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� � � �
� � � � � � � � � � � � �
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)�* +�,-/.
12 0
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�#"�$:e 6 � )���� ����µ����KTS)(
ν1(t)
ν2(t)
)
=
(
e−iE1t 0
0 e−iE2t
)(
ν1(0)
ν2(0)
)
Xt�|#w"s#&) νe → νµ % ��¯:° �!&�'KTA)P (νe → νµ) = sin22θ · sin2
(
1.27∆m2L
E
)
� ��eFX �]�/ÑtÒ 6 W(X�XIa E T8�7���f����� ��õ�ö�2/÷��A) L T�(.' t ����8��� �I��!) 6 "�)(cFdM� ∆m2 T�) ν1 � ν2 �����+* �-,�.�a7� 6 W1.2.2 MSW /10���I�l���w��TI)32���Á8-4�L8�6587�9SJ8���I�l���w�B¯�°�[G±OX]e8WSXG�.T νe � W+( :
�:Þ;���(� ) � Z0( ÁM®�Þ;���K� ) [=<?>sd���� ��@ �A�I�3�t�w�BA?CF[�±OX]e���G¬sdÖ) νµ(τ )T Z0 �?D�[E<F>�e 6 � �)E2.�(ÁAa-GIH 6-J+K �-L?MG2�N* (Ve =√
2GF Ne, GF : 9!Ow2ßPn��� .D , Ne : ��� ��D ��� ) ��� 6 "3#Ma7� 6 WlXw��#P2��Á��RQ�¤$[ �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
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PMT
HV, signal cables
818
mm
102 mm
T 3.11: LINAC O endcap
�3 � rHt\�5�R_\9����2 28
-1500
-1000
-500
0
500
1000
1500
-1500 -1000 -500 0 500 1000 1500
x(cm)
Z (
cm)
0200040006000
-1500 -1000 -500 0 500 1000 1500
010
0020
0030
00
-150
0-1
000
-500
050
010
0015
00
X (cm)
T 3.12: LINAC OI�/\*���'TMKIX �
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
4 6 8 10 12 14 16 18
WT = 83m
combined deviation=0.11%
total energy in water from Ge measurement(MeV)
(MC
- D
AT
A)/
DA
TA
�3.13: LINAC energy scale
�3 � rHt\�5�R_\9����2 29
position dependence of observed energy deviation
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0 1 2 3 4 5 6 7 8 9 10
WT = 83m
IHGFEDCBA
position tag
(MC
-DA
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)/D
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A
�3.14: LINAC position dependence
3.4 Ni-Cf � ��������� �� ����� ���
Ni-Cf ��������� �"!�#%$%&(' 1p.e. �*)�+-,/. PMT .10324.6587:9-'<; MeV �=)8+.<>3?<+A@8�8B-C-�6+EDGF-HJILK�M � 3.15 .ANPO Q�RTS�UWVESYX�DGZ\[�](^/_-`JIGab . Ni-Cf source &1' Ni(n,γ)Ni cedEMPNAfg; MeV �=):+/. γ hTDji/kJIGa b . γ h�MNmlY](n�o:p-'6qE&"r/$(XsUL$ut�vEM\Nml1]6i:o�w1xLy-zA.(i3k\Im{/|E�6$6r<}L0�DL~8�k4I��JM4Nml(]<'6�\>-?6+\@:�G���A."�8�J�L��� �"!A#m$mM1ZP[���`\I(a3x��Jw='"�(�:�� w�] Ni source .1��p �(� 9�ze�3�"�m���:'8�8�A�-�������"��IL�:�e9-�:�8 T¡%,/.G¢£:¤3¥ '<�� /,/.L0E.1c�¦PQT§ ���P�jI%�<�-9/¨m©TªA�=Q���Qe[Y��'8«�S(¬-8®P¯:$T�°.± wL²P³YM/N8I�´ ± '6µ3�"¶�·<¸JM6¹�º<¨e�e�/I��P���W'(»e¼P,-&G½e¾"k\I DT generator
DLZP[�]3¿%7J."�����L��� �"!�#m$mDL^TlY]:[\I%a
3.5 DT � �À�Á�Â��� �s �T�Ã� �Ä�
DT �<�A���E�j��!J#%$ [20] &�'Y�eÅJÆ8MG^ÇO b � M/N\fÈ'e>e?Y+J@<�6B:C-�(+/.1´ ± 'É/Ê1Ë-Ì 9:'ÍUG�jÎ:�:. efficiency QJ§1.GÏe�AM%Z"[��*`\I(a LINAC M/NmI8�e�\����� �!J#%$ � .LÐA[-&1'6Ñ Ê .(Ò:Ó\¨ANJfÔ��Õ/,-Ö"I<xe×-MLØA[1Ù3Ú/, ÉJÊ1Ë-Ì 94¨(Ïe��Û�ÜI��3' β �8��.(7:ÝA¨eÞ8ß4,Yà/á�M1â-Ú-ãä�Wå�æ�Û1Ü�I��A¨-ç\è�� `AI(a � 3.16 &mµ4�¶�·e¸�.%^:é�D�ê"k6a
DT generator NAf°i8osªG`JI � 9:z�&Yë/ì3.AN"O�QYc-dAM4NelY](i�oíª�`JI(a3H +2 H →4 He + n
�3 � ��������� ����� 30
20m
m
200m
m
130m
m
125m
m
50mm
10m
m 30m
m
Nickel wire + Water
�3.15: Ni-Cf ����������� ������������� �"!
