2019 ೥౓ɹम࢜࿦จ

εʔύʔΧϛΦΧϯσʹ͓͚Δେ‫ؾ‬ϛϡʔχϡʔτϦϊ/൓ϛϡʔχϡʔτϦϊࣝผʹΑΔ࣭ྔ֊૚ੑͷ‫ڀݚ‬໊‫ݹ‬԰େֶେֶӃཧֶ‫ڀݚ‬ՊૉཻࢠӉ஦෺ཧֶઐ߈Ӊ஦஍‫ٿ‬෺ཧ‫ܥ‬Ӊ஦ઢ෺ཧֶ‫ࣨڀݚ‬ത࢜՝ఔʢલ‫ظ‬՝ఔʣ2 ೥ֶ੶൪߸ 261801306

୮Ӌ ޼2020 ೥ 1 ݄ 24 ೔֓ཁχϡʔτϦϊ͸ૉཻࢠͷඪ४໛‫ܕ‬Λߏ੒͢ΔதੑϨϓτϯͰ͋ΔɻχϡʔτϦϊ͸ऑ͍૬‫༻࡞ޓ‬ͷ‫ݻ‬༗ঢ়ଶͱ͠
ͯ 3 छྨͷϑϨʔόʔ νe , νµ , ντ ͱɺ3 ͭͷ࣭ྔ‫ݻ‬༗ঢ়ଶ ν1 , ν2 , ν3 Λ࣋ͪɺͦͷ࣭ྔ‫ݻ‬༗஋ͱͯ͠ m1 , m2 , m3 Λ࣋ͭɻ ͜ͷ࣭ྔ‫ݻ‬༗஋ͷઈର஋͸൑໌͓ͯ͠Βͣɺ࣭ྔͷೋ৐͔ࠩ͠෼͔Βͳ͍ͨΊɺ͜ͷ࣭ྔͷॱং͕ਖ਼ৗ֊૚

(m1 < m2 ≪ m3 ) Ͱ͋Δ͔‫֊ٯ‬૚ (m3 ≪ m1 < m2 ) Ͱ͋Δ͔ܾఆ͍ͯ͠ͳ͍ɻ͜ͷ࣭ྔ֊૚ͷܾఆ͸χϡʔτϦϊͷੑ࣭Λ໌Β͔ʹ͢Δ͚ͩͰͳ͘ɺ෺࣭༏੎Ӊ஦Λઆ໌͢Δཻࢠ൓ཻࢠඇରশੑͷ‫͢ݙߩʹڀݚ‬ΔͨΊɺੈքதͷχϡʔτϦϊ‫؍‬ଌ࣮‫Ͱݧ‬ଌఆ͕ਐΊΒΕ͍ͯΔɻεʔύʔΧϛΦΧϯσ࣮‫Ͱݧ‬͸େ‫ؾ‬χϡʔτϦϊৼಈղੳͱɺ
Ճ଎‫ث‬ϏʔϜΛ༻͍ͯੜ੒͞ΕͨχϡʔτϦϊΛ༻͍ͨ T2K ࣮‫ݧ‬ͷ‫ڀݚ‬Λ౷߹ͨ݁͠ՌͰɺ‫ࡏݱ‬໿ 2 σ Ͱਖ਼ৗ֊૚Λ͍ࣔࠦͯ͠Δ͕ɺະͩͦͷܾఆʹ͸ࢸ͍ͬͯͳ͍ɻ
࣭ྔ֊૚ͷܾఆʹ͸χϡʔτϦϊৼಈͷৼΔ෣͍Λ‫؍‬ଌ͢Δ͜ͱ͕༗ޮͰ͋ΔɻχϡʔτϦϊৼಈͱ͸χϡʔτϦϊͷϑϨʔόʔ͕ۭؒΛ఻೻தʹผͷछྨʹมԽ͢Δ‫ݱ‬৅Ͱ͋Γɺ஍‫಺ٿ‬෦Λ௨ա͢Δࡍͷ෺࣭ޮՌͷӨ‫ʹڹ‬Αͬͯਖ਼ৗ֊૚ͱ‫֊ٯ‬૚ͷ৔߹ͰৼΔ෣͍͕ҟͳΔɻεʔύʔΧϛΦΧϯσͰ͸͜ͷ‫؍‬ଌʹେ‫ؾ‬χϡʔτϦϊΛ༻
͍͍ͯΔɻେ‫ؾ‬χϡʔτϦϊͱ͸Ӊ஦ઢ͕஍‫ٿ‬ͷେ‫ؾ‬தͷ‫ͱ֩ࢠݪ‬িಥͯ͠ੜ੒͞ΕͨχϡʔτϦϊͷ͜ͱͰɺେ
‫ࢠిؾ‬χϡʔτϦϊ (νe , ν¯e ) ͱେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊ (νµ , ν¯µ ) ͷ 2 छྨ͕͋Δ͕ɺ‫ࡏݱ‬͸େ‫ࢠిؾ‬χϡʔτϦϊͷΈ෺࣭ޮՌͷղੳʹ༻͍ΒΕ͍ͯΔɻ·ͨେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊ΋࣭ྔ֊૚ͷܾఆ‫౓ײ‬Λ͕࣋ͭɺνµ ͱ ν¯µ Λ෼཭͢Δ͜ͱͰɺΑΓҰ૚ܾఆ‫্͢޲͕౓ײ‬Δ͜ͱ͕஌ΒΕ͍ͯΔɻઌߦ‫Ͱڀݚ‬͸ likelihood ๏ʹΑΔνµ /ν¯µ ࣝผ͕։ൃ͞ΕɺεʔύʔΧϛΦΧϯσͰ‫؍‬ଌ͞ΕΔ࠷΋୯७ͳ 1 Ϧϯά (νΣϨϯίϑϦϯά͕ 1 ͭͷ) ࣄ৅ʹಋೖ͞Ε͕ܾͨఆ‫౓ײ‬ͷ޲্ʹ͸ࢸΒͳ͔ͬͨɻ͜ͷཁҼͱͯ͠‫౓ײ‬ͷߴ͍χϡʔτϦϊΤωϧΪʔ 10 GeV෇ۙͰͷ౷‫ྔܭ‬ͷগͳ͕͞‫͛ڍ‬ΒΕ͍ͯΔɻ
ຊ‫Ͱڀݚ‬͸εʔύʔΧϛΦΧϯσʹ͓͚Δ֊૚ܾఆ‫্޲౓ײ‬Λ໨ࢦͯ͠ɺ֊૚ܾఆ‫౓ײ‬ͷߴ͍ΤωϧΪʔྖҬͰࣄ৅਺ͷଟ͍ଟཻࢠࣄ৅Λ‫ؚ‬Ίͨେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊࣄ৅Ͱͷɺlikelihood ๏ʹΑΔ νµ /ν¯µ ࣝผํ๏ͷ։ൃΛߦ͍ɺͦͷॳΊͯͷ݁ՌΛࣔ͢ɻ͜ͷࣝผΛ 3 ੈ୅େ‫ؾ‬χϡʔτϦϊৼಈΛߟྀٖͨ͠ࣅσʔλʹಋೖͨ͠৔߹ɺνµ -like αϯϓϧʹ͓͚Δਅͷνµ ࣄ৅ͷׂ߹͸ࣝผ͍ͯ͠ͳ͍ঢ়ଶʹൺ΂ͯɺ1 Ϧϯάࣄ৅Ͱ͸ 14.7±0.4%, ϚϧνϦϯά (νΣϨϯίϑϦϯά

͕ 2 ͭҎ্ͷ) ࣄ৅Ͱ͸ 2.9±0.3% ޲্ͨ͠ɻ·ͨ ν¯µ -like αϯϓϧʹ͓͚Δਅͷ ν¯µ ࣄ৅ͷׂ߹͸ 1 Ϧϯάࣄ৅Ͱ͸ 7.8±0.3%, ϚϧνϦϯάࣄ৅Ͱ͸ 12.7±0.5% ޲্ͨ͠ɻ

·ͨɺ͜ͷࣝผΛಋೖͨ͠ µ-like αϯϓϧʹ͍ͭͯ 200 ೥෼ͷαϯϓϧͰ࣭ྔ֊૚ͷܾఆ‫౓ײ‬Λ‫ੵݟ‬΋ͬͨ݁Ռɺࣝผલͷ µ-like ࣄ৅ʹൺ΂ͯ࠷େͰ໿ 2.9 ഒ‫্͠޲͕౓ײ‬ɺ͜ͷαϯϓϧΛ෺࣭ޮՌͷղੳ‫ʹڀݚ‬Ճ͑Δ͜ͱͰɺ‫ࡏݱ‬ͷ‫౓ײ‬Λ࠷େͰ 1.18 ഒʹ޲্͢Δ͜ͱΛ֬ೝͨ͠ɻ
࠷‫ʹޙ‬কདྷ࣮‫Ͱݧ‬ͷࣝผੑೳͱ౷‫ྔܭ‬ͷ૿ՃྔΛ‫ੵݟ‬΋ͬͨɻ७ਫͰຬͨ͞Ε͍ͯΔ‫ݕ‬ग़‫ࢎེʹث‬ΨυϦχ΢Ϝ
ΛՃ͑ͯதੑࢠ‫ݕ‬ग़ޮ཰͕޲্ͨ͠৔߹ʹɺνµ /ν¯µ ࣝผੑೳ͕ߋʹ޲্͢Δ͜ͱΛ֬ೝͨ͠ɻಛʹ 1 Ϧϯάࣄ৅Ͱࣝผੑೳ͕େ্͖͘ঢ͢Δɻ·ͨϋΠύʔΧϛΦΧϯσ࣮‫Ͱݧ‬͸༗ޮମੵ͕໿ 8.3 ഒʹͳΔ͜ͱʹՃ͑ͯɺߴΤωϧΪʔϛϡʔΦϯχϡʔτϦϊࣄ৅ͷ౷‫͕ྔܭ‬ಛʹ૿Ճ͢ΔͨΊɺಉ͡‫؍‬ଌ‫( ؒظ‬3244.4 ೔) ΛԾఆͨ͠৔߹ɺεʔύʔΧϛΦΧϯσʹൺ΂ͯ֊૚ܾఆ‫͕౓ײ‬໿ 12.3 ഒʹͳΔͱ͍͏݁ՌΛಘͨɻ

iii

໨࣍

ୈ1ষ

ং࿦

1

1.1

ૉཻࢠͱχϡʔτϦϊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2

χϡʔτϦϊ࣭ྔ֊૚ੑ໰୊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.3

χϡʔτϦϊৼಈ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.4

SK ʹ͓͚Δେ‫ؾ‬χϡʔτϦϊৼಈղੳ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.5

େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊͷ֊૚ܾఆ‫͜ͱ౓ײ‬Ε·Ͱͷ νµ /ν¯µ ࣝผ . . . . . . . . . . . . . . . .

5

1.6‫ڀݚ‬໨త . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6εʔύʔΧϛΦΧϯσ࣮‫ݧ‬

72.1࣮‫ݧ‬ͷ֓ཁ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.2‫ݕ‬ग़‫ ث‬. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.3

ਫνΣϨϯίϑޫ‫ݕ‬ग़ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.4

σʔλऩूγεςϜ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.5

ϋΠύʔΧϛΦΧϯσ‫ܭ‬ը . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13େ‫ؾ‬χϡʔτϦϊ

15

ୈ2ষ

ୈ3ষ

3.1

େ‫ؾ‬χϡʔτϦϊͷੜ੒

3.2

େ‫ؾ‬χϡʔτϦϊϑϥοΫε . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

3.3

χϡʔτϦϊ૬‫ ༻࡞ޓ‬. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

3.4

NEUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.5

‫ݕ‬ग़‫ث‬γϛϡϨʔγϣϯ

ୈ4ষ

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

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

χϡʔτϦϊࣄ৅બผͱࣄ৅࠶ߏ੒

21

4.1

SK Ͱ‫؍‬ଌ͞ΕΔχϡʔτϦϊࣄ৅ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2ࣄ৅࠶ߏ੒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

4.3

தੑࢠ‫ݕ‬ग़ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

4.4

SK-Gd ‫ܭ‬ը . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

ୈ5ষ

νµ ͱ ν¯µ ͷ૬‫͚͓ʹ༻࡞ޓ‬Δ‫؍‬ଌ্ͷ૬ҧ఺

27

5.1

ϛϡʔΦϯ่յిࢠ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

5.2

தੑࢠ਺ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

5.3

ଟཻࢠࣄ৅ʹ͓͚Δ νµ ͱ ν¯µ ͷӡಈֶతಛ௃ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

likelihood ๏ʹΑΔ νµ /ν¯µ ࣝผ

37

ୈ6ষ

6.1

likelihood ๏ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

iv

໨࣍

6.2

େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊࣄ৅બผͷಋೖ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.3

likelihood ֬཰ີ౓෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6.4

֤ࣄ৅ͷΠϯϓοτύϥϝʔλ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.5

3 ੈ୅େ‫ؾ‬χϡʔτϦϊৼಈΛߟྀٖͨ͠ࣅσʔλΛ༻͍ͨ νµ /ν¯µ ࣝผͷධՁ . . . . . . . . . . . 42

6.6

∆L ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43࣭ྔ֊૚ੑܾఆ‫౓ײ‬ͷߟ࡯

47

7.1

ఱ௖֯෼෍ͱΞοϓμ΢ϯൺ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

7.2

µ-like ࣄ৅ͷΞοϓμ΢ϯൺ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

7.3

e-like ࣄ৅ͷΞοϓμ΢ϯൺ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.4

SK-IV ‫؍‬ଌ‫ ؒظ‬3244.4 ೔Ͱͷ݁Ռ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

7.5֊૚ੑܾఆ‫౓ײ‬ͷධՁ·ͱΊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

কདྷ࣮‫Ͱݧ‬ͷ֊૚ܾఆ‫౓ײ‬ͷ‫ڀݚ‬

57

ୈ7ষ

ୈ8ষ

37
41

8.1

SK-Gd ϑΣʔζͰͷ νµ /ν¯µ ࣝผ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

8.2

ϋΠύʔΧϛΦΧϯσ࣮‫Ͱݧ‬ͷ֊૚ܾఆ‫ ౓ײ‬. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

݁࿦

65

9.1

·ͱΊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

9.2

՝୊ͱల๬ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

ୈ9ষ

ँࣙ

67

v

ਤ໨࣍

1.1

χϡʔτϦϊͷ࣭ྔ֊૚ͷൺֱ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.2

χϡʔτϦϊΤωϧΪʔʹର͢Δ্޲͖χϡʔτϦϊͱԼ޲͖χϡʔτϦϊͷࣄ৅਺ͷൺ . . . . .

5

1.3

େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊͷભҠ֬཰ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.1εʔύʔΧϛΦΧϯσ‫ݕ‬ग़‫ ث‬. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.2ޫిࢠ૿ഒ؅ͱεʔύʔϞδϡʔϧͷ໛ࣜਤ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.3νΣϨϯίϑ์ࣹͷΠϝʔδ [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.4

QBEE ಺෦ͷϒϩοΫμΠΞάϥϜ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1

Ұ࣍Ӊ஦ઢཅࢠͷϑϥοΫεɻຊాϞσϧͰͷ‫݁ࢉܭ‬Ռ (ࠇઢ)ɺ‫؍‬ଌσʔλ (֤఺) . . . . . . . . .

16

3.2

֤ΤωϧΪʔຖͷେ‫ؾ‬χϡʔτϦϊϑϥοΫεͷఱ௖֯෼෍ . . . . . . . . . . . . . . . . . . . . .

16

3.3

େ‫ؾ‬χϡʔτϦϊϑϥοΫεͷൺֱ

3.4

֤χϡʔτϦϊ૬‫༻࡞ޓ‬ͷ൓Ԡஅ໘ੵ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1

SK Ͱ‫؍‬ଌ͞ΕΔχϡʔτϦϊࣄ৅ͷ໛ࣜਤ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2

SK-IV ͰͷϦϯά਺Χ΢ϯτ likelihood ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.3

SK-IV Ͱͷ FC multi-GeV ࣄ৅ͷ PID likelihood ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . 24

5.1

่յిࢠ਺෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

5.2

ϛϡʔΦϯӡಈྔͱඈఔͷؔ܎ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

5.3

Ӊ஦ઢετοϓϛϡʔΦϯͰͷ d ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

5.4

େ‫ؾ‬χϡʔτϦϊ 1 Ϧϯά µ-like ՙిΧϨϯτ४஄ੑࢄཚ (CCQE) ࣄ৅Ͱͷ d ෼෍ [2] . . . . . .

30

5.5

่յిࢠ਺ = 1 ͷ৔߹ͷ d ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

5.6

่յిࢠ਺ = 2, Ϧϯά߹‫ܭ‬ӡಈྔ 1.33 GeV ҎԼͷ৔߹ͷ d ෼෍ . . . . . . . . . . . . . . . . . .

32

5.7

่յిࢠ਺ = 2, Ϧϯά߹‫ܭ‬ӡಈྔ 1.33 GeV Ҏ্ 5.0 GeV ະຬͷ৔߹ͷ d ෼෍ . . . . . . . . . . .

32

5.8

่յిࢠ਺ = 2, Ϧϯά߹‫ܭ‬ӡಈྔ 5.0 GeV Ҏ্ͷ৔߹ͷ d ෼෍ . . . . . . . . . . . . . . . . . . .

33

5.9

ϛϡʔΦϯ่յ࣌ؒ෼෍

5.10

่յిࢠώοτ਺ N 50 ෼෍

5.11தੑࢠ਺෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

5.12

ԣํ޲ӡಈྔ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

5.13

Ϧϯά਺෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

6.1

1 Ϧϯάࣄ৅ͷΠϯϓοτதੑࢠ਺෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6.2

ϚϧνϦϯάࣄ৅ͷΠϯϓοτதੑࢠ਺෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

6.3

Πϯϓοτ่յిࢠ਺෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
19

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

vi

ਤ໨࣍

6.4

ΠϯϓοτϛϡʔΦϯ่յ࣌ؒ෼෍

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6.5Πϯϓοτ่յిࢠώοτ਺෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

6.6

Πϯϓοτԣํ޲ӡಈྔɺϦϯά਺෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

6.7

1 Ϧϯάࣄ৅ͷ ∆L ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.8ϚϧνϦϯάࣄ৅ (߹‫ܭ‬ӡಈྔ > 1.33 GeV) ͷ ∆L ෼෍

6.9

ϚϧνϦϯάࣄ৅ (Ϧϯά߹‫ܭ‬ӡಈྔ ≤ 1.33 GeV) ͷ ∆L ෼෍ . . . . . . . . . . . . . . . . . . . .

44

7.1

ࣝผલ µ-like ࣄ৅ͷΞοϓμ΢ϯਤ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

7.2

MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠ µ-like 1 Ϧϯάࣄ৅ͰͷΞοϓμ΢ϯਤ . . . . . . . . . . . . . . . 49

7.3

MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠ µ-like ϚϧνϦϯάࣄ৅ͰͷΞοϓμ΢ϯਤ . . . . . . . . . . . . 49

7.4

νµ /ν¯µ ࣝผΛಋೖͨ͠ µ-like 1 Ϧϯάࣄ৅ͰͷΞοϓμ΢ϯਤ . . . . . . . . . . . . . . . . . . . .

50

7.5

νµ /ν¯µ ࣝผΛಋೖͨ͠ µ-like ϚϧνϦϯάࣄ৅ͰͷΞοϓμ΢ϯਤ . . . . . . . . . . . . . . . . .

51

7.6

ࣝผલ e-like ࣄ৅ͷΞοϓμ΢ϯਤ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

7.7

MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠ e-like 1 Ϧϯάࣄ৅ͰͷΞοϓμ΢ϯਤ . . . . . . . . . . . . . . . 52

7.8MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠ e-like ϚϧνϦϯάࣄ৅ͰͷΞοϓμ΢ϯਤ . . . . . . . . . . . . 53

7.9

νe /ν¯e ࣝผΛಋೖͨ͠ e-like 1 Ϧϯάࣄ৅ͰͷΞοϓμ΢ϯਤ . . . . . . . . . . . . . . . . . . . .

54

7.10

νe /ν¯e ࣝผΛಋೖͨ͠ e-like ϚϧνϦϯάࣄ৅ͰͷΞοϓμ΢ϯਤ . . . . . . . . . . . . . . . . . .

54

8.1

1 Ϧϯάࣄ৅ʹ͓͚Δਅͷதੑࢠ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

8.2

ϚϧνϦϯάࣄ৅ʹ͓͚Δਅͷதੑࢠ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

8.3

ਅͷதੑࢠ෼෍Λ༻͍ͨ ∆L ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

8.4

HK ༗ޮମੵͰͷࣄ৅‫؍‬ଌγϛϡϨʔγϣϯͷ໛ࣜਤ . . . . . . . . . . . . . . . . . . . . . . . . . 61

8.5

SK ͱ HK ͷ FC ࣄ৅ͱ PC ࣄ৅ͷϑϥοΫεͷൺֱ . . . . . . . . . . . . . . . . . . . . . . . . . 61

8.6

ಉ͡ exposure Ͱͷ SK ͱ HK ͷ FC ࣄ৅ͷϑϥοΫεͷൺֱ . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . 43

62

vii

ද໨࣍

1.1

ૉཻࢠඪ४໛‫͚͓ʹܕ‬ΔϨϓτϯͷ·ͱΊ [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2.1εʔύʔΧϛΦΧϯσͷาΈ [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.2

50 cm ‫૿ࢠిޫܘ‬ഒ؅ͷ࢓༷·ͱΊ [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.3

ཻ֤ࢠͷ७ਫதͰͷνΣϨϯίϑޫ์ग़ᮢΤωϧΪʔ [2] . . . . . . . . . . . . . . . . . . . . . . .

11

2.4

ͦΕͧΕͷήΠϯνϟϯωϧͷిՙμΠφϛοΫϨϯδͱ෼ղೳ [5] . . . . . . . . . . . . . . . . .

12

2.5

ιϑτ΢ΣΞτϦΨʔλΠϓͷৄࡉ

2.6

SK ͱ HK ͷ‫ݕ‬ग़‫ث‬ͷൺֱ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6.1

Likelikelihod ‫͍༻ʹࢉܭ‬ΔΠϯϓοτύϥϝʔλͷ·ͱΊ . . . . . . . . . . . . . . . . . . . . . . 41

6.2

1 Ϧϯάࣄ৅ʹ͓͚Δ νµ /ν¯µ ࣝผ݁Ռͷൺֱ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.3ϚϧνϦϯάࣄ৅ʹ͓͚Δ νµ /ν¯µ ࣝผ݁Ռͷൺֱ . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

6.4

ઌߦ‫Ͱڀݚ‬ͷ νµ /ν¯µ ࣝผ݁Ռ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

6.5

ઌߦ‫Ͱڀݚ‬ͷ νe /ν¯e ࣝผ݁Ռ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

7.1

MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠৔߹ͷ χ2 ஋ͷ݁Ռ . . . . . . . . . . . . . . . . . . . . . . . . . . 49

7.2

νµ /ν¯µ ࣝผΛಋೖͨ͠ χ2 ஋ͷ݁Ռ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.3

MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠ e-like ࣄ৅ͷ χ ஋ͷ݁Ռ . . . . . . . . . . . . . . . . . . . . . . 53

7.4

νe /ν¯e ࣝผΛಋೖͨ͠ χ2 ஋ͷ݁Ռ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.5

SK-IV ‫͚͓ʹؒظ‬Δ νµ /ν¯µ ࣝผΛಋೖͨ͠ χ ஋ͷ݁Ռ . . . . . . . . . . . . . . . . . . . . . . . . 55

7.6

SK-IV ‫؍‬ଌ‫͚͓ʹؒظ‬Δ νe /ν¯e ࣝผΛಋೖͨ͠ χ2 ஋ͷ݁Ռ . . . . . . . . . . . . . . . . . . . . . 55

7.7֊૚ੑܾఆ‫౓ײ‬ͷධՁͷ·ͱΊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

8.1

ਅͷதੑࢠ਺෼෍Λ༻͍ͨ৔߹ͷ νµ /ν¯µ ࣝผ݁Ռ . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

8.2

େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊ֤ΤωϧΪʔϏϯຖͷࣄ৅਺ͷൺ . . . . . . . . . . . . . . . . . . . .

62

8.3

HK ໿ 24 ೥෼ (SK200 ೥෼ͱಉ͡ exposure ) ʹ͓͚Δ χ2 ஋ͷ݁Ռ . . . . . . . . . . . . . . . . . 63

8.4

SK-IV ‫؍‬ଌ‫( ؒظ‬3244.4 ೔) ʹ͓͚Δ SK ͱ HK Ͱͷ χ2 ஋ͷ݁Ռͷൺֱ . . . . . . . . . . . . . . 63

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

50

2

54

2

1

ୈ1ষ

ং࿦
1.1 ૉཻࢠͱχϡʔτϦϊૉཻࢠ͸෺࣭ͷ࠷খ୯ҐͰ͋Γɺ͜ͷ͏ͪ෺࣭Λߏ੒͢Δཻࢠͱͯ͠ɺ‫͍ڧ‬૬‫༻࡞ޓ‬Λ͢ΔΫΦʔΫͱ‫͍ڧ‬૬‫ޓ‬࡞༻Λ͠ͳ͍Ϩϓτϯ͕ଘࡏ͢Δɻ͜ͷϨϓτϯͷ͏ͪిՙΛ࣋ͭ΋ͷΛՙిϨϓτϯɺిՙΛ࣋ͨͳ͍தੑϨϓτϯΛχϡʔτϦϊͱ‫Ϳݺ‬ɻՙిϨϓτϯ͸ 3 छྨ͋Γɺ࣭ྔͷখ͍͞ॱʹిࢠɺϛϡʔΦϯɺλ΢ͱ‫ݺ‬͹Ε͍ͯΔɻχϡʔτϦϊ͸͜ͷՙిϨϓτϯͱऑ͍૬‫༻࡞ޓ‬Λ௨ͯ݁͡ͼ෇͖ɺͦΕͧΕʹରԠ͢ΔՙిϨϓτϯ͔ΒిࢠχϡʔτϦϊɺϛϡʔΦϯχϡʔτϦϊɺλ΢χϡʔτϦϊͱ‫ݺ‬͹ΕΔɻ͜ΕΒ͸ϑϨʔόʔͱ‫ݺ‬͹ΕΔऑ͍૬
‫༻࡞ޓ‬ͷ‫ݻ‬༗ঢ়ଶͰ͋ΔɻχϡʔτϦϊͷ࣭ྔ͸ૉཻࢠͷඪ४໛‫͍͓ͯʹܕ‬θϩͩͱߟ͑ΒΕ͍͕ͯͨɺχϡʔτϦϊৼಈͱ͍͏ϑϨʔόʔͷछྨ͕มԽ͢Δ‫ݱ‬৅͕‫؍‬ଌ͞ΕͨͨΊʹ࣭ྔΛ࣋ͭ͜ͱ͕໌Β͔ʹͳͬͨɻ͔͠͠ɺ
χϡʔτϦϊͷ࣭ྔ͸ͱͯ΋খ͘͞ɺ௨ৗͷ෺࣭ͱ͸΄ͱΜͲ૬‫༻࡞ޓ‬Λ͠ͳ͍ͨΊʹ‫؍‬ଌ͕೉͍͠ɻ‫ࡏݱ‬൑໌͠
͍ͯΔ͜ͱ͸ɺχϡʔτϦϊͷ࣭ྔ‫ݻ‬༗஋͕ 3 ੈ୅ (m1 , m2 , m3 ) ͋Δ͜ͱͱɺͦͷ 2 ৐ࠩ ∆m221 , ∆m232 ͷ஋͚ͩ
Ͱ͋Δɻ
ද 1.1

γϯϘϧ

ૉཻࢠඪ४໛‫͚͓ʹܕ‬ΔϨϓτϯͷ·ͱΊ [3]

໊শ

࣭ྔ

e

ిࢠ

0.511 MeV/c

µ

ϛϡʔΦϯ

105.7 MeV/c2τλ΢1777 MeV/cνeిࢠχϡʔτϦϊ

<2 eV/c2νµϛϡʔΦϯχϡʔτϦϊ

<0.19 MeV/c2λ΢χϡʔτϦϊ

<18.2 MeV/c

ντ

ిՙ

εϐϯ

2

-1

2

1/2
0

2

1.2 χϡʔτϦϊ࣭ྔ֊૚ੑ໰୊
χϡʔτϦϊ࣭ྔ֊૚ͱ͸ 3 ੈ୅ (m1 , m2 , m3 ) ͋ΔχϡʔτϦϊͷ࣭ྔ‫ݻ‬༗஋ͷॱংͷ͜ͱͰɺͦͷॱং͕ܾఆ
͞Ε͍ͯͳ͍͜ͱΛ࣭ྔ֊૚ੑ໰୊ͱ͍͏ɻਤ 1.1 ʹ࣭ྔ֊૚ͷ໛ࣜਤΛࣔͨ͠ɻχϡʔτϦϊͷ࣭ྔ֊૚ͷީิ͸ਖ਼ৗ֊૚ (NH, Normal Hierarchy) ͱ‫֊ٯ‬૚ (IH, Inverted Hierarchy) ͷ 2 छྨ͋Γɺਖ਼ৗ֊૚Ͱͷ࣭ྔͷॱং͸

m3 > m2 > m1 , ‫֊ٯ‬૚Ͱ͸ m2 > m1 > m3 Ͱ͋ΔɻଠཅχϡʔτϦϊৼಈͷଌఆ͔Β m2 > m1 ͸൑໌͍ͯ͠Δ
͕ɺm3 ͱ m2 ͷେখؔ܎͸൑໌͍ͯ͠ͳ͍ͨΊɺ͜ͷॱং͸ܾఆ͞Ε͍ͯͳ͍ɻ
࣭ྔ֊૚ͷܾఆ͸ɺະͩಾͷଟ͍χϡʔτϦϊͷੑ࣭ͷղ໌ʹߩ‫͢ݙ‬Δ͚ͩͰ͸ͳ͘ɺӉ஦ͷ੒ΓཱͪʹؔΘΔ

2

ୈ 1 ষ ং࿦ཻࢠ൓ཻࢠඇରশੑͷ‫ʹڀݚ‬໾ཱͭɻ͜ͷΑ͏ʹ࣭ྔ֊૚ͷܾఆ͸ɺχϡʔτϦϊ෺ཧʹͱͲ·ΒͣɺૉཻࢠӉ஦෺ཧֶͷൃలʹେ͖͘ߩ‫͢ݙ‬ΔɻͦͷͨΊ೔ຊʹ͓͚ΔεʔύʔΧϛΦΧϯσ࣮‫͘ͳͰ͚ͩݧ‬ɺੈքதͷχϡʔτϦϊ࣮‫( ݧ‬IceCube[6], ANTARES[7] ͳͲ) ͕͜ΕΛܾఆ͢ΔͨΊʹ‫ڝ‬૪͍ͯ͠ΔɻεʔύʔΧϛΦΧϯσ࣮‫Ͱݧ‬͸ɺ࣭ྔ֊૚ੑͷܾఆ‫౓ײ‬Λ޲্ͤ͞ΔͨΊʹ༷ʑͳղੳΞϓϩʔν͕ࢼΈΒΕ͓ͯΓɺ৽͍͠ղੳख๏ͷ։ൃ͕‫ٸ‬຿ͱͳ͍ͬͯΔɻຊ‫Ͱڀݚ‬͸֊૚ܾఆ‫্޲౓ײ‬ͷͨΊͷ৽ͨͳղੳख๏ͱͯ͠ɺେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊ(νµ ) ͱ൓ϛϡʔΦϯχϡʔτϦϊ (ν¯µ ) Λࣝผ͢Δख๏Λ։ൃ͢Δɻ

ਤ 1.1

χϡʔτϦϊͷ࣭ྔ֊૚ͷൺֱɻࠨ͕ਖ਼ৗ֊૚ (NH)ɻӈ͕‫֊ٯ‬૚Λද͍ͯ͠Δɻ3 ͭͷ࣭ྔ‫ݻ‬༗ঢ়ଶ͸χϡʔτϦϊϑϨʔόʔͷॏͶ߹ΘͤͰද͞ΕΔɻ

1.3

χϡʔτϦϊৼಈ

1.3.1 χϡʔτϦϊࠞ߹χϡʔτϦϊ͸θϩͰͳ͍࣭ྔΛ࣋ͭ͜ͱͰɺϑϨʔόʔ͕ਅۭதͰભҠ͢Δɻલड़ͷ௨ΓɺχϡʔτϦϊ͸ऑ͍૬‫༻࡞ޓ‬ͷ‫ݻ‬༗ঢ়ଶͱͯ͠ϑϨʔόʔΛ͕࣋ͭɺಉ࣌ʹ࣭ྔ‫ݻ‬༗ঢ়ଶͱͯ͠ͷ ν1 , ν2 , ν3 Λ࣋ͪɺͦͷ‫ݻ‬༗஋ͱͯ͠ m1 , m2 , m3 Λ࣋ͭɻχϡʔτϦϊϑϨʔόʔ͸͜ΕΒͷ࣭ྔ‫ݻ‬༗ঢ়ଶͷࠞ͟Γ߹ΘͤͰද͞ΕΔɻχϡʔτϦϊ͕ۭؒΛ఻೻͢ΔաఔͰɺ࣭ྔ‫ݻ‬༗ঢ়ଶͷࠞ߹ׂ߹͕มԽ͠ɺ‫؍‬ଌ͞ΕΔχϡʔτϦϊϑϨʔόʔ͕มԽ͢Δ‫ݱ‬৅͕χϡʔτϦϊৼಈͰ͋Δɻऑ͍૬‫Ͱ༻࡞ޓ‬ͷ‫ݻ‬༗ঢ়ଶͱ࣭ྔ‫ݻ‬༗ঢ়ଶͷؔ܎͸ ࣜ 1.1 Ͱද͞ΕΔɻ|ν¯α ⟩ =

3
!
i

(1.1)

Uαi |ν¯i ⟩͜͜Ͱ νi (i = e, ν, τ ) ͸࣭ྔ‫ݻ‬༗ঢ়ଶɺνα ͸ϑϨʔόʔɺUαi ͸຀-த઒-ࡔా (MNS) ߦྻͱ‫ݺ‬͹Εɺࣜ 1.2 ͷΑ͏ʹද͞ΕΔ [8]ɻ⎛1
U = ⎝000
cos θ23− sin θ23⎞⎛0cos θ13sin θ23 ⎠ ⎝0cos θ23− sin θ13 eiδCP

0
1
0

⎞⎛
sin θ13 e−iδCPcos θ12⎠ ⎝− sin θ1200
cos θ13sin θ12cos θ12
0

⎞
0
0⎠
1

͜͜Ͱθi,j ͸࣭ྔ‫ݻ‬༗ঢ়ଶνi , νj ͷࠞ߹֯ɺδCP ͸ CP ରশੑͷഁΕͷେ͖͞Λද͢ύϥϝʔλʔͰ͋Δɻ

(1.2)

3

1.3 χϡʔτϦϊৼಈ

1.3.2 ਅۭதͰͷχϡʔτϦϊৼಈਅۭதͰͷχϡʔτϦϊͷϑϨʔόʔͷมԽ (α → β ) ͷ࣌ؒൃల͸ࣜ 1.3 Ͱද͞ΕΔɻ⟨νβ | e−iĤt |να ⟩ =

3
!

(1.3)

∗
e−iEi t Uβi Uαii&p2 + m2i ͸ӡಈྔ p Λ࣋ͭࣗ༝ཻࢠͷΤωϧΪʔ‫ݻ‬༗஋Ͱ͋

͜͜ͰɺĤ ͸ࣗ༝ཻࢠͷϋϛϧτχΞϯɺEi =Δɻ·ͨɺ3 ੈ୅χϡʔτϦϊৼಈͷભҠ֬཰ P (να → νβ ) ͸ɺα, β = e, µ, τ ͱͯ͠ɺࣜ 1.4 Ͱද͞ΕΔɻ

P (να → νβ ) = δαβ − 4

!

'

(
∗

∗
Re UαiUβi Uαj Uβj sin2i>j)∆m2ij L
4E

*

+2

!

'

(
∗

∗
Im UαiUβi Uαj Uβj sini>j)∆m2ij L
2E

*

(1.4)

͜͜Ͱɺ∆m2i,j = m2i − m2j Ͱ͋Γɺmi , mj ͸χϡʔτϦϊ࣭ྔ‫ݻ‬༗஋ m1 , m2 , m3 Λද͢ɻ·ͨ L ͸χϡʔτϦϊͷඈఔͰ͋Δɻ3 ੈ୅χϡʔτϦϊৼಈ͸ҰൠʹෳࡶͰ͋Δ͕ɺೋͭͷ࣭ྔͷೋ৐ࠩͷؔ܎͕ |∆m221 | ≪ |∆m232 |ͱ͍͏͜ͱͱɺҰͭͷࠞ߹֯ θ13 ͕খ͍͜͞ͱ͕ա‫ڈ‬ͷ࣮‫͔ݧ‬Β൑໌͓ͯ͠Γɺ|∆m221 | ͱ |∆m232 | ͷৼಈΛ෼཭͠
ͯߟ͑Δ͜ͱ͕Ͱ͖ΔͨΊɺ͜͜Ͱ͸ 2 ੈ୅ৼಈΛߟ͑Δɻ࣭ྔ‫ݻ‬༗ঢ়ଶ ν1 , ν2 , ϑϨʔόʔ‫ݻ‬༗ঢ়ଶ νe , νµ ͷ 2 ੈ୅χϡʔτϦϊͷࠞ߹ঢ়ଶ͸

+

|νe ⟩
|νµ ⟩

,

=

+

cos θ
− sin θ

sin θ
cos θ

,+

ͱͳΓɺ࣌ؒൃల͸ h̄ ΛσΟϥοΫఆ਺ͱͯ͠ɺࣜ 1.6 ͰදͤΔɻ

|ν1 ⟩
|ν2 ⟩

,

(1.5)

+
,
+
,
iE1 t
iE2 t
|να (t)⟩ = − |ν1 ⟩ sin θ exp −+ |ν2 ⟩ cos θ exp −
h̄
h̄

(1.6)

t = 0 Ͱ να Ͱ͋ͬͨχϡʔτϦϊ͕࣌ࠁ t ʹ να Ͱ͋Δ֬཰ P (να → να ) ͸sin2 2θP (να → να ) = 1 −
2-.

