �� ;��%� f � ; < - w =rg1eq�� j c Reduction w ��� � � c���c k�� e�&������ visible��� ���0� e������ *,+�-� f ���?w $�q9&

�4 � ��� ����� 50

0

1

2

3

4

5

6

7

8

9

10

8 10 12 14 16 18 20Energy(MeV)

Upp

er li

mit

(%

: 9

0%C

L)

1.75%

d 4.15: z !5�(�+c νe

� � 4 � @c ���������� 1�� � f � ��� � �0� :����� z ! jlki�4� � � 8B

,�;������ �K� ��� n " j νe

�� �B�7e8B��� � � �� c9�� �(� �rw��� � � �9� �� �o� � � � �� � ��� . � 1

� � f e *+�- ����w���� � e SK k�1�� � f � *,+�- ���.w ��g j �$c�� �9� (90%CL)w�y� � �"�l�

�4 � ����� ��� 51

��� c���� k �Φ(νe)/ΦBP98(

8B) ≤ 1.75%(90%CL)

≤ 1.77%(95%CL)

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g ¿#c6td� n H {�e�� TnfK Ë K C E Ì C�F r H rfK �+�>-�gwq 5 � a spallation products -�¬`� b<c�d#h ¯iFkj g�lfm1n �`o#p g.M `#N É#ÊO9"m:¹�ºa � MeV

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65

� � � �

[1] R.Davis,Jr. et al.,Phys.Rev.Lett.,20,1205(1968)

[2] The Super-Kamiokande Collaboration, Phys. Rev. Lett. 81 (1998) 1562-1567

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J.Schechter and J.W.F.Valle, Phys. Rev. D24(1981)1883

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Apr1997, arXiv:hep-ph/9705451

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School,Ed.Roca Cortes and F.Sanchez,Cambridge University Pres 1996 p.299.

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�5 � ¹ V

66

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67

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