#$#$#$#$#$#$##$#$#$#$#$#$#%$%$%$%$%$%$%%$%$%$%$%$%$% &$&$&$&$&$&$&$&$&&$&$&$&$&$&$&$&$&'$'$'$'$'$'$'$'$''$'$'$'$'$'$'$'$'
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n
nnn
nn N16
2 m
(a) (b) (c)
E =14.2 MeVn
O(n,p) N16
�3.16: DT generator data taking
DT generator M\NmI(µ/�3¶�·e¸3a (a): µ��/¶:D�<>="k\I É4Ê M DT generator D6ì@?Jª�AI1a (b):
� 9�z�D�i�osª�AJI(a (c):DT generator D 2m ç"Bsª�Ae'PµP�3¶�DC<�=3kAI(a
�3 � ��������� ����� 31
� �������������� �� SK � ���� ���������������16O + n →16 N + p
16N ���! �" � � 16N � 7.12 # �%$'&�(��*)�+��-,. �0/�132 β 4'5�16N →16 O + e− + γ + νe
6 /078��9;: 4.3MeV ��<� =� 6.1MeV � γ >���?;@A B"DC �FE;�HG MeV �HI;JLK0M N'O PK � ������� C��RQ"� 6TS�U �V0WHX�Y� %" � 3.17 �[Z�\R]�2�^A_�XL`baHc�dDT � � ����� �0Q�� 6 /�7feg�3cd NHh � �iK��j�k��*l-mPKDn �boBp � �qQ � 6/P �r's�t-X�u- F"bvHd%� � 3.18,
�3.19 �T� � � � ����� C �AQ"� 6 /Lw%xPey�zcd
I�JPK�M NHO BK �F^A_%{H|��'�P}0~%���H{�|H���3����x U %"R�B+0���z���'�H����X���H�0WL� ±0.5% X;u�78� LINAC � � �C��C ��Q"�"�F�����F�F�0Xu- F"
Energy (MeV)
0
1000
2000
3000
4000
5000
6000
7000
8000
2 4 6 8 10 12 14
�3.17: Z�\!]�2 DT � � ����C��qQ��"� N�h � �8K� -� ( �C��� ) ���DoPp C��RQ"� � � ( ��� � ) ���H�����a���x U
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-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-1500 -1000 -500 0 500 1000 1500z-position (cm)
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r-position (cm)
(MC
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-0.03
-0.02
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0
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0 50 100 150 200 250 300 350Azimuthal Angle (degrees)
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cos(Zenith Angle)
(MC
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-0.03
-0.02
-0.01
0
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0.02
0.03
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3.7 Trigger efficiencyN �� �mqo� bm � � X����IJ�K0M ����¾���� ��� %� � @A FE 6 � Low Energy
Trigger(LE), Super Low Energy Trigger(SLE) �����HcA 2 ������������� � S�U x U!�"$# c&%'�(�)����� efficiency �+*-, !�.0/ Ni-cf 1�}A~ DT generator W S0U % c !W�1 # c /�2)3(4 d6587 . ��9:%�� G MeV ;=<:��>�W@?'�BA�wLd�IJPKDM=�8�BC-D !'EX;u !�" ���F��� efficiency
/)GIH ��ÂEfficiency =
NLE(SLE)trigger
NDT (Ni)trigger. 5HwTxT�@��c !+"$#�#�J NLE(SLE)trigger
/LE(SLE) trigger
J ��¾$K$�LNM�OP�Fc�dQ �3� 4 1 NDT (Ni)trigger
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0
0.2
0.4
0.6
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DATAMC
Energy (MeV)
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�3.20: LE trigger � efficiency
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�3 � ����������-�X��K 34
0
0.2
0.4
0.6
0.8
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3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
DATAMC
threshold:-260mV
Energy (MeV)
SL
E t
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eff
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0
0.2
0.4
0.6
0.8
1
3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
DATAMC
threshold:-260mV
Energy (MeV)
SL
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0
0.2
0.4
0.6
0.8
1
3 4 5 6 7 8
DATAMC
threshold:-222mV
Energy (MeV)
SL
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0
0.2
0.4
0.6
0.8
1
3 4 5 6 7 8
DATAMC
threshold:-212mV
Energy (MeV)
SL
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�3.24: SLE �+����� -212mV
35
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L(dir) =∑
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a(θi) : PMT �4���:��� � DL� ���IQG�&�����
�4 � 8X�G� 0�1 36