(E1 − E2 )t
1 − cos
h̄

/0

(1.7)

Ͱ͋Δɻ͜͜ͰχϡʔτϦϊͷ࣭ྔ͕খ͍͜͞ͱ͔Β pc ≫ m1 , m2 Λ༻͍ͯɺ
1

1

E2 − E1 = [(pc)2 + (m2 c2 )] 2 − [(pc)2 + (m1 c2 )] 2
=

(1.8)

(m22 − m21 )c3
2pͱۙࣅͰ͖Δɻ͜ΕΛ༻͍ͯࣜ 1.7 ͸ࣜ 1.9 ͱද͞Εɺ͜ΕΑΓ t = 0 Ͱ να Ͱ͋ͬͨχϡʔτϦϊ͕࣌ࠁ t ʹ

νβ Ͱ͋Δ֬཰ P (να → νβ ) ͸P (να → να ) = 1 − sin2 2θ sin2
P (να → νβ ) = sin2 2θ sin2.

.

1.27∆m2 [eV2 ]L[km]
E[GeV]

1.27∆m2 [eV2 ]L[km]
E[GeV]//(1.9)(1.10)

ͱදͤΔɻ2 ੈ୅χϡʔτϦϊৼಈ֬཰͸χϡʔτϦϊͷ L/E (ඈఔ/ΤωϧΪʔ) ͷؔ਺ͱͳ͍ͬͯΔ͜ͱ͕Θ
͔Δɻ

4

ୈ 1 ষ ং࿦1.3.3 ෺࣭தͰͷχϡʔτϦϊৼಈ෺࣭தͰͷϑϨʔόʔͷมԽ͸෺࣭ͱχϡʔτϦϊͷ൓ԠʹΑͬͯɺਅۭதͱ͸ৼΔ෣͍Λม͑Δɻ͜Ε͸෺࣭ޮՌͱ‫ݺ‬͹ΕɺWolfenstein [9] ͕ఏҊ͠ɺMikheev ͱ Smirnov[10] ͕͜ΕΛ·ͱΊͨɻ෺࣭ޮՌ͸χϡʔτϦϊ͕෺࣭தΛ఻೻தʹɺχϡʔτϦϊͷ࣮࣭తͳ࣭ྔ͕มԽ͠ɺ͋Δ৚݅ʹΑͬͯ‫͜ى‬Δ‫ڞ‬໐ʹΑΔޮՌͷ͜ͱͰɺ͜Ε͸෺࣭தͷిࢠʹΑͬͯҾ͖‫͜͞ى‬ΕΔͨΊɺిࢠχϡʔτϦϊͷΈ͜ͷӨ‫ڹ‬Λड͚ɺࣜ 1.11 ͷΑ͏ͳ VCC ͕͔͔Δɻಛʹɺ෺࣭ͷີ౓͕ߴ͍ͱ͜Ζ (஍‫಺ٿ‬෦) Ͱͷ‫ڞ‬໐͸ɺνe (ν¯e ) ʹରͯ͠ਖ਼ৗ֊૚ (‫֊ٯ‬૚) Ͱ‫͜ى‬Γɺ‫֊ٯ‬૚ (ਖ਼ৗ֊૚) Ͱ‫͜ى‬Βͳ͍ɻ͜ͷޮՌͷ‫د‬༩ʹΑͬͯɺχϡʔτϦϊৼಈ֬཰͸ਖ਼ৗ֊૚ͱ‫֊ٯ‬૚ͰҟͳΔ͕ɺಉ࣌ʹ νe ͱ ν¯e ʹରͯ͠΋‫͔͔ʹ͖޲ٯ‬Δɻ͜ͷͨΊਖ਼ৗ֊૚ͱ‫֊ٯ‬૚ͷৼಈ֬཰ͷҧ͍Λ໌Β͔ʹ͍ͨ͠৔߹ɺχϡʔτϦϊ/൓χϡʔτϦϊΛ۠ผͯ͠ৼಈ֬཰Λଌఆ͢Δ͜ͱ͕ෆՄܽͰ͋Δɻ

√VCC = ± 2GF Ne(1.11)

͜͜ GF ͸ϑΣϧϛ݁߹ఆ਺ɺNe ͸ిࢠີ౓Ͱ͋Δɻਖ਼ෛͷූ߸͸ νe (ν¯e ) ʹରԠ͍ͯ͠Δɻ͜ͷ‫د‬༩ΛߟྀʹೖΕͨ෺࣭தͰͷ 2 ੈ୅χϡʔτϦϊৼಈͷγϡϨσΟϯΨʔํఔࣜ͸i∂x Ψ(x) =

∆m2M
4E

+

− cos 2θM
sin 2θM,
sin 2θM
Ψ(x)cos 2θM(1.12)ͱද͞ΕΔɻ͜͜Ͱ͸ɺ

Γ=

2EVCC
∆m2

(1.13)

ͱͯ͠ ∆m2M , sin2 2θM ΛҎԼͷΑ͏ʹఆ͍ٛͯ͠Δɻ

∆m2M = ∆m2
sin2 2θM =1(1.14)

sin2 2θ + (cos 2θ − Γ)2sin2 2θ
sin 2θ + (cos 2θ − Γ)2(1.15)

2Ҏ্͔Βɺ෺࣭தͰͷχϡʔτϦϊৼಈ֬཰ͷࣜ͸ਅۭதͷ৔߹ͱಉ༷ʹࣜ 1.16, 1.17 ͷΑ͏ʹද͢͜ͱ͕Ͱ͖Δɻ

P (να → να ) = 1 − sin2 2θM sin22

P (να → νβ ) = sin 2θM sin

2

.

.

1.27∆m2M [eV2 ]L[km]
E[GeV]

1.27∆m2M [eV2 ]L[km]
E[GeV]//(1.16)(1.17)

1.4 SK ʹ͓͚Δେ‫ؾ‬χϡʔτϦϊৼಈղੳ͜ͷΑ͏ͳχϡʔτϦϊৼಈͷৼΔ෣͍Λར༻ͯ͠ɺεʔύʔΧϛΦΧϯσ࣮‫( ݧ‬SK) Ͱ͸࣭ྔ֊૚ͷܾఆͷͨΊʹɺେ‫ࢠిؾ‬χϡʔτϦϊͷఱ௖֯ (౸དྷํ޲) ෼෍Λ༻͍ͯ෺࣭ޮՌͷղੳΛߦ͍ͬͯΔɻνe /ν¯e ࣝผ [11] ʹΑͬͯ νe ͱ ν¯e Λ෼཭ͨ͠αϯϓϧͷ֤ΤωϧΪʔྖҬʹ͓͚Δ্޲͖ (෺࣭ޮՌΛड͚Δ) ࣄ৅ͱԼ޲͖ (෺࣭ޮՌΛड͚ͳ͍) ࣄ৅ͷࣄ৅਺ͷൺ (Ξοϓμ΢ϯൺ) Λൺ΂Δ͜ͱͰ֊૚ͷҧ͍͕ఱ௖֯෼෍ͷҧ͍ΛੜΜͰ͍Δ͜
ͱΛ֬ೝ͢Δ͜ͱ͕Ͱ͖Δɻਤ 1.2 ʹ νe /ν¯e ࣝผʹ͓͍ͯ۠ผ͞Εͨ νe -like ࣄ৅ͱ ν¯e -like ࣄ৅ͷΞοϓμ΢ϯൺ

1.5 େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊͷ֊૚ܾఆ‫͜ͱ౓ײ‬Ε·Ͱͷ νµ /ν¯µ ࣝผͷ෼෍ΛͦΕͧΕࣔͨ͠ɻਖ਼ৗ֊૚ΛԾఆͨ͠৔߹ͷ෼෍ (੨ઢ) ͱ‫֊ٯ‬૚ΛԾఆͨ͠৔߹ͷ෼෍ (ᒵઢ) ͕ҟͳͬ
͍ͯΔ͜ͱ͕෼͔Δɻσʔλ‫؍‬ଌͷ݁Ռ (ࠇ఺) ͸ਖ਼ৗ֊૚Λ͓ࣔࠦͯ͠Γɺ͜ͷ SK Ͱͷ݁ՌͱՃ଎‫ث‬ϏʔϜΛ༻͍ͯੜ੒͞ΕͨχϡʔτϦϊΛ༻͍ͨ T2K ࣮‫ݧ‬ͷ݁ՌΛ౷߹ͨ݁͠ՌͰɺ‫ࡏݱ‬໿ 2 σ Ͱਖ਼ৗ֊૚Λ͍ࣔࠦͯ͠Δ[12]ɻ SK Ͱ͸ɺ‫ͳߋࡏݱ‬Δ‫্޲౓ײ‬Λ໨ࢦͯ͠ɺ༗ޮମੵͷ֦ுɺχϡʔϥϧωοτϫʔΫΛ༻ཻ͍ͨࢠࣝผɺλ΢χϡʔτϦϊղੳͳͲɺຊ‫ڀݚ‬Λ‫ؚ‬Ίͨෳ਺ͷղੳΛ௥Ճ͢Δ͜ͱͰɺࠓ‫ ޙ‬5 ೥ؒͰ࣭ྔ֊૚ܾఆ‫ ౓ײ‬3 σ ͷୡ੒Λ໨ඪʹ‫͍ͯ͛ܝ‬Δɻ

ਤ 1.2

χϡʔτϦϊΤωϧΪʔʹର͢Δ্޲͖χϡʔτϦϊͱԼ޲͖χϡʔτϦϊͷࣄ৅਺ͷൺ [12]ɻࠇ఺͕

σʔλͰ‫ࠩޡ‬๮͸౷‫ܭ‬Τϥʔɺ੨ઢ͕ਖ਼ৗ֊૚ΛԾఆͨ͠஋ɺᒵ৭͕‫֊ٯ‬૚ΛԾఆͨ͠஋Ͱ͋Δɻ

1.5 େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊͷ֊૚ܾఆ‫͜ͱ౓ײ‬Ε·Ͱͷ νµ /ν¯µ ࣝผ‫ࡏݱ‬ͷεʔύʔΧϛΦΧϯσͰͷେ‫ؾ‬χϡʔτϦϊৼಈղੳʹɺϛϡʔΦϯχϡʔτϦϊ (νµ , ν¯µ ) ࣄ৅͸༻͍ΒΕ͍ͯͳ͍͕ɺϛϡʔΦϯχϡʔτϦϊ΋ిࢠχϡʔτϦϊ (νe , ν¯e ) ͱಉ༷ʹ֊૚ੑʹ‫౓ײ‬Λ࣋ͭɻ νµ ͱ ν¯µ ͦΕͧΕͷભҠ֬཰Λਤ 1.3 (a) ͱ 1.3 (b) ʹࣔͨ͠ɻॎ࣠ΛχϡʔτϦϊΤωϧΪʔɺԣ࣠ΛχϡʔτϦϊ౸དྷํ޲ͱ
ͨ࣌͠ͷɺਖ਼ৗ֊૚ΛԾఆͨ͠৔߹ͷ࢒ଘ֬཰͔Β‫֊ٯ‬૚ΛԾఆͨ͠৔߹ͷ࢒ଘ֬཰ΛҾ͍ͨ΋ͷͰ͋Γɺ৭͕ೱ͍෦෼΄ͲԾఆͨ͠֊૚ʹΑΔ࢒ଘ֬཰ͷ͕ࠩେ͖͍ɻcos(ఱ௖֯) = 0 ͕ਫฏํ޲Ͱ͋Γɺcos(ఱ௖֯) > 0 ͕Լ޲͖ (େ‫ؾ‬தΛ௨ա͖ͯͨ͠) χϡʔτϦϊɺcos(ఱ௖֯) < 0 ্͕޲͖ (஍‫಺ٿ‬෦Λ௨ա͖ͯͨ͠) χϡʔτϦϊͰ
͋Δɻ৭͕ೱ͍෦෼͕ cos(ఱ௖֯) < 0 Ͱଟ͍ͷ͸্޲͖χϡʔτϦϊ͕஍‫಺ٿ‬෦ͷ෺࣭ޮՌΛड͚ΔͨΊͰ͋Δɻ͜ͷ νµ ͱ ν¯µ ͷ෼෍͸൓సͨ͠‫͍ͯࣅͰܗ‬Δ͜ͱ͕࢕͑Δɻ͜ͷͨΊ νµ ͱ ν¯µ ͕ࠞࡏͨ͠αϯϓϧͰ͸ɺͦΕͧΕͷޮՌΛଧͪফ͋ͬͯ͠͠·͍ɺ࣭ྔ֊૚ͷܾఆ‫͕౓ײ‬௿Լͯ͠͠·͏ɻ͜ͷ͜ͱ͔Β֊૚ܾఆ‫্޲౓ײ‬ͷͨΊʹɺ͜ͷ νµ ͱ ν¯µ Λࣝผ͢Δ͜ͱ͸‫ۃ‬ΊͯॏཁͰ͋Δ͜ͱ͕Θ͔Δɻνµ /ν¯µ ࣝผͷ༗ޮੑ͔Βઌߦ‫[ ڀݚ‬2] ͰɺχϡʔτϦϊ൓Ԡͷ࠶ߏ੒͕͠΍͍͢࠷΋୯७ͳχϡʔτϦϊ൓Ԡ (४஄ੑࢄཚࣄ৅, ‫ޙ‬ड़) ʹ͍ͭͯɺϛϡʔΦϯͷ่յిࢠͱதੑࢠͷ৘ใΛ༻͍ͨ likelihood ๏ʹΑΔ νµ /ν¯µ ࣝผͷख๏͕։ൃ͞Εͨɻ͔͠͠ɺ͜ͷ୯७ͳࣄ৅͸Ұൠ

5

6

ୈ 1 ষ ং࿦ʹ࣭ྔ֊૚ੑ‫͞ͱ͍ߴ͕౓ײ‬ΕΔχϡʔτϦϊΤωϧΪʔ 10 GeV ෇ۙ (ਤ 1.3 ͷ৭ͷೱ͍ྖҬ) Ͱ౷‫͕ܭ‬গͳ͘ɺ༗ޮͳ‫͕౓ײ‬ಘΒΕͳ͔ͬͨɻ

ਤ 1.3େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊͷભҠ֬཰ɻਖ਼ৗ֊૚ͷ৔߹ͷભҠ֬཰͔Β‫֊ٯ‬૚ͷ৔߹ͷભҠ֬཰ΛҾ͍ͨਤɻԣ͕࣠χϡʔτϦϊΤωϧΪʔ (GeV)ɺॎ͕࣠χϡʔτϦϊఱ௖֯෼෍Ͱ͋Δɻ৭͕ೱ͍෦෼͕֊૚ຖ
ͷભҠ֬཰ͷ͕ࠩେ͖͍ [2]ɻ(a) νµ → νµ (b) ν¯µ → ν¯µ1.6‫ڀݚ‬໨త

લड़ͷΑ͏ʹ֊૚ੑܾఆ‫্޲౓ײ‬ͷͨΊʹ νµ /ν¯µ ࣝผΛ͢Δ͜ͱ͸ॏཁͰ͋Δɻຊ‫Ͱڀݚ‬͸ɺχϡʔτϦϊ࣭ྔ֊૚ͷܾఆ‫্޲౓ײ‬Λ໨ࢦ͠ɺܾఆ‫౓ײ‬ͷߴ͍ྖҬͰࣄ৅਺ͷଟ͍ɺଟཻࢠࣄ৅ʹ͍ͭͯ νµ ͱ ν¯µ Λࣝผ͢Δख๏Λ։ൃ͢ΔɻεʔύʔΧϛΦΧϯσ࣮‫͍͓ͯʹݧ‬ɺ͜Ε·Ͱଟཻࢠࣄ৅ʹ͍ͭͯ͸ νµ /ν¯µ ࣝผ͸ߦΘΕ͓ͯΒͣɺຊ‫ॳ͕ڀݚ‬ͷࢼΈͰ͋Δɻ͜Ε·Ͱຊ‫ߦ͕ڀݚ‬ΘΕͯ͜ͳ͔ͬͨཁҼͱͯ͠ɺϛϡʔΦϯχϡʔτϦϊ͕ిࢠχϡʔτϦϊʹൺ΂ͯҰൠʹܾఆ‫͕౓ײ‬௿͍ͱ༧૝͞Ε͍ͯΔ͜ͱ͕‫͛ڍ‬ΒΕΔɻ͔͠͠ɺ૷ஔͷվྑʹΑΔΤϨ
ΫτϩχΫεͷ޲্΍ɺࠓ‫ޙ‬༧ఆ͞Ε͍ͯΔེࢎΨυϦχ΢ϜΛ७ਫதʹՃ͑Δ࣮‫͍͓ͯʹݧ‬ɺνµ ͱ ν¯µ ͷࣝผʹ༗ޮͱ͞Ε͍ͯΔϛϡʔΦϯ่յిࢠ΍தੑࢠͷ‫ݕ‬ग़ޮ཰ͷେ෯ͳ޲্͕ΈΒΕɺνe /ν¯e ࣝผΑΓ΋ߴ͍ࣝผੑೳΛಘΒΕΔՄೳੑ͕ߴ͍͜ͱɺ·ܾͨఆ‫౓ײ‬Λ๦͛ΔཁҼͷҰͭͰ͋ͬͨߴΤωϧΪʔͷϛϡʔΦϯχϡʔτϦϊ൓Ԡ͕‫ݕ‬ग़‫ث‬ͷ‫ݕ‬ग़ՄೳྖҬ֎·Ͱ‫ٴ‬ΜͰ͠·͏ͱ͍͏໰୊͕ɺεʔύʔΧϛΦΧϯσ࣮‫͚͓ʹݧ‬Δ༗ޮମੵ֦ு‫ݚ‬‫ڀ‬΍‫ܭࡏݱ‬ըதͷϋΠύʔΧϛΦΧϯσ࣮‫ʹݧ‬Αͬͯɺ‫ݕ‬ग़ՄೳྖҬ͕֦͕Δ͜ͱͰղফ͞ΕΔՄೳੑ͕͋Γɺ͜ͷҙຯͰ νµ /ν¯µ ࣝผΛಋೖ͢Δ͜ͱ͸֊૚ܾఆ‫ݙߩʹ্޲౓ײ‬Λ͢ΔՄೳੑ͕ߴ͍ɻ
·ͨɺಉ༷ʹ֊૚ੑܾఆΛ໨ࢦ͢ IceCube ࣮‫ݧ‬ɺANTARES ࣮‫ݧ‬͸ώοτύλʔϯ͔Β ν/ν̄ ࣝผΛ͢Δ͜ͱ͕
ग़དྷͳ͍ͨΊɺੈքతʹ‫ͯݟ‬΋ຊ‫ڀݚ‬͸৽͍࣭͠ྔ֊૚‫ڀݚ‬ͷख๏ͱͯ͠ಛචʹ஋͢Δɻ
͜ͷ࿦จͰ͸ɺνµ /ν¯µ ࣝผํ๏ͷ։ൃͱࣝผ͞ΕͨαϯϓϧͰͷ࣭ྔ֊૚ͷܾఆ‫౓ײ‬ͷධՁΛߦ͏ɻୈ 2 ষͰεʔύʔΧϛΦΧϯσ࣮‫ݕͱݧ‬ग़‫ث‬ͷ֓ཁɺୈ 3 ষͰେ‫ؾ‬χϡʔτϦϊͱͦͷ૬‫༻࡞ޓ‬ɺୈ 4 ষͰχϡʔτϦϊͷ৘ใͷ࠶ߏ੒ͷख๏ʹ͍ͭͯड़΂ͨ‫ޙ‬ɺୈ 5 ষʹ͓͍ͯ νµ /ν¯µ ͷৼΔ෣͍ͷߟ࡯ɺୈ 6 ষͰ νµ /ν¯µ ࣝผ likelihood๏ͷ֓ཁͱͦͷࣝผ݁ՌΛड़΂Δɻ·ͨୈ 7 ষͰ͸ɺνµ /ν¯µ ࣝผΛಋೖͨ͠αϯϓϧΛ༻͍࣭ͯྔ֊૚ͷܾఆਫ਼౓Λ‫͠ڀݚ‬ɺୈ 8 ষͰ͸কདྷ࣮‫͚͓ʹݧ‬Δࣝผਫ਼౓΍ܾఆਫ਼౓Λߟ࡯͢Δɻ࠷‫ʹޙ‬ୈ 9 ষͰຊ‫ڀݚ‬ͷ·ͱΊͱࠓ‫ޙ‬ͷల๬Λड़΂Δɻ7ୈ2ষ

εʔύʔΧϛΦΧϯσ࣮‫ݧ‬
2.1 ࣮‫ݧ‬ͷ֓ཁεʔύʔΧϛΦΧϯσ͸‫ذ‬ෞ‫ݝ‬ඈଭࢢɺ෋ࢁ‫ͱݝ‬ͷ‫͋ʹڥݝ‬ΔਆԬ߭ࢁͷ஍Լ 1000 m ʹҐஔ͢ΔਫνΣϨϯίϑ‫ݕ‬ग़‫͋Ͱث‬Δɻத͸ 5 ສτϯͷ௒७ਫͰຬͨ͞Ε͓ͯΓɺ໿ 13000 ຊͷޫిࢠ૿ഒ؅ (Photomultiplier tube,

PMT) ͰғΘΕɺՙిཻࢠʹΑΔνΣϨϯίϑ์ࣹΛଊ͑Δ͜ͱ͕Ͱ͖Δɻ·ͨ‫ݕ‬ग़‫ث‬͸಺ਫ૧ͱ֎ਫ૧ͷ 2 ͭʹ෼͔Ε͓ͯΓɺχϡʔτϦϊ൓ԠͱӉ஦ઢཻࢠΛ۠ผͰ͖ΔΑ͏ʹͳ͍ͬͯΔ (ਤ 2.1)ɻओͳ໨త͸ཅࢠ่յ୳ࡧ
ͱ༷ʑͳχϡʔτϦϊ‫( ݯ‬ଠཅɺେ‫ؾ‬ɺՃ଎‫ث‬ɺӉ஦) Ͱੜ੒͞ΕͨχϡʔτϦϊΛ༻͍ͨ‫͋Ͱڀݚ‬Δɻ

ਤ 2.1 εʔύʔΧϛΦΧϯσ‫ݕ‬ग़‫[ ث‬13]

2.1.1 ‫ݕ‬ग़‫ث‬ͷาΈεʔύʔΧϛΦΧϯσͰͷ‫؍‬ଌ͸ 1996 ೥ 4 ݄ 1 ೔ʹ։࢝͞Εɺ‫ݕͰ·ࡏݱ‬ग़‫ث‬΍ಡΈग़͠ճ࿏ͷվྑΛॏͶͯ‫؍‬ଌΛଓ͚͍ͯΔɻ͜Ε·Ͱͷ‫؍‬ଌ‫ؒظ‬͸‫ݕ‬ग़૷ஔͷҧ͍ʹΑͬͯɺSK-I ∼ SK-V ·Ͱେ͖͘ 5 ͭͷϑΣʔζʹ෼͚ΒΕ͍ͯΔ (ද 2.1)ɻॳΊͷ 5 ೥ؒͷ‫؍‬ଌΛ SK-I ͱ‫Ϳݺ‬ɻޫిࢠ૿ഒ؅ͷަ‫׵‬Λ͠ɺ࠶౓‫؍‬ଌΛ։࢝͢ΔͨΊͷ஫ਫ࡞‫ۀ‬தʹఈ໘ͷޫిࢠ૿ഒ؅ׂ͕Εɺ࿈࠯తʹ಺ਫ૧Ͱ 6777 ຊɺ֎ਫ૧ 1100 ຊͷޫిࢠ૿ഒ؅͕ഁଛͨ͠ɻ

8

ୈ2ষ

εʔύʔΧϛΦΧϯσ࣮‫ݧ‬͜ͷ SK-II ‫Ͱؒظ‬͸࢒ͬͨޫిࢠ૿ഒ؅Ͱ‫؍‬ଌΛߦͬͨͨΊɺ಺ਫ૧ͷޫిࢠ૿ഒ؅ͷ‫ ͕਺ݸ‬5182 ຊͱগͳ͍ɻ

SK-III ͔Β͸ޫిࢠ૿ഒ؅ͷຊ਺Λ‫ݩ‬ʑͱ΄΅ಉ͡ 11129 ຊʹ໭ͨ͠ɻ2008 ೥ 9 ݄͔Β͸ɺSK-IV ͱͯ͠ɺ৽ͨ
ʹ։ൃ͞ΕͨΤϨΫτϩχΫε QBEE Λಋೖ͠ɺσʔλऩूγεςϜΛҰ৽ͨ͜͠ͱͰ௕‫ظ‬తͰ҆ఆͨ͠‫؍‬ଌΛଓ͚ΒΕΔΑ͏ʹͳΓɺ໿ 10 ೥ؒɺ2018 ೥ 5 ݄·Ͱ‫؍‬ଌ͕ଓ͚ΒΕͨɻ2018 ೥ 5 ݄ 31 ೔͔Β͸ 12 ೥ͿΓʹଌఆ‫ث‬λϯΫΛ։͖ɺλϯΫͷਫ࿙Ε෦෼ͷम෮ɺޫిࢠ૿ഒ؅ͷަ‫׵‬ɺλϯΫ಺ͷԚΕ΍ࡺͷআ‫ڈ‬ɺਫ॥‫؀‬ͷͨΊ഑؅ͷ௥ՃͳͲͷվम޻ࣄ͕ߦΘΕͨɻͦͯ͠ 2019 ೥ 1 ݄ 31 ೔͔Β SK-Gd (‫ޙ‬ड़) ʹ޲͚ͨ৽ϑΣʔζ SK-V ͕։࢝͞Εͨ [1]ɻද 2.1εʔύʔΧϛΦΧϯσͷาΈ [1]

SK-I

SKII

SKIII

SK-IV

SK-V

1996 ೥ 4 ݄͔Β2002 ೥ 10 ݄͔Β

2006 ೥ 7 ݄͔Β2008 ೥ 9 ݄͔Β2019 ೥ 1 ݄2001 ೥ 7 ݄

2005 ೥ 10 ݄2008 ೥ 8 ݄

2018 ೥ 5 ݄Ҏ߱ӡసத಺ਫ૧ PMT

11146 ຊ5182 ຊ

11129 ຊ11129 ຊ11129 ຊ֎ਫ૧ PMT1885 ຊ

1885 ຊ

1885 ຊ

1885 ຊ

1885 ຊ

ΤϨΫτϩχΫε

ATM

ATM

ATM

QBEE

QBEE

ϑΣʔζ
࣌‫ظ‬

2.2

‫ݕ‬ग़‫ث‬2.2.1 ‫ݕ‬ग़‫֓ث‬ཁ௒७ਫͷ٧·ͬͨλϯΫ͸ԁப‫Ͱܗ‬ɺߴ͞ 41.4 m, ௚‫ ܘ‬39.3 m ͷେ͖͕͋͞Γɺ಺ਫ૧ͱ֎ਫ૧ʹ෼͚ΒΕΔɻ
಺ਫ૧͸ओͱͳΔ‫ݕ‬ग़‫ ͞ߴͰث‬36.2 m, ௚‫ ܘ‬33.8 m Ͱ໿ 3 ສ 2 ઍτϯͷ༰ੵΛ༗͢Δɻ֎ਫ૧͸಺ਫ૧ͷपғΛғΈɺଆ໘͸ 2.2 m, ্Լ͸ 2.05 m ͷް͕͋͞Γɺ໿ 1 ສ 8 ઍτϯͷ༰ੵΛ༗͢Δɻ಺ਫ૧ͱ֎ਫ૧ͷؒ͸εʔύʔϞδϡʔϧ 2.2(b) ͱ͍͏ޫిࢠ૿ഒ؅Λ഑ஔͨ͠ϞδϡʔϧΛऔΓ෇͚ͨ 55 cm ෯ͷεςϯϨε੡ͷϑϨʔϜͰғ·Εɺ಺ਫ૧ଆʹ͸߹‫ ܭ‬11129 ຊͷ 50 cm ‫૿ࢠిޫܘ‬ഒ؅͕ɺ֎ਫ૧ଆʹ͸ 1885 ຊͷ 20 cm ‫૿ࢠిޫܘ‬ഒ؅͕औΓ෇͚ΒΕ͍ͯΔɻ಺ਫ૧ͷޫిࢠ૿ഒ؅͸಺ଆΛ޲͍͓ͯΓɺਫ૧಺෦ͰͷՙిཻࢠʹΑΔνΣϨϯίϑ
ޫΛ‫ݕ‬ग़͍ͯ͠Δɻ·ͨɺ֎ਫ૧ͷޫిࢠ૿ഒ؅͸֎ଆΛ޲͍͓ͯΓɺ‫ݕ‬ग़‫ث‬ΛғΉ‫ؠ‬൫͔ΒͷதੑࢠΛःณ͢Δ
ͱͱ΋ʹӉ஦ઢͳͲͷՙిཻࢠΛ‫ݕ‬ग़͢Δ͜ͱͰɺόοΫάϥ΢ϯυࣄ৅ͱχϡʔτϦϊࣄ৅ͱ۠ผ͍ͯ͠Δɻ·ͨޫిࢠ૿ഒ؅ΛғΉྖҬͱ‫ݕ‬ग़‫ث‬ΛғΉน໘͸λΠϕοΫγʔτͱ͍͏ന৭Ͱ൓ࣹ཰໿ 90% ͷ൓ࣹࡐͰ෴ΘΕ
͍ͯΔɻ͜Ε͸಺ਫ૧ͱ֎ਫ૧ͷؒ΍‫ݕ‬ग़‫΁֎ث‬ͷޫ࿙ΕΛ๷͙໨త͕͋Δ [13]ɻ

9

2.2 ‫ݕ‬ग़‫ث‬
(a)

(b)

ਤ 2.2 (a) 50 cm ޫిࢠ૿ഒ؅ͷ໛ࣜਤ (b) εʔύʔϞδϡʔϧͷ໛ࣜਤ [13]2.2.2 50 cm ‫૿ࢠిޫܘ‬ഒ؅εʔύʔΧϛΦΧϯσ‫ݕ‬ग़‫ʹث‬ΑΔ‫؍‬ଌྔ͸શͯޫిࢠ૿ഒ؅ʹΑΔޫࢠͷ৴߸Ͱ͋ΔɻͦͷͨΊɺޫిࢠ૿ഒ
؅ͷੑ࣭Λཧղ͢Δ͜ͱ͕ͱͯ΋ॏཁͰ͋Δɻ͜͜Ͱ͸಺ਫ૧ʹ࢖༻͞Ε͍ͯΔ 50 cm ޫిࢠ૿ഒ؅ͷ࢓༷Λࣔ͢ɻ͜ͷޫిࢠ૿ഒ؅͸඿দϗτχΫε R3600 ‫͋Ͱܕ‬Δɻද 2.2 ʹ࢓༷Λ·ͱΊͨ [4]ɻ
ද 2.2

50 cm ‫૿ࢠిޫܘ‬ഒ؅ͷ࢓༷·ͱΊ [4]ޫి໘௚‫ ܘ‬50 cm

ޫి෺࣭όΠΞϧΧϦ (Sb-K-Cs)

ྔࢠޮ཰

22% (೾௕ 360-400 nm)

ޫిࢠऩूޮ཰

70%μΠϊʔυߏ଄

ϕωνΞϯϒϥΠϯυ‫( ܕ‬11 ஈ)య‫૿ܕ‬ഒ཰

107య‫ܕ‬ҹՃిѹ

2000 V҉ిྲྀ

200 nAμʔΫϨʔτ

3 kHz (૿ഒ཰ 107 ͷ৔߹ )య‫ؒ࣌ߦ૸ࢠిܕ‬90 nsec (૿ഒ཰ 107 ͷ৔߹ )ిࢠ૸ߦ࣌ؒͷ֦͕Γ

2.2 nsec

ॏྔ

13 kg

଱ਫѹ

6 kg/cm2 ๷ਫੑޫి໘ʹ͸όΠΞϧΧϦ (Sb-K-Cs) ͱ‫ݺ‬͹ΕΔޫి෺࣭͕ৠண͞Ε͓ͯΓɺ͜͜ͰޫࢠΛ‫ٵ‬ऩ͠ɺҰ࣍ిࢠΛൃ
ੜͤ͞Δɻޫి໘ʹଓ͘μΠϊʔυͷߏ଄͸ 11 ஈͷϕωνΞϯϒϥΠϯυ‫͋Ͱܕ‬Δɻయ‫ܕ‬తʹ 1500-2200 V ͷҹ

10

ୈ2ষ

εʔύʔΧϛΦΧϯσ࣮‫ݧ‬ՃిѹͰҰ࣍ిࢠΛ 107 ഒ·Ͱ૿෯ͤ͞Δ͜ͱͰɺ‫ݕ‬ग़Մೳͳి‫ؾ‬৴߸Λൃੜ͍ͤͯ͞Δɻޫిࢠ૿ഒ؅͸࣓৔ͷӨ‫ڹ‬Λड͚ɺ૿ഒ཰͕มԽ͢ΔͳͲੑೳ͕ѱԽͯ͠͠·͏ɻͦͷͨΊεʔύʔΧϛΦΧϯσͰ͸‫ݕ‬ग़‫ث‬ͷपғʹϔϧϜϗϧπίΠϧΛ‫͖ר‬ɺ͜ΕʹిྲྀΛྲྀ͢͜ͱʹΑͬͯ஍࣓‫ؾ‬ͷӨ‫ڹ‬Λ‫ݮ‬Β͍ͯ͠Δɻ‫ܭࡏݱ‬ըதͷϋΠύʔΧϛΦΧϯσ࣮‫ݧ‬ͷͨΊʹ৽‫ܕ‬ͷޫిࢠ૿ഒ؅͕։ൃதͰ͋Δɻ͜Ε͸ɺޫి໘ͷߏ଄΍μΠϊʔυͷ‫ܗ‬ঢ়Λมߋ͢Δ͜ͱʹΑͬͯɺޫిࢠ (ޫి໘Ͱੜͨ͡ిࢠ) ऩूޮ཰͕ 90%ɺిࢠ૸ߦ࣌ؒͷ֦͕Γ 1.0 ns ͳͲେ෯ʹੑೳΛ޲্͍ͤͯ͞ΔɻεʔύʔΧϛΦΧϯσͰ΋ SK-V ͔Β͸Ұ෦Λ͜ͷޫిࢠ૿ഒ؅ʹ‫ʹط‬ஔ͖‫͍ͯ͑׵‬Δɻ

ਤ 2.3

2.3

νΣϨϯίϑ์ࣹͷΠϝʔδ [1]ਫνΣϨϯίϑޫ‫ݕ‬ग़νΣϨϯίϑ์ࣹͱ͸ՙిཻࢠ͕۶ં཰ n Λ࣋ͭഔ࣭தͰɺ෺࣭தͰͷޫ଎౓ c/n Λ௒͑ͨ଎౓ v = βc Λ࣋ͭ࣌ɺཻࢠͷਐߦํ޲ʹରͯ֯͠౓ θc ͰνΣϨϯίϑޫΛൃੜ͢Δ‫ݱ‬৅Ͱ͋Δ (ਤ 2.3)ɻ

cos θc =

1
nβ

(2.1)

७ਫ͸ n ∼ 1.34 ͳͷͰՙిཻࢠ͕ β = 1 ͰਐΉ࣌ θc ∼ 42◦ ͱͳΔɻ୯Ґ௕͞ dx ਐΉ࣌ʹ์ग़͞ΕΔνΣϨϯί
ϑޫͷޫࢠ਺ N ͸

d2 N
2παq 21=(1 − 2 2 )
2
dxdλ
λ
n β

(2.2)

Ͱ༩͑ΒΕΔɻ͜͜Ͱ α ͸ඍࡉߏ଄ఆ਺ α = 1/137, q ͸ՙిཻࢠͷిՙΛ͍ࣔͯ͠Δɻޫిࢠ૿ഒ؅͸ 300-600

nm ʹ‫ݕ‬ग़‫౓ײ‬Λ࣋ͭͷͰ 1/nβ = cos θ Λ୅ೖ͠ɺࣜ 2.2 Λม‫ͯ͠ܗ‬dN= 2παq 2 sin2 θc
dx

2 λ2

dλ
2
λ1 λ
1
1
= 2παq 2 sin θc ( − )
λ1
λ2

(2.3)

11

2.4 σʔλऩूγεςϜ
ͱ͢Δɻ͜͜Ͱ λ1 = 300, λ2 = 600, q = 1, θc ∼ 42◦ ͱͯ͠‫͢ࢉܭ‬Δͱɺཻࢠ͕ 1 cm ਐΜͩ࣌ʹฏ‫ ۉ‬340 ‫ݸ‬ͷޫࢠ͕์ग़͞ΕΔɻ·ͨՙిཻࢠ͕νΣϨϯίϑޫΛग़͢ͷʹඞཁͳΤωϧΪʔ Ethr ͸ m Λՙిཻࢠͷ੩ࢭ࣭ྔͱ
ͯ͠ɺ

nmc2
Ethr = √n2 − 1(2.4)

Ͱද͞ΕΔɻ७ਫத (n ∼ 1.34) Ͱͷཻ֤ࢠͷνΣϨϯίϑޫ์ग़ͷᮢ஋͸ද 2.3 ʹ·ͱΊΒΕ͍ͯΔɻ1 ͭͷཻࢠ(ओʹϨϓτϯ) ͕νΣϨϯίϑᮢ஋Λ௒͑Ϧϯάͱͯ͠‫؍‬ଌ͞Εͨ΋ͷΛγϯάϧϦϯάɺ2 ͭҎ্ͷཻࢠ͕ (Ϩϓτϯͷଞʹϋυϩϯ΋ಉ࣌ʹ) ‫؍‬ଌ͞Εͨ΋ͷΛϚϧνϦϯάͱ͍͏ɻ࣮ࡍʹཻࢠ͕์ग़͞Ε͍ͯͯ΋ɺதੑཻࢠ
΍νΣϨϯίϑᮢ஋Λ௒͑ͳཻ͍ࢠ͸Ϧϯάͱͯ͠‫؍‬ଌ͞Εͳ͍ͷͰɺҰൠʹϦϯάͷ৘ใ͔Β‫׬‬શʹχϡʔτϦϊ૬‫༻࡞ޓ‬Λ࠶ߏ੒͢Δ͜ͱ͸೉͍͠ɻ͔͠͠εʔύʔΧϛΦΧϯσͰ͸༷ʑͳࣄ৅બผख๏ʹΑͬͯ͜ͷ࠶ߏ੒ਫ਼౓Λ޲্͍ͤͯ͞Δɻ
ද 2.3 ཻ֤ࢠͷ७ਫதͰͷνΣϨϯίϑޫ์ग़ᮢΤωϧΪʔ [2]ཻࢠ੩ࢭ࣭ྔ (MeV/c2 )ᮢ஋ (MeV)

e±

0.511

0.767

µ±

105.7

157.4

±

139.7

207.9

±

493.7

735.5

938.3

1413

π

K

p

2.4 σʔλऩूγεςϜ
SK-I ͔Β SK-III ·ͰͷΤϨΫτϩχΫε͸ ATM (Analog-Timing-Module) ͱ‫ݺ‬͹ΕΔΤϨΫτϩχΫε͕࢖ΘΕ͍͕ͯͨ SK-IV ͔Β͸ΤϨΫτϩχΫεΛ QBEE (QTC-Based Electronics with Ethernet) ʹ࡮৽ͨ͠ɻ͜ΕʹΑΓϋʔυ΢ΣΞʹ͓͚ΔΠϕϯττϦΨʔΛແ͘͠ɺશͯͷޫిࢠ૿ഒ؅ʹΑΔޫࢠͷώοτ৘ใΛ‫ه‬࿥Ͱ͖Δ
Α͏ʹͳͬͨͨΊɺຊ‫Ͱڀݚ‬ॏཁࢹ͍ͯ͠Δதੑࢠ৴߸‫ݕ‬ग़΍่յిࢠͷ‫ݕ‬ग़ޮ཰ʹେ෯ͳ޲্Λ΋ͨΒͨ͠ɻ͜ͷઅͰ͜ͷσʔλऩूγεςϜʹ͍ͭͯઆ໌͢Δɻ

2.4.1 QBEEҰͭͷ QBEE Ϟδϡʔϧ͸ 8 ͭͷ QTC (࣌ؒిՙม‫׵‬ૉࢠ) Λ‫ؚ‬ΈɺͦΕͧΕͷ QTC ͸ 3 ͭͷ PMT ͷ৴߸Λѻ͍ͬͯΔ (ਤ 2.4)ɻQTC ͸ PMT ͔ΒͷΞφϩά৴߸Λड͚औΔͱɺͦͷిՙʹઢ‫ܗ‬ൺྫͨ͠෯Λ࣋ͭ୹‫ܗ‬೾ʹม‫͢ܗ‬ΔɻQTC ͔Βͷ୹‫ܗ‬೾͸Ϛϧνώοτ TDC ʹૹΒΕɺͦͷ্ཱ͕ͪΓ࣌ؒΛ৴߸‫ݕ‬ग़։࢝࣌ؒɺ෯Λిՙͱͯ͠σδλϧԽ͞ΕΔɻσδλϧԽ͞Εͨ৴߸͸ FPGA Ͱॲཧ͞ΕϑϩϯτΤϯυίϯϐϡʔλʹૹΒΕΔɻϑϩϯτΤϯυίϯϐϡʔλͰ͸σʔλΛ‫ن‬ଇతʹฒͼସ͑ɺ͞Βʹ merge PC ʹૹΔɻmerge PC Ͱ‫ޙ‬ड़ͷιϑτ΢ΣΞτϦΨʔ͕͔͚ΒΕɺΠϕϯτΛநग़͍ͯ͠ΔɻQTC ಺ͷ৴߸૿෯ճ࿏ʹ 3 छྨͷҟͳΔ૿෯཰ (small, medium, high) Λઃఆ͢Δ͜ͱͰɺQBEE Ͱ͸ ATM ʹൺ΂ͯ໿ 5 ഒ޿͍μΠφϛοΫϨϯδΛՄೳʹͨ͠ɻͦΕͧΕͷ૿෯཰͸ 1, 1/7, 1/49 ഒʹઃఆ͞Ε͍ͯΔɻද 2.4
ʹ‫؍‬ଌͰ͖ΔిՙͷϨϯδͱిՙ෼ղೳΛࣔͨ͠ɻೖࣹ p.e. ਺ʹ߹Θͤͯ૿෯཰Λద੾ʹม͑Δ͜ͱͰɺ3 νϟϯωϧΛ߹Θͤͯ 0.2 pC ͔Β 2500 pC ·ͰͷൣғͰͷ‫؍‬ଌΛՄೳʹ͍ͯ͠Δ [5]ɻ

12

ୈ2ষ

εʔύʔΧϛΦΧϯσ࣮‫ݧ‬ද 2.4 ͦΕͧΕͷήΠϯνϟϯωϧͷిՙμΠφϛοΫϨϯδͱ෼ղೳ [5]ήΠϯνϟϯωϧ

ిՙμΠφϛοΫϨϯδ

ిՙ෼ղೳ

small

0.2 ∼ 51 pC

0.1 pC/count5 ∼ 2500 pC

4.9 pC/countmedium1 ∼ 357 pC

large

0.7 pC/count

2.4.2 τϦΨʔ
merge PC ʹ͸શͯͷ PMT ͷ৘ใ͕ूΊΒΕΔɻ͜͜Ͱ͸৴߸‫ݕ‬ग़։͔࢝࣌ؒΒ 200 nsec Ҏ಺ (λϯΫͷ୺͔Β୺·Ͱޫ͕ਐΉͷʹ͔͔Δ࣌ؒʹରԠ) ʹώοτͨ͠ PMT ͷ਺ N200 ͕͋Β͔͡Ίઃఆͨ͠ᮢ஋Λ௒͑ͨࣄ৅ΛϋʔυσΟεΫʹ‫ه‬࿥͢Δ (ιϑτ΢ΣΞτϦΨʔ)ɻSK-IV Ҏ߱ͷϑΣʔζͰ͸ɺτϦΨʔͷᮢ஋ͷҧ͍ʹΑͬͯɺ

4 छྨͷτϦΨʔΛ͔͚͍ͯΔɻͦΕͧΕͷτϦΨʔλΠϓͷৄࡉΛද 2.5 ʹ·ͱΊͨɻϋʔυ΢ΣΞτϦΨʔ͔Βιϑτ΢ΣΞτϦΨʔʹมߋͨ͜͠ͱͰ֤ࣄ৅ͷλΠϛϯά෯Λࣗ༝ʹબ୒Ͱ͖ΔΑ͏ʹͳͬͨɻATM Ͱ͸ LE(Low Energy) ͱ HE (High Energy) ͷ 2 ͭͷτϦΨʔ͸ͱ΋ʹ 1.3 µsec Ͱ͕͋ͬͨɺQBEE Ͱ͸ LE ͱ HE Ͱ 40
µsec ͷ෯Λ‫ه‬࿥Ͱ͖Δɻ͜ΕʹΑͬͯࣄ৅ൃੜ‫ޙ‬ͷϛϡʔΦϯ่յిࢠͷ‫ݕ‬ग़ޮ཰͕޲্ͨ͠ɻSLE (Super Low

Energy) ͷΈΠϕϯτ෯͕୹͍ͷ͸์ࣹઢόοΫάϥ΢ϯυͷσʔλྔΛ཈͑ΔͨΊͰ͋ΔɻSK-IV ͔Β͸৽ͨͳτϦΨʔͱͯ͠ SHE (Super High Energy) ͱ AFT (After) τϦΨʔ͕ಋೖ͞ΕͨɻSHE τϦΨʔࣄ৅͕ OD τϦΨʔʹ͔͔Βͳ͔ͬͨ৔߹ɺAFT τϦΨʔ͕Ҿ͖‫͜͞ى‬Εɺࣄ৅ൃੜ‫ ޙ‬500 µsec ؒΛᮢ஋ͳ͠ͰσʔλΛશͯऔಘ͢Δɻ͜ΕʹΑͬͯதੑࢠั֫ʹΑΔ 2.2 MeV ΨϯϚઢͷ‫ݕ‬ग़͕Մೳʹͳͬͨɻ͜ΕΒͷվྑ͸ಛʹ௒৽੕എ‫ܠ‬χϡʔτϦϊ‫ݕ‬ग़Λ໨తʹͨ͠΋ͷ͕ͩɺχϡʔτϦϊϑϨʔόʔͷಛఆ΍χϡʔτϦϊ/൓χϡʔτϦϊͷࣝผੑೳͷ޲্ʹ΋‫͍͕ͯͬܨ‬Δɻ
ද 2.5

ιϑτ΢ΣΞτϦΨʔλΠϓͷৄࡉτϦΨʔλΠϓ

ώοτ਺ͷᮢ஋ N200 (ώοτ/200 nsec)Πϕϯτ෯ (µsec)τϦΨʔϨʔτ

SLE

34

LE

47

1.5(-0.5 ∼+1.0)

3.0 ∼3.4 kHz

HE

50

SHE

70 (2011 ೥ 9 ݄Ҏલ)40 (-5 ∼ +35)

∼ 40 HzSHE

58 (2011 ೥ 9 ݄Ҏ߱)

OD

22 in OD

40 (-5 ∼ +35)
40 (-5 ∼ +35)
40 (-5 ∼ +35)
40 (-5 ∼ +35)

∼ 40 Hz13

2.5 ϋΠύʔΧϛΦΧϯσ‫ܭ‬ըਤ 2.4

QBEE ಺෦ͷϒϩοΫμΠΞάϥϜ

2.5 ϋΠύʔΧϛΦΧϯσ‫ܭ‬ըεʔύʔΧϛΦΧϯσ࣮‫( ݧ‬SK) Λ௒͑Δ౷‫ͱྔܭ‬ଌఆਫ਼౓ͷ޲্Λ໨ࢦͯ͠ϋΠύʔΧϛΦΧϯσ࣮‫( ݧ‬HK,

Hyper Kamiokande) ͕ਐΊΒΕ͓ͯΓ 2026 ೥ଌఆ։࢝Λ༧ఆ͍ͯ͠ΔɻSK ͷ‫͍͑ͱܧޙ‬Δ͜ͷ࣮‫ݧ‬͸ɺSK ͰͷχϡʔτϦϊৼಈղੳͷ‫ڀݚ‬Λߋʹߴਫ਼౓Ͱ޲্͢Δɻຊ࿦จதͰ΋ຊ‫ڀݚ‬Λ HK ʹಋೖͨ͠৔߹ͷ‫ظ‬଴͞ΕΔ
݁ՌΛ SK ͷ৔߹ͱ߹Θͤͯߟ࡯͢Δɻ
ද 2.6 ʹ SK ͱ HK ͷ‫ݕ‬ग़‫ث‬ͷ֓ཁΛൺֱͯࣔͨ͠͠ɻHK ͸‫ذ‬ෞ‫ݝ‬ೋे‫ࢁޒ‬ͷ஍Լ 650 m ʹ‫ݐ‬ઃ͕༧ఆ͞Εͯ
͍Δ௒େ‫ܕ‬νΣϨϯίϑޫ‫ݕ‬ग़‫͋Ͱث‬Δɻ૯ମੵ 258 kton, ༗ޮମੵ͸ 187 kton Ͱ͋Γɺ͜Ε͸ SK ͷ༗ޮମੵͷ໿ 8.3 ഒͰ͋Δɻલड़ͷΑ͏ʹ৽‫ܕ‬ͷ PMT ͕ SK ͱಉ͡ 40% ͷޫి໘ඃ෴཰Ͱઃஔ͞ΕΔ༧ఆͰ͋Γɺ‫ݕ‬ग़ޮ཰͸໿ 2 ഒɺ࣌ؒ෼ղೳ΋ 2 ∼3 ഒʹ޲্͢Δɻຊ‫͍͓ͯʹڀݚ‬༗ޮମੵͷ૿Ճ͸ॏཁͰɺ୯७ͳ౷‫ྔܭ‬ͷ૿Ճ΋໪࿦ɺߴΤωϧΪʔͷχϡʔτϦϊ൓ԠʹΑͬͯੜཻͨ͡ࢠ͕‫ݕ‬ग़‫ث‬ͷ֎ਫ૧ʹඈͼग़ͯ͠͠·͏ࣄ৅͕‫ݮ‬গ͢ΔɻSK Ͱ͸֊૚ܾఆʹ‫౓ײ‬ͷ͋Δ 10GeV ෇ۙͷϛϡʔχϡʔτϦϊ൓Ԡ͕‫ݕ‬ग़‫ث‬ͷ֎ਫ૧·Ͱ‫ٴ‬ΜͰ͠·͏͜ͱͰɺղੳʹ༻͍Δ͜ͱ͕Ͱ͖ͣɺ͜ͷྖҬͰͷ౷‫͕ྔܭ‬গͳ͍ͱ͍͏໰୊͕͋Δ͕ɺHK Ͱ͸͜ͷྖҬͰे෼ͳ౷‫ܭ‬Λ֬อͰ͖ΔՄೳੑ͕͋Δɻৄࡉͳ‫ੵݟ‬΋Γʹ͍ͭͯ͸‫ޙ‬ड़͢Δɻ
ද 2.6 SK ͱ HK ͷ‫ݕ‬ग़‫ث‬ͷൺֱ

SKHK‫ݕ‬ग़‫ث‬ͷҐஔ

1000 m650 m‫ݕ‬ग़‫ث‬ͷ௚‫ܘ‬

39 m

74 m

‫ݕ‬ग़‫ث‬ͷߴ͞

42 m

60 m

૯ମੵ

50 kton258 kton༗ޮମੵ

22.5 kton

187 kton֎ਫ૧ͷް͞

∼2m

1∼2m

಺ਫ૧ͷ PMT ਺

11129 ຊ40000 ຊ֎ਫ૧ͷ PMT ਺1885 ຊ

6700 ຊ

ޫి໘ඃ෴཰

40%

40%

1 ޫࢠ‫౓ײ‬

12%

24%

࣌ؒ෼ղೳ

2∼3 nsec

1 nsec15ୈ3ষେ‫ؾ‬χϡʔτϦϊνµ ͱ ν¯µ Λࣝผ͢ΔͨΊʹେ‫ؾ‬χϡʔτϦϊͷੑ࣭Λཧղ͢Δ͜ͱ͸ෆՄܽͰ͋Δɻ͜ͷষͰ͸ຊ‫͍༻Ͱڀݚ‬Δେ‫ؾ‬χϡʔτϦϊͷੑ࣭ͱͦͷ૬‫͍ͯͭʹ༻࡞ޓ‬આ໌͢Δɻ

3.1 େ‫ؾ‬χϡʔτϦϊͷੜ੒େ‫ؾ‬χϡʔτϦϊͱ͸Ӊ஦͔Β౸དྷͨ͠Ұ࣍Ӊ஦ઢʢओʹཅࢠʣ͕஍‫ٿ‬େ‫ؾ‬தͷࢎૉ΍஠ૉͳͲͷ‫ͱ֩ࢠݪ‬൓Ԡ͠ɺੜͨ͡ೋ࣍Ӊ஦ઢʹ‫·ؚ‬ΕΔύΠΦϯ (π ± ), έΠΦϯ (K ± ), ϛϡʔΦϯ (µ± ) ͷ่յʹΑͬͯੜͨ͡χϡʔτϦϊͷ͜ͱͰ͋Δɻେ‫ؾ‬χϡʔτϦϊͱͯ͠ੜ੒͞ΕΔͷ͸ϛϡʔχϡʔτϦϊͱిࢠχϡʔτϦϊͷΈͰλ΢χϡʔτϦϊ͸‫·ؚ‬Εͳ͍ɻεʔύʔΧϛΦΧϯσͰ͸‫؍‬ଌͨ͠େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊͱిࢠχϡʔτϦϊͷଘࡏൺ͕ཧ࿦༧ଌͱҰக͠ͳ͍͜ͱ͔ΒχϡʔτϦϊৼಈ‫ݱ‬৅ͷଘࡏΛ໌Β͔ʹͨ͠ɻԼ‫ه‬ͷࣜ͸‫ج‬ຊతͳେ‫ؾ‬χϡʔτϦϊ͕ੜ੒͞ΕΔաఔΛࣔͨ͠΋ͷͰ͋Δɻ

π + → µ+ + ν µµ+ → e+ + νe + ν¯µ−−

π → µ + ν¯µµ− → e− + ν¯e + νµ

(3.1)
(3.2)
(3.3)
(3.4)

3.2 େ‫ؾ‬χϡʔτϦϊϑϥοΫε
SK Ͱ͸େ‫ؾ‬χϡʔτϦϊϑϥοΫε‫ࢉܭ‬ϞσϧʹຊాϞσϧ [14] Λ࠾༻͍ͯ͠ΔɻຊాϞσϧͰ͸Ұ࣍Ӊ஦ઢͷϑϥοΫεΛ AMS (Alpha Magnetic Spectrometer) ࣮‫[ ݧ‬15] ΍ BESS (Ballon-born experiment with aSuperconducting Spectrometer) ࣮‫[ ݧ‬16] ʹΑͬͯଌఆ͞Εͨ݁ՌΛ‫͓ͯ͠ࢉܭʹݩ‬Γɺଠཅ෩ͱ஍࣓‫͕ؾ‬Ұ࣍Ӊ஦ઢʹ‫ޮ͢΅ٴ‬Ռ΋‫ʹࢉܭ‬૊Έࠐ·Ε͍ͯΔ (ਤ 3.1)ɻྫ͑͹ɺ1 GeV ఔ౓ͷӉ஦ઢͰ͸ଠཅͷ‫ۃ‬େͱ‫ۃ‬খͷ͕ࠩ
໿ 2 ഒ͋Δ͕ɺ10 GeV Ҏ্ͩͱ 10% ఔ౓·Ͱ‫ݮ‬গ͢Δɻେ‫ؾ‬χϡʔτϦϊ͸ϑϥοΫε͸͜ͷҰ࣍Ӊ஦ઢ͕େ‫ؾ‬‫ͱ֩ࢠݪ‬૬‫ͯ͠༻࡞ޓ‬ੜ੒͞Εͨೋཻ࣍ࢠͰ͋ΔύΠதؒࢠ΍ K தؒࢠͷ่յ͔Βੜ੒͔Β‫͞ࢉܭ‬ΕΔɻਤ 3.2 ʹେ‫ؾ‬χϡʔτϦϊϑϥοΫεͷ౸དྷํ޲ (ఱ௖֯) ෼෍Λࣔͨ͠ɻχϡʔτϦϊͷϑϥοΫε͸ਫฏํ޲ͰΑΓେ͖͘ͳ͍ͬͯΔɻ‫ݕ‬ग़‫͔ث‬Β‫ͨݟ‬େ‫ؾ‬ͷްΈ͕ਫฏํ޲ͷํ͕ް͘ͳ͍ͬͯΔɻ͜ͷޮՌ͸ಛʹ 1 GeV ҎԼͷ௿ΤωϧΪʔχϡʔτϦϊͰ‫ݦ‬ஶͰ͋Δɻ
·ͨɺSK ʹ͓͚Δେ‫ؾ‬χϡʔτϦϊৼಈղੳͰ͸ɺχϡʔτϦϊϑϥοΫεʹʹχϡʔτϦϊৼಈύϥϝʔλΛ༻͍֤ͯࣄ৅ͷΤωϧΪʔͱ౸དྷํ޲ʹԠͯ͡χϡʔτϦϊৼಈͷ֬཰ͷॏΈ෇͚Λߦ͏͜ͱͰٙࣅతʹχϡʔτϦϊৼಈΛߟྀ͍ͯ͠Δɻ

16

ୈ3ষ

େ‫ؾ‬χϡʔτϦϊ

ਤ 3.3 ʹຊాϞσϧͱͦΕҎ֎ͷϞσϧʹΑΔϑϥοΫε‫݁ࢉܭ‬ՌΛࣔͨ͠ɻߴΤωϧΪʔͰϛϡʔΦϯχϡʔτϦϊͷׂ߹͕૿Ճ͠ɺಛʹ ν¯µ ʹൺ΂ͯ νµ ͷׂ߹͕૿Ճ͢Δ͜ͱ͕Θ͔Δɻ

ਤ 3.1 Ұ࣍Ӊ஦ઢཅࢠͷϑϥοΫεɻຊాϞσϧͰͷ‫݁ࢉܭ‬Ռ (ࠇઢ)ɺ‫؍‬ଌσʔλ (֤఺)ਤ 3.2֤ΤωϧΪʔຖͷେ‫ؾ‬χϡʔτϦϊϑϥοΫεͷఱ௖֯෼෍ɻ(ࠨ) 0.32 GeVɺ(த) 1.0 GeVɺ(ӈ) 3.2

GeVɻcos θ = 1 ͸ਨ௚Լ޲͖ํ޲ͷχϡʔτϦϊɻcos θ = −1 ͸ਨ௚্޲͖ํ޲ͷχϡʔτϦϊΛද͍ͯ͠Δɻ͜͜ͰχϡʔτϦϊৼಈ͸ߟྀ͞Ε͍ͯͳ͍ɻ

17

3.3 χϡʔτϦϊ૬‫༻࡞ޓ‬
(a)

(b)

ਤ 3.3 େ‫ؾ‬χϡʔτϦϊϑϥοΫεͷൺֱ [14]ɻ(a) શํ޲ͷฏ‫ۉ‬ɺ(b) ϑϨʔόʔຖͷൺ཰ɻ੺͕ Honda-fluxɺೱ͍੨͕ Bartol flux[17]ɺ྘఺ઢ͕ FLUKA flux[18]ɺ໌Δ͍੨ͷ఺ઢ͕ Honda 06 fluxɻ

3.3 χϡʔτϦϊ૬‫༻࡞ޓ‬͜͜Ͱ͸େ‫ؾ‬χϡʔτϦϊͷਫதͰͷ૬‫༻࡞ޓ‬Λઆ໌͢ΔɻχϡʔτϦϊ൓Ԡ͸ 2 ͭʹେผ͞Εɺ͕̍ͭ W ± Ϙκϯͷަ‫׵‬Λ௨͠ɺχϡʔτϦϊ͕ಉҰϑϨʔόʔͷՙిϨϓτϯʹస‫͢׵‬ΔՙిΧϨϯτ (CC, Charged Current) ൓Ԡɺ΋͏ 1 ͭ͸ Z 0 Ϙκϯͷަ‫׵‬Λ௨ͯ͠‫͜ى‬ΔχϡʔτϦϊ͕൓Ԡཻͨ͠ࢠʹΤωϧΪʔͱӡಈྔΛड͚౉͢தੑΧϨϯτ (NC, Neutral Current ) ൓ԠͰ͋Δɻ൓ԠʹΑΔՙిϨϓτϯ͔ΒχϡʔτϦϊϑϨʔόʔΛಉఆͰ͖Δͷ͸ CC ૬‫༻࡞ޓ‬ͷΈͰ͋Γɺຊ‫Ͱڀݚ‬΋͜ΕΛબΜͰ༻͍͍ͯΔɻ୅දతͳ૬‫༻࡞ޓ‬ΛҎԼʹࣔ͢ɻCC ४஄ੑࢄཚCC ୯Ұϝιϯੜ੒CC ਂඇ஄ੑࢄཚ

ν + N → l + N′

(3.5)

ν + N → l + N′ + π(3.6)

ν + N → l + N ′ + hadrons(3.7)͜͜Ͱ ν ͸χϡʔτϦϊ͔൓χϡʔτϦϊɺN, N ′ ͸ཅࢠ·ͨ͸தੑࢠͰ͋Δɻl ͸χϡʔτϦϊϑϨʔόʔͱಉ͡ϑϨʔόʔΛ࣋ͭՙిϨϓτϯͰ͋ΔɻNC ൓ԠͰ͸্‫ه‬ͷࣜதͷՙిϨϓτϯΛχϡʔτϦϊʹஔ͖‫ͨ͑׵‬ࣜͰ‫ه‬ड़͢Δ͜ͱ͕Ͱ͖Δɻ·ͨ CC ४஄ੑࢄཚΛ CCQE (Charged Current Quasi-Elastic) ൓Ԡͱ‫ͼݺ‬ɺ࢒Γͷ 3ͭͷ൓ԠΛ૯শͯ͠ CC nonQE ൓Ԡͱ‫Ϳݺ‬ɻઌߦ‫[ ڀݚ‬2] Ͱ͸ɺνµ /ν¯µ ࣝผͷͨΊʹ CCQE ൓ԠͷΈΛ༻͍͍ͯΔ͕ɺຊ‫ڀݚ‬͸ CC nonQE ൓Ԡ΋ࣝผର৅ͱ͍ͯ͠Δɻ࣍ʹ֤૬‫͍ͯͭʹ༻࡞ޓ‬ɺେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊʹண໨ͯ͠આ໌͢Δɻ

3.3.1 ४஄ੑࢄཚ
४஄ੑࢄཚ൓Ԡ͸χϡʔτϦϊͱ֩ࢠͷ 2 ମ൓ԠͰ 1 GeV ҎԼͷ௿ΤωϧΪʔྖҬͰࢧ഑తͳ൓ԠͰ͋Δɻ֩ࢠ
͕੩ࢭ͍ͯ͠ΔͱΈͳ͢ͱɺՙిϨϓτϯͷ৘ใͷΈͰχϡʔτϦϊΤωϧΪʔͷ࠶ߏ੒͕ՄೳͰ͋Δɻνµ ͱν¯µ ͷ

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େ‫ؾ‬χϡʔτϦϊ

CCQE ൓Ԡ͸ҎԼͷ௨ΓʹͳΔɻν µ + n → µ− + p(3.8)

ν¯µ + p → µ+ + n(3.9)

νµ ͸‫֩ࢠݪ‬தͷதੑࢠͱ 2 ମ൓Ԡ͠ɺµ− ͱཅࢠΛɺν¯µ ͸‫֩ࢠݪ‬தͷཅࢠͱ 2 ମ൓Ԡ͠ɺµ+ ͱதੑࢠΛ์ग़͢
Δɻ͜ͷ µ− (µ+ ) ͸่յ͠ɺ่յిࢠͱ‫ݺ‬͹ΕΔిࢠ (ཅిࢠ) ΛͦΕͧΕ์ग़͢Δɻ

µ− → e− + ν¯e + νµ(3.10)µ+ → e+ + νe + ν¯µ(3.11)

४஄ੑࢄཚࣄ৅Ͱ͸ɺν¯µ ൓ԠʹΑΔதੑࢠΛதੑࢠ‫ݕ‬ग़ख๏ (‫ޙ‬ड़) Λ༻͍ͯநग़͢Δ͜ͱͰɺνµ ൓Ԡͱ ν¯µ ൓ԠΛ෼཭͢Δ͜ͱ͕Ͱ͖Δɻ·ͨ์ग़͞Ε่ͨյిࢠͷ৘ใΛ༻͍Δ͜ͱͰ µ+ ͱ µ− ͷৼΔ෣͍ͷҧ͍Λಛఆ͢
Δ͜ͱ͕Ͱ͖Δɻৄࡉ͸ୈ 5 ষͰड़΂Δɻ

3.3.2 ୯ҰύΠΦϯੜ੒୯ҰύΠΦϯੜ੒൓Ԡ͸χϡʔτϦϊͱ֩ࢠͷ൓Ԡͷ݁Ռ ∆ ཻࢠ͕ੜ੒͞Εɺ∆ ͷ่յʹΑΓύΠΦϯ͕ੜ੒͞
ΕΔ൓ԠͰ͋Δɻ1∼3 GeV ෇ۙͰ͸͜ͷ൓Ԡ͕ࢧ഑తͰ͋ΔɻεʔύʔΧϛΦΧϯσͰ͸ύΠΦϯͷΤωϧΪʔ͕νΣϨϯίϑᮢ஋Λ௒͑ͨ৔߹ɺϦϯάͱͯ͠‫؍‬ଌ͞ΕɺՙిϨϓτϯͷϦϯάͱ߹ΘͤͯϚϧνϦϯάΠϕϯτ
ʹબఆ͞ΕΔɻ

ν+N →l+∆(3.12)∆ → π + N′

(3.13)

νµ + p(n) → µ− + p(n) + π +(3.14)

νµ + p(n) → µ+ + p(n) + π −(3.15)

νµ ͱ ν¯µ ͷ൓Ԡ͸ҎԼͷ௨ΓͰ͋Δɻ

൓Ԡ֩ࢠͱ์ग़֩ࢠ͕ಉ͡छྨͷ৔߹ɺνµ Ͱ͸ π + ͕ ν¯µ Ͱ͸ π − ͕์ग़͞ΕΔɻ͜ͷ π + ͸ µ+ ʹ่յ͢Δ͕ɺ

π − ͸่յલʹ‫֫͞ัʹ֩ࢠݪ‬Εͯ͠·͏ͨΊɺµ− ͸์ग़͞Εͳ͍ɻ่յ‫ޙ‬ͷ µ+ ͷΈࣜ 3.11 ͷաఔͰ่յిࢠ
Λग़ͨ͢Ίɺ่յిࢠͷ਺ʹҧ͍͕ੜ͡Δɻ

3.3.3 ਂඇ஄ੑࢄཚ
ਂඇ஄ੑࢄཚ͸ 2 GeV Ҏ্ͷྖҬͰχϡʔτϦϊΤωϧΪʔʹൺྫͯ͠൓Ԡஅ໘ੵ͕େ͖͘ͳΓɺߴΤωϧΪʔʹ͓͍ͯࢧ഑తͱͳΔ൓ԠͰ͋ΔɻߴΤωϧΪʔͷͨΊ֩ࢠΑΓ΋ΫΦʔΫͷߏ଄͕‫͑ݟ‬ɺΫΦʔΫͱࢄཚ͍ͯ͠
ΔͱۙࣅͰ͖ΔɻϨϓτϯͱϋυϩϯʹ౉ͨ͠ΤωϧΪʔͱχϡʔτϦϊͷΤωϧΪʔ͕౳͍͠ͱۙࣅͰ͖ΔͨΊɺೋཻ࣍ࢠͷΤωϧΪʔΛଌఆ͢Δ͜ͱͰχϡʔτϦϊͷΤωϧΪʔΛਪఆͰ͖Δɻ·ͨɺνµ ͱ ν¯µ ͷεϐϯ֯ӡಈྔͷҧ͍ʹΑͬͯɺϨϓτϯͱϋυϩϯʹ౉͢ΤωϧΪʔͷׂ߹͕ҟͳΔͨΊɺ͜ͷੑ࣭Λ νµ /ν¯µ ࣝผʹར༻͢Δɻ
ਤ 3.4 ͸‫ޙ‬ड़ͷ NEUT ʹΑͬͯγϛϡϨʔτ͞Ε֤ͨ૬‫༻࡞ޓ‬ͷ൓Ԡஅ໘ੵͱ࣮‫ݧ‬σʔλΛ·ͱΊͨ΋ͷͰ͋Δ[19] [20] [21] ɻ֊૚ੑܾఆ‫͞ͱ͍ߴ͕౓ײ‬Ε͍ͯΔ 10 GeV ۙลͷྖҬͰ͸ਂඇ஄ੑࢄཚ (DIS) ࣄ৅͕ࢧ഑తͰ
͋Γɺ͍ͭͰ‫ڞ‬໐ࣄ৅ (RES) ∼ ୯ҰύΠΦϯੜ੒ࣄ৅͕ଟ͍͜ͱ͕෼͔ΔɻͦͷͨΊ νµ /ν¯µ ࣝผͰ͸ಛʹ͜ΕΒͷࣄ৅ͷࣝผੑೳ͕ॏཁͱͳΔɻ

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3.4 NEUT

ਤ 3.4

֤χϡʔτϦϊ૬‫༻࡞ޓ‬ͷ൓Ԡஅ໘ੵɺ࣮ઢ͕ NEUT ʹΑΔγϛϡϨʔγϣϯ݁Ռ [19]ɺ֤఺͕‫؍‬ଌσʔλ [21] Ͱ͋Δɻࠨਤ͕ ν ࣄ৅ɺӈਤ͕ ν̄ ࣄ৅ɻQE (४஄ੑࢄཚࣄ৅)ɺRES (‫ڞ‬໐ࣄ৅)ɺDIS (ਂ஄ੑࢄཚࣄ৅)ɺTOTAL (߹‫ܭ‬஋) Ͱ͋Δɻ

3.4 NEUT
NEUT ͱ͸ɺલड़ͷϑϥοΫεϞσϧΛΠϯϓοτͱͯ͠ɺχϡʔτϦϊ͕‫ݕ‬ग़‫಺ث‬΍पΓͷ‫ؠ‬൫ͰͲͷΑ͏ͳ૬‫༻࡞ޓ‬ΛͲΕ͘Β͍ͷස౓Ͱߦ͏͔‫͢ࢉܭ‬ΔͨΊͷχϡʔτϦϊ૬‫༻࡞ޓ‬δΣωϨʔλʔͰ͋Δɻ‫ݩ‬ʑεʔύʔΧϛΦΧϯσ࣮‫͚͓ʹݧ‬ΔਫதͰͷେ‫ؾ‬χϡʔτϦϊ૬‫༻࡞ޓ‬ΛϞσϧԽ͢ΔͨΊʹ։ൃ͞Ε͕ͨɺ‫ػ‬ೳΛ֦ॆ͠ɺ‫͍༻͘޿Ͱ·ࡏݱ‬ΒΕ͍ͯΔɻຊ‫Ͱڀݚ‬͸ MC (Monte Carlo) γϛϡϨʔγϣϯΛ༻͍ͯલड़ͷΑ͏ͳେ‫ؾ‬χϡʔτϦϊ૬‫༻࡞ޓ‬ͷৼΔ෣͍Λߟ࡯͢ΔͨΊɺNEUT ͷੑೳ͸ඇৗʹॏཁͱͳΔɻͦΕͧΕͷ૬‫༻࡞ޓ‬͸֤࣮‫ݧ‬σʔλΛ‫ʹݩ‬γϛϡϨʔτ͞Ε͍ͯΔ [19]ɻ

3.4.1 ֩಺ޮՌࢎૉ‫Ͱ֩ࢠݪ‬ͷ૬‫༻࡞ޓ‬ͷ৔߹ʹੜ੒͞Εͨϋυϩϯ͸͔֩Βඈͼग़Δલʹೋ࣍૬‫༻࡞ޓ‬Λड͚Δ৔߹͕͋Δɻ

NEUT Ͱ͜ΕΒͷ૬‫༻࡞ޓ‬ΛγϛϡϨʔγϣϯ͢ΔͨΊʹɺ͜ΕΒͷཻࢠ͸֩Λൈ͚ͨ‫ޙ‬΋่յ͢Δ͔‫ٵ‬ऩ͞ΕΔ·Ͱ௥੻͞ΕΔɻߋʹɺൃੜͨ͠ೋཻ࣍ࢠͷ૬‫༻࡞ޓ‬͸࣍ʹड़΂Δ௥੻εςοϓͰ‫͞ࢉܭ‬Ε͍ͯΔɻ

3.5 ‫ݕ‬ग़‫ث‬γϛϡϨʔγϣϯ
NEUT ʹ͓͍ͯχϡʔτϦϊ΍ϛϡʔΦϯͷ૬‫Ͱ༻࡞ޓ‬ੜ੒͞Εͨೋཻ࣍ࢠ͸ SKDetSim ͱ‫ݺ‬͹ΕΔ GEANT3ϕʔεͷ‫ݕ‬ग़‫ث‬γϛϡϨʔγϣϯʹΑͬͯͦͷ‫ޙ‬ͷӡಈΛ௥੻͞ΕΔɻ͜ΕΒͷཻࢠ͸ɺਫதͰͷཻࢠͷ఻೻΍่յɺϋυϩϯ૬‫༻࡞ޓ‬Λ‫ࢠ༷͢͜ى‬ΛγϛϡϨʔγϣϯ͞Εɺͦͷ‫ޙ‬ɺՙిཻࢠʹΑΔνΣϨϯίϑޫͷ์ग़աఔͱͦͷޫࢠͷৼΔ෣͍Λܾఆ͞ΕΔɻ·ͨɺPMT Ԡ౴΋γϛϡϨʔγϣϯ͞Εɺ࣮ࡍͷΩϟϦϒϨʔγϣϯ݁Ռ͔Βશͯͷ PMT ͷੑೳΛߟྀ͠ɺMC γϛϡϨʔγϣϯͷ݁Ռ΋࣮ࡍͷσʔλͱಉ͡Α͏ʹղੳ͢Δ͜ͱ͕Ͱ͖Δɻ

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ୈ4ষ

χϡʔτϦϊࣄ৅બผͱࣄ৅࠶ߏ੒
εʔύʔΧϛΦΧϯσͰ͸ 1 ೔ʹ‫؍‬ଌ͞ΕΔࣄ৅͕໿ 106 ‫͋ݸ‬Γɺͦͷଟ͕͘‫ݕ‬ग़‫֎ث‬෦͔Βඈདྷͨ͠Ӊ஦ઢ΍์ࣹੑ෺࣭͔Β์ࣹ͞Εͨ γ ઢͳͲͰ͋Δɻνµ ͱ ν¯µ Λࣝผ͢ΔͨΊʹ͸ɺେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊࣄ৅Λਖ਼͘͠બͼɺͦͷ૬‫༻࡞ޓ‬ͷ༷ࢠΛਖ਼͘͠࠶ߏ੒͢Δ͜ͱ͕ඞཁͰ͋ΔɻεʔύʔΧϛΦΧϯσͰ͸ϦμΫγϣϯͱ‫ݺ‬͹ΕΔ 5 ஈ֊ͷࣄ৅બผख๏Λ༻͍ͯɺ‫؍‬ଌ͞Εͨશͯͷࣄ৅͔ΒχϡʔτϦϊࣄ৅Λࣗಈతʹબ୒͍ͯ͠Δɻ
͜͏ͯ͠બ͹ΕͨχϡʔτϦϊࣄ৅Λ༷ʑͳղੳͰ༻͍ΔͨΊʹɺχϡʔτϦϊ൓Ԡͷ৘ใΛܾఆ͢Δࣄ৅࠶ߏ੒
͕ߦΘΕΔɻ͜ͷষͰ͸͜ͷࣄ৅࠶ߏ੒ख๏ʹ͍ͭͯઆ໌͢Δɻ

4.1 SK Ͱ‫؍‬ଌ͞ΕΔχϡʔτϦϊࣄ৅χϡʔτϦϊࣄ৅͸ SK Ͱͷ‫؍‬ଌͷ͞ΕํʹΑͬͯɺ3 ͭͷछྨʹେผ͞ΕΔɻҰͭ໨͕χϡʔτϦϊ൓Ԡ͕‫ݕ‬ग़‫ث‬ͷ༗ޮମੵ (಺ਫ૧ͷน໘͔Βগͳ͘ͱ΋ 2 m Ҏ্಺ଆͷྖҬ) ಺Ͱ‫݁͢׬‬Δ Fully Contained (FC) Πϕϯτɺೋͭ໨͕χϡʔτϦϊ൓Ԡ͕‫ݕ‬ग़‫ث‬ͷ༗ޮମੵ֎΁‫ٴ‬ΜͰ͍Δ Partially Contained (PC) Πϕϯτɺࡾͭ໨͕‫ݕ‬ग़‫ث‬Լଆͷ‫ؠ‬൫ͰχϡʔτϦϊ͕૬‫݁ͨ͠༻࡞ޓ‬Ռɺ์ग़͞ΕͨϛϡʔΦϯ͕‫ݕ‬ग़‫ث‬ͷԼଆ͔Βඈདྷͨ͠ Upward-going

muon (UPMU) ΠϕϯτͰ͋Δɻ‫ݕ‬ग़‫ث‬Լଆ͔Βඈདྷ͢ΔϛϡʔΦϯ͸χϡʔτϦϊ൓ԠʹΑΔ΋ͷ͚ͩͳͷͰ
UPMU ΠϕϯτΛχϡʔτϦϊΠϕϯτͱఆٛ͢Δ͜ͱ͕Ͱ͖Δɻ͜ͷ͏ͪϛϡʔΦϯ͕‫ݕ‬ग़‫಺ث‬෦Ͱࢭ·ͬͨΠϕϯτΛ Upward stopping muonɺ‫ݕ‬ग़‫ث‬Λ௨աͨ͠ΠϕϯτΛ Upward through going-muon ͱ‫Ϳݺ‬ɻਤ 4.1 ʹ֤χϡʔτϦࣄ৅ͷ໛ࣜਤΛࣔͨ͠ɻPC ΠϕϯτɺUPMU Πϕϯτ͸χϡʔτϦϊ൓ԠΛશͯ‫؍‬ଌ͢Δ͜ͱ͕Ͱ͖
ͳ͍ͨΊɺ͍͔ͭ͘ͷղੳ͕ࠔ೉ʹͳΔɻͦͷͨΊຊղੳͰ͸ FC ࣄ৅ͷΈΛղੳʹ༻͍͍ͯΔɻ

ਤ 4.1 SK Ͱ‫؍‬ଌ͞ΕΔχϡʔτϦϊࣄ৅ͷ໛ࣜਤ

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ୈ 4 ষ χϡʔτϦϊࣄ৅બผͱࣄ৅࠶ߏ੒

4.2

ࣄ৅࠶ߏ੒

ࣄ৅બผΛ௨աͯ͠ೖཻࣹࢠ͕χϡʔτϦϊͩͱ൑ఆ͞Εͨࣄ৅͸ɺνΣϨϯίϑޫͷ৘ใ͔Βඈདྷͨ͠χϡʔτϦϊͷछྨ΍ӡಈྔΛܾఆ͢ΔͨΊʹࣄ৅࠶ߏ੒͕ߦΘΕΔɻ͜͜Ͱ͸ͦͷखॱʹ͍ͭͯઆ໌͢Δɻࣄ৅࠶ߏ੒
͸ҎԼͷ 8 ͭͷϓϩηεʹେผ͞ΕΔɻ͜͜Ͱ͸ͦͷ֓ཁΛઆ໌͢ΔɻΑΓৄࡉͳ৘ใ͸ [11] Λࢀরɻ

1. όʔςοΫε ϑΟοςΟϯά
όʔςοΫεͱ͸χϡʔτϦϊͷ൓Ԡ఺Ͱ͋ΔɻόʔςοΫε͸ώοτͨ͠ PMT ͷώοτλΠϛϯά࢒ࠩΛ࠷΋࠷΋খ͘͢͞ΔνΣϨϯίϑޫ์ग़఺ͱͯ͠ఆٛ͞ΕΔɻ͜͜Ͱ͸ߋʹɺ࠷΋େ͖ͳΤωϧΪʔΛ࣋
ͭ 1 ͭ໨ͷϦϯάͷํ޲΍֎ԑΛܾఆ͢Δɻ

2. Ϧϯά਺Χ΢ϯτಘΒΕͨόʔςοΫεͱϦϯάͷํ޲Λ༻͍ͯଞͷϦϯάީิΛ୳ࡧ͢ΔɻϦϯάީิ͸ likelihood ๏ʹΑͬͯϦϯάͰ͋ΔͱೝΊΒΕΔ͔Ͳ͏͔൑ఆ͞ΕɺϦϯά਺͕ܾఆ͞ΕΔɻ

3. ཻࢠࣝผ (Particle identification, PID)ͦΕͧΕͷϦϯά͸νΣϨϯίϑޫͷώοτύλʔϯͱ։‫֯ޱ‬Λ༻͍ͨ likelihood ๏ʹΑΓɺϦϯάͷ‫ܗ‬ঢ়͕γϟϫʔ‫͋Ͱܕ‬Δ e-like (e± , γ ) ࣄ৅͔ඇγϟϫʔ‫ܕ‬ͷ µ-like (µ,π ) ࣄ৅͔ͷ 2 छྨʹ෼ྨ͞ΕΔɻ

4. ΑΓਖ਼֬ͳ όʔςοΫε ϑΟοςΟϯά (MS-fit) (1 Ϧϯάࣄ৅ͷΈ)
3 Ͱܾఆͨ͠ϦϯάͷछྨΛ‫͞ʹݩ‬ΒʹৄࡉʹόʔςοΫεΛܾఆ͢Δɻ
5. ӡಈྔͷܾఆ֤ϦϯάͷνΣϨϯίϑޫͷԁਲ਼಺Ͱ‫ݕ‬ग़͞Εͨ PMT ͷిՙྔ͔ΒɺMC γϛϡϨʔγϣϯͱ‫ݕ‬ग़‫ֱث‬ਖ਼͔ΒಘΒΕͨରԠΛ༻͍ͯɺͦΕͧΕͷϦϯάͷӡಈྔΛ‫ٻ‬ΊΔɻ

6. ่յిࢠ୳ࡧ
χϡʔτϦϊ൓ԠͰ์ग़͞ΕཻͨࢠʹΑͬͯ࡞ΒΕ่ͨյిࢠΛ୳͢ɻ

7. Ϧϯά਺ͷֱਖ਼ (FC ϚϧνϦϯάࣄ৅ͷΈ)࠶ߏ੒͞Εͨ৘ใΛ༻͍ͯɺ‫ͯͬޡ‬ϑΟοςΟϯάͨ͠Ϧϯά͕͋Ε͹ީิ͔Β֎͢ɻ

8. π 0 ϑΟοςΟϯά
1 Ϧϯά e-like ࣄ৅ͱબ୒͞Εͨࣄ৅ͷத͔Β π 0 ࣄ৅ͷީิΛ୳͢ɻ

4.2.1 όʔςοΫε ϑΟοςΟϯά
όʔςοΫε͸ PMT ͷώοτλΠϛϯά৘ใΛ༻͍ͯ 3 ͭͷखॱ͔Βܾఆ͞ΕΔɻॳΊ͸શͯͷޫࢠ͕ 1 ͭͷ఺‫͔ݯ‬Βಉ࣌ʹ์ग़͞ΕͨͱԾఆͯ͠ϑΟοςΟϯάΛߦ͍ɺόʔςοΫεΛਪఆ͢Δɻ͜ΕΛ Point-fit ͱ‫Ϳݺ‬ɻͦͷ‫ޙ‬ɺ‫ੵݟ‬΋ͬͨόʔςοΫεͰͷɺ֤ PMT ΁ͷώοτλΠϛϯά͔Βޫͷ TOF (Time of flight) Λࠩ͠Ҿ͍
ͨ PMT ώοτλΠϛϯάͷ࣌ؒΛ‫͠ࢉܭ‬ɺ͜ͷώοτλΠϛϯά࢒ࠩ෼෍͕࠷΋খ͘͞ͳΔҐஔΛόʔςοΫεͱܾͯ͠ఆ͢Δɻ࣍ʹɺӡಈํ޲ͱ 1 ͭ໨ͷϦϯάͷ֎ԑΛܾఆ͢Δɻӡಈํ޲ͱ։‫֯ޱ‬͸ҎԼʹࣔ͢ύϥϝʔλΛ༻͍ܾͯఆ͞ΕΔɻ

Q(θedge ) =3 θedge
0

P E(θ)dθ×sin θedge

)

*2
4
+
,
dP E(θ) 44(θedge − θexp )2
× exp −dθ 4θ=θedge
2σθ2

(4.1)

͜͜Ͱ θexp ͱσθ ͸νΣϨϯίϑޫͷԁਲ਼಺ͷిՙྔ͔Β‫ظ‬଴͞ΕΔ։‫ͦͱ֯ޱ‬ͷ෼ղೳͰ͋ΔɻP E(θ) ͸։‫֯ޱ‬

23

4.2 ࣄ৅࠶ߏ੒
ͷؔ਺ͱͯ͠ͷɺ‫؍‬ଌ͞Εͨిՙྔͷ֯౓෼෍Ͱ͋Δʢ͜ͷ‫؍‬ଌిՙྔ͸ਫͷಁ໌౓ͱ PMT ͷΞΫηϓλϯεͷޮՌΛิਖ਼͞Εͨ΋ͷͰ͋Δʣɻ͜ͷ Q(θedge ) Λ࠷େԽͤ͞Δӡಈํ޲ͱϦϯάͷ֎ԑΛ Point-fit ͷ݁Ռͱͯ͠࠾༻
͢Δɻ࠷‫ ʹޙ‬TDC-fit Λ༻͍ͯਖ਼֬ʹόʔςοΫεΛఆΊΔɻ͜͜Ͱ͸ޫࢠ͸ཻࢠͷ‫ʹ੻ي‬Ԋͬͯ์ग़͞ΕΔνΣ
ϨϯίϑޫͩͱԾఆͯ͠νΣϨϯίϑϦϯά಺ʹ͋Δ PMT ͷώοτλΠϛϯά࢒ࠩΛ‫͢ࢉܭ‬ΔɻϦϯά֎ͷޫࢠʹ͍ͭͯ͸όʔςοΫεͷҐஔͰੜ੒͞ΕͨͱԾఆͯ͠‫͞ࢉܭ‬ΕΔɻ͜ͷ‫੻ي‬தͰ‫؍‬ଌ͞ΕͨλΠϛϯά࢒ࠩ෼෍ͷϐʔΫʹͳΔ఺͕όʔςοΫεͱͯ͠બ͹ΕΔɻϚϧνϦϯάࣄ৅ʹ΋͜ͷ TDC-fit ͸༗ޮͰ͋Δɻ

Point fit Ͱ͸ώοτλΠϛϯάͷ৘ใͷΈ࢖͍ͬͯΔɻΑΓਖ਼֬ʹόʔςοΫεͱӡಈํ޲Λ‫ٻ‬ΊΔͨΊʹɺ1 Ϧϯάࣄ৅ʹ͍ͭͯ͸‫ޙ‬ड़ͷཻࢠࣝผʹΑͬͯ൑ఆ͞Εཻͨࢠ (µ-likeɺe-like) ͷϦϯάͷయ‫ܕ‬తͳώοτύλʔϯΛ‫ ʹݩ‬MS-fit ͱ‫ݺ‬͹ΕΔϑΟοςΟϯάΛ࠶౓ߦ͏ɻMS-fit ͸όʔςοΫεΛɺpoint fit ͰಘΒΕཻͨࢠͷӡಈํ޲ʹฏߦͳ੒෼Λ‫܁‬Γฦ͠ௐ੔͍͖ͯ͠ɺόʔςοΫεͱӡಈํ޲ͷมԽ͕ͦΕͧΕ 5 cm ҎԼɺ0.5 ౓ҎԼʹͳΔͱ
όʔςοΫεΛܾఆ͠ɺऴྃ͢Δɻ·ͨɺϚϧνϦϯάࣄ৅ʹ͸ MS-fit ͸ߦΘΕͳ͍͕ɺಉ༷ʹ࠶ߏ੒͞Εͨ৘ใΛར༻͢Δ͜ͱͰɺ‫ͯͬޡ‬Ϧϯάͱͯ͠൑ఆͯ͠͠·ͬͨϦϯάΛநग़͠ɺϦϯάͷީิ͔Β֎͍ͯ͠Δɻ͜ΕΒͷੑೳ͸ MC ͔Βਪఆ͞ΕΔҐஔ෼ղೳͰධՁ͞Εɺ1 Ϧϯάࣄ৅ͷํ͕͕ϚϧνϦϯάࣄ৅ʹൺ΂ͯҐஔܾఆਫ਼౓͸ߴ͍ɻ

4.2.2 Ϧϯά਺Χ΢ϯτ
1 ͭ໨ͷνΣϨϯίϑϦϯάͱͦͷόʔςοΫε͕ܾΊΒΕΔͱɺHough ๏Λ༻͍ͯ PMT ώοτը૾͔Β 42౓ͷ։‫֯ޱ‬Λ࣋ͭԁΛ‫ݕ‬ग़͠ɺଞͷϦϯάީิͷ୳ࡧΛߦ͏ɻ͜ͷ Hough ๏͸ SK ಠࣗͷ΋ͷͰ͸ͳ͘෯޿͍෼
໺Ͱ޿͘༻͍ΒΕ͍ͯΔਤ‫ܗ‬நग़๏Ͱ͋ΔɻHough ๏Ͱ͸·ͣɺώοτͨ͠ PMT Λબͼͦͷ PMT ͷҐஔΛத৺ͱ͢ΔԾ૝ͷԁΛඳ͘ɻ֤ PMT Λத৺ʹਾ͑ͨෳ਺ͷԾ૝ԁ͸ɺ͍͔ͭ͘ͷ఺Ͱަࠩ͢ΔͨΊɺ͜ͷަࠩͨ͠఺
ͱ‫ݩ‬ʑͷόʔςοΫεΛൺ΂Δ͜ͱͰద੾ͳνΣϨϯίϑϦϯάͷ౸དྷํ޲Λಛఆ͠ɺ͜ͷํ޲ʹ͓͚ΔϦϯάީิΛ୳͢͜ͱͰ 2 ൪໨ͷϦϯάΛಛఆ͢ΔɻϦϯά͔Ͳ͏͔ͷ൑ఆʹ͸ likelihood ๏͕༻͍ΒΕɺ2 ൪໨ͷϦϯά͕‫͔ͨͬͭݟ‬৔߹ʹ͸͜ͷ޻ఔΛ‫܁‬Γฦ͢͜ͱͰɺ࠷େ 5 ͭͷϦϯάΛ‫͚ͭݟ‬Δ͜ͱ͕ՄೳͰ͋Δɻਤ 4.2 ʹ SK-I

V ͰͷϦϯά਺Χ΢ϯτ likelihood ෼෍Λࣔ͢ɻ
(a)

ਤ 4.2

(b)

SK-IV ͰͷϦϯά਺Χ΢ϯτ likelihood ෼෍ɻࠇ఺͕ଌఆͨ͠σʔλ఺ɺ֤৭ͷώετάϥϜ͕ಉ͡‫ظ‬ؒͰͷͦΕͧΕͷχϡʔτϦϊ૬‫༻࡞ޓ‬ͷਅͷ෼෍Ͱ͋Δɻ(a)sub-GeV (b)multi-GeVɻ

24ୈ 4 ষ χϡʔτϦϊࣄ৅બผͱࣄ৅࠶ߏ੒
͜͜Ͱ sub-GeV ͱ͸࠷΋ΤωϧΪʔ͕ߴ͍ϦϯάͷՄࢹΤωϧΪʔ͕ 1.33 GeV ҎԼͷࣄ৅ɺmulti-GeV ͸ՄࢹΤωϧΪʔ͕ 1.33 GeV Ҏ্ͷࣄ৅ͷ૯শͰ͋Δɻ࣭ྔ֊૚ܾఆʹ‫౓ײ‬ͷ͋ΔྖҬ͸ओʹɺmulti-GeV ʹ‫·ؚ‬ΕΔɻ
͜ͷߦఔͰɺϦϯά͕ 1 ͭͱ൑ఆ͞Εͨࣄ৅Λ 1 Ϧϯά (γϯάϧϦϯά) ࣄ৅ɺϦϯάΛෳ਺࣋ͭͱ൑ఆ͞Εͨࣄ৅ΛϚϧνϦϯάࣄ৅ͱ‫Ϳݺ‬ɻਤ 4.2 Λ‫ݟ‬ΔͱɺϚϧνϦϯάͰ CC single π ͳͲͷ CC nonQE(ՙిΧϨϯτඇ஄ੑࢄཚ) ࣄ৅ͷׂ߹͕૿͍͑ͯΔ͜ͱ͕෼͔Δɻ͜ΕΒͷ CC nonQE ࣄ৅͸ՙిϨϓτϯҎ֎ʹ π ± ͳͲͷՙిཻࢠΛ࡞ΓɺͦΕΒ͕Ϧϯάͱͯ͠‫؍‬ଌ͞ΕΔ͔ΒͰ͋Δɻ

4.2.3 ཻࢠࣝผ‫؍‬ଌ͞ΕͨνΣϨϯίϑϦϯά͸ཻࢠࣝผΞϧΰϦζϜ (PID, Particle Identification) Λ༻͍ͯ e-like Ϧϯάͱ µ-like Ϧϯάʹ෼ྨ͞ΕΔɻిࢠ (ΨϯϚઢ) ͸ి࣓γϟϫʔΛ‫ͨ͜͠ى‬Γɺ௿ΤωϧΪʔͰଟॏࢄཚΛ‫͢͜ى‬ͨΊɺPMT ͷώοτ෼෍͕֦͕Γɺ‫ڥ‬ք͕΅΍͚ͨϦϯάΛ࡞Δɻ൓ରʹϛϡʔΦϯ (ՙిύΠΦϯ) ͸͜ΕΒͷ൓ԠΛҾ͖‫͍ͨͳ͜͞ى‬Ί‫ڥ‬ք͕͸͖ͬΓͱͨ͠ϦϯάΛ࡞Δɺ·ͨϛϡʔΦϯ (ՙిύΠΦϯ) ͕ඇ૬ର࿦త

(β = v/c < 1) ͷ৔߹ʹɺ͜ΕΒͷνΣϨϯίϑϦϯά͸։‫֯ޱ‬ͷখ͞ͳώοτ෼෍ͱͳΔɻPID ΞϧΰϦζϜͰ͸͜ͷΑ͏ͳҧ͍Λར༻ཻͯ͠ࢠΛࣝผ͍ͯ͠Δɻਤ 4.3 ͸ SK-IV ͷ FC multi-GeV ࣄ৅ʹର͢Δ PID likelihood෼෍Λ͍ࣔͯ͠ΔɻϚϧνϦϯάࣄ৅Ͱ͸ϦϯάͷҰ෦͕ॏͳΔ͜ͱͰϦϯάͷ‫ڥ‬ք͕ᐆດʹͳΔɻͦͷͨΊώοτύλʔϯ͔ΒཻࢠΛࣝผ͢Δͷ͕ࠔ೉ʹͳΓɺ1 Ϧϯάࣄ৅΄Ͳࣝผੑೳ͸Α͘ͳ͍ɻ
(a)

(b)

ਤ 4.3 SK-IV Ͱͷ FC multi-GeV ࣄ৅ͷ PID likelihood ෼෍ɻࠇ఺͕ଌఆͨ͠σʔλ఺ɺ྘৭ͷώετάϥϜ
͕ಉ͡‫Ͱؒظ‬ͷϛϡʔΦϯχϡʔτϦϊͷਅͷ෼෍Ͱ͋Δɻ (a) 1 Ϧϯάࣄ৅ (b) ϚϧνϦϯάࣄ৅

4.2.4 ӡಈྔͷ࠶ߏ੒ཻ֤ࢠͷӡಈྔ͸ରԠ͢ΔϦϯάΛத৺ͱͨ͠൒։‫ ͕֯ޱ‬70 ౓ͷԁਲ਼಺ʹ‫·ؚ‬ΕΔ p.e. ਺͔Β‫͞ࢉܭ‬ΕΔ (͢΂ͯͷώοτΛ‫ͤ·ؚ‬ΔͨΊ 70 ౓ʹઃఆ͞Ε͍ͯΔʣɻ֤ϦϯάͷӡಈྔΛܾΊΔͨΊʹɺώοτͨ͠ PMT ͷ p.e.
਺͸ͲͷϦϯάʹΑΔ΋ͷͳͷ͔ಛఆ͠෼཭͢Δඞཁ͕͋Δɻp.e. ਺ͷ෼཭͸֤ϦϯάΛ։‫ ֯ޱ‬θ ͷؔ਺ͱΈͳͨ࣌͠ʹ༧૝͞ΕΔ p.e. ਺Λ༻͍ͯߦΘΕΔɻi ൪໨ͷ PMT ͔Β n ൪໨ͷϦϯά΁ͷ p.e. ਺͸࣍ͷࣜ 4.2 Ͱ‫͞ࢉܭ‬
ΕΔɻ

25

4.3 தੑࢠ‫ݕ‬ग़

exp
qi,n
obs
qi,n
= qiobs × 5 exp
n′ qi,n′

(4.2)

obs
͜͜Ͱ qi,n͸ i ൪໨ͷ PMT Ͱͷ p.e. ͷ͏ͪɺn ൪໨ͷϦϯάʹଐ͍ͯ͠Δͱਪఆ͞Εͨ p.e. ਺Ͱ͋Γɺqiobs ͸
expi ൪໨ͷ PMT ͷ p.e. ਺ɺqi,n͸༧ଌ͞Ε͍ͯΔ p.e. ਺Ͱ͋Δɻ͜ͷ࣌ɺώοτλΠϛϯάʹ΋੍‫ݶ‬Λ͔͚ɺTOFΛҾ͍ͨώοτλΠϛϯά࢒ࠩ෼෍ͷϐʔΫΛғΉ −50 < t < +250 nsec Ҏ಺ʹώοτͨ͠ p.e. ͷΈநग़͍ͯ͠
Δɻ͜Ε͸ϛϡʔΦϯ่յిࢠͷΑ͏ͳ஗ԆώοτͷόοΫάϥ΢ϯυΛऔΓআͨ͘ΊͰ͋Δɻ߹‫ܭ‬ͷ p.e. ਺͸ҎԼͷࣜ 4.3 Ͱ‫͞ࢉܭ‬ΕΔɻ͜ͷ࣌ิਖ਼߲ͱͯ͠ɺਫதͰͷޫ‫ݮ‬ਰɺPMT ͷΞΫηϓλϯεɺࢄཚޫ͔Βͷ‫د‬༩ΛߟྀʹೖΕ͍ͯΔɻ

⎡GMC ⎣RT OTn =
α×
Gdata

!

θi,n ʻ 70◦ &&−50 ʻ ti ʻ 250 nsec

+

ri
cosΘi
qiobs × exp( ) ×Lf (Θi )

,

−

!

θi,n

ʻ 70◦

Si −

!

θi,n

ʻ 70◦

⎤

Ri ⎦

(4.3)

ͦΕͧΕͷม਺͸α=‫֨ن‬ԽҼࢠ
Gdata , GMC =σʔλͱ MC ʹର͢Δ૬ରతͳ PMT ήΠϯύϥϝʔλθi.n =i ൪໨ͷ PMT ͷํ޲ͱ n ൪໨ͷϦϯάํ޲ͷؒͷ։‫֯ޱ‬
ti =i ൪໨ͷ PMT ͷޫࢠͷ TOF ΛҾ͍ͨώοτλΠϛϯά
L = ਫதͰͷޫͷ‫ݮ‬ਰ௕
ri =όʔςοΫε͔Β i ൪໨ͷ PMT ·Ͱͷ‫཭ڑ‬f (Θi )= ޫࢠೖࣹ֯ (Θi ) ͷؔ਺ͱͯ͠ͷ PMT ΞΫηϓλϯεʹର͢Δิਖ਼ؔ਺Si =ࢄཚޫʹΑͬͯ i ൪໨ͷ PMT ʹೖΔͱ༧ଌ͞ΕΔ p.e. ਺
Ri =‫ݕ‬ग़‫಺ث‬ͷϒϥοΫγʔτʹΑΔ൓ࣹޫࢠͷӨ‫ڹ‬Λߟྀͨ͠ิਖ਼Ͱද͞ΕΔɻ͜͜ͰɺL ʹؔͯ͠͸ through-going muon Λ༻͍ͯৗ࣌ଌఆ͞Ε͍ͯΔɻಘΒΕͨ RT OT ͸ΤωϧΪʔεέʔϧֱਖ਼Λ༻͍ͯӡಈྔͷ஋ʹม‫͞׵‬ΕΔɻ

4.2.5 ่յిࢠ୳ࡧ
่յిࢠ͸χϡʔτϦϊ൓ԠʹΑͬͯੜ੒͞Εͨ µ± ΍ɺπ + ͷ่յʹΑͬͯͰ͖ͨ µ+ ͷ่յʹΑͬͯൃੜ͢Δ
ిࢠͷ͜ͱͰ͋Δɻຊ‫Ͱڀݚ‬͸ϛϡʔΦϯͷՙిΛ൑ఆ͢ΔͨΊʹ่յిࢠͷ৘ใΛ༻͍͍ͯΔɻͦΕΏ͑ʹ่յిࢠͷ‫ݕ‬ग़ޮ཰͸ νµ /ν¯µ ࣝผੑೳʹ‫ݦ‬ஶʹӨ‫ڹ‬Λ‫͢΅ٴ‬ɻ่յిࢠ͸ɺ࠷ॳͷࣄ৅ͷλΠϛϯά΢Οϯυ΢ɺ΋͘͠͸ 900 nsec ؒͷλΠϛϯά΢Πϯυ΢಺Ͱଌఆ͞ΕΔɻ

SK-IV Ͱͷ‫ݕ‬ग़ޮ཰͸ µ+ ͷ่յిࢠͰ 96% ɺµ− ͔Βͷ่յిࢠͰ 83% Ͱ͋ΔɻSK-IV ͔Β͸ µ− ั֫୤ྭ‫ى‬γ ઢ΋่յిࢠͱͯ͠‫ݕ‬ग़͞Ε͍ͯΔɻ͜ΕʹΑΓɺSK-I ∼SK-III ·Ͱͱൺ΂ͯ‫ݕ‬ग़ޮ཰͕޲্͍ͯ͠Δɻ

4.3 தੑࢠ‫ݕ‬ग़νΣϨϯίϑޫ‫؍‬ଌͰ͸௨ৗՙిཻࢠͷΈ‫؍‬ଌ͕Մೳ͕ͩɺεʔύʔΧϛΦΧϯσͰ͸ࣜ 4.4 ͷΑ͏ͳաఔͰத
ੑࢠ͕ਫૉ‫֫͞ัʹ֩ࢠݪ‬Εͨࡍʹൃੜ͢Δ 2.2 MeV ͷ γ ઢ༝དྷͷඍऑͳνΣϨϯίϑޫΛଊ͑ɺதੑࢠ৴߸ΛબͿಛผͳτϦΨʔΛ͔͚Δ͜ͱͰɺؒ઀తʹதੑࢠͷ‫؍‬ଌΛՄೳʹ͍ͯ͠Δɻதੑࢠั֫ʹΑΔ 2.2 MeV ͷ γ ઢͷ૞ࡧ͸ 2 ͭͷεςοϓʹ෼͚ΒΕΔ [20] [22]ɻ

26

ୈ 4 ষ χϡʔτϦϊࣄ৅બผͱࣄ৅࠶ߏ੒

n+H→d+γ(4.4)

4.3.1 தੑࢠީิબ୒
ॳΊͷεςοϓͱͯ͠ɺPMT ͷώοτλΠϛϯάσʔλͷϐʔΫΛ‫ݕ‬ग़͢Δ͜ͱʹΑͬͯதੑࢠ৴߸ͷީิΛબͿɻ18 µs ͔Β 535 µs ͷ࣌ؒ෯Λ 10 ns ຖͷ࣌ؒ΢Οϯυ΢ʹ۠੾ͬͯɺ2.2 MeV ͷީิΛ૞ࡧ͢Δɻ͜ͷ࣌ؒ෯͸ॳ‫ࣄظ‬৅ൃੜ͔Β‫ܦ‬աͨ࣌ؒ͠Ͱ͋Δɻ18 µs ͷԼ‫͍ͯͭʹݶ‬͸ 12 ͔Β 18 µs ͷ PMT ͷΞϑλʔύϧεΛআ‫ڈ‬͢ΔͨΊʹઃఆ͞Ε͍ͯΔɻ
۠੾ͬͨ 10 ns ͷ࣌ؒ෯Ͱͷώοτ਺͕ 7 Ҏ্ͷࣄ৅Λ 2.2 MeV ͷ γ ઢ ͷީิͱͯ͠બ୒͢Δ͕ɺ͜ͷ࣌ɺ1ͭͷதੑࢠީิΛෳ਺ͷީิͱͯ͠਺͑͋͛ΔͷΛ๷͙ͨΊʹɺγ ઢ ͷީิͱͯ͠બ୒͞ΕͨҰ൪ॳΊͷώοτ͔Β 20 ns Ҏ಺ͷީิ͸ 1 ͭͷ γ ઢީิͱͯ͠·ͱΊΔɻ20 ns Ҏ‫ޙ‬ͷώοτʹ͍ͭͯ͸ 2 ͭͷ γ ઢީิͱͯ۠͠ผ
ͯ͠બ୒͠ɺ࣌ؒ෯಺Ͱ͜ͷૢ࡞Λ‫܁‬Γฦ͢ɻ·ͨɺߴΤωϧΪʔͷόοΫάϥ΢ϯυࣄ৅Λআ‫͢ڈ‬ΔͨΊʹ 10 ns
෯Ͱ 51 ώοτҎ্ɺ200 ns ෯Ͱ 201 ώοτҎ্ͷ΋ͷ͸ީิ͔Βআ֎͍ͯ͠Δɻ͜ΕΒͷૢ࡞ʹΑͬͯɺީิࣄ
৅Ͱ͸શମͷ 33.2% ͷதੑࢠࣄ৅Λநग़͢Δ͜ͱ͕Ͱ͖Δɻ

4.3.2 χϡʔϥϧωοτϫʔΫॳΊͷεςοϓͰબ͹Εͨީิࣄ৅Λߋʹ 16 ‫ݸ‬ͷม਺Λ༻͍ͨχϡʔϥϧωοτϫʔΫʹ͔͚όοΫάϥ΢ϯ
υࣄ৅ͱ෼཭ͤ͞Δ͜ͱͰ࠷ऴީิΛબΜͰ͍͘ɻ͜ͷૢ࡞ʹΑΓɺॳΊͷεςοϓͰ͸தੑࢠࣄ৅ͷ 4.45 ഒ‫ؚ‬·Ε͍ͯͨόοΫάϥ΢ϯυࣄ৅Λ 0.018 ഒʹ·Ͱ௿‫͍ͯ͠ݮ‬Δɻ·ͨɺ࠷ऴతͳதੑࢠͷ‫ݕ‬ग़ޮ཰͸ 20.5% Ͱ
͋Δɻ

4.4 SK-Gd ‫ܭ‬ը͜Ε·Ͱͷ७ਫ͕٧·ͬͨ‫ݕ‬ग़‫Ͱث‬΋தੑࢠ‫ݕ‬ग़͸Մೳ͕ͩɺͦͷ‫ݕ‬ग़ޮ཰͸ 20.5% Ͱ͋ΔɻͦͷओͳཁҼ͸൓௓ిࢠͷΤωϧΪʔ͕νΣϨϯίϑᮢ஋෇ۙͷ 3.3 MeV ఔ౓Ͱ͋ΓɺόοΫάϥ΢ϯυࣄ৅ʹຒ΋Εͯ͠·͏͔ΒͰ͋Δɻͦͷ‫ݕ‬ग़ޮ཰޲্Λ໨ࢦͯ͠ɺ७ਫʹེࢎΨυϦχ΢Ϝ (Gd2 (SO4 )3 ) ΛՃ͑Δ‫ܭ‬ը͕ SK-Gd ‫ܭ‬ըͰ͋Δɻ
ΨυϦχ΢Ϝ‫֩ࢠݪ‬͸ࣜ 4.5, 4.6 ͷΑ͏ʹதੑࢠั֫ͷࡍɺγ ઢΛ 3∼4 ຊ์ग़͢Δɻ͜ΕΒ͸ 80.5% ͕ 7.9 MeV
Λɺ19.3% ͕ 8.5 MeV ͷΤωϧΪʔΛ࣋ͭɻͦͷ‫ ޙ‬γ ઢ͸ίϯϓτϯࢄཚΛ͢Δ͜ͱͰ໿ 4.5 MeV ͷిࢠʹ౳͍͠ΤωϧΪʔΛ࣋ͭͷͰɺνΣϨϯίϑᮢ஋Λ༰қʹ௒͑Δ͜ͱ͕Ͱ͖Δɻ·ͨΨυϦχ΢Ϝ‫֩ࢠݪ‬͸େ͖ͳ೤த
ੑࢠั֫அ໘ੵ 49700 b Λ࣋ͭ͜ͱͰগͳ͍ྔͰଞͷ‫֩ࢠݪ‬ΑΓ΋͸Δ͔ʹߴ͍தੑࢠั֫ྗΛ࣋ͭɻ७ਫதʹ

0.2% ͷེࢎΨυϦχ΢ϜΛ౤ೖ͢Δ͜ͱͰதੑࢠ‫ݕ‬ग़ޮ཰͸໿ 90% ·Ͱ޲্͢Δ͜ͱ͕༧ଌ͞Ε͍ͯΔɻ͜ΕʹΑΓɺ• ௒৽੕എ‫ܠ‬χϡʔτϦϊ‫ݕ‬ग़• χϡʔτϦϊ/൓χϡʔτϦϊϑϨʔόʔࣝผੑೳͷ޲্• ଠཅχϡʔτϦϊ‫؍‬ଌͰͷόοΫάϥ΢ϯυ௿‫ݮ‬ͳͲଟ͘ͷ࣮‫͕͋ݙߩͰݧ‬Δɻ

n +155 Ge →156 Gd∗ →156 Gd + γ ′ s(4.5)

n +157 Ge →158 Gd∗ →158 Gd + γ ′ s

(4.6)

27

ୈ5ষ

νµ ͱ ν¯µ ͷ૬‫͚͓ʹ༻࡞ޓ‬Δ‫؍‬ଌ্ͷ૬ҧ఺νµ ͱ ν¯µ ͷࣝผʹ͸ҰൠʹͦΕͧΕͷ൓Ԡ͔Β์ग़͞ΕΔՙిϛϡʔΦϯʹ࣓৔Λ͔͚ɺ‫͕ۂ‬Δํ޲͔Β۠ผ͢
Δํ๏ͳͲ͕༗ޮͰ͋Δɻ͔͠͠ɺSK ͸࣓৔Λ࣋ͨͳ͍‫ݕ‬ग़‫͋Ͱث‬Δ͜ͱ͔Β͜ͷख๏͸࢖͑ͳ͍ͨΊɺҰൠʹࣝผ͸೉͍͠ɻ͔͠͠ɺSK-IV Ͱ่յిࢠɺதੑࢠͳͲͷ‫ݕ‬ग़ޮ཰͕޲্͠ɺνµ ͱ ν¯µ ͷ૬‫༻࡞ޓ‬ͷҧ͍Λ͜Ε·ͰΑΓ‫؍‬ଌͰ͖ΔΑ͏ʹͳͬͨɻຊ‫Ͱڀݚ‬͸ɺ͜ͷΑ͏ͳ૬‫༻࡞ޓ‬ͷҧ͍Λࣔ͢ύϥϝʔλ͕ෳ਺͋Δ͜ͱΛར༻͠ɺlikelihood ๏ʹΑͬͯ νµ ͱν¯µ Λࣝผ͢Δɻlikelihood ๏ͱ͸ɺ͋Δύϥϝʔλͷ‫؍‬ଌྔ͕ νµ Β͍͠஋͔ ν¯µ Β͍͠஋͔Ͳ͏͔ɺ͋Β͔͡Ίνµ , ν¯µ ʹ͍ͭͯ༧૝ͨ֬͠཰ີ౓ؔ਺ (ͦͷύϥϝʔλͷ֬཰෼෍) Λ༻͍ͯ൑ఆ͢Δํ๏Ͱ͋Δɻৄࡉͳղઆ͸ୈ

6 ষͰߦ͏ɻ
ߴ͍ࣝผੑೳΛୡ੒͢ΔͨΊʹɺνµ ͱ ν¯µ ͷ૬‫༻࡞ޓ‬ͷҧ͍͕ͲͷΑ͏ͳύϥϝʔλʹͲͷΑ͏ʹදΕΔ͔ཧղ
͢Δඞཁ͕͋Δɻຊ‫Ͱڀݚ‬͸ SK Ͱ‫؍‬ଌ͞ΕΔύϥϝʔλΛ૞ࡧ͠ɺ࠷ऴతʹ 6 छྨ (่յిࢠ਺ɺϛϡʔΦϯ่յ࣌ؒɺ่յిࢠώοτ਺ɺதੑࢠ਺ɺԣํ޲ӡಈྔɺϦϯά਺) Λ νµ ͱ ν¯µ ͷ૬‫༻࡞ޓ‬ͷҧ͍Λࣔ͢ύϥϝʔλͱͯ͠બ୒ͨ͠ɻ͜͜Ͱ͸͜ΕΒͷύϥϝʔλʹ͍ͭͯղઆ͢Δɻ

5.1 ϛϡʔΦϯ่յిࢠ5.1.1 ่յిࢠ਺
νµ ͱ ν¯µ ͷ CCQE (ՙిΧϨϯτ४஄ੑࢄཚ) ൓Ԡ͸ҎԼͷ௨ΓʹͳΔɻν µ + n → µ− + p(5.1)

ν¯µ + p → µ+ + n(5.2)

͜ͷ µ− ͱµ+ ͸่յ͠ɺͱ΋ʹ่յిࢠΛ 1 ͭ์ग़͢ΔͷͰɺ่յిࢠͷ਺ʹࠩ͸ੜ͡ͳ͍ɻ

µ− → e− + ν¯e + νµ

(5.3)µ+ → e+ + νe + ν¯µ(5.4)

͔͠͠ɺCCQE ൓ԠҎ֎ͷ CC nonQE (ՙిΧϨϯτඇ஄ੑࢄཚ) ൓ԠͰ͸ࣜ 5.5∼5.8 ͷΑ͏ʹύΠΦϯ͕์ग़͞ΕΔɻπ + ͸ µ+ ʹ่յ͠ɺ่յిࢠΛ์ग़͢Δ͕ɺπ − ͸่յલʹ‫ٵ‬ऩ͞Εͯ͠·͏ͷͰɺ่յిࢠ͸์ग़͞Εͳ͍ɻνµ ൓ԠͰ͸ࣜ 5.5, 5.6 ͷΑ͏ʹ์ग़֩ࢠͱ π ͷిՙͷ࿨͕ͦΕͧΕ +1, +2 Ͱ͋Δͷʹର͠ɺν¯µ ൓ԠͰ͸ࣜ

5.7, 5.8 ͷΑ͏ʹ์ग़֩ࢠͱ π ͷిՙͷ࿨͕ͦΕͧΕ-1, 0 Ͱ͋ΔͨΊ νµ ൓Ԡͷํ͕ π + Λ์ग़͢ΔՄೳੑ͕ߴ͍ɻ
͜ΕʹΑΓɺνµ ࣄ৅ͷํ͕ ν¯µ ࣄ৅ʹൺ΂่ͯյిࢠΛΑΓଟ͘์ग़͢Δɻ1 Ϧϯάࣄ৅ɺϚϧνϦϯάࣄ৅ʹ͍ͭͯͦΕͧΕਤ 5.1(a), 5.1(b) ʹ่յిࢠ਺෼෍Λࣔ͢ɻ͜͜Ͱ͸෼෍ͷ‫ܗ‬ͷҧ͍Λ෼͔Γ΍͘͢͢ΔͨΊʹࣄ৅਺

28

ୈ 5 ষ νµ ͱ ν¯µ ͷ૬‫͚͓ʹ༻࡞ޓ‬Δ‫؍‬ଌ্ͷ૬ҧ఺Ͱ‫֨ن‬Խͯ͠ද͍ࣔͯ͠Δɻ͜ͷ‫ޙ‬ͷ‫؍‬ଌྔͷ෼෍ʹ͍ͭͯ΋ಉ༷ʹදࣔ͢ΔɻϚϧνϦϯάࣄ৅Ͱ͸ CC nonQE൓Ԡ͕ࢧ഑తͷͨΊɺνµ ͱ ν¯µ ͷ͕ࠩΑΓ‫ݦ‬ஶʹ‫͑ݟ‬Δɻνµ + n → µ− + N ′ + π ′ s (N ′ ͱπ ′ s ͷిՙͷ࿨͸ + 1)

(5.5)

νµ + p → µ− + N ′ + π ′ s (N ′ ͱπ ′ s ͷిՙͷ࿨͸ + 2)

(5.6)

ν¯µ + n → µ+ + N ′ + π ′ s (N ′ ͱπ ′ s ͷిՙͷ࿨͸ − 1)

(5.7)

ν¯µ + p → µ+ + N ′ + π ′ s (N ′ ͱπ ′ s ͷిՙͷ࿨͸ 0)

(5.8)

(a)

(b)

ਤ 5.1 νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷ่յిࢠ਺෼෍ɻ(a) 1 Ϧϯάࣄ৅ɻ(b) ϚϧνϦϯάࣄ৅

5.1.2

primary ϛϡʔΦϯ༝དྷͷ่յిࢠநग़

primary ϛϡʔΦϯͱ͸ϛϡʔΦϯχϡʔτϦϊ૬‫༻࡞ޓ‬ͷҰཻ࣍ࢠͱͯ͠์ग़͞ΕͨϛϡʔΦϯͷࣄͰ͋Γɺຊ‫Ͱڀݚ‬͸ π + ͷ่յʹΑͬͯੜͨ͡ϛϡʔΦϯͱ۠ผͯ͜͠͏‫Ϳݺ‬ɻ

primary ϛϡʔΦϯͷՙిΛಛఆ͢Δํ๏ͱͯ͠ɺϛϡʔΦϯ่͕յ͢Δ·Ͱͷ͕࣌ؒ༗ޮͳࣄ͸ઌߦ‫[ ڀݚ‬2]Ͱࣔ͞Ε͍ͯΔɻ͜Ε͸ϛϡʔΦϯͷण໋͸ిՙʹґଘ͠ͳ͍͕ɺµ− ͷΈ‫֫͞ัʹ֩ࢠݪ‬ΕΔͨΊ‫͚͔ݟ‬ͷ่յ͕࣌ؒ୹͘ͳΔ͜ͱΛར༻͍ͯ͠Δ (‫ޙ‬ड़)ɻϛϡʔΦϯͷ่յ࣌ؒ͸‫ݕ‬ग़͞Ε่ͨյిࢠ͔Βܾఆ͢Δ͜ͱ͕Ͱ͖
Δɻ͔͠͠ɺCC nonQE ࣄ৅Ͱ͸ π + ͷ่յ͔Βੜ͡ΔϛϡʔΦϯ΋ଘࡏ͢ΔͨΊɺෳ਺͋ΔϛϡʔΦϯͱ่յిࢠ͔Βਖ਼͍͠૊Έ߹ΘͤΛܾఆ͢Δඞཁ͕͋Δɻຊ‫Ͱڀݚ‬͸ઌߦ‫[ ڀݚ‬2] ΛࢀߟʹϛϡʔΦϯӡಈྔ͔Βਪఆͨ͠ϛϡʔΦϯ่յ஍఺Λ࢖ͬͯɺ૊Έ߹ΘͤΛܾఆ͢Δख๏Λ։ൃͨ͠ɻԼ‫Ͱه‬͸ͦͷํ๏ʹ͍ͭͯৄ͘͠આ໌͢Δɻ

29

5.1 ϛϡʔΦϯ่յిࢠਤ 5.2

ϛϡʔΦϯӡಈྔͱඈఔͷؔ܎ [2]ਤ 5.2 ͸Ӊ஦ઢϛϡʔΦϯͷӡಈྔͱඈఔͷؔ܎Ͱ͋ΔɻϛϡʔΦϯͷӡಈྔͱඈఔͷؔ܎͸͓͓ΑͦҰ࣍૬ؔͰ͋Γࣜ 5.9 Ͱද͢͜ͱ͕Ͱ͖Δɻ

y = ax + 200(5.9)͜͜Ͱఆ਺ a ͸ϛϡʔΦϯͷඈఔຖʹ 0-400 [cm]ɺ400-1000 [cm]ɺ1000-4000 [cm] ͷ 3 ͭͷྖҬʹΘ͚ɺͦΕͧΕϑΟοςΟϯά͢Δ͜ͱʹΑͬͯ‫ٻ‬Ίͨ஋Ͱɺa = 2.043 ± 0.003, 2.083 ± 0.001, 2.253 ± 0.000 [MeV/c/cm]
Ͱ͋Δɻ͜ͷ૬ؔؔ܎Λར༻ͯ͠‫؍‬ଌྔͰ͋ΔϛϡʔΦϯͷόʔςοΫε Vµ , ϛϡʔΦϯͷӡಈྔ Pµ , ϛϡʔΦϯͷ์ग़ํ޲ Dµ Λ༻͍ͯɺϛϡʔΦϯͷ่յ஍఺ Vstop ͸ࣜ 5.10 Ͱද͞ΕΔɻ

Vstop = Vµ + (Pµ ×

1 200−) × Dµaa(5.10)

͜ͷΑ͏ʹਪఆͨ͠ϛϡʔΦϯͷ่յ஍఺ Vstop ͱ่յిࢠͷόʔςοΫε (Ґஔ) Ve ͷ‫཭ڑ‬Λ d ͱ͢Δͱɺd͸ɺd = Vstop − Ve

(5.11)

ͱͯ͠‫͖Ͱࢉܭ‬ΔɻӉ஦ઢϛϡʔΦϯΛ༻͍ͨσʔλͱ MC ͷ d ෼෍Λൺֱͨ͠ઌߦ‫??ڀݚ‬ͷ݁ՌΛਤ 5.3 ʹࣔ͢ɻਤ 5.3 Ӊ஦ઢετοϓϛϡʔΦϯͰͷ d ෼෍ɻࠇ఺͕σʔλɺ੺ઢ͕ MC Λࣔ͢ [2]ɻ30

ୈ 5 ষ νµ ͱ ν¯µ ͷ૬‫͚͓ʹ༻࡞ޓ‬Δ‫؍‬ଌ্ͷ૬ҧ఺MC ͱσʔλͷ߹͍΋Α͘ɺ֦͕Γ͸ϛϡʔΦϯͷඈఔ < 1000 cm Ͱ͸ |d| < 150 cm ʹ཈͑ΒΕ͍ͯΔɻϛϡʔΦϯ༝དྷͷ่յిࢠͷόʔςοΫε͸ϛϡʔΦϯͷ่յ༧ଌ஍఺ͷपลʹ෼෍͍ͯ͠Δ͜ͱ͕‫͑ݴ‬Δɻ͞Βʹɺେ‫ؾ‬χϡʔτϦϊ MC 1 Ϧϯά µ-like FC ͷՙిΧϨϯτ४஄ੑࢄཚ (CCQE) ൓ԠͰಉ༷ʹ‫ ͨ͠ࢉܭ‬d ෼෍Λਤ 5.4
ʹࣔ͢ɻ͜ͷࣄ৅͸Ұൠʹ primary ϛϡʔΦϯ༝དྷͷ่յిࢠ͕ 1 ͚ͭͩग़‫͢ݱ‬ΔͨΊɺπ + ༝དྷͷϛϡʔΦϯ่յిࢠͷόοΫάϥ΢ϯυ͕ͳ͘ɺ։ൃ͞Εͨ primary ϛϡʔΦϯ༝དྷͷ่յిࢠநग़๏ͷੑೳΛ͔֬ΊΔͷʹ࠷
దͰ͋ΔɻϛϡʔΦϯඈఔ 1000 cm Ҏ্ͷ΋ͷ͸ࣄ৅਺͕গͳ͘লུ͞Ε͍ͯΔ͕ɺਤ 5.4 Ͱͷ݁Ռ͸Ӊ஦ઢετοϓϛϡʔΦϯͱಉ༷ͷ෼෍ʹͳ͍ͬͯΔɻ͜ͷͨΊ͜ͷ่յిࢠநग़๏͸େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊࣄ৅ʹ΋༗ޮͰ͋Δͱ‫͑ݴ‬Δɻ

ਤ 5.4 େ‫ؾ‬χϡʔτϦϊ 1 Ϧϯά µ-like ՙిΧϨϯτ४஄ੑࢄཚ (CCQE) ࣄ৅Ͱͷ d ෼෍ [2]ϚϧνϦϯάࣄ৅΁ͷϛϡʔΦϯ༝དྷͷ่յిࢠநग़ͷద༻ϛϡʔΦϯ่յిࢠநग़ํ๏ΛϚϧνϦϯάࣄ৅ʹಋೖ͢Δɻਤ 5.5(a) ∼ ਤ 5.5(c) ͸่յిࢠ਺ = 1 ͷࣄ৅ͷd ෼෍ΛϦϯά߹‫ܭ‬ӡಈྔʹΑͬͯ 3 ͭͷྖҬʹ෼͚ͯදࣔͨ͠΋ͷͰ͋Δɻ੺ઢ͕ νµ ࣄ৅ɺ੨ઢ͕ ν¯µ ࣄ৅Ͱ͋Δɻνµ ࣄ৅ͷ෼෍Λ‫ݟ‬Δͱɺν¯µ ࣄ৅ͷ෼෍ʹൺ΂ͯ d > 300 cm Ҏ্Λ่࣋ͭյిࢠͷׂ߹͕૿͍͑ͯΔɻνµ ࣄ৅͸ π + ‫ݯى‬ͷ่յిࢠΛ࣋ͭͷͰɺ͜ͷ෼෍ͷҧ͍͸ π + ‫ݯى‬ͷ่յిࢠʹΑΔ΋ͷͱਪଌͰ͖Δɻਤ 5.6(a) ∼5.8(b) ʹ่յిࢠ਺ = 2 ͷࣄ৅ͷ d ෼෍Λେ‫ ؾ‬νµ , ν¯µ ࣄ৅ͦΕͧΕʹ͍ͭͯࣔͨ͠ɻ

͜͜Ͱͷ੺ઢ͸ 2 ͭͷ่յిࢠͷ͏ͪϛϡʔΦϯ่յ༧ଌ஍఺ʹΑΓ͍ۙ‫ ཭ڑ‬d Λ่࣋ͭյిࢠΛબΜͩ dmin෼෍Ͱ͋Γɺ੨ઢ͕ΑΓԕ͍‫ ཭ڑ‬d Λ่࣋ͭյిࢠΛબΜͩ dmax ෼෍Ͱ͋Δɻ͜ͷ෼෍Ͱ͸ primary ϛϡʔΦϯ༝དྷͱ π + ༝དྷͷ่յిࢠͷ྆ํΛ‫ؚ‬Ήࣄ৅͕ଟ਺Ͱ͋Γɺ૒ํͷ෼෍ͷҧ͍ΛΑΓৄ͘͠‫ݟ‬Δ͜ͱ͕Ͱ͖Δɻ
ਤ 5.6(a), 5.6(b) Ͱ͸Ϧϯά߹‫ܭ‬ӡಈྔ 1.33 GeV ະຬͷࣄ৅ΛબΜͰ͍Δɻ௿ΤωϧΪʔͷ൓ԠͰ͸ µ ͱ π ͷඈఔ͕ͱ΋ʹ୹͘ɺ่յిࢠόʔςοΫεͷ‫཭ڑ‬ͷ͕ࠩখ͘͞ͳ͍ͬͯΔɻਤ 5.7(a), 5.7(b) ͸Ϧϯά߹‫ܭ‬ӡಈྔ

1.33 GeV Ҏ্ 5.0 GeV ະຬͷࣄ৅Ͱ͋Δɻd = 300cm ҎԼͰ͸ dmin ͕ࢧ഑తͰ͋Δ͕ɺ͜ΕҎ্Ͱ͸ dmax ͕ࢧ഑తʹͳΔɻਤ 5.8(a), 5.8(b) ͸Ϧϯά߹‫ܭ‬ӡಈྔ 5.0 GeV Ҏ্ͷࣄ৅Ͱ͋ΔɻߴΤωϧΪʔͷࣄ৅ͳͷͰΑΓ µͱπ ͷ‫཭͕཭ڑ‬ΕΔɻd = 600 cm ҎԼͷྖҬͰ dmin ͕ࢧ഑తͰ͋Γɺ͜͜Λ‫ ʹڥ‬dmin ෼෍ͷ‫ܗ‬΋มΘ͍ͬͯΔɻ͜ͷ͜ͱ͔ΒɺϛϡʔΦϯ༝དྷͷ่յిࢠΛબ୒͢Δ৚݅ͱͯ͠

• dmin < 300 cm (ϛϡʔΦϯ [Ϧϯά߹‫ ]ܭ‬ӡಈྔ< 5.0 GeV ͷ৔߹)• dmin < 600 cm (ϛϡʔΦϯ [Ϧϯά߹‫ ]ܭ‬ӡಈྔ ≥ 5.0 GeV ͷ৔߹)Λ՝͢ɻ·่ͨյిࢠ͕ 1 ͭͷ৔߹΍ 3 ͭҎ্ͷ৔߹ʹ΋͜ͷ‫ج‬४͸༗ޮͰ͋ΔͨΊɺશͯͷࣄ৅ʹରͯ͜͠ͷ31

5.1 ϛϡʔΦϯ่յిࢠ৚݅Λద༻͢Δɻ
(a)

(b)

(c)

ਤ 5.5 ่յిࢠ਺ = 1 ͷ৔߹ͷ d ෼෍ɻ੺ઢ͕ νµ ੨ઢ͕ ν¯µ ࣄ৅Ͱ͋Δɻ(a) Ϧϯά߹‫ܭ‬ӡಈྔ 1.33 GeV ҎԼ (b) Ϧϯά߹‫ܭ‬ӡಈྔ 1.33 GeV Ҏ্ 5.0 GeV ະຬ (c) Ϧϯά߹‫ܭ‬ӡಈྔ 5.0 GeV Ҏ্ɻ

32ୈ 5 ষ νµ ͱ ν¯µ ͷ૬‫͚͓ʹ༻࡞ޓ‬Δ‫؍‬ଌ্ͷ૬ҧ఺
(a)

(b)

ਤ 5.6 ่յిࢠ਺ = 2, Ϧϯά߹‫ܭ‬ӡಈྔ 1.33 GeV ະຬͷ৔߹ͷ d ෼෍ɻ੺ઢ͕ 2 ͭͷ่յిࢠͷ͏ͪɺϛϡʔΦϯ่յ༧ଌ஍఺ʹΑΓ่͍ۙյిࢠΛબΜͩ dmin ෼෍ɻ੨ઢ͕‫͕཭ڑ‬ԕ͍΋ͷΛબΜͩ dmax ෼෍ɻ(a) େ‫ ؾ‬νµ ࣄ৅ (b) େ‫ ؾ‬ν¯µ ࣄ৅

(a)

ਤ 5.7

(b)

่յిࢠ਺ = 2, Ϧϯά߹‫ܭ‬ӡಈྔ 1.33 GeV Ҏ্ 5.0 GeV ະຬͷ৔߹ͷ d ෼෍ɻ੺ઢ͕ 2 ͭͷ่յిࢠͷ͏ͪɺϛϡʔΦϯ่յ༧ଌ஍఺ʹΑΓ่͍ۙյిࢠΛબΜͩ dmin ෼෍ɻ੨ઢ͕‫͕཭ڑ‬ԕ͍΋ͷΛબΜͩ

dmax ෼෍ɻ(a) େ‫ ؾ‬νµ ࣄ৅ (b) େ‫ ؾ‬ν¯µ ࣄ৅

33

5.1 ϛϡʔΦϯ่յిࢠ
(a)

ਤ 5.8

(b)

่յిࢠ਺ = 2, Ϧϯά߹‫ܭ‬ӡಈྔ 5.0 GeV Ҏ্ͷ৔߹ͷ d ෼෍ɻ੺ઢ͕ 2 ͭͷ่յిࢠͷ͏ͪɺϛϡʔΦϯ่յ༧ଌ஍఺ʹΑΓ่͍ۙյిࢠΛબΜͩ dmin ෼෍ɻ੨ઢ͕‫͕཭ڑ‬ԕ͍΋ͷΛબΜͩ dmax ෼෍ɻ(a) େ‫ ؾ‬νµ ࣄ৅ (b) େ‫ ؾ‬ν¯µ ࣄ৅

5.1.3 ϛϡʔΦϯ่յ࣌ؒ (Decay time)่յిࢠ͔Βͷ৘ใͷҰͭͱͯ͠ϛϡʔΦϯ่յ࣌ؒ (Decay time) ͱ͍͏ύϥϝʔλΛ༻͍Δɻ͜Ε͸χϡʔτϦϊ͕൓Ԡͨ࣌ؒ͠ (t = 0) ͔Β primary ϛϡʔΦϯ༝དྷͷ่յిࢠ͕ੜ੒͞ΕΔ·Ͱͷ࣌ؒࠩͰ͋Δɻ͜ͷ࣌ؒࠩ͸ϛϡʔΦϯͷ‫͚͔ݟ‬ͷण໋Λද͍ͯ͠ΔɻϛϡʔΦϯͷण໋͸࣮ࡍ͸ͦͷූ߸ʹΑΒͳ͍͕ɺµ− ͷΈ‫֩ࢠݪ‬ʹั֫͞ΕΔͨΊɺ‫͚͔ݟ‬ͷण໋͕ µ+ ʹൺ΂ͯ୹͘ͳΔɻ͜ͷ µ+ ͱ µ− ͷ‫͚͔ݟ‬ͷण໋ͷҧ͍Λར༻͢Δ͜ͱͰ νµ ͱν¯µ Λࣝผ͢Δɻ่յిࢠ਺ = 0 ͷࣄ৅Ͱ͸ϛϡʔΦϯ่յ࣌ؒ͸ଌఆ͢Δ͜ͱ͸ग़དྷͳ͍ɻ
(a)

(b)

ਤ 5.9 νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷϛϡʔΦϯ่յ࣌ؒ෼෍ɻ(a) 1 Ϧϯάࣄ৅ɻ(b) ϚϧνϦϯάࣄ৅

5.1.4 ่յిࢠώοτ਺µ− ͕‫֫͞ัʹ֩ࢠݪ‬Εͨࡍɺࣜ 5.12, 5.13 ͷΑ͏ͳաఔͰ γ ઢΛ์ग़͢Δɻ͜ͷ γ ઢ͸χϡʔτϦϊ൓Ԡ‫ޙ‬

50 nsec Ҏ಺ʹνΣϨϯίϑޫΛ์ग़͠‫؍‬ଌ͞ΕΔɻγ ઢ͸ 0.5-30 MeV ఔͷΤωϧΪʔΛ࣋ͪɺ໿ 6 MeV ʹϐʔ34ୈ 5 ষ νµ ͱ ν¯µ ͷ૬‫͚͓ʹ༻࡞ޓ‬Δ‫؍‬ଌ্ͷ૬ҧ఺ΫΛ࣋ͭɻ͜ͷΤωϧΪʔ෼෍ͷҧ͍Λ‫ݟ‬ΔͨΊʹࣄ৅ൃੜपล 50 nsec ෯Ͱώοτͨ͠ PMT ਺Λ‫ٻ‬ΊҐஔґଘੑΛิਖ਼ͨ͠஋Λ N50 ͱͯ͠ఆٛͯ͠ɺ͜ͷ෼෍Λ༻͍ΔɻΤωϧΪʔ෼෍Λ֬ೝ͢ΔͨΊʹ PMT ͷશޫྔͰ͸ͳ͘ώοτ਺෼෍Λ༻͍Δཧ༝ͱͯ͠͸௿ΤωϧΪʔྖҬͰώοτ਺෼෍ͷํ͕ΤωϧΪʔ෼ղೳ͕ߴ͍͔ΒͰ͋Δ [23]ɻ N50 = 6 ͕໿ 1 MeV ʹ૬౰͠ɺµ− ͷ෼෍Ͱ͸ N50 = 40 ͷลΓʹϐʔΫ͕‫͑ݟ‬Δ͜ͱ͕෼͔Δɻ

N50 = 250 ลΓͷϐʔΫΛ࡞Δ෼෍͸่յిࢠΤωϧΪʔʹΑΔ෼෍Ͱ͋Δɻµ− +16 O → νµ + n +15 N∗(5.12)

N∗ →15 N + γ (6.32MeV)(5.13)

15(a)ਤ 5.105.2(b)νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷ่յిࢠώοτ਺෼෍ɻ(a) 1 Ϧϯάࣄ৅ (b) ϚϧνϦϯάࣄ৅தੑࢠ਺

CCQE ൓ԠͰ͸ࣜ 5.1 ͱࣜ 5.2 ͷΑ͏ʹ ν¯µ ͷΈதੑࢠΛ์ग़͢ΔɻਫதͰͷೋ࣍తͳ૬‫ʹ༻࡞ޓ‬Αͬͯதੑࢠ
͕࡞ΒΕΔՄೳੑ͸௿͍ͷͰதੑࢠ਺Λଌఆ͢Δ͜ͱͰ νµ ͱν¯µ Λޮ཰Αࣝ͘ผ͢Δ͜ͱ͕Ͱ͖ΔɻCC nonQE ࣄ৅ͷΑ͏ͳߴΤωϧΪʔࣄ৅ͷ৔߹ɺύΠΦϯͷ֩಺ޮՌɺϋυϩϯ૬‫༻࡞ޓ‬ɺྭ‫ى‬஠ૉ‫͔֩ࢠݪ‬Βͷதੑࢠ์ग़
ͳͲʹΑͬͯଟ਺ͷதੑࢠ͕‫؍‬ଌ͞Εɺνµ ͱ ν¯µ ͷ෼෍ͷࠩ͸খ͍͞ɻਤ 5.11(a), 5.11(b) ʹ 1 Ϧϯάࣄ৅ɺϚϧνϦϯάࣄ৅Ͱͷதੑࢠ਺෼෍Λࣔͨ͠ɻ1 Ϧϯάࣄ৅Ͱ͸ CCQE ࣄ৅͕ࢧ഑తͳͨΊ νµ ͱ ν¯µ ͷ෼෍ͷ͕ࠩ‫ݦ‬
ஶͰ͋ΔɻҰํɺϚϧνϦϯάࣄ৅Ͱ͸ non QE ࣄ৅ͷׂ߹͕૿Ճ͢ΔͨΊ෼෍ͷࠩ͸‫͑ݟ‬ਏ͘ͳΔɻ

35

5.3 ଟཻࢠࣄ৅ʹ͓͚Δ νµ ͱ ν¯µ ͷӡಈֶతಛ௃
(a)

(b)

ਤ 5.11νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷதੑࢠ਺෼෍ɻ(a) 1 Ϧϯάࣄ৅ (b) ϚϧνϦϯάࣄ৅

5.3 ଟཻࢠࣄ৅ʹ͓͚Δ νµ ͱ ν¯µ ͷӡಈֶతಛ௃
5.3.1 ԣํ޲ӡಈྔ
CC nonQE ࣄ৅ͷΑ͏ͳଟཻࢠࣄ৅Ͱ͸ӡಈֶతಛ௃Λ༻͍ͯ νµ ͱ ν¯µ Λࣝผ͢Δ͜ͱ͕Ͱ͖Δɻ͜Ε͸ νµ ͱν¯µ ͷεϐϯͷҧ͍ʹΑͬͯϨϓτϯ‫ͱܥ‬ϋυϩϯ‫ʹܥ‬ड͚౉͢ӡಈྔͷׂ߹͕ҟͳΔͨΊͰ͋ΔɻҰൠʹ νµ ͷํ͕ϋυϩϯ‫͢౉ʹܥ‬ӡಈྔ͕େ͖͘ɺϨϓτϯ‫͢౉ʹܥ‬ӡಈྔ͕খ͍͞ɻ͜ͷׂ߹Λൺ΂ΔͨΊʹɺਤ 5.12(b) ͸߹‫ܭ‬ӡಈྔʹର͢Δԣํ޲ӡಈྔͷׂ߹"ԣํ޲ӡಈྔ/߹‫ܭ‬ӡಈྔ"ͷ෼෍Λ͍ࣔͯ͠Δɻ͜͜Ͱɺԣํ޲ӡಈྔͱ͸χϡʔτϦϊ൓ԠʹΑͬͯ์ग़͞ΕɺϦϯάΛ࡞ͬͨϛϡʔΦϯҎ֎ͷՙిཻࢠͷӡಈྔͷϛϡʔΦϯͷਐߦํ޲ʹਨ௚ͳӡಈྔ੒෼ͷઈର஋ͷ߹‫͋Ͱܭ‬Δ (ਤ 5.12(a) Λࢀর) ɻ·ͨ߹‫ܭ‬ӡಈྔ͸ϦϯάΛ࡞ཻͬͨࢠͷӡಈྔͷઈର஋ͷ߹‫͋Ͱܭ‬Δɻԣํ޲ӡಈྔ͸Ϧϯάͷӡಈྔ͔Β‫͢ࢉܭ‬ΔͨΊɺෳ਺ͷϦϯάΛ࣋ͭϚϧνϦϯάࣄ৅ͷΈ͜ΕΛར༻Ͱ͖Δɻ(a)ਤ 5.12(b)νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷશӡಈྔʹର͢Δԣํ޲ӡಈྔͷׂ߹ɻશӡಈྔ͸ϦϯάΛ࡞ͬͨӡಈྔͷ߹‫ܭ‬ɺԣํ޲ӡಈྔ͸ϛϡʔΦϯϦϯάҎ֎ͷϦϯάͷϛϡʔΦϯਐߦํ޲ʹਨ௚ͳӡಈྔͷ߹‫ܭ‬ɻ(a) ԣํ޲ӡಈྔͷఆٛ (b) ϚϧνϦϯάࣄ৅ ʹ͓͍ͯɺશӡಈྔʹରͯ͠ԣํ޲ӡಈྔͷ઎ΊΔׂ߹

36

ୈ 5 ষ νµ ͱ ν¯µ ͷ૬‫͚͓ʹ༻࡞ޓ‬Δ‫؍‬ଌ্ͷ૬ҧ఺

5.3.2 Ϧϯά਺લड़ͷΑ͏ʹ νµ ͕ ν¯µ ʹൺ΂ͯϋυϩϯ‫͢౉ʹܥ‬ΤωϧΪʔ͕ଟ͍ͷͰɺύΠΦϯͳͲͷՙిཻࢠ͕νΣϨϯί
ϑᮢ஋Λ௒͑ͯϦϯάͱͯ͠‫؍‬ଌ͞ΕΔ֬཰͕ߴ͘ͳΔɻ͜Ε΋ϚϧνϦϯάࣄ৅ͷΈར༻Ͱ͖ΔͨΊ෼෍͸Ϧϯά਺͕ 2 ͭҎ্ͷ෼෍Λ͍ࣔͯ͠Δɻ(a)ਤ 5.13νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷϚϧνϦϯάࣄ৅ʹ͓͚ΔϦϯά਺෼෍

37

ୈ6ষ

likelihood ๏ʹΑΔ νµ/ν¯µ ࣝผ
6.1 likelihood ๏likelihood ๏ʹ༻͍ΒΕΔ νµ /ν¯µ ࣝผͷͨΊͷ likelihood ؔ਺͸࣍ͷΑ͏ʹఆٛ͞ΕΔɻ
Lνµ =

3
!

log(ΓSi (xi ))(6.1)

log(ΓBi (xi ))

(6.2)

i=1

Lν¯µ =

3!
i=1∆L = Lνµ − Lν¯µ

(6.3)

B
͜͜Ͱ ΓSi (xi ), Γi (xi ) ͸ CCνµ (CCν¯µ ) ࣄ৅ͷ i ൪໨ͷύϥϝʔλʔͷ֬཰ີ౓ؔ਺Λද͠ɺxi ͸‫؍‬ଌྔͰ͋Δɻνµ ͱν¯µ ͦΕͧΕͷ L ͷ஋ͷࠩ ∆L ͷ஋Λશͯͷࣄ৅ʹ͍ͭͯ‫ٻ‬ΊΔɻ͜͜ͰಘΒΕͨ ∆L ͷ஋͕ɺ͋Β͔͡ΊఆΊͨΧοτ஋ΑΓେ͖͍͔খ͍͔͞ʹΑͬͯ νµ Β͍͠ (νµ -like) ͔ ν¯µ Β͍͠ (ν¯µ -like) ͔൑ఆ͢Δɻ͜͜Ͱͷ֬཰ີ౓ؔ਺ͱ͸֤ύϥϝʔλ෼෍ͷ͜ͱͰ͋Δɻຊ‫Ͱڀݚ‬͸ likelihood ‫ࢉܭ‬ͷͨΊͷύϥϝʔλ෼෍ͷ࡞੒ʹɺMC ͷਅͷ৘ใΛ༻͍ͯબΜͩେ‫ ؾ‬νµ ͱ ν¯µ ࣄ৅Λ༻͍Δɻਖ਼͘͠େ‫ ؾ‬νµ ͱ ν¯µ ࣄ৅Λબ୒͢ΔͨΊʹҎԼͷΑ͏ͳࣄ৅બผΛಋೖͨ͠ɻ

6.2 େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊࣄ৅બผͷಋೖ
likelihood ‫͍༻ʹࢉܭ‬Δ֬཰ີ౓෼෍Λ࡞੒͢ΔͨΊͷࣄ৅બผΛಋೖ͢ΔɻNEUT ͷਅͷ৘ใΛ༻͍ͯେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊ νµ ͱ ν¯µ ࣄ৅Λ SK Ͱͷେ‫ؾ‬χϡʔτϦϊৼಈղੳͰ༻͍ΒΕ͍ͯΔࣄ৅બผख๏Λ༻͍ͯબͼɺ࣮ࡍͷଌఆͱಉ༷ͷखॱͰ࠶ߏ੒͞Εͨ৘ใ͔Β෼෍Λ࡞੒͢ΔɻҎԼʹͦͷखॱΛࣔͨ͠ɻ• ਅͷ νµ , ν¯µ ࣄ৅બ୒NEUT ͷਅͷ৘ใΛ༻͍ͯਅͷ νµ ͱ ν¯µ ΛͦΕͧΕબͿɻ• ՙిΧϨϯτࣄ৅બ୒χϡʔτϦϊϑϨʔόʔͷಛఆ΍ΤωϧΪʔͷ࠶ߏ੒͕ՄೳͳՙిΧϨϯτ (CC) ࣄ৅Λਅͷ৘ใ͔Βબ୒͢Δɻ• ՄࢹΤωϧΪʔ > 30 [MeV]௿ΤωϧΪʔͷόοΫάϥ΢ϯυΠϕϯτΛআ‫͢ڈ‬Δɻ

38

ୈ6ষ

likelihood ๏ʹΑΔ νµ /ν¯µ ࣝผ• น͔ΒͷϛϡʔΦϯͷ‫ ≥ ཭ڑ‬200 [cm]ࣄ৅࠶ߏ੒ΞϧΰϦζϜ͕ਖ਼͘͠ಈ࡞͢Δ༗ޮମੵ಺ࣄ৅ͷબ୒Λ͢Δɻ

• ֎ਫ૧ (OD) Ͱͷώοτ਺ < 16 [hits]Ӊ஦ઢϛϡʔΦϯͳͲͷόοΫάϥ΢ϯυࣄ৅Λআ‫͢ڈ‬Δɻ

• νΣϨϯίϑϦϯάͷ਺ = 1 or 2 Ҏ্
1 ͭͷ΋ͷ͕ 1 Ϧϯάɺ2 ͭҎ্ͷ΋ͷΛϚϧνϦϯάͱͯ͠ѻ͏ɻɹ• PID ʹΑΔϦϯάͷछྨ µ
1 Ϧϯάͷ৔߹͸ͦͷϦϯάͷɺϚϧνϦϯάͷ৔߹͸ΤωϧΪʔ͕࠷΋ߴ͍Ϧϯάͷ PID ͕ µ-like ͱ൑ఆ͞Εͨ΋ͷΛબΜͰ͍Δɻ• ϛϡʔΦϯͷӡಈྔ > 200 [MeV/c]µ-like ࣄ৅ͷϛϡʔΦϯ͕࣋ͭӡಈྔͷԼ‫ݶ‬஋ͷ৚݅ɻSK ͷղੳͰҰൠతʹ༻͍ΒΕΔɻ• ӡಈྔ (Ϧϯάͷӡಈྔ͔Βਪఆͨ͠χϡʔτϦϊΤωϧΪʔͷ) ৚݅
1 Ϧϯά ϛϡʔΦϯӡಈྔ > 1.33 [GeV]ϚϧνϦϯά Ϧϯά߹‫ܭ‬ӡಈྔ > 1.33 [GeV]͜ͷྖҬͰ µ ༝དྷͱ π + ༝དྷͷ่յిࢠΛΑΓΑ۠͘ผͰ͖Δɻ·ͨɺ࣭ྔ֊૚ੑ‫౓ײ‬ͷߴ͍ߴΤωϧΪʔࣄ৅ʹಛԽͯࣝ͠ผΛߦ͏ͨΊ௿ΤωϧΪʔͰͷৼΔ෣͍Λແࢹ͍ͯ͠Δɻ• ϛϡʔΦϯ่յ༧ଌ஍఺ͱ่յిࢠόʔςοΫεͷ࠷খ‫ ཭ڑ‬dmin ৚݅· dmin < 300 [cm] (ϛϡʔΦϯ [Ϧϯά߹‫ ]ܭ‬ӡಈྔ< 5.0 GeV ͷ৔߹)· dmin < 600 [cm] (ϛϡʔΦϯ [Ϧϯά߹‫ ]ܭ‬ӡಈྔ ≥ 5.0 GeV ͷ৔߹)d ෼෍͔Β‫ੵݟ‬΋ͬͨϛϡʔΦϯ༝དྷͷ่յిࢠબผ৚݅Λ͜ͷΑ͏ʹઃఆ͢Δɻ• ༗ޮମੵ಺่յిࢠόʔςοΫε· |Ze | < 1610 [cm]&· Xe2 + Ye2 < 1490 [cm]dmin Λ่࣋ͭյిࢠ͕༗ޮମੵ಺ʹ‫·ؚ‬Ε͍ͯΔ͔ࣝผ͢Δɻͨͩ͜͠ͷ஋͸಺ਫ૧͔Β 2 m ͷ‫཭ڑ‬ΑΓ΋͞Βʹ಺ଆͷྖҬͰ͋Δɻ͜ͷྖҬͷ֎ଆͰ่յిࢠͷ‫ݕ‬ग़ޮ཰͕௿Լͯ͠͠·͏ͨΊ͜ͷΑ͏ͳ஋Λઃఆ͍ͯ͠Δɻ͜͜Ͱ Z ͸‫ݕ‬ग़‫ث‬ͷਨ௚ํ޲ɻX,Y ͸ਫฏํ޲Ͱ͋Δɻ• ่յిࢠϑΟοτͷྑ͞ > 0.5่յిࢠͱؒҧ͑΍͍͢Ξϑλʔύϧεࣄ৅Λআ‫͢ڈ‬Δɻ

39

6.3 likelihood ֬཰ີ౓෼෍

6.3 likelihood ֬཰ີ౓෼෍
લड़ͷࣄ৅બผΛ༻͍ͯ 300 ೥෼ͷ MC γϛϡϨʔγϣϯΛ༻͍ͯ֬཰ີ౓෼෍Λ࡞੒ͨ͠ɻ͜ͷαϯϓϧͰ͸χϡʔτϦϊৼಈͷߟྀ͸͞Ε͍ͯͳ͍ɻ࡞੒ͨ֬͠཰ີ౓෼෍ΛҎԼʹࣔͨ͠ɻ౷‫ʹܭ‬ΑΔ෼෍͕͹Β͖͕ͭখ
͘͞ͳΔΑ͏ʹɺશͯͷ෼෍ʹ͍ͭͯ 10 Ϗϯʹௐઅͨ͠ɻͨͩ͠தੑࢠ਺෼෍ʹ͍ͭͯ͸લड़ͷΑ͏ʹɺCCQE
൓Ԡͱ CC nonQE ൓ԠͰ෼෍͕ҟͳΔͨΊ͜ΕΛ۠ผͯ֬͠཰ີ౓Λ‫͢ࢉܭ‬Δඞཁ͕͋ΔɻͦͷͨΊʹɺ1 Ϧϯάࣄ৅Ͱ͸่յిࢠ਺ = 0, 1 ͷ৔߹ͱ่յిࢠ਺ ≥ 2 ͷ৔߹ʹ෼͚ͯ෼෍Λ࡞੒ͨ͠ɻ·ͨϚϧνϦϯάࣄ৅ͷ৔߹ʹ͸ɺ߹‫ܭ‬ӡಈྔ 5.0 GeV Ҏ্ɺͱ 5.0 GeV ະຬͷࣄ৅ʹ෼͚ͯ෼෍Λ࡞੒ͨ͠ɻ
(a)

(b)

ਤ 6.1

1 Ϧϯάࣄ৅ͷΠϯϓοτதੑࢠ਺෼෍ νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷதੑࢠ෼෍ɻ(a) ่յిࢠ਺ = 0,
1 (b) ่յిࢠ਺ ≥ 2

(a)

(b)

ਤ 6.2 ϚϧνϦϯάࣄ৅ͷΠϯϓοτதੑࢠ਺෼෍ νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷதੑࢠ෼෍ɻ(a) ߹‫ܭ‬ӡಈྔ

< 5.0 GeV (b) ߹‫ܭ‬ӡಈྔ ≥ 5.0 GeV

40

ୈ6ষ
(a)

likelihood ๏ʹΑΔ νµ /ν¯µ ࣝผ(b)ਤ 6.3 νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷΠϯϓοτ่յిࢠ਺෼෍ɻ(a) 1 Ϧϯάࣄ৅ (b) ϚϧνϦϯάࣄ৅

(a)

(b)

ਤ 6.4 νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷΠϯϓοτϛϡʔΦϯ่յ࣌ؒ෼෍ɻ(a) 1 Ϧϯάࣄ৅ (b) ϚϧνϦϯάࣄ৅

(a)

(b)

ਤ 6.5 νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷ่յిࢠώοτ਺෼෍ɻ(a) 1 Ϧϯάࣄ৅ (b) ϚϧνϦϯάࣄ৅41

6.4 ֤ࣄ৅ͷΠϯϓοτύϥϝʔλ
(a)

(b)

ਤ 6.6

νµ (੨ઢ)ɺν¯µ (੺ઢ) ࣄ৅ຖͷ (a) શӡಈྔʹର͢Δԣํ޲ӡಈྔͷׂ߹ (b) Ϧϯά਺

6.4 ֤ࣄ৅ͷΠϯϓοτύϥϝʔλ֬཰ີ౓෼෍ͱͯ͠ಡΈࠐΉΠϯϓοτύϥϝʔλͷ਺ͱछྨ͸Ϧϯάͷ਺ͱલड़ͷ primary ϛϡʔΦϯ༝དྷͷ่յిࢠબผʹద߹่ͨ͠յిࢠީิ͕͋Δ͔ͳ͍͔ʹΑܾͬͯΊɺද 6.1 ʹ͜ΕΛ·ͱΊͨɻྫ͑͹Ϧϯάͷ਺͕̍ͭͰ่յిࢠީิΛ࣋ͭࣄ৅͸ɺϛϡʔΦϯ่յ࣌ؒɺ่յిࢠ਺ώοτ N50 ਺ɺதੑࢠ਺ɺ่յిࢠ਺ͷ̐ͭͷ֬཰ີ౓෼෍ΛಡΈࠐΉɻதੑࢠ਺ͷ෼෍ʹ͍ͭͯ͸ 1 Ϧϯάࣄ৅Ͱ่յిࢠ਺ = 0 ·ͨ͸ 1 ͷ৔߹ʹ͸ਤ

6.1(a) Λɺ ่յిࢠ਺ ≥2 ͷ৔߹ʹਤ 6.1(b) ΛಡΈࠐΈɺϚϧνϦϯάࣄ৅ͰϦϯά߹‫ܭ‬ӡಈྔ͕ 5.0 GeV ະຬͷ৔߹ʹਤ 6.2(a) Λɺ5.0 GeV Ҏ্ͷ৔߹ʹਤ 6.2(b) ΛͦΕͧΕಡΈࠐΉɻ·ͨ SK-I ∼SK-III Ͱ͸தੑࢠ਺ͷ৘ใ͕࢖͑ͳ͍͜ͱΛߟྀͯ͠શͯͷࣄ৅ʹ͍ͭͯ֬཰ີ౓෼෍ͱͯ͠தੑࢠ਺෼෍ΛಡΈࠐ·ͳ͍৔߹ͷ likelihood‫ࢉܭ‬΋߹Θͤͯߦ͏ɻ
ද 6.1

Likelikelihod ‫͍༻ʹࢉܭ‬ΔΠϯϓοτύϥϝʔλͷ·ͱΊ

1 ϦϯάϛϡʔΦϯ༝དྷͷ่յిࢠ͕͋Δ͔ʁ͋Δ

ͳ͍ϚϧνϦϯά
͋Δͳ͍ϛϡʔΦϯ่յ࣌ؒ

!

!

่յిࢠώοτ਺

!

!

தੑࢠ਺

!

!

!

!

่յిࢠ਺

!

!

!

!

ԣํ޲ӡಈྔ

!

!

Ϧϯά਺

!

!

6

4

Πϯϓοτͷ਺

4

2

42

ୈ6ষ

likelihood ๏ʹΑΔ νµ /ν¯µ ࣝผ

6.5 3 ੈ୅େ‫ؾ‬χϡʔτϦϊৼಈΛߟྀٖͨ͠ࣅσʔλΛ༻͍ͨ νµ /ν¯µ ࣝผͷධՁ։ൃͨ͠ νµ /ν¯µ ࣝผΛ 3 ੈ୅χϡʔτϦϊৼಈΛߟྀٖͨ͠ࣅσʔλαϯϓϧΛ༻͍ͯධՁ͢Δɻٖࣅσʔλͷ࡞੒ʹ͸ 200 ೥෼ͷ MC Λ༻͍ͨɻ͜Ε͸֬཰ີ౓෼෍࡞੒ʹ༻͍ͨαϯϓϧͱ͸ಠཱͨ͠αϯϓϧͰ͋Δɻ͜ͷαϯϓϧʹ‫ޙ‬ड़ͷৼಈύϥϝʔλʹΑΔॏΈ෇͚Λߦ͏͜ͱͰɺχϡʔτϦϊৼಈΛಋೖ͢Δɻ͜ͷαϯϓϧ͸࣮ࡍͷσʔλͱಉ༷ʹѻ͏͜ͱ͕Ͱ͖ɺͳ͓͔ͭ MC ͷਅͷ৘ใ΋֬ೝ͢Δ͜ͱ͕Ͱ͖ΔͷͰղੳͷੑೳධՁʹ࠷ద
Ͱ͋Δɻ͜͜Ͱ͸ likelihood ‫ʹࢉܭ‬Αͬͯ‫ٻ‬Ίͨ ∆L ͷ෼෍Λਅͷ νµ , ν¯µ ʹ͍ͭͯͦΕͧΕ֬ೝࣝ͠ผੑೳΛ֬
ೝ͢Δɻ

6.5.1 χϡʔτϦϊৼಈύϥϝʔλ༻͍Δ MC αϯϓϧʹ͸χϡʔτϦϊৼಈ͸ߟྀ͞Ε͍ͯͳ͍ͨΊɺ࣮ࡍͷσʔλͱಉ༷ʹѻ͏ͨΊԼ‫ه‬ͷࣜͷχϡʔτϦϊৼಈύϥϝʔλΛԾఆ͠ɺશͯͷࣄ৅ʹ͍ͭͯॏΈ෇͚Λ͢Δ͜ͱͰৼಈٖͨ͠ࣅσʔλαϯϓϧΛ
࡞੒͢Δɻ͜ΕΒͷ஋͸ܾఆ͞Ε͍ͯͳ͍͕ɺ͜Ε·ͰͷχϡʔτϦϊৼಈ࣮‫ݧ‬ͷ݁Ռ͔ΒಘΒΕͨϕετϑΟοτͷ஋Λ༻͍͍ͯΔɻ

sin2 θ12 = 0.309(6.4)

sin θ13 = 0.025(6.5)

sin2 θ23 = 0.50

(6.6)∆m221 = 7.49 × 10−5

(6.7)

2

∆m232 = ±2.44 × 10−3
δCP = 0

(6.8)
(6.9)

͜͜Ͱ ∆m223 ͷ஋͕ਖ਼ͷ৔߹ʹਖ਼ৗ֊૚ (NH)ɺෛͷ৔߹ʹ‫֊ٯ‬૚ (IH) Ͱ͋Δɻ∆L ෼෍Λ࡞੒͢Δࡍ͸ਖ਼ৗ֊૚ΛԾఆͯ͠ਖ਼ͷ஋Λ༻͍Δɻ

6.5.2 େ‫ؾ‬χϡʔτϦϊٖࣅσʔλࣄ৅બ୒ٖࣅσʔλΛ࣮ࡍͷଌఆσʔλͱಉ༷ʹղੳ͢ΔͨΊʹɺ‫ط‬ଘͷେ‫ؾ‬χϡʔτϦϊσʔλղੳʹ࢖ΘΕ͍ͯΔࣄ
৅બผ৚݅Λ༻͍Δɻ͜ͷ৚݅Ͱબ͹Εͨࣄ৅ΛҰൠʹ µ-like FC αϯϓϧͱ‫Ϳݺ‬ɻࣄ৅બผ‫ޙ‬ͷαϯϓϧʹ͸ νµ ,

ν¯µ ͷଞʹ NC ࣄ৅ νe , ν¯e ࣄ৅ͳͲͷόοΫάϥ΢ϯυࣄ৅͕‫·ؚ‬ΕΔɺ͜ΕΒΛ·ͱΊͯͦͷଞͷࣄ৅ (Other) ͱ͍ͯ͠Δɻ• น͔ΒͷϛϡʔΦϯͷ‫ ≤ ཭ڑ‬200 [cm]• ֎ਫ૧Ͱͷώοτ਺ < 16 [hits]• ཻࢠࣝผ (PID) ʹΑΔχϡʔτϦϊϑϨʔόʔͷಛఆ࠷΋ΤωϧΪʔͷେ͖͍Ϧϯά µ-like• ՄࢹΤωϧΪʔ (visible energy) > 30 MeV• multi-GeV ࣄ৅બ୒1 Ϧϯάࣄ৅ ՄࢹΤωϧΪʔ > 1.33 GeVϚϧνϦϯάࣄ৅ ՄࢹΤωϧΪʔ > 0.6 GeV , ϛϡʔΦϯӡಈྔ > 0.6 GeV/c

43

6.6 ∆L ෼෍

6.6 ∆L ෼෍ࣄ৅બผΛ௨աͨ͠αϯϓϧΛ༻͍ͯɺlikelihood ‫ࢉܭ‬Λߦ͍ɺ∆L ෼෍Λ࡞੒͢Δɻਤ 6.7 ͸ 1 Ϧϯάࣄ৅ɺਤ

6.8 ͸ϚϧνϦϯάࣄ৅ͷ߹‫ܭ‬ӡಈྔ ≥ 1.33 GeV ͷࣄ৅ɺਤ 6.8 ͸ϚϧνϦϯάࣄ৅ͷ߹‫ܭ‬ӡಈྔ < 1.33 GeV ͷࣄ৅ʹ͍ͭͯͷ ∆L ෼෍Ͱ͋ΔɻϚϧνϦϯάࣄ৅ʹؔͯ͠͸Πϯϓοτύϥϝʔλͷ෼෍ͷ࡞੒ͷͨΊʹϦϯά

߹‫ܭ‬ӡಈྔ > 1.33 GeV Ҏ্ͷࣄ৅Λબ୒͍ͯ͠ΔͨΊɺಉ͡৚݅Ͱͷ෼෍ͱͦͷଞͷ෼෍Λ۠ผͯ͠෼෍ʹ͍ͯ͠Δɻ·ͨͦΕͧΕʹ͍ͭͯ (a) Πϯϓοτʹதੑࢠ਺෼෍Λ༻͍Δ৔߹ɺ(b) Πϯϓοτʹதੑࢠ਺෼෍Λ༻͍ͳ͍৔߹ɺΛൺֱͯ͠ࡌͤͯ͋Δɻશͯͷ෼෍ʹ͍ͭͯਤதͷ੨ઢ͕ਅͷ νµ ࣄ৅ɺ੺ઢ͕ਅͷ ν¯µ ࣄ৅ɺࢵઢ͕ͦͷଞͷࣄ৅Ͱ͋Δɻ
(a)

ਤ 6.7

(b)

1 Ϧϯάࣄ৅ͷ ∆L ෼෍ɻνµ ࣄ৅ (੨ઢ)ɺν¯µ ࣄ৅ (੺ઢ)ɺͦͷଞͷࣄ৅ (ࢵઢ) ຖʹ෼෍Λ͍ࣔͯ͠Δɻ(a) શͯͷΠϯϓοτΛ༻͍ͨ৔߹ (b) Πϯϓοτʹதੑࢠ਺Λ༻͍ͳ͍৔߹ Χοτ஋ ∆L = 0.2 Λઃఆ͠ɺ͜ΕΑΓ ∆L ͕ߴ͍ࣄ৅Λ νµ -like, ௿͍ࣄ৅Λ ν¯µ -like ͱ͢Δɻ

(a)

(b)

ਤ 6.8 ϚϧνϦϯά (Ϧϯά߹‫ܭ‬ӡಈྔ > 1.33 GeV) ࣄ৅ͷ ∆L ෼෍ɻνµ ࣄ৅ (੨ઢ)ɺν¯µ ࣄ৅ (੺ઢ)ɺͦͷଞͷࣄ৅ (ࢵઢ) ຖʹ෼෍Λ͍ࣔͯ͠Δɻ(a) શͯͷΠϯϓοτΛ༻͍ͨ৔߹ (b) Πϯϓοτʹதੑࢠ਺Λ༻͍ͳ͍৔߹ ʹ͍ͭͯΧοτ஋ ∆L = -0.8 Λઃఆ͠ɺ͜ΕΑΓ ∆L ͕ߴ͍ࣄ৅Λ νµ -like, ௿͍ࣄ৅Λ ν¯µ -like ͱ͢Δɻ

44

ୈ6ষ
(a)

likelihood ๏ʹΑΔ νµ /ν¯µ ࣝผ(b)ਤ 6.9 ϚϧνϦϯά (Ϧϯά߹‫ܭ‬ӡಈྔ ≤ 1.33 GeV) ࣄ৅ͷ ∆L ෼෍ɻνµ ࣄ৅ (੨ઢ)ɺν¯µ ࣄ৅ (੺ઢ)ɺͦͷଞͷࣄ৅ (ࢵઢ) ຖͷ෼෍ɻ(a) શͯͷΠϯϓοτΛ༻͍ͨ৔߹ (b) Πϯϓοτʹதੑࢠ਺Λ༻͍ͳ͍৔߹ ʹ͍ͭͯΧοτ஋ ∆ L = -0.8 Λઃఆ͠ɺ͜ΕΑΓ ∆ L ͕ߴ͍ࣄ৅Λ νµ -like, ௿͍ࣄ৅Λ ν¯µ -like ͱ͢Δɻ

1 Ϧϯάࣄ৅ʹ͍ͭͯ͸ ∆L Χοτ஋Λ ∆L = 0.2 ʹઃఆ͠ɺ∆L ≥ 0.2 ͷࣄ৅Λ νµ -likeɺ∆L < 0.2 ͷࣄ৅Λν¯µ -like ͱ͢Δɻಉ༷ʹϚϧνϦϯάࣄ৅ʹؔͯ͠͸Χοτ஋Λ ∆L = −0.8 ʹઃఆ͍ͯ͠Δɻ͜ͷΧοτ஋ʹ͍ͭͯ͸ৼಈΛ͔͚͍ͯͳ͍ MC αϯϓϧʹ͍ͭͯಉ༷ʹ ∆L ෼෍Λ࡞੒͠ɺࣝผੑೳ͕ߴ͘ɺ͔ͭ෼෍ͷҧ͍ʹΑΔࣝผੑೳͷ‫ܥ‬౷‫͕ࠩޡ‬খ͘͞ͳΔΑ͏ͳ஋Λ͋Β͔͡ΊબΜͰ͍Δɻ‫ܥ‬౷‫ࠩޡ‬Λ‫ݮ‬Βͨ͢ΊʹɺΧοτ஋पลͷ∆L Λ࣋ͭࣄ৅Λআ‫͢ڈ‬Δͱ͍͏ํ๏΋͋Δ͕ɺࠓճ͸શͯͷࣄ৅Λ νµ ·ͨ͸ ν¯µ ͱͯ͠બ୒͢ΔΑ͏ͳΧοτ஋Λઃఆ͍ͯ͠Δɻ

6.6.1 νµ /ν¯µ ࣝผͷੑೳධՁ∆L ͷ஋ʹΑͬͯબ୒͞Εͨ νµ -like ࣄ৅ͱ ν¯µ -like ࣄ৅ΛͦΕͧΕਅͷ৘ใͱൺ΂Δ͜ͱͰࣝผੑೳΛධՁ͢
ΔɻධՁͷ؆୯ͷͨΊʹ purity ͱ eﬃciency Λಋೖ͢Δɻpurity ͱ eﬃciency ͷఆٛΛҎԼʹࣔ͢ɻCCνµ (CCν¯µ , others) ࣄ৅਺νµ (ν¯µ ) − like શࣄ৅਺(6.10)

෼฼ͷ͏ͪνµ (ν¯µ ) − like ͱ൑ఆ͞Εͨࣄ৅਺CCνµ (CCν¯µ ) શࣄ৅਺(6.11)

purity =eﬃcincy =࣮ࡍͷղੳͰ͸ඈདྷͨ͠χϡʔτϦϊͷछྨ͸෼͔Βͳ͍ͷͰ νµ (ν¯µ ) -like ͱ൑ఆͨ͠ࣄ৅ͷ purity ͷߴ͕ࣝ͞ผੑೳͱͯ͠ॏཁͰ͋Δɻද 6.2, 6.3 ʹ 1 ϦϯάɺϚϧνϦϯάࣄ৅ʹ͓͚Δ purity ͷ஋ΛͦΕͧΕ·ͱΊͨɻ͜͜Ͱͷ‫ࠩޡ‬͸౷‫͋Ͱࠩޡܭ‬Δɻࣝผલͷ νµ ͱ ν¯µ Ͱ͸χϡʔτϦϊ൓Ԡஅ໘ੵͷҧ͍͔Β νµ ͷࣄ৅਺͕ଟ͘ͳͬ
͍ͯΔɻ·ͨόοΫάϥ΢ϯυࣄ৅ͷׂ߹͸ϚϧνϦϯάࣄ৅Ͱ૿Ճ͍ͯ͠Δɻ

1 Ϧϯάࣄ৅Ͱ͸ɺதੑࢠ਺෼෍ΛΠϯϓοτʹ༻͍ͨ৔߹ɺࣝผલͷ µ-like ࣄ৅ʹର͢Δׂ߹ (ຊ‫Ͱڀݚ‬͸͜ΕΛࣝผલͷ purity ͱ͢Δ) ͸ 62.4% ͩͬͨ νµ ࣄ৅ ͸ࣝผ‫ ޙ‬77.1±0.4% ʹͳΓɺν¯µ purity ͸ࣝผલ 37.2% ͔Βࣝผ‫ ޙ‬45.0±0.3% ͱͳΓɺͦΕͧΕ 14.7±0.4% ɺ7.8±0.3% purity ͕޲্ͨ͠ɻதੑࢠ਺෼෍Λ༻͍ͳ͔ͬͨ
৔߹͸ࣝผ‫ޙ‬ɺνµ ͕ 74.0±0.4%ɺν¯µ ͕ 44.8±0.3 % ͱͳͬͨɻதੑࢠ਺෼෍Λ༻͍Δ͜ͱͰɺ༻͍ͳ͍৔߹ʹൺ΂ͯɺpurity ͸ νµ Ͱ 3.1±0.8% ͷ޲্͠ɺν¯µ ͷ޲্͸ͳ͔ͬͨɻ

ϚϧνϦϯάࣄ৅Ͱ͸ɺதੑࢠ਺෼෍ΛΠϯϓοτʹ༻͍ͨ৔߹ɺࣝผલ 73.5% ͩͬͨ νµ purity ͸ࣝผ‫ޙ‬76.4±0.3%, ν¯µ purity ͸ࣝผલ 22.0% ͔Βࣝผ‫ ޙ‬34.7±0.5% ͱͳΓɺͦΕͧΕ 2.9±0.3%, 12.7±0.5% purity ͕45

6.6 ∆L ෼෍޲্ͨ͠ɻதੑࢠ਺෼෍Λ༻͍ͳ͔ͬͨ৔߹͸ࣝผ‫ޙ‬ɺνµ ͕ 76.4±0.3%, ν¯µ ͕ 34.3±0.5% ͱͳΓɺͦΕͧΕ

2.9±0.3%, 12.7±0.5% purity ͕޲্ͨ͠ɻϚϧνϦϯάͰ͸தੑࢠ਺෼෍ʹΑͬͯࣝผੑೳ͸޲্͠ͳ͔ͬͨɻ
தੑࢠΛ์ग़͢Δաఔ͕χϡʔτϦϊ૬‫༻࡞ޓ‬Ҏ֎ʹ΋ଟ͘ɺνµ ͱ ν¯µ ͷҧ͍͕‫͑ݟ‬ਏ͘ͳ͍ͬͯΔ͜ͱ͕ͦͷཁҼͩͱߟ͑ΒΕΔɻ
ද 6.4,6.5 ʹͦΕͧΕઌߦ‫Ͱڀݚ‬ͷ νµ /ν¯µ ࣝผ݁Ռ [2] ͱ νe /ν¯e ࣝผ݁Ռ [11] Λ·ͱΊͨɻ[2] Ͱ͸ 3 ੈ୅ৼಈΛߟྀͨ͠αϯϓϧɺ[11] Ͱ͸ 2 ੈ୅ৼಈΛߟྀͨ͠αϯϓϧ͕༻͍ΒΕ͍ͯΔɻ༻͍͍ͯΔαϯϓϧ͕ҧ͏ͨΊ୯७ͳൺֱ͸ग़དྷͳ͍͕ɺઌߦ‫ʹڀݚ‬ൺ΂ͯ΋ࣝผੑೳ͸ྼ͍ͬͯͳ͍ɻಛʹࣄ৅͕ෳࡶͰࣝผ͕೉͍͠ͱ͞Ε͍ͯͨ µ-like ϚϧνϦϯάࣄ৅ʹ͓͍ͯɺຊ‫ॳͰڀݚ‬Ίͯߴ͍ਫ४ͷࣝผੑೳΛ‫͛ڍ‬Δ͜ͱʹ੒ޭͨ͠ɻ
ද 6.2 1 Ϧϯάࣄ৅ʹ͓͚Δ νµ /ν¯µ ࣝผ݁Ռͷൺֱɻ஋͸ purity Λࣔ͢ɻ

1 Ϧϯάࣄ৅CC νµCC ν¯µOthersதੑࢠ਺෼෍Λνµ -like༻͍ͨ৔߹ν¯µ -like

77.1±0.4%22.2±0.4%

0.7±0.1%

தੑࢠ਺෼෍Λνµ -like༻͍ͳ͍৔߹ν¯µ -like

74.0±0.4%25.2±0.4%

0.9±0.1%ࣝผલµ-like

37.2%

0.4%

ද 6.3

54.7±0.3%

45.0±0.3%

55.0±0.3%

0.3%44.8±0.3%

62.4%

0.1%

ϚϧνϦϯάࣄ৅ʹ͓͚Δ νµ /ν¯µ ࣝผ݁Ռͷൺֱɻ஋͸ purity Λࣔ͢ɻϚϧνϦϯάࣄ৅CC νµCC ν¯µOthersதੑࢠ਺෼෍Λνµ -like༻͍ͨ৔߹ν¯µ -like

76.4±0.3%

18.4±0.2%

5.3±0.1%

தੑࢠ਺෼෍Λνµ -like༻͍ͳ͍৔߹ν¯µ -like

76.4±0.3%

18.3±0.2%

5.3±0.1%ࣝผલµ-like63.6±0.6%
64.0±0.5%73.5%

34.7±0.5%34.3±0.5%
22.0%

1.6±0.1%
1.7±0.1%
4.5%

ද 6.4 ઌߦ‫[ ڀݚ‬2] Ͱͷ νµ /ν¯µ ࣝผ݁Ռɻ஋͸ purity Λࣔ͢ɻ

ࣝผ‫ޙ‬
ࣝผલ

1 Ϧϯάࣄ৅CC νµCC ν¯µOthersνµ -like

67.4±0.3%31.8±0.3%

0.8%

62.3%

36.9%

ν¯µ -likeµ-like49.8±0.5%49.2±0.5%

0.9 ±0.1%
0.9%

ද 6.5 ઌߦ‫[ ڀݚ‬11] Ͱͷ νe /ν¯e ࣝผ݁Ռɻ஋͸ purity Λࣔ͢ɻ

1 Ϧϯάࣄ৅

ϚϧνϦϯάࣄ৅CC νe

CC ν¯eOthersνe -like

62.8%

10.8%

26.3%

ν¯e -like

55.9%

36.7%

7.4%

ࣝผલ e-like

57.6%

30.6%

12.0%

νe -like

59.4%

17.9%

22.5%

ν¯e -like

53.1%

21.0%

25.9%

ࣝผલ e-like

56.1%

19.5%

24.5%

47

ୈ7ষ

࣭ྔ֊૚ੑܾఆ‫౓ײ‬ͷߟ࡯ࣝผͨ͠ νµ -like, ν¯µ -like ࣄ৅Λ༻͍࣭ͨྔ֊૚ੑܾఆ‫౓ײ‬Λ‫ੵݟ‬΋Δɻਤ 1.3 ͷΑ͏ʹ νµ , ν¯µ ࣄ৅ͦΕͧΕͰχϡʔτϦϊৼಈͷৼΔ෣͍͕ਖ਼ৗ֊૚ (NH) ͱ‫֊ٯ‬૚ (IH) ͰҟͳΔͨΊɺ‫ੵݟ‬΋Γʹ͸ਤ 1.2 ͷΑ͏ͳΞοϓμ΢ϯൺΛ༻͍ͯ νµ -like ͱ ν¯µ -like αϯϓϧͦΕͧΕʹ͍ͭͯਖ਼ৗ֊૚ͱ‫֊ٯ‬૚ΛԾఆͨ͠৔߹ͰͷৼΔ෣͍ͷҧ͍Λ֬ೝ͢Δɻαϯϓϧ͸લষͰࣝผʹ༻͍ͨ 200 ೥෼ٙࣅσʔλαϯϓϧશͯΛ༻͍Δɻ‫؍‬ଌ‫ ؒظ‬200 ೥͸࣮‫ظݧ‬ؒͱͯ͠աଟͰ͋ΔΑ͏ʹ‫͡ײ‬Δ͕ɺ‫ݧ࣮ܧޙ‬ͷϋΠύʔΧϛΦΧϯσ࣮‫( ݧ‬HK) Ͱ͸༗ޮମੵ͕໿ 8.3 ഒʹ֦͕Δ༧ఆͰ͋ΓɺSK Ͱͷ 200 ೥෼αϯϓϧ͸ HK Ͱͷ໿ 24 ೥෼αϯϓϧͰ͋Δɻ͜Ε͸‫Ͱ·ࡏݱ‬ͷ SK ‫؍‬ଌ‫ؒظ‬ͱ΄΅ಉ౳Ͱ͋Γɺ‫࣮ݱ‬తͳαϯϓϧྔͰ͋Δͱ‫͑ݴ‬ΔɻSK-IV ‫؍‬ଌ‫ؒظ‬΍ HK ‫؍‬ଌ‫Ͱؒظ‬ͷ֊૚ੑܾఆ‫౓ײ‬Λ‫ݟ‬ੵ΋Δࡍʹ͸ɺ͜ͷ 200 ೥෼αϯϓϧʹ‫؍‬ଌ‫Ͱؒظ‬ॏΈΛ͚ͭͯར༻͢Δɻνµ -like αϯϓϧͱ ν¯µ -like αϯϓϧ͸
લষͰ։ൃͨ͠தੑࢠ਺෼෍Λ༻͍ͨ νµ /ν¯µ ࣝผʹΑͬͯಘΒΕͨαϯϓϧΛͦͷ··༻͍͍ͯΔɻ·ͨ νµ ͱ ν¯µͷΞοϓμ΢ϯൺ͕࣮ࡍʹ͸ͲͷΑ͏ͳ૿‫ݮ‬Λ͢Δ͔֬ೝ͢ΔͨΊʹ MC ਅͷ৘ใΛ༻͍ͯબΜͩ νµ ͱ ν¯µ ࣄ৅ʹ͍ͭͯ΋߹Θͤͯ֬ೝ͢Δɻ

7.1 ఱ௖֯෼෍ͱΞοϓμ΢ϯൺΞοϓμ΢ϯൺͱ͸ɺࣜ 7.1 ʹࣔ͞ΕΔΑ͏ͳχϡʔτϦϊͷ্޲͖ࣄ৅ͷ਺ͱԼ޲͖ࣄ৅ͷ਺ͷൺͰ͋Δɻ͜
͜Ͱ্޲͖ࣄ৅ͱ͸χϡʔτϦϊ͕஍‫಺ٿ‬෦Λ௨աͯ͠‫ݕ‬ग़‫ʹث‬ಧ͘ఱ௖֯ cos θ < −0.4, Լ޲͖ࣄ৅ͱ͸஍‫ٿ‬େ‫ؾ‬தΛ௨աͯ͘͠Δఱ௖֯ cos θ > 0.4 ͷ౸དྷํ޲Λ࣋ͭࣄ৅Ͱ͋Δɻ্޲͖ࣄ৅ͷχϡʔτϦϊ͸஍‫಺ٿ‬෦ͷ෺࣭ޮՌͷӨ‫ڹ‬Λड͚ɺਖ਼ৗ֊૚ (NH) ͱ‫֊ٯ‬૚ (IH) Ͱ νµ ͱ ν¯µ ͷࣄ৅਺ͷ૿‫ͳʹٯ͕޲ํݮ‬ΔͨΊɺ͜ͷൺΛ֬ೝ͢Δ͜ͱͰ࣭ྔ֊૚ੑ‫౓ײ‬Λେ·͔ʹਪఆ͢Δ͜ͱ͕Ͱ͖Δɻॎ࣠ΛR=(্޲͖ࣄ৅ͷ਺) − (Լ޲͖ࣄ৅ͷ਺)ɺ(্޲͖ࣄ৅ͷ਺) + (Լ޲͖ࣄ৅ͷ਺)(7.1)

ԣ࣠ΛશϦϯάͷ߹‫ܭ‬ӡಈྔʹͨ͠ 2 ࣍‫ݩ‬ϓϩοτΛΞοϓμ΢ϯਤͱ‫Ϳݺ‬ɻ͜͜Ͱͷ‫ࠩޡ‬๮͸֤ϏϯͰͷ౷‫ܭ‬Τϥʔ (∆Ri ) Ͱ͋Δɻ·ͨ͜ΕΒͷ஋͔Β‫ٻ‬Ί࣭ͨྔ֊૚ੑ‫౓ײ‬Λද͢ύϥϝʔλͱͯ͠ i ൪໨ͷϏϯͷ χ2i Λ࣍ͷΑ͏ʹఆٛ͢Δɻ

χ2i =

+

Ri [NH] − Ri [IH]
∆Ri

,2

(7.2)

͜͜Ͱ Ri [NH] ͕ਖ਼ৗ֊૚ΛԾఆͨ࣌͠ͷ i ൪໨ͷϏϯͷ R ͷ஋ɺRi [IH] ͕‫֊ٯ‬૚ΛԾఆͨ͠৔ͷ i ൪໨ͷϏϯͷ R ͷ஋Ͱ͋Γ ∆Ri ͕ i ൪໨ͷϏϯͷ Ri ͷ౷‫ܭ‬ΤϥʔͰ͋Δɻ֤Ϗϯʹରͯ͜͠ΕΛ‫͠ࢉܭ‬ɺχ2i ͷ૯࿨ χ2 ΛͦΕͧΕͷαϯϓϧͰͷ࣭ྔ֊૚ੑ‫౓ײ‬Λ‫ੵݟ‬΋ͬͨ஋ͱͯ͠ධՁ͢Δɻ

48

ୈ7ষ

7.2

࣭ྔ֊૚ੑܾఆ‫౓ײ‬ͷߟ࡯µ-like ࣄ৅ͷΞοϓμ΢ϯൺҎԼʹ 1 Ϧϯάࣄ৅ͱϚϧνϦϯάࣄ৅ʹ͍ͭͯͦΕͧΕࣝผલͱࣝผ‫ ޙ‬νµ -like, ν¯µ -like ࣄ৅ͷΞοϓμ΢ϯ
ਤΛࣔ͢ɻϏϯ͸ 1 Ϧϯάࣄ৅Ͱ 3 Ϗϯ (1.0-2.5 GeV, 2.5-5.0 GeV, >5.0 GeV)ɺϚϧνϦϯάࣄ৅Ͱ 4 Ϗϯ ( -1.0

GeV, 1.0-2.5 GeV, 2.5-5.0 GeV, >5.0 GeV) ʹ෼͚Δɻ͜Ε͸ [11] Λࢀߟʹͨ͠ɻਤதͷࠇઢ͸ਖ਼ৗ֊૚ (NH)ɺ੺
࢛֯͸‫֊ٯ‬૚ (IH) Λද͍ͯ͠Δɻ෺࣭தͷχϡʔτϦϊৼಈΛߟྀ͢ΔͱɺҰൠʹ্޲͖ࣄ৅ͷ৔߹ʹਖ਼ৗ֊૚Ͱν¯µ ͷׂ߹͕૿͑ɺ‫֊ٯ‬૚Ͱ νµ ͷׂ߹͕૿͑Δɻ

7.2.1 ࣝผલ µ-like ࣄ৅ࣝผલͷΞοϓμ΢ϯਤ͸ҎԼͷΑ͏ʹͳΔɻ7.1(a) ͕ 1 Ϧϯάࣄ৅ɺ7.1(b) ͕ϚϧνϦϯάࣄ৅Ͱ͋Δɻνµ ͱν¯µ ͕ࠞࡏͨ͠αϯϓϧͰ͸֊૚ʹΑΔΞοϓμ΢ϯൺͷ͕ࠩখ͍͞ɻ
(a)

(b)

ਤ 7.1 ࣝผલ µ-like ࣄ৅ͷΞοϓμ΢ϯਤɻਖ਼ৗ֊૚ (NH)(ࠇઢ)ɺ‫֊ٯ‬૚ (IH)(੺࢛֯) ͰͷΞοϓμ΢ϯਤͷൺֱɻ(a) 1 Ϧϯάࣄ৅ (b) ϚϧνϦϯάࣄ৅ɻ

7.2.2 ਅͷ৘ใΛ༻͍ͯࣝผͨ͠৔߹ͷ݁ՌॳΊʹɺࣝผʹ MC ਅͷ৘ใΛ༻͍ͯ νµ ͱ ν¯µ ࣄ৅ΛબΜͩ৔߹ͷΞοϓμ΢ϯൺΛ‫ͨ͠ࢉܭ‬ɻҎԼʹͦͷΞοϓμ΢ϯਤͱ χ2 ͷ஋Λ·ͱΊͨදΛ͍ࣔͯ͠ΔɻΞοϓμ΢ϯਤ͸ 1 Ϧϯάࣄ৅͕ਤ 7.2ɺϚϧνϦϯάࣄ৅͕ਤ

7.3 Ͱ͋Δɻ͜ΕΛ‫ݟ‬Δͱਅͷ νµ ͱ ν¯µ ͸‫ʹ͍ޓ‬Ξοϓμ΢ϯൺͷ૿‫ʹ޲ํٯ͕޲ํݮ‬ಈ͖ɺࠞࡏͨ͠ µ-like αϯϓϧʹൺ΂ͯ֊૚ͷ͕ࠩ‫ݦ‬Ε͍ͯΔ͜ͱ͕෼͔Δɻ·ͨද 7.1 ͔Βࣝผ‫ޙ‬ͷ χ2 ͸ 1 Ϧϯάࣄ৅Ͱ χ2 = 3.454ɺϚϧνϦϯάࣄ৅Ͱ χ2 = 3.508 Ͱ͋Γɺಛʹ νµ ʹൺ΂ͯ ν¯µ ͷํ͕֊૚ܾఆ‫͑࢕͕ͱ͍͜ߴ͕౓ײ‬Δɻ͜ΕΛࣝผੑ
ೳ 100% ͷ৔߹ͷ‫ج‬४ͱ࣮ͯ͠ࡍʹຊ‫ࣝͰڀݚ‬ผͨ͠ νµ -like αϯϓϧɺν¯µ -like αϯϓϧͷ֊૚ੑܾఆਫ਼౓Λߟ࡯
͢Δɻ

49

7.2 µ-like ࣄ৅ͷΞοϓμ΢ϯൺද 7.1 MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠৔߹ͷ χ2 ஋ͷ݁Ռ

1 Ϧϯά
ࣝผલ

ਅͷ νµ

ϚϧνϦϯάਅͷ ν¯µ< 1.0GeVਅͷ νµਅͷ ν¯µ

0.077

0.051

0.065

1.0-2.5GeV

0.000

0.129

0.199

0.080

0.096

1.169

2.5-5.0GeV

0.176

0.113

1.190

0.005

0.176

0.760

> 5.0GeV∼

0.110

1.22

0.608

0.172

0.798

0.394

1.457

1.997

1.120

2.388

߹‫ܭ‬

(a)

ࣝผલ

0.287

3.454

0.334

3.508

(b)

ਤ 7.2

MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠ µ-like 1 Ϧϯάࣄ৅Ͱͷɺਖ਼ৗ֊૚ (NH)(ࠇઢ)ɺ‫֊ٯ‬૚ (IH)(੺࢛֯)ͷΞοϓμ΢ϯਤͷൺֱɻ(a) νµ -like ࣄ৅ (b) ν¯µ -like ࣄ৅ɻ

(a)

ਤ 7.3

(b)

MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠ µ-like ϚϧνϦϯάࣄ৅Ͱͷɺਖ਼ৗ֊૚ (NH)(ࠇઢ)ɺ‫֊ٯ‬૚ (IH)(੺࢛֯) ͷΞοϓμ΢ϯਤͷൺֱɻ(a) νµ -like ࣄ৅ (b) ν¯µ -like ࣄ৅ɻ

50

ୈ7ষ

࣭ྔ֊૚ੑܾఆ‫౓ײ‬ͷߟ࡯

7.2.3 ຊ‫Ͱڀݚ‬։ൃͨ͠ νµ /ν¯µ ࣝผΛಋೖͨ݁͠Ռ
ਤ 7.4 ʹ 1 Ϧϯάࣄ৅ɺਤ 7.5 ʹϚϧνϦϯάࣄ৅ͷΞοϓμ΢ϯਤΛͦΕͧΕࣔͨ͠ɻ200 ೥෼αϯϓϧͰ΋౷‫਺ܭ‬͸΍͸Γେ͖͘ͳ͘ɺਖ਼ৗ֊૚ͱ‫֊ٯ‬૚ͷҧ͍ʹΑͬͯ‫ݦ‬ΕΔΞοϓμ΢ϯൺͷࠩ͸౷‫ࠩޡܭ‬ൣғ಺ʹཹ·͍ͬͯΔɻ͔͠͠ɺಛʹ౷‫਺ܭ‬ͷগͳ͍ 1 Ϧϯά 5.0 GeV Ҏ্ͷϏϯҎ֎ͷϏϯͰ͸ɺਅͷ νµ , ν¯µ ΛબΜͩ৔߹ͷΞοϓμ΢ϯൺͷ૿‫ͱ޲ํݮ‬ಉ͡ํ޲ʹಈ͍͍ͯΔͨΊɺνµ /ν¯µ ࣝผʹΑΔࣝผ͸ҰఆͷޮՌ͕͋Δͱ‫͑ݴ‬Δɻ
ද 7.2 ʹΞοϓμ΢ϯਤͷ֤Ϗϯຖͷ χ2 ͷ஋Λ·ͱΊͨɻ1 Ϧϯάࣄ৅Ͱ χ2 ͷ஋͸ࣝผલ 0.287 ͔Βࣝผ‫ޙ‬

0.922, ϚϧνϦϯάࣄ৅Ͱࣝผલ 0.334 ʹର͠ɺ0.884 ʹͳͬͨɻνµ /ν¯µ ࣝผʹΑͬͯ࠷େͰɺࣝผલ µ-like αϯϓϧʹൺ΂ͯɺ1 Ϧϯάࣄ৅Ͱ໿ 3.2 ഒɺϚϧνϦϯάࣄ৅Ͱ͸໿ 2.6 ഒɺµ-like ࣄ৅ͷ࣭ྔ֊૚ੑ‫্޲౓ײ‬ͷՄೳੑ͕͋Δɻ
·ͨ 1 Ϧϯάࣄ৅ 5.0 GeV Ҏ্ͷྖҬͰ૿‫ͨͬͳʹٯ͕޲ํݮ‬ཁҼͱͯ͠౷‫ܭ‬ͷ༳Β͗ͷଞʹɺ͜ͷྖҬͰͷνµ ͱ ν¯µ ͷৼΔ෣͍͕֬཰ີ౓෼෍Ͱ༧૝ͨ͠΋ͷͱҟͳͬͨৼΔ෣͍Λͨ͠ͱߟ͑ΒΕΔɻ1 Ϧϯάࣄ৅͸ 1 Ϧϯάࣄ৅͸४஄ੑࢄཚ (QE) ࣄ৅ͱඇ஄ੑࢄཚ (nonQE) ࣄ৅͕ࠞࡏ͓ͯ͠Γɺ֬཰ີ౓ؔ਺͸௿ΤωϧΪʔଆͰࣄ৅਺ͷଟ͍ QE ࣄ৅ͷ෼෍ʹґΔͱ͜Ζେ͖͍ͨΊ nonQE ࣄ৅ͷׂ߹͕૿͑ΔߴΤωϧΪʔྖҬͰࣝผੑೳ͕௿
Լͯ͠͠·ͬͨɻ֤ΤωϧΪʔϏϯຖʹ֬཰ີ౓Λ‫͢ࢉܭ‬Δ͜ͱͰɺ֤ྖҬͰͷ νµ ͱ ν¯µ ͷৼΔ෣͍ΛΑΓਖ਼֬ʹ‫ه‬ड़ͯ͠ likelihood ‫ͦʹࢉܭ‬ΕͧΕ༻͍Δ͜ͱͰࣝผੑೳΛվળ͢Δ͜ͱ͕Ͱ͖Δͱߟ͑ΒΕΔɻ
ද 7.2 νµ /ν¯µ ࣝผΛಋೖͨ͠ χ2 ஋ͷ݁Ռ

1 Ϧϯά
ࣝผલ

νµ -likeϚϧνϦϯάν¯µ -like< 1.0GeVνµ -likeν¯µ -like

0.077

0.028

0.055

1.0-2.5GeV

0.000

0.285

0.131

0.080

0.113

0.002

2.5-5.0GeV

0.176

0.012

0.197

0.005

0.038

0.370

> 5.0GeV

0.110

0.020

0.276

0.172

0.259

0.019

0.318

0.604

0.438

0.446

߹‫ܭ‬

0.287

0.922

(a)

ਤ 7.4

ࣝผલ

0.334

0.884

(b)

νµ /ν¯µ ࣝผΛಋೖͨ͠ µ-like 1 Ϧϯάࣄ৅Ͱͷɺਖ਼ৗ֊૚ (NH)(ࠇઢ)ɺ‫֊ٯ‬૚ (IH)(੺࢛֯) ͷΞοϓμ΢ϯਤͷൺֱɻ(a) νµ -like ࣄ৅ (b) ν¯µ -like ࣄ৅ɻ

51

7.3 e-like ࣄ৅ͷΞοϓμ΢ϯൺ
(a)

(b)

ਤ 7.5 νµ /ν¯µ ࣝผΛಋೖͨ͠ µ-like ϚϧνϦϯάࣄ৅Ͱͷਖ਼ৗ֊૚ (NH)(ࠇઢ)ɺ‫֊ٯ‬૚ (IH)(੺࢛֯) ͰͷΞοϓμ΢ϯਤͷൺֱɻ(a) νµ -like ࣄ৅ (b) ν¯µ -like ࣄ৅ɻ

7.3 e-like ࣄ৅ͷΞοϓμ΢ϯൺެࣜʹ༻͍ΒΕ͍ͯΔ e-like ࣄ৅ͱൺ΂ͯɺࣝผ‫ ޙ‬µ-like ࣄ৅͕ SK ʹ͓͚Δ֊૚ੑ‫Ͳʹ্޲౓ײ‬Ε΄Ͳߩ‫͢ݙ‬Δͷ͔֬ೝ͢ΔͨΊʹɺલষͰ༻͍ͨ΋ͷͱಉҰͷٖࣅσʔλαϯϓϧΛ࢖ͬͯ e-like ࣄ৅ʹ͍ͭͯͷΞοϓμ΢
ϯਤΛ࡞੒͠ɺχ2 ͷ஋Λ µ-like ࣄ৅ͱൺ΂Δɻ͜͜Ͱ͸ 1 Ϧϯάࣄ৅ɺϚϧνϦϯάͱ΋ʹ multi-GeV ࣄ৅Λબ
୒͢ΔɻϏϯ͸ 1 Ϧϯάࣄ৅Ͱ 4 Ϗϯ (1.33-2.5 GeV, 2.5-5.0 GeV, 5.0-10.0 GeV, 10.0-20.0 GeV)ɺϚϧνϦϯά
ࣄ৅Ͱ 3 Ϗϯ (1.33 GeV, 2.5-5.0 GeV, 5.0-20.0 GeV) ʹ෼͚Δɻ͜Ε͸ [11] Λࢀߟʹͨ͠ɻਤதͷࠇઢ͸ਖ਼ৗ֊૚ (NH)ɺ੺࢛֯͸‫֊ٯ‬૚ (IH) Λද͍ͯ͠Δɻ෺࣭தͷχϡʔτϦϊৼಈΛߟྀ͢ΔͱɺҰൠʹ্޲͖ࣄ৅ͷ৔߹ʹਖ਼ৗ֊૚Ͱ ν¯e ͷׂ߹͕૿͑ɺ‫֊ٯ‬૚Ͱ νe ͷׂ߹͕૿͑Δɻ

7.3.1 ࣝผલ e-like ࣄ৅ͷ݁Ռνe ͱ ν¯e Λࣝผ͍ͯ͠ͳ͍ e-like αϯϓϧͷΞοϓμ΢ϯਤΛࣔ͢ɻࠞࡏͨ͠ঢ়ଶͰ΋ਖ਼ৗ֊૚ͱ‫֊ٯ‬૚ͰͷΞοϓμ΢ϯൺʹ͕ࠩੜ͍ͯ͡Δ͜ͱ͕Θ͔Δɻ

52

ୈ7ষ
(a)

࣭ྔ֊૚ੑܾఆ‫౓ײ‬ͷߟ࡯(b)

ਤ 7.6 ࣝผલ e-like ࣄ৅ͷΞοϓμ΢ϯਤɻਖ਼ৗ֊૚ (NH)(ࠇઢ)ɺ‫֊ٯ‬૚ (IH)(੺࢛֯) ͰͷΞοϓμ΢ϯਤͷൺֱɻ(a) 1 Ϧϯάࣄ৅ (b) ϚϧνϦϯάࣄ৅ɻ

7.3.2 ਅͷ৘ใΛ༻͍ͯࣝผͨ͠৔߹ͷ݁Ռνe ͱ ν¯e Λਅͷ৘ใΛ༻͍ͯબΜͩ৔߹ͷ݁ՌΛҎԼʹࣔ͢ɻਤ 7.7, 7.8 ͷΞοϓμ΢ϯਤΛ‫ݟ‬Δͱ NH ͱ IH
ͷΞοϓμ΢ϯൺ͕େ͖͘ҟͳ͍ͬͯΔ͜ͱ͕෼͔Δɻ
(a)

ਤ 7.7

(b)

MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠ e-like 1 Ϧϯάࣄ৅ͰͷΞοϓμ΢ϯਤɻਖ਼ৗ֊૚ (NH)(ࠇઢ)ɺ‫֊ٯ‬૚(IH)(੺࢛֯) ͷൺֱɻ(a) νe -like ࣄ৅ (b) (ν¯e )-like ࣄ৅ɻ

53

7.3 e-like ࣄ৅ͷΞοϓμ΢ϯൺ
(a)

ਤ 7.8

(b)

MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠ e-like ϚϧνϦϯάࣄ৅ͰͷΞοϓμ΢ϯਤɻਖ਼ৗ֊૚ (NH)(ࠇઢ)ɺ‫ٯ‬֊૚ (IH)(੺࢛֯) Ͱͷൺֱɻ(a) νe -like ࣄ৅ (b) (ν¯e )-like ࣄ৅ɻද 7.3

MC ਅͷ৘ใΛ༻͍ͯࣝผͨ͠ e-like ࣄ৅ͷ χ2 ஋ͷ݁Ռ

1 ϦϯάϚϧνϦϯά

ࣝผલ

νe -likeν¯e -likeࣝผલνe -likeν¯e -like

1.33∼2.5GeV

0.002

0.565

1.361

0.044

0.648

0.831

2.5∼5.0GeV

0.647

10.75

9.316

2.231

10.73

5.759

5.0∼10.0GeV

0.999

26.05

24.00

10.0GeV∼

0.056

0.462

0.272

2.700

14.16

6.544

37.83

34.95

25.54

13.13

߹‫ܭ‬

1.704

72.78

4.975

38.67

7.3.3 νe /ν¯e ࣝผʹΑΔ݁Ռ
SK Ͱͷৼಈղੳʹ༻͍ΒΕ͍ͯΔ νe /ν¯e ࣝผΛಋೖͨ݁͠ՌΛҎԼʹࣔ͢ɻಛʹ νe -like αϯϓϧͷ 2.5 GeV Ҏ্Ͱਖ਼ৗ֊૚ͱ‫֊ٯ‬૚ͷ෼෍ͷ͕ࠩ‫ݦ‬ஶͰ͋Δɻ͔͠͠ϚϧνϦϯάࣄ৅Ͱ͸ࣝผલͱൺ΂ͯେ෯ͳ޲্͸‫ݟ‬ΒΕͳ͍ɻ͜Ε͸ਤ 1.2 ʹ‫ݟ‬ΒΕΔੑ࣭ͱಉ༷Ͱ͋Δɻ
ද 7.4 ʹ χ2 ͷ஋Λ·ͱΊͨɻ1 Ϧϯάࣄ৅Ͱࣝผલ 1.704 ͔Βࣝผ‫ ޙ‬5.115 ʹϚϧνϦϯάࣄ৅Ͱ͸ࣝผલ

2.891 ͔Βࣝผ‫ ޙ‬3.847 ʹ޲্͍ͯ͠Δɻ͜Ε͸ 1 Ϧϯάࣄ৅Ͱ໿ 3.0 ഒɺϚϧνϦϯάࣄ৅Ͱ͸໿ 1.3 ഒͷ্ঢ
཰Ͱ͋Δɻχ2 ͷ஋͸େ͖͍͕ਅͷ৘ใͰࣝผͨ݁͠Ռͱൺ΂Δͱ 1 ׂʹ΋ຬͨͳ͍ɻ͜ͷཁҼͱͯ͠ e-like ࣄ৅ʹ‫·ؚ‬Εͯ͠·͏ NC ࣄ৅΍ϛϡʔΦϯχϡʔτϦϊࣄ৅ͳͲͷόοΫάϥ΢ϯυࣄ৅͕ଟ͘‫·ؚ‬Ε νe ͱ ν¯e ͷੑ࣭Λअຐͯ͠͠·͏ͨΊͰ͋Δɻ[11] Ͱ͸ 1 Ϧϯά e-like ࣄ৅ʹ઎ΊΔόοΫάϥ΢ϯυࣄ৅ͷׂ߹ 12.0%ɺϚϧνϦϯά e-like ࣄ৅ʹ‫·ؚ‬ΕΔόοΫάϥ΢ϯυࣄ৅ͷׂ߹ 24.5% ͱ͞Ε͍ͯΔɻ͜ΕΒΛޮ཰Α͘෼཭͢Δ͜
ͱ͕೉͍ͨ͠Ίɺνe /ν¯e ࣝผੑೳ͸͋·Γߴ͘ͳ͍ɻ

54

ୈ7ষ
ද 7.4

࣭ྔ֊૚ੑܾఆ‫౓ײ‬ͷߟ࡯νe /ν¯e ࣝผΛಋೖͨ͠ χ2 ஋ͷ݁Ռ

1 ϦϯάϚϧνϦϯά

ࣝผલ

νe -likeν¯e -likeࣝผલνe -likeν¯e -like

1.33∼2.5GeV

0.002

0.293

0.084

0.044

0.127

0.001

2.5∼5.0GeV

0.647

1.906

0.036

2.231

1.911

0.538

5.0∼10.0GeV

0.999

2.702

0.005

10.0GeV∼

0.056

0.086

0.002

2.700

2.367

0.535

4.988

0.127

4.404

1.075

߹‫ܭ‬

1.704

5.115

(a)

4.975

5.479

(b)

ਤ 7.9 νe /ν¯e ࣝผΛಋೖͨ͠ e-like 1 Ϧϯάࣄ৅ͰͷΞοϓμ΢ϯਤɻਖ਼ৗ֊૚ (NH)(ࠇઢ)ɺ‫֊ٯ‬૚ (IH)(੺࢛֯) ͷൺֱɻ (a) νe -like ࣄ৅ (b) (ν¯e )-like ࣄ৅ɻ(a)ਤ 7.10(b)νe /ν¯e ࣝผΛಋೖͨ͠ e-like ϚϧνϦϯάࣄ৅ͰͷΞοϓμ΢ϯਤɻ(a) νe -like ࣄ৅ (b) (ν¯e )-like ࣄ৅ɻ

55

7.4 SK-IV ‫؍‬ଌ‫ ؒظ‬3244.4 ೔Ͱͷ݁Ռ

7.4 SK-IV ‫؍‬ଌ‫ ؒظ‬3244.4 ೔Ͱͷ݁ՌSK-IV ‫؍‬ଌ‫Ͱؒظ‬ͷ݁ՌΛ µ-like, e-like ࣄ৅ʹ͍ͭͯͦΕͧΕද 7.5, 7.6 ʹ·ͱΊͨɻલड़ͷ 200 ೥෼ͷ MCͰͷ݁ՌʹॏΈΛ͚ͭ SK-IV ‫؍‬ଌ‫ ؒظ‬3244.4 ೔Ͱͷ݁Ռʹ‫͍ͯ͠ࢉ׵‬Δɻe-like ࣄ৅Ͱ΋ χ2 ͷ஋͕খ͘͞౷‫ܭ‬ͷ༳Β͗ʹӅΕͯ͠·͏Α͏ͳ஋Ͱ͋Δ͕ɺ࣮ࡍͷεʔύʔΧϛΦΧϯσͰͷ e-like ࣄ৅Λ༻͍ͨৼಈղੳͷܾఆ‫౓ײ‬͸ɺSK-IV ‫ؒظ‬ͷΈͰ 1.58 σ Ͱਖ਼ৗ֊૚Λࣔࠦ͢Δ݁ՌΛಘ͍ͯΔɻͦͷͨΊಉ‫ ͍͓ͯʹؒظ‬µ-like ࣄ৅ͷ௥Ճ͢Δ͜ͱʹΑͬͯߋͳΔ‫ظ্͕޲౓ײ‬଴Ͱ͖Δɻ

7.4.1 νµ /ν¯µ ࣝผΛಋೖͨ͠ µ-like ࣄ৅ͷ݁Ռද 7.5

SK-IV ‫͚͓ʹؒظ‬Δ νµ /ν¯µ ࣝผΛಋೖͨ͠ χ2 ஋ͷ݁Ռ

1 Ϧϯά
ࣝผલ

∼1.0GeVνµ -likeϚϧνϦϯάν¯µ -likeࣝผલνµ -likeν¯µ -like

0.003

0.001

0.002

1.0∼2.5GeV

0.000

0.013

0.006

0.003

0.005

0.000

0.008

0.001

0.009

0.000

0.002

0.016

5.0GeV∼

0.005

0.001

0.012

0.008

0.012

0.001

0.014

0.026

0.019

0.019

2.5∼5.0GeV
߹‫ܭ‬

0.012

0.040

0.015

0.038

7.4.2 νe /ν¯e ࣝผΛಋೖͨ͠ e-like ࣄ৅ͷ݁Ռ
ද 7.6 SK-IV ‫؍‬ଌ‫͚͓ʹؒظ‬Δ νe /ν¯e ࣝผΛಋೖͨ͠ χ2 ஋ͷ݁Ռ

1 ϦϯάϚϧνϦϯά

ࣝผલ

νe -likeν¯e -likeࣝผલνe -likeν¯e -like

0.000

0.013

0.004

0.002

0.006

0.000

2.5∼5.0GeV

0.0287

0.085

0.002

0.099

0.085

0.024

0.044

0.120

0.000

10.0GeV∼

0.002

0.004

0.000

0.120

0.105

0.024

0.222

0.006

0.196

0.048

1.33∼2.5GeV
5.0∼10.0GeV
߹‫ܭ‬

0.076

0.228

0.221

0.244

7.5 ֊૚ੑܾఆ‫౓ײ‬ͷධՁ·ͱΊ؆୯ͷͨΊ஋ͷେ͖ͳ 200 ೥෼Ͱͷ݁ՌΛൺֱ͢Δɻද 7.7 ʹ µ-likeɺe-like ࣄ৅ͷ࣭ྔ֊૚ͷܾఆ‫౓ײ‬ͷਪఆ஋Ͱ͋Δ χ2 ͷ݁ՌΛ·ͱΊͨɻχ2 ͷ஋͸ɺµ-like αϯϓϧͰ͸ 0.621 ͔Β 1.806 ΁໿ 2.9 ഒ޲্ͨ͠ɻe-like ࣄ৅Ͱ͸ 6.679 ͔Β 10.594 ͱ໿ 1.6 ഒͷ޲্ʹͱͲ·͍ͬͯΔɻಛʹϚϧνϦϯάࣄ৅ͷ৔߹ʹͦͷࣝผੑೳͷ͕ࠩ‫ݦ‬ஶͰ͋ΓɺͦͷཁҼͱͯ͠ɺߴΤωϧΪʔࣄ৅ͷׂ߹͕େ͖͍ µ-like ࣄ৅ʹରͯ͠ɺຊ‫ॳͰڀݚ‬Ίͯ likelihood ‫ʹࢉܭ‬ಋೖͨ͠ӡಈֶతͳύϥϝʔλʔͰ͋Δ่յిࢠɺԣ
ํ޲ӡಈྔɺϦϯά਺ͷ෼෍ͷҧ͍͕ νµ ͱ ν¯µ Ͱେ͖͘ɺࣝผʹΑ͘ޮ͍ͨͨΊͰ͋Δɻࣝผ͞ΕͨαϯϓϧͰͷ

56

ୈ7ষ

࣭ྔ֊૚ੑܾఆ‫౓ײ‬ͷߟ࡯ਖ਼ৗ֊૚ͱ‫֊ٯ‬૚ͰͷΞοϓμ΢ϯൺͷࠩ͸౷‫ܭ‬ͷ༳Β͗ʹӅ͞Εͯ͠·͏Մೳੑ͕͋ΔͨΊɺ͜ͷޮՌΛΑ͘ߟ࡯͢Δඞཁ͕͋Δ͕ɺࠓճಘΒΕͨ χ2 ͷ஋͔Β‫ͨ͠ࢉܭ‬৔߹ʹ͸ɺࣝผ͞Εͨ νµ -like, ν¯µ -like αϯϓϧΛৼಈղੳ‫ʹڀݚ‬ಋೖ͢Δ͜ͱͰɺe-like αϯϓϧͷΈΛ༻͍Δ৔߹ʹൺ΂ͯ࠷େͰ 1.18 ഒఔ౓ɺ֊૚ܾఆ‫౓ײ‬Λ޲্ͤ͞ΔՄೳੑ͕͋Δɻ
ද 7.7

֊૚ੑܾఆ‫౓ײ‬ͷධՁͷ·ͱΊࣝผલ χ2ࣝผ‫ ޙ‬χ2

1 Ϧϯά µ-like

0.287

0.922

ϚϧνϦϯά µ-like

0.334

0.884

µ-like ߹‫ܭ‬

0.621

1.806

1 Ϧϯά e-like

1.704

5.115

ϚϧνϦϯά e-like

4.975

5.479

e-like ߹‫ܭ‬

6.679

10.594

57

ୈ8ষ

কདྷ࣮‫Ͱݧ‬ͷ֊૚ܾఆ‫౓ײ‬ͷ‫ڀݚ‬͜Ε·Ͱ͸‫ࡏݱ‬ਐߦதͷεʔύʔΧϛΦΧϯσ‫ݕ‬ग़‫ث‬ΛԾఆͨ͠֊૚ܾఆ‫౓ײ‬ͷ‫ڀݚ‬Λ͖͕ͯͨ͠ɺSK ͷ‫ܧޙ‬࣮‫ ͯ͠ͱݧ‬SK-Gd ϑΣʔζɺϋΠύʔΧϛΦΧϯσ࣮‫͕͋ݧ‬Δɻલड़ͷΑ͏ʹ͜ΕΒͷ࣮‫ࡏݱͰݧ‬ͷ νµ /ν¯µ ࣝผੑೳͱ֊૚ܾఆ‫্͢޲͕౓ײ‬Δͱ༧૝͞ΕΔͨΊɺຊষͰ͸͜ΕΛ‫ੵݟ‬΋Δɻ

8.1 SK-Gd ϑΣʔζͰͷ νµ /ν¯µ ࣝผSK-Gd ϑΣʔζͰ͸ɺ͜Ε·Ͱ७ਫͰຬͨ͞Εͨ‫ݕ‬ग़‫಺ث‬෦ʹེࢎΨυϦχ΢ϜΛՃ͑Δ͜ͱͰதੑࢠͷ‫ݕ‬ग़ޮ཰͕‫ݱ‬ঢ়ͷ໿ 20% ͔Β໿ 90% ·Ͱ޲্͢Δɻ։ൃͨ͠ νµ /ν¯µ ࣝผͰ͸‫ݕ‬ग़ޮ཰ 20% ͷ৔߹ͷதੑࢠ਺෼෍Λ༻
͍͍ͯΔ͕ɺதੑࢠ‫ݕ‬ग़ޮ཰͕޲্͢Δ͜ͱͰࣝผੑೳ͕ΑΓ޲্͢ΔՄೳੑ͕͋ΔɻຊষͰ͸͜ΕΛ‫ੵݟ‬΋Δɻ

8.1.1 SK-Gd ΛԾఆͨ͠தੑࢠ෼෍
͜͜Ͱ͸ SK-Gd ΛԾఆͯ͠ɺ͜Ε·Ͱ༻͍͍ͯͨ࠶ߏ੒͞Εͨதੑࢠ਺෼෍ (‫ݕ‬ग़ޮ཰ 20%) ͷ୅ΘΓʹ MC ͷਅͷ৘ใʹΑΔதੑࢠ਺෼෍ (‫ݕ‬ग़ޮ཰ 100%) Λ likelihood ‫͍ͯ༻ʹࢉܭ‬ɺνµ /ν¯µ ࣝผΛߦ͏ɻਤ 8.1, 8.2 ʹ 1 Ϧϯάࣄ৅ɺϚϧνϦϯάࣄ৅ʹ͍ͭͯਅͷதੑࢠ਺෼෍Λࣔͨ͠ɻલষͱಉ༷ʹ 1 Ϧϯάࣄ৅͸่յిࢠ਺ = 0, 1ͷࣄ৅ͱ่յిࢠ਺ ≥2 ͷࣄ৅ʹ۠ผ͠ɺϚϧνϦϯάࣄ৅͸Ϧϯά߹‫ܭ‬ӡಈྔ 5.0 GeV Ҏ্ͱ 5.0 GeV ະຬͰ۠ผ͍ͯ͠Δɻ͜ΕΛ‫ݟ‬Δͱಛʹ 1 Ϧϯάࣄ৅Ͱ νµ ͱ ν¯µ ͷ෼෍ͷҧ͍͕‫ݦ‬ஶͰ͋Δɻ֩಺ޮՌͳͲʹΑΔೋ࣍త
ͳதੑࢠͷൃੜ͕গͳ͍ 1 Ϧϯάࣄ৅Ͱ͸ɺνµ ൓ԠͰ͸தੑࢠ͕์ग़͞Εͣɺν¯µ ൓ԠͰ͸தੑࢠ͕ൃੜ͢Δͱ͍͏ҧ͍͕ΑΓ໌֬ʹ‫ݦ‬ΕΔ͔ΒͰ͋Δɻ͜ΕΒͷ෼෍Λதੑࢠ਺ͷ֬཰ີ౓ؔ਺ͱͯ͠ಡΈࠐΈ likelihood ‫ࢉܭ‬Λ
ߦ͏ɻ

58

ୈ8ষ
(a)

কདྷ࣮‫Ͱݧ‬ͷ֊૚ܾఆ‫౓ײ‬ͷ‫ڀݚ‬

(b)

ਤ 8.1

1 Ϧϯάࣄ৅ʹ͓͚Δਅͷதੑࢠ෼෍ɻ੨ઢ͕ਅͷ νµ ࣄ৅ɺ੺ઢ͕ਅͷ ν¯µ Ͱ͋Δɻ(a) ่յిࢠ਺ =0, 1ɺ(b) ่յిࢠ਺ ≥ 2
(a)

(b)

ਤ 8.2 ϚϧνϦϯάࣄ৅ʹ͓͚Δਅͷதੑࢠ෼෍ɻ੨ઢ͕ਅͷ νµ ࣄ৅ɺ੺ઢ͕ਅͷ ν¯µ Ͱ͋Δɻ(a) 5.0 GeV
ະຬɺ(b) 5.0 GeV Ҏ্

8.1.2 ∆L ෼෍ͱ νµ /ν¯µ ࣝผ݁Ռਅͷதੑࢠ෼෍Λ༻͍ͯ‫∆ ͨ͠ࢉܭ‬L ෼෍Λਤ 8.3 ʹࣔͨ͠ɻ͜͜Ͱ΋લষͱಉҰͷ 3 ੈ୅ৼಈΛߟྀٖͨ͠ࣅσʔλαϯϓϧ 200 ೥෼Λ༻͍͍ͯΔɻ∆L Χοτ஋͸ 1 Ϧϯάࣄ৅Ͱ ∆L= 0.4, ϚϧνϦϯάࣄ৅Ͱ∆L= −0.6 Λઃఆͯ͠ɺνµ -like ࣄ৅ͱ ν¯µ ࣄ৅ʹ෼཭ͨ͠ɻࣝผͷ eﬃciency ͸ 1 Ϧϯάࣄ৅ νµ Ͱ 60.2±0.3%,ν¯µ Ͱ 81.5±0.3%, ϚϧνϦϯάࣄ৅ νµ Ͱ 74.3±0.3%, ν¯µ Ͱ 48.4±0.5% ͱͳΓɺ͜Ε·Ͱͷ νµ /ν¯µ ࣝผੑೳΑΓ΋େ෯ʹվળͨ͠ɻಛʹதੑࢠ਺෼෍ͷ͕ࠩ‫ݦ‬ஶͩͬͨ 1 Ϧϯάࣄ৅Ͱߴ͍ࣝผੑೳΛಘΒΕͨɻ·ͨɺ1 Ϧϯάࣄ৅͸ likleihood ‫ࢉܭ‬ͷύϥϝʔλͷ਺͕ 2 छྨɺ·ͨ͸ 4 छྨͰ͋ΔͨΊதੑࢠ਺෼෍ͷҧ͍ʹΑΔӨ‫͕ڹ‬େ͖͘ޮ͍͍ͯΔͱߟ͑ΒΕΔɻνµ /ν¯µ ࣝผʹΑΔ purity ͷ஋ΛΛද 8.1 ʹࣔͨ͠ɻߴ͍ eﬃciency ʹΑͬͯ 1 Ϧϯάࣄ৅Ͱ͸ɺࣝผલ 62.4%
ͩͬͨ νµ purity ͸ࣝผ‫ ޙ‬84.2±0.3%, ν¯µ purity ͸ࣝผલ 37.2% ͔Βࣝผ‫ ޙ‬54.7±0.3% ͱͳΓɺͦΕͧΕ

59

8.1 SK-Gd ϑΣʔζͰͷ νµ /ν¯µ ࣝผ21.8±0.3%, 17.5±0.3% purity ͕޲্ͨ͠ɻ·ͨϚϧνϦϯάࣄ৅Ͱ͸ࣝผલ 73.5% ͩͬͨ νµ purity ͸ࣝผ‫ޙ‬

78.5±0.3%, ν¯µ purity ͸ࣝผલ 22.0% ͔Βࣝผ‫ ޙ‬35.1±0.5% ͱͳΓɺͦΕͧΕ 5.0±0.3%,13.1±0.5% purity ͕޲্ͨ͠ɻ࣮ࡍͷ SK-Gd ΛͰ͸தੑࢠ‫ݕ‬ग़ޮ཰͸ 90% ͷͨΊࣝผੑೳ͸͜ͷ஋ΑΓ΋௿Լ͢Δ͜ͱ͕͕༧૝͞ΕΔ͕ɺதੑࢠ‫ݕ‬ग़ޮ཰ 20 % ͷ৔߹ʹൺ΂Δͱ֤αϯϓϧͷ purity ͕޲্͢Δ͜ͱΛ֬ೝͨ͠ɻ
(a)

(b)

(c)

ਤ 8.3

ਅͷதੑࢠ෼෍Λ༻͍ͨ ∆L ෼෍ɻ(a) 1 Ϧϯάࣄ৅ (b) ϚϧνϦϯά (Ϧϯά߹‫ܭ‬ӡಈྔ > 1.33 GeV)ࣄ৅ (c) ϚϧνϦϯάࣄ৅ (Ϧϯά߹‫ܭ‬ӡಈྔ ≤ 1.33 GeV) ࣄ৅ද 8.1 ਅͷதੑࢠ਺෼෍Λ༻͍ͨ৔߹ͷ νµ /ν¯µ ࣝผ݁Ռ1 Ϧϯάࣄ৅
νµ -like

1 Ϧϯάࣄ৅ν¯µ -likeࣝผલνµ -likeϚϧνϦϯάࣄ৅ν¯µ -like
ࣝผલ

CC νµ

CC ν¯µOthers

84.2±0.3%

15.5±0.3%

0.3%

62.4%

44.8±0.3%54.7±0.3%

0.5%

37.2%

0.4%

78.5±0.3%

16.3±0.2%

5.2±0.1%

73.5%

22.0%

4.5%

62.2±0.5%35.1±0.5%

2.6±0.2%

60

ୈ8ষ

8.2

কདྷ࣮‫Ͱݧ‬ͷ֊૚ܾఆ‫౓ײ‬ͷ‫ڀݚ‬ϋΠύʔΧϛΦΧϯσ࣮‫Ͱݧ‬ͷ֊૚ܾఆ‫౓ײ‬µ-like ࣄ৅ͷ֊૚ܾఆ‫౓ײ‬Λ੍‫͢ݶ‬ΔཁҼͷҰͭʹ౷‫͕ྔܭ‬গͳ͍͜ͱ͕͋͛ΒΕΔɻຊ‫Ͱڀݚ‬͸ νµ /ν¯µ ࣝผʹ༻͍͍ͯΔϛϡʔΦϯͷ่յిࢠͷ‫ݕ‬ग़΍χϡʔτϦϊΤωϧΪʔͷ࠶ߏ੒͕ՄೳͳχϡʔτϦϊ൓Ԡ͕‫ݕ‬ग़‫಺ث‬Ͱऩ·Δ FC (Fully Contained) ࣄ৅ͷΈΛར༻͍ͯ͠Δɻ͔͠͠ɺಛʹ֊૚ܾఆ‫͞ͱ͍ߴ͕౓ײ‬ΕΔ 10 GeV ෇ۙͷߴΤωϧΪʔྖҬͰɺχϡʔτϦϊ൓ԠʹΑͬͯੜཻͨ͡ࢠͷ‫͕੻ي‬༗ޮମੵ֎ʹ‫ٴ‬ΜͰ͠·͏ PC (Partially

Contained) ࣄ৅͕૿Ճ͠༻͍Δ͜ͱ͕Ͱ͖ͳ͍ࣄ৅͕૿Ճ͢ΔͨΊɺಛʹ͜ͷྖҬͰ౷‫े͕਺ܭ‬෼Ͱͳ͍ɻਤ
8.5(a) ʹεʔύΧϛΦΧϯσ (SK) ʹ͓͚Δେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊࣄ৅ͷਅͷΤωϧΪʔ෼෍Λ FC ࣄ৅ (੨ઢ) ͱ PC ࣄ৅ (ᒵ৭) ʹ͍ͭͯൺֱͯࣔͨ͠͠ɻ5.0 GeV Ҏ্Ͱ͸ PC ࣄ৅͕ࢧ഑తʹͳ͍ͬͯΔ͜ͱ͕Θ͔Δɻ౷‫ྔܭ‬ͷ૿ՃΛҰͭͷ໨తͱͯ͠εʔύʔΧϛΦΧϯσ࣮‫ݧ‬ͷ‫ͯ͠ͱݧ࣮ܧޙ‬ϋΠύʔΧϛΦΧϯσ࣮‫( ݧ‬HK)
͕‫ܭ‬ը͞Ε͓ͯΓɺͦͷ༗ޮମੵ͸εʔύʔΧϛΦΧϯσͷ໿ 8.3 ഒͰ͋ΔͨΊɺϋΠύʔΧϛΦΧϯσ͸εʔύʔΧϛΦΧϯσ 8.3 ೥෼ͷ౷‫ྔܭ‬Λ໿ 1 ೥Ͱୡ੒͢Δ͜ͱ͕Ͱ͖ΔɻಛʹϛϡʔΦϯχϡʔτϦϊ͸ɺ൓ԠͰ์ग़͞ΕΔϛϡʔΦϯͷඈఔ͕ΤωϧΪʔʹ͓͓Αͦൺྫͯ͠৳ͼΔͨΊɺ༗ޮମੵ͕૿Ճ͢ΔϋΠύʔΧϛΦΧϯσͰ͸‫ڐ‬༰Ͱ͖Δඈఔ͕૿͑ɺΑΓߴΤωϧΪʔͳࣄ৅Λ FC ࣄ৅ͱͯ͠‫؍‬ଌର৅ʹ͢Δ͜ͱ͕Ͱ͖ΔͨΊ୯७ͳ౷‫ྔܭ‬ͷ 8.3 ഒͷ૿ՃΑΓ΋ߋͳΔ૿ՃྔΛ‫ࠐݟ‬Ή͜ͱ͕Ͱ͖ΔɻిࢠχϡʔτϦϊࣄ৅Ͱ͸์ग़͞Εͨిࢠ͕ΧεέʔυγϟϫʔΛੜ͡Δ͜ͱͰ‫ٸ‬଎ʹΤωϧΪʔΛࣦ͏ͨΊɺεʔύʔΧϛΦΧϯσͷ༗ޮମੵͰ΋େ൒͕ FC ࣄ৅ʹͳΔͨΊɺ͜ΕʹΑΔ౷‫ྔܭ‬ͷ૿Ճ͸΄ͱΜͲͳ͍ɻͦͷͨΊϋΠύʔΧϛΦΧϯσͰͷ౷‫਺ܭ‬ͷ૿Ճ͸ϛϡʔΦϯχϡʔτϦϊࣄ৅ʹରͯ͠ಛʹ༗ޮͰ͋Δɻ͜ͷͨΊຊষͰ͸͜ͷ༗ޮମੵͷ૿ՃʹΑΔϛϡʔΦϯχϡʔτϦϊͷ౷‫ྔܭ‬ͷ૿ՃΛ MC γϛϡϨʔγϣϯͰ‫ੵݟ‬΋Δ͜ͱͰϋΠύʔΧϛΦΧϯσͰͷ֊૚ܾఆ‫౓ײ‬Λߟ࡯͢Δɻ

8.2.1

HK ༗ޮମੵͰͷࣄ৅‫؍‬ଌͷ‫ڀݚ‬SK Ͱ PC ࣄ৅ͱ൑ఆ͞Εͨࣄ৅ʹ͍ͭͯɺHK ͷ༗ޮମੵΛԾఆͨ͠৔߹Ͱ͸ FC ࣄ৅ʹͳΔ͔ PC ࣄ৅ʹͳΔ
͔Λɺ؆୯ͷͨΊʹ SK ͷ MC γϛϡϨʔγϣϯ 200 ೥෼Λ༻͍ͯԼ‫ه‬ͷํ๏Ͱ൑ఆΛߦ͏ɻ
ਤ 8.4 ͷΑ͏ʹɺϋΠύʔΧϛΦΧϯσͷ‫ݕ‬ग़‫ث‬༗ޮମੵͱͯ͠ఈ໘ͷ൒‫ ܘ‬35 mɺߴ͞ 56 m ͷԁபΛԾఆ͢Δɻ1 ͭͷϛϡʔΦϯχϡʔτϦϊࣄ৅ʹ͍ͭͯɺχϡʔτϦϊ൓Ԡ఺ΛԾఆͨ͠ԁப಺ʹϥϯμϜʹઃఆ͠ɺMC
ͷ৘ใͰ͋ΔਅͷϛϡʔΦϯӡಈྔɺਅͷ์ग़ํ޲Λ༻͍ͯϛϡʔΦϯ่յ஍఺Λ‫ੵݟ‬΋Δɻ͜͜ͰϛϡʔΦϯͷΤωϧΪʔଛࣦ͸؆୯ͷͨΊɺ2 MeV/cm, ·ͨϛϡʔΦϯ͸์ग़ํ޲ʹ௚ਐ͢ΔͱԾఆ͓ͯ͠Γɺͦͷ‫ੵݟ‬΋่ͬͨյ஍఺͕ԁப಺ʹऩ·Δ৔߹Λ FC ࣄ৅ͱ൑ఆ͠ɺऩ·Βͳ͍৔߹Λ PC ࣄ৅ͱ൑ఆ͢Δɻ͜͜Ͱ༻͍͍ͯΔ
χϡʔτϦϊϑϥοΫεͳͲ͸શͯ SK ΛԾఆͨ͠ MC γϛϡϨʔγϣϯʹ४‫͍ͯ͠ڌ‬Δɻ
ਤ 8.5(b) ʹϋΠύʔΧϛΦΧϯσΛԾఆͨ͠৔߹ͷେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊࣄ৅ͷਅͷΤωϧΪʔ෼෍Λࣔͨ͠ɻ੨ઢ͕ HK Ͱͷ FC ࣄ৅ɺᒵઢ͕ HK Ͱͷ PC ࣄ৅Ͱ͋Δɻ8.5(a) ͱൺֱ͢ΔͱɺPC ࣄ৅͕໿൒਺ʹͳΓɺ

10 GeV ෇ۙ·Ͱ FC ࣄ৅ͷׂ߹͕ PC ࣄ৅ʹൺ΂ͯେ͖͘ͳ͍ͬͯΔɻ·ͨɺද 8.2 ʹେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊࣄ৅ͷ֤ΤωϧΪʔϏϯͰͷࣄ৅਺ΛɺSK, HK ͷͲͪΒͰ΋ FC ࣄ৅ʹͳͬͨࣄ৅ɺHK ͰͷΈ FC ࣄ৅ʹͳͬ
ͨࣄ৅ɺHK Ͱ΋ PC ࣄ৅ʹͳͬͨࣄ৅ Λൺֱͯ͠·ͱΊͨɻεʔύʔΧϛΦΧϯσʹ͓͍ͯ 5.0 GeV Ҏ্ͷ FC
ࣄ৅͸ 18766 Πϕϯτͱ௿ΤωϧΪʔͷࣄ৅ʹରͯ͠গͳ͍͕ɺϋΠύʔΧϛΦΧϯσͰ͸ 17300 Πϕϯτ૿͑ɺ͓͓Αͦ౷‫ ͕ྔܭ‬2 ഒʹͳΔɻ͜ͷ౷‫ܭ‬ͷ૿ՃྔΛߟྀͯ͠ HK ʹ͓͚Δ֊૚ܾఆ‫౓ײ‬Λ‫͢ࢉܭ‬Δɻ61

8.2 ϋΠύʔΧϛΦΧϯσ࣮‫Ͱݧ‬ͷ֊૚ܾఆ‫౓ײ‬

ਤ 8.4

HK ༗ޮମੵͰͷࣄ৅‫؍‬ଌγϛϡϨʔγϣϯͷ໛ࣜਤ

(a)

(b)

ਤ 8.5 SK ͱ HK ͷʹ͓͚Δ FC ࣄ৅ (੨ઢ) ͱ PC ࣄ৅ (ᒵઢ) ͷϑϥοΫεɻ(a) SK ͷ৔߹ (b) HK ͷ৔߹Ͱಉ͡ exposure Ͱൺֱ͍ͯ͠Δɻ

62

ୈ8ষ

কདྷ࣮‫Ͱݧ‬ͷ֊૚ܾఆ‫౓ײ‬ͷ‫ڀݚ‬

ਤ 8.6 ಉ͡ exposure Ͱͷ SK ͱ HK ͷ FC ࣄ৅ͷϑϥοΫεͷൺֱɻHK ͷ৔߹ (੨ઢ) SK ͷ৔߹ (ᒵઢ)

ද 8.2

8.2.2

େ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊ֤ΤωϧΪʔϏϯຖͷࣄ৅਺ͷൺɻಉ͡ exposure ͷ৔߹Λൺֱ͍ͯ͠Δɻ

SK, HK Ͱ FC ࣄ৅HK ͰͷΈ FC ࣄ৅

SK, HK Ͱ PC ࣄ৅< 1.0 GeV200798304

34

1.0-2.5 GeV

132670

11390

1996

2.5-5.0 GeV

46287

16963

6544

> 5.0 GeV

18766

17300

37168

HK Ͱͷ֊૚ܾఆ‫౓ײ‬ͷ‫ڀݚ‬౷‫ܭ‬ͷ૿ՃྔͷӨ‫ڹ‬ͷΈΛ‫ੵݟ‬΋ΔͨΊɺ༗ޮମੵҎ֎ͷ‫ݕ‬ग़‫ث‬ͷੑೳ͸‫ࡏݱ‬ͷεʔύʔΧϛΦΧϯσ࣮‫ͱݧ‬ಉ༷ͷੑೳΛԾఆ͠ɺຊ‫Ͱڀݚ‬։ൃ͞Εͨ νµ /ν¯µ ࣝผʹΑΔ νµ -like, ν¯µ -like ࣄ৅Λ༻͍ͯɺ7 ষͱಉ༷ʹΞοϓμ΢
ϯൺΛ֬ೝ͢Δɻ֬ೝʹ͸͜Ε·ͰͱಉҰͷ MC γϛϡϨʔγϣϯ SK200 ೥෼ (HK ͷ༗ޮମੵͰ͸໿ 24 ೥෼)Λ༻͍ΔɻHK ༗ޮମੵͰͷࣄ৅਺ΛԾఆ͢ΔͨΊʹɺ֤ΤωϧΪʔϏϯຖͷ౷‫ʹྔܭ‬ॏΈΛ͚ͭͯ‫ͨ͠ࢉܭ‬ɻॏΈ͸ද 8.2 ΑΓ‫ͯ͠ࢉܭ‬ɺ <1.0 GeV Ͱ 1.0015 ഒɺ1.0-2.5 GeV Ͱ 1.0858 ഒɺ2.5-5.0 GeV Ͱ 1.3665 ഒɺ >5.0

GeV Ͱ 1.9219 ഒʹઃఆ͍ͯ͠Δɻ
ද 8.3 ʹ HK ༗ޮମੵΛԾఆͨ͠৔߹ͷɺHK ໿ 24 ೥෼ (SK200 ೥෼ͱಉ͡ exposure ) Ͱͷ χ2 ͷ஋Λ·ͱΊͨɻ͜ΕʹΑΓ༗ޮମੵͷ֦େʹΑͬͯ FC ࣄ৅͕૿Ճͨ͜͠ͱʹΑΔ χ2 ͷ஋ͷมԽͷΈ͕ χ2 ͷ஋ʹ‫ݦ‬ΕΔɻ

2.5-5.0 GeV, >5.0 GeV ͷൣғͰ౷‫૿͕ྔܭ‬Ճͨ͜͠ͱͰɺಛʹ͜ͷྖҬͰͷ χ2 ͷ஋͕૿Ճͨ͠ɻϚϧνϦϯάͰ͜ͷӨ‫ڹ‬͸‫ݦ‬ஶͰ͋Δɻµ-like ࣄ৅શମͰ͸ χ2 ∼ 2.6 ͱͳͬͨɻSK Ͱ͸ χ2 ∼ 1.8 Ͱ͋ͬͨͷͰɺHK ʹ͓͍ͯ FC
ࣄ৅͕૿Ճͨ͜͠ͱʹΑͬͯ֊૚‫౓ײ‬͸ 1.4 ഒఔ౓޲্͢Δɻ

·ͨɺද 8.4 ʹ͸ SK ͱ HK ͰಉҰ‫( ؒظ‬SK-IV ‫؍‬ଌ‫ ؒظ‬3244.4 ೔) ଌఆΛͨ͠৔߹ͷ χ2 ͷ஋Λൺֱͨ͠ɻ༗
ޮମੵͷ૿Ճͱ FC ࣄ৅͕૿͑ΔޮՌ͕߹Θ͞Γɺ౷‫૿͕ྔܭ‬Ճ͢Δ͜ͱͰɺµ-like ࣄ৅ͷ χ2 ͷ஋͸ 0.078 ͔Β

63

8.2 ϋΠύʔΧϛΦΧϯσ࣮‫Ͱݧ‬ͷ֊૚ܾఆ‫౓ײ‬
0.964 ʹ໿ 12.3 ഒʹͳΔ͜ͱΛ֬ೝͨ͠ɻ

͜ͷΑ͏ʹɺνµ /ν¯µ ࣝผͷಋೖ͸কདྷ࣮‫͍͓ͯʹݧ‬͸‫ࡏݱ‬ͷ࣮‫ݧ‬ΑΓ΋ߋʹ༗ޮͰ͋Δͱ͍͏݁Ռ͕ಘΒΕͨɻ
·ͨɺࠓճ͸༗ޮମੵͷ૿ՃʹΑΔޮՌͷΈΛ‫ੵݟ‬΋͕ͬͨɺϋΠύʔΧϛΦΧϯσ࣮‫Ͱݧ‬͸ޫిࢠ૿ഒੁͷੑೳ޲্ͳͲʹΑΓɺதੑࢠ‫ݕ‬ग़ޮ཰͸ 50% ఔ౓ʹͳΔͱ͞Ε͓ͯΓ νµ /ν¯µ ࣝผੑೳ͸ɺΑΓҰ૚޲্͢ΔՄೳੑ͕ߴ͘ɺߋͳΔ‫ʹ্޲౓ײ‬΋‫ظ‬଴Ͱ͖Δ͜ͱΛ࠷‫ʹޙ‬ड़΂͓ͯ͘ɻද 8.3

HK ໿ 24 ೥෼ (SK200 ೥෼ͱಉ͡ exposure ) ʹ͓͚Δ χ2 ஋ͷ݁Ռ

1 Ϧϯά
ࣝผલ

∼1.0GeVνµ -likeϚϧνϦϯάν¯µ -likeࣝผલνµ -likeν¯µ -like

0.077

0.028

0.055

1.0∼2.5GeV

0.000

0.310

0.142

0.087

0.012

0.002

0.241

0.017

0.269

0.007

0.052

0.506

5.0GeV∼

0.212

0.039

0.531

0.331

0.499

0.036

0.366

0.943

0.701

0.599

2.5∼5.0GeV
߹‫ܭ‬

ද 8.4

0.453

1.309

0.502

1.300

SK-IV ‫؍‬ଌ‫( ؒظ‬3244.4 ೔) ʹ͓͚Δ SK ͱ HK Ͱͷ χ2 ஋ͷ݁ՌͷൺֱSK-IV ͷ৔߹ࣝผલ χ2ࣝผ‫ ޙ‬χHK ͷ৔߹
2

ࣝผલ χ2ࣝผ‫ ޙ‬χ2

1 Ϧϯά µ-like

0.012

0.040

0.167

0.483

ϚϧνϦϯά µ-like

0.015

0.038

0.185

0.481

µ-like

0.027

0.078

0.352

0.964

65

ୈ9ষ

݁࿦
9.1 ·ͱΊχϡʔτϦϊ࣭ྔ֊૚ੑ໰୊ͷղܾ͸χϡʔτϦϊͷੑ࣭ղ໌΍෺࣭༏੎Ӊ஦ͷ‫͍͓ͯʹڀݚ‬ඇৗʹॏཁͰ͋Δɻຊ‫Ͱڀݚ‬͸εʔύʔΧϛΦΧϯσ࣮‫͚͓ʹݧ‬Δ֊૚ܾఆ‫্޲౓ײ‬Λ໨ࢦͯ͠ɺৼಈղੳ‫΁ڀݚ‬ͷେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊࣄ৅ͷಋೖʹ޲͚ͨ likelihood ๏ʹΑΔ νµ /ν¯µ ࣝผํ๏Λ։ൃͨ͠ɻ
ಛʹɺࣄ৅͕ෳࡶʹͳΓࣝผ͕೉͍͠ͱ͞ΕΔଟཻࢠࣄ৅ʹ͍ͭͯॳΊͯ νµ /ν¯µ ࣝผΛ։ൃ͠ɺ৽ͨͳύϥϝʔλͱͯ͠ νµ ͱ ν¯µ ͷӡಈֶతͳҧ͍Λར༻ͨ͠ԣํ޲ӡಈྔɺϦϯά਺ɺ่յిࢠ਺෼෍Λ likelihood ‫ʹࢉܭ‬ಋೖ
ͨ͠ɻ·ͨɺϛϡʔΦϯͷ่յ࣌ؒɺ่յిࢠώοτ਺Λࣝผʹ༻͍ΔͨΊʹɺෳ਺ͷ่յిࢠͷத͔ΒχϡʔτϦϊ൓ԠʹΑͬͯ์ग़͞ΕͨҰ࣍ϛϡʔΦϯ༝དྷͷ่յిࢠͷநग़๏Λ։ൃ͢ΔͳͲଟཻࢠࣄ৅Ͱͷࣄ৅બผ๏Λ࠷దԽͨ͠ɻ1 Ϧϯάࣄ৅ʹ͍ͭͯ͸่յిࢠ਺ɺϛϡʔΦϯ่յ࣌ؒɺ่յిࢠώοτ਺ɺதੑࢠ਺ΛɺϚϧνϦϯάͰ͸ߋʹԣํ޲ӡಈྔɺϦϯά਺Λ௥Ճͨ͠ΠϯϓοτύϥϝʔλΛ likelihood ‫͍ͨ༻ʹࢉܭ‬ɻ͜ΕΛ 3 ੈ୅χϡʔτϦϊৼಈΛߟྀٖͨ͠ࣅσʔλαϯϓϧʹద༻ͨ݁͠Ռɺࣝผલͷ µ-like αϯϓϧͰ 1Ϧϯάࣄ৅ 62.4%, ϚϧνϦϯάࣄ৅ 73.4% ͷׂ߹ͩͬͨ CCνµ ͸ࣝผ‫ ޙ‬νµ -like αϯϓϧͰ purity ͕ͦΕͧ
Ε 77.1±0.4%,76.0±0.3% ʹͳΓɺͦΕͧΕ 14.7±0.4%, 2.9±0.3% ޲্ͨ͠ɻ·ͨ CCν¯µ ͸ࣝผલ µ-like αϯϓϧͰ 1 Ϧϯάࣄ৅ 37.2%, ϚϧνϦϯάࣄ৅ 22.9% ͷׂ߹͔Βࣝผ‫ ޙ‬ν¯µ -like αϯϓϧͰ purity ͕ͦΕͧΕ

45.0±0.3%, 37.2±0.5% ʹͦΕͧΕ 7.8±0.3%, 14.3±0.5% ޲্ͤ͞Δ͜ͱʹ੒ޭͨ͠ɻ͜Ε͸ઌߦ‫͚͓ʹڀݚ‬Δνµ /ν¯µ ࣝผ΍ νe /ν¯e ࣝผͷ݁Ռʹൺ΂ͯ΋ߴ͍ࣝผੑೳͰ͋Δɻ

200 ೥෼ͷٖࣅσʔλʹ͓͚Δࣝผͨ͠ νµ -like, ν¯µ -like αϯϓϧͷ࣭ྔ֊૚ੑ‫౓ײ‬ΛΞοϓμ΢ϯൺΛ༻͍ͯ֬ೝͨ͠ɻ1 Ϧϯά 5.0 GeV Ҏ্ͷϏϯΛআ͍ͯɺ΄΅શͯͷϏϯͰਅͷ νµ , ν¯µ ࣄ৅ͷΞοϓμ΢ϯൺͷ૿‫ʹ޲ํݮ‬ࣝผͨ͠ νµ -like, ν¯µ -like αϯϓϧͷ૿‫͕޲ํݮ‬Ұகͨͨ͠Ίɺνµ /ν¯µ ࣝผͷಋೖ͸‫ʹ্޲౓ײ‬ҰఆͷޮՌ͕͋Δͱ
‫͑ݴ‬Δɻ͔͠͠ɺ֤Ϗϯຖͷ૿‫ݮ‬͸খ͘͞౷‫ܭ‬ͷ༳Β͗ʹΑΔ૿‫ʹݮ‬ɺ֊૚ͷҧ͍ʹΑΔޮՌ͕Ӆ͞Εͯ͠·͏Մೳੑ͕͋Γɺ͜ͷ఺ʹ͍ͭͯ͸ߟ࡯͢Δඞཁ͕͋Δɻ‫ݱ‬ঢ়ͷ χ2 ͷ஋Λͦͷ··༻͍ͨ৔߹ʹ͸ɺࣝผલ µ-like ࣄ৅ͷ χ2 = 0.621 ͔ΒࣝผΛಋೖͨ݁͠Ռɺµ-like ࣄ৅શମͰ χ2 = 1.806 ͱͳΓɺ࠷େͰ 2.9 ഒఔ౓ µ-like ࣄ৅ͷ֊૚ܾఆ‫౓ײ‬Λ޲্ͤ͞ΔՄೳੑ͕͋Δɻ·ͨࣝผ‫ޙ‬ͷ µ-like αϯϓϧΛ‫ࡏݱ‬ͷεʔύʔΧϛΦΧϯσͰͷৼಈղੳ‫ʹڀݚ‬ಋೖͨ͠৔߹ʹ࠷େͰ 1.18 ഒɺ࣭ྔ֊૚ͷܾఆ‫౓ײ‬ͷ޲্͕͋ΔࣄΛ֬ೝͨ͠ɻ

9.2 ՝୊ͱల๬
‫ࡏݱ‬ͷεʔύʔΧϛΦΧϯσ࣮‫͚͓ʹݧ‬Δ νµ /ν¯µ ࣝผΛಋೖͨ͠ µ-like αϯϓϧͷਖ਼ৗ֊૚ͱ‫֊ٯ‬૚ͷΞοϓμ
΢ϯൺͷҧ͍͸౷‫ܭ‬ͷ༳Β͗ʹൺ΂ͯখ͍ͨ͞Ί࣭ྔ֊૚ͷܾఆ‫͞ݶ੍͕౓ײ‬ΕΔɻͦͷղܾͷͨΊ͸ࣝผਫ਼౓Λߋʹ޲্ͤ͞Δ͔౷‫ྔܭ‬Λ૿Ճͤ͞Δඞཁ͕͋ΔɻεʔύʔΧϛΦΧϯσͰ͸‫ͯ͠ͱݧ࣮ܧޙ‬εʔύʔΧϛΦΧϯ

66

ୈ 9 ষ ݁࿦σ‫ݕ‬ग़‫ث‬ͷ७ਫதʹེࢎΨυϦχ΢ϜΛೖΕΔ͜ͱͰதੑࢠͷ‫ݕ‬ग़ޮ཰Λ‫ࡏݱ‬ͷ໿ 20% ͔Β໿ 90% ʹ޲্ͤ͞Δ

SK-Gd ࣮‫ݧ‬ɺ·ͨ༗ޮମੵ͕໿ 8.3 ഒʹͳΓ‫ݕ‬ग़‫ث‬ੑೳ΋େ෯ʹ޲্͢ΔϋΠύʔΧϛΦΧϯσ࣮‫͕ݧ‬༧ఆ͞Ε͓ͯΓɺຊ‫Ͱڀݚ‬͸͜ΕΒͷকདྷ࣮‫Ͱݧ‬ͷ νµ /ν¯µ ࣝผੑೳͱ֊૚ܾఆ‫౓ײ‬ͷ‫ڀݚ‬Λ͋Θͤͯߦͬͨɻ
ॳΊʹ SK-Gd ࣮‫ݧ‬ΛԾఆͯ͠ɺਅͷதੑࢠ਺෼෍ (தੑࢠ‫ݕ‬ग़ޮ཰ 100%) Λ༻͍ͯ likleihood ‫ࢉܭ‬Λߦ͍ɺνµͱ ν¯µ Λࣝผͨ͠ɻࣝผੑೳ͸ɺ‫ࡏݱ‬ͷ࣮‫ݧ‬ͷ৔߹ʹൺ΂ͯߋʹੑೳ͕޲্͠ɺಛʹ 1 Ϧϯάࣄ৅Ͱ͜Ε͕‫ݦ‬ஶͰ͋ͬͨɻதੑࢠ‫ݕ‬ग़ޮ཰͕ 90% ͷ SK-Gd ࣮‫Ͱݧ‬΋ಉఔ౓ͷࣝผੑೳͷ޲্͕༧૝͞ΕΔɻ·ͨϋΠύʔΧϛΦΧϯσ࣮‫Ͱݧ‬ͷϛϡʔΦϯχϡʔτϦϊͷ༗ޮମੵ಺ࣄ৅ͷ૿ՃྔΛ MC γϛϡϨʔγϣϯΛ༻͍ͯ‫݁ͨ͠ࢉܭ‬Ռɺಛʹ 5.0 GeV Ҏ্ͷߴΤωϧΪʔྖҬͰɺεʔύʔΧϛΦΧϯσ࣮‫ݧ‬ͷ༗ޮମੵ಺ࣄ৅ʹൺ΂ͯɺ౷‫ ͕ྔܭ‬2 ഒۙ͘૿Ճͨ͠ɻ͜ͷޮՌΛߟྀͯ͠ϋΠύʔΧϛΦΧϯσ࣮‫͚͓ʹݧ‬ΔࣝผΛಋೖͨ͠ µ-like αϯϓϧͷ χ2 ͷ஋͸ɺಉ͡‫؍‬ଌ‫( ؒظ‬3244.4 ೔) ͰͷεʔύʔΧϛΦΧϯσ࣮‫Ͱݧ‬ͷ χ2 ͷ஋ͷ໿ 12.3 ഒʹͳΔ͜ͱΛ֬ೝͨ͠ɻ
͜ͷΑ͏ʹকདྷ࣮‫ ͍͓ͯʹݧ‬νµ /ν¯µ ࣝผͷੑೳ͕ߋʹ޲্͢Δ͜ͱ͸໌֬Ͱ͋Γɺେ‫ؾ‬ϛϡʔΦϯχϡʔτϦϊͷ౷‫ྔܭ‬ͷ૿Ճ΋‫ࠐݟ‬ΊΔͨΊɺ௕‫ظ‬తͳ໨ઢͰ‫ͯݟ‬΋ຊ‫ڀݚ‬͸େ͖ͳҙٛΛ࣋ͭɻεʔύʔΧϛΦΧϯσͰ͸࣭ྔ֊૚ੑͷ‫্޲౓ײ‬Λ໨ࢦ͠ɺ༷ʑͳղੳΞϓϩʔνΛߦ͍ͬͯΔɻຊ‫ڀݚ‬΋ͦͷҰ‫ৼͯ͠ͱ؀‬ಈղੳ‫ݙߩʹڀݚ‬
͢Δ͜ͱͰҰ೔Ͱ΋ૣ͍࣭ྔ֊૚ͷܾఆɺͻ͍ͯ͸෺࣭༏੎Ӊ஦ͷઆ໌ͳͲૉཻࢠӉ஦෺ཧ෼໺શମͷൃలʹࢿ͢
Δ͜ͱ͕‫ظ‬଴͞ΕΔɻ

67

ँࣙຊ‫ڀݚ‬ΛਐΊΔʹ͋ͨΓɺଟ͘ͷํͷ͝ࢦಋͱ͝‫ྗڠ‬ΛࣀΓ·ͨ͠ɻ͜ͷ৔ΛआΓ͓ͯྱਃ্͛͠·͢ɻࢦಋ‫ڭ‬һͰ͋Δҏ౻޷޹ઌੜʹ͸χϡʔτϦϊৼಈղੳͱ͍͏ૉ੖Β͍͠‫ڀݚ‬ςʔϚΛ༩͑ͯ௖͖ɺ͜Ε·Ͱେมଟ͘ͷ͝ࢦಋΛ௖͖·ͨ͠ɻେֶೖֶલΑΓ෺࣭༏੎Ӊ஦ͷಾΛղ໌͍ͨ͠ͱߟ͑ɺຊֶ෦ʹೖֶ͠·͕ͨ͠ɺ‫ڀݚ‬ੜ‫͍͓ͯʹ׆‬ඍྗͳ͕Β͜ͷ‫ͱ͖ͨ͜Ͱݙߩʹڀݚ‬Λେม‫͘͠خ‬ଘ͡·͢ɻUCI ͷๆढ़Ұઌੜ͸ଟ๩Λ‫ۃ‬ΊΔதɺ໘ࣝͷͳ͍ࢲʹຖिͷΑ͏ʹ࣌ؒΛׂ͍ͯ௖͖ɺͦͷ౎౓࠙੾ஸೡʹ͝ࢦಋΛͯ͠௖͖·ͨ͠ɻຊ‫ڀݚ‬ͷਐΊํʹ͍ͭͯӈ΋ࠨ΋෼͔Βͳ͔ͬͨࢲ͸ๆઌੜͷॿ‫ʹݴ‬ΑͬͯԿ౓‫ٹ‬ΘΕ͔ͨ෼͔Γ·ͤΜɻ·ͨɺ‫ڀݚ‬άϧʔϓͰͷձٞͷࡍʹ͸ൃදͷखॿ͚΍ࢲͷ੿͍ӳ‫ޠ‬ͷαϙʔτ·Ͱ͍͖ͯͨͩ͠
·ͨ͠ɻໟड߂জઌੜʹ͸ൃදεϥΠυ΍จॻͷ࡞੒ํ๏ͳͲࡉ෦·Ͱஸೡʹ͝ࢦಋΛ௖͖·ͨ͠ɻ͍ͭ΋‫͔ʹؾ‬͚ͯ௖͖ɺਫ਼ਆ໘Ͱେม͓ੈ࿩ʹͳΓ·ͨ͠ɻ·ͨɺେ‫ؾ‬χϡʔτϦϊৼಈ‫ڀݚ‬άϧʔϓͷઌੜํɺઌഐํʹ͸‫ݚ‬‫಺ڀ‬༰ʹؔ͢Δଟ͘ͷॿ‫ݴ‬Λ௖͖·ͨ͠ɻԞଜᐁઌੜʹ͸ຊ‫ ͍ͨ༻Ͱڀݚ‬PC ͷηοτΞοϓɺղੳπʔϧͰ͋Δ

ROOT ͷߨशɺ࿦จςϯϓϨʔτͷ࡞੒ͳͲΛ͍͖ͯͨͩ͠ɺຊ‫ڀݚ‬Λԁ‫ʹ׈‬ਐΊΔ͜ͱ͕Ͱ͖·ͨ͠ɻ·ͨɺಉ‫ࣨڀݚ‬ͷઌੜํʹ͸ຊ‫ʹڀݚ‬ର͢Δॿ‫͘ͳͰ͚ͩݴ‬ɺ෯޿͍‫ڀݚ‬෼໺ʹؔ͢Δ͝ࢦಋΛ௖͖ɺ෺ཧֶ෼໺શମ΁ͷ‫ݟ‬ฉΛਂΊΔ͜ͱ͕Ͱ͖·ͨ͠ɻ౦‫ژ‬େֶ΍ຊେֶɺಉ‫ࣨڀݚ‬ͷࣄ຿ͷํʑʹ͸ɺग़ுਃ੥΍֤छॻྨͷ࡞੒ํ๏ͳͲʹॿྗΛ௖͖·ͨ͠ɻ‫ڀݚ‬Λ௨ͯ͠਌ກΛਂΊͨଞେֶͷֶੜͷօ༷ʹ͸ීஈͷੜ‫Ͱ׆‬େม͓ੈ࿩ʹͳΓ·ͨ͠ɻ֎ք͔Βด͟͞ΕͨਆԬͰੜ‫͢׆‬Δ͜ͱ͸͍͔͞͞ࠔ೉Ͱ͕ͨ͠ɺ੠Λ͔͚ͯ͘Εͨօ༷ͷ͓ӂͰॆ࣮ͨ͠΋ͷͱͳΓ·ͨ͠ɻಛʹΤσΟϯόϥେֶ͔ΒͷཹֶੜͰ͋Δ Mahdi ͞Μ͸ӳ‫͕ۤޠ‬खͳࢲʹɺ͍ͭ΋‫ʹ͘͞ؾ‬ɺͦͯ͠ͱͯ΋਌੾ʹ࿩͔͚ͯͩ͘͠͞Γ·ͨ͠ɻӳจʹͯ‫ँײ‬Λ఻͍͖͑ͤͯͨͩ͞·͢ɻI’m greateful to Mahdi for always kindly talking to me even though I am not very good at English.
ಉ‫ࣨڀݚ‬ͷ্‫ڃ‬ੜͷํʑʹ͸ɺ‫ڀݚ‬ੜ‫ʹ׆‬ඞཁͳ४උ΍‫ڀݚ‬ͷਐΊํͷΞυόΠεΛ௖͖·ͨ͠ɻ·ͨҿΈձΛ
‫ا‬ը͍͍ͯͨͩͨ͠Γɺҿ৯୅Λᇋͬͯͩ͘͞Γͱීஈͷੜ‫Ͱ׆‬΋͓ੈ࿩ʹͳΓ·ͨ͠ɻ·ͨԼ‫ڃ‬ੜͷօ༷ʹ͸‫ݚ‬‫ڀ‬ੜ‫͏͍ͱ׆‬ΑΓ΋Ή͠Ζීஈͷੜ‫Ͱ׆‬େม͓ੈ࿩ʹͳΓ·ͨ͠ɻ೐΍͔ͳۭؒ͸‫ڀݚ‬ੜ‫׆‬ͷർΕͷ༊͠ͱͳΓɺ‫ʹࣨڀݚ‬଍ΛӡͿࣄָ͕͠ΈʹͳΓ·ͨ͠ɻಉ‫ڃ‬ੜͷُҪ༔ฏ͘Μɺ౻Ҫେᠳ͘Μɺࢁ઒஛‫͘ݰ‬Μͷ͓ӂͰࢲ͸ಉ‫ࣨڀݚ‬ͷଘࡏΛ஌Δࣄ͕Ͱ͖·ͨ͠ɻֶ෦ੜ࣌୅͔Β࠷΋͓ੈ࿩ʹͳͬͨํʑͰ͋Γɺ3 ೥ؒ൴Βͱ‫੾ʹڞ‬᛭ୖຏͰ͖ͨ͜ͱΛ‫ތ‬Γʹࢥ͍·͢ɻςΧϙ‫ބ‬ͷຬ఺ͷ੕ۭΛࢲ΋Ұ౓͸‫ͯݟ‬Έ͔ͨͬͨͰ͢ɻ
͜ͷΑ͏ʹଟ͘ͷํʑͷࢧ͑ͷ͓ӂͰຊ࿦จΛ‫׬‬੒͢ΔʹࢸΓ·ͨ͠ɻॏͶͯ‫ྱޚ‬ਃ͋͛͠Δͱ‫ʹڞ‬ɺօ༷ͷ༷ʑͳ෼໺Ͱͷ͝‫׆‬༂Λ‫ف‬೦͓