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4.1.3 � ��������������������E��! "�SK ��# 0�1�$ yL�(5&%��s�'%:�-��(��]�-�-�X�*) $ yL��5,+�%-(/.+y��&�,021 n m�Wm4365�7X���8)��9�6��g���8X����v�:/;&�*����<=% 0(1 �?> ��@BA6�C< ~ED �*� SK �Lowenergy
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– First electronic noise cut
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1 ��� ATM v8:��T �B����¹���LXZY� f [B��% 95 �TJE^(� HIT ]�% 1 �G�ATM ����]�y�z D � PMT �?_I`6% � ���LXZY��fR�
• goodness cut��� <'� goodness �4{E] 0.4 JIK21I\(�9_I`B� � ���LXZY� fR�&U�V�½ $4�6� )��� dgfp+�%9UG��s�V�½ 7 �{¤ ^:_ ]8A?¢�f�N�v�� goodness ]� !B� � D [2%�XPY�v"�=�?��" 4.1 +�%�#%$'&47(��X��)b)+*�j�� goodness ��,��C�.- <Lz D �{�• Flasher cutR�/=��@9�4¹*º�)��W�� f [=�'%9RIf"g"§6¨,©B� HIT ]104�,B�26¢2y{z D �/_,`�.3P<Å% � ����X�Y� fd�
0
50
100
150
200
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1goodness
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SK ��)*½2�:� à �I2 "1��*��J�h i�j�k:���/S�U�V µ +�%%KI®'L���M:N%O2g�PPepJEK��@�AL7QO"g�P�R�S ( J K�%TF�U¾¼e�DV@W�)6e=X�9 ) À�YI%µ +16 O → µ + X
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Isotope τ 1
2
(sec) Decay mode Kinetic Energy(MeV)
82He 0.122 β− 10.66 + 0.99 ( γ )
β− n ( 11 % )83Li 0.84 β− 12.5 ∼ 1385B 0.77 β+ 13.7393Li 0.178 β− 13.5 ( 75 % )
11.0 + 2.5 ( γ )
β− n ∼ 10 ( 35 % )96C 0.127 β+ p 3 ∼ 13
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 �%$'&�? �! z)(�* ± :Ã�d�F�GaH m�I-J ?�+�, ÝtÞ W.-�q�º6»�� � :Rj v ?)à \ ? νe /10 l6m_u d \ ?�2?43©?�Ñ�Ò�W�5�6 ��7 q :�j�Æ Ý νe /10 l'm£u d � 8 ± : © Å W98: Æ<; W�¤�¥± :)j v ?�Ã�d9C[D � w>= · ± : νe /10 l'm �@?ACB�DFE1G uIH© M9J© G�Ñ�Ò �0�E j � � �LKNM GPO�Q �Eu dRTS � w G νe /10 l'm z]�VUg�¨� Ã�W cos θsun ≤ 0.5G�Ñ�Ò
( H© )z��Eq9W j
SK 1260 days data(E ≥ 8MeV)
0
250
500
750
1000
1250
1500
1750
2000
2250
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1cosθsun
cosθsun < 0.5
① ②
③
24.7: SK 1260days cos θsun distribution
4.1.8 Reduction summaryX ãGZY)[�\�]'^ l z�� � W � G /.0 l6m z]d.�9���_GPO<Q'`��[q�Eba9c�dfe Ô�gÄl�h�Ci ± E jNj W d1klY�[�\�]m^ l�n1oZp�h�irq 5 � W /104s'tvu `%w�q 7.x 4.1`�� ±%y
�4 � d e Ô O�Q 44
Reduction step numer of events for data numer of events for MC
After real time selection 164771273 1533207
First reduction
Fidutial Volume cut 29528788 1103678
Time different cut 23248492
OD trigger cut 21711646
Electronic noise cut 21636900 1103678
goodness cut 21077368 1088997
Flasher cut 15249791 1085178
Spallation cut
Spallation cut 10797241 21% dead time
Second Reduction
New goodness cut 2910763 10.2% cut
Cherencov ring pattern cut 2183473 12.5% cut
Clusfit cut 1497559 1.8% cut
Gamma cut 267996 9.6% cut
lowenergy final sample(E≥4.5MeV) 267996 591005
Final Reduction
Energy ≥ 8.0MeV 40781 346849
cos θsun ≤ 0.5 25004 258852a9c�dfe Ô)g s h)� 25004 258852
x 4.2:k YP[�\�]4^ s n1omp@h�irq 5 /10's4tvu
�4 � d e Ô O�Q 45
4.2 ��� ������ �� ������������������� ���2
4.7G H© G�Ñ�Ò�� �RTS �"! G
νe /10'smt �%?<ACB�D_E�Ñ9Ò �0� E ii$# `%�'&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)
g.)���� w�� � &[ � e�� ������� - � � �� - ��� �� ������� - � ��w ��� 4 � � -�� � �,� ���w�� g1e��@A�c�� �%x�W�c���� w�� � � � e� "! n ��# t e $&% ��',��(*)yw%�r� e+��-,K�'g �"�l� w%� � e1&�" � �&��� -.� � �0/ � j ��� 4 � � -�� � � �'c w $K� � c n d 4.16 k�� e�& @lA �d 4.17
� ��-��1� � ������0� -�� � ��/ q�e ��c w $�� j g e'&
1
10
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10 3
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10
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65
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�5 � ¹ V
66
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67
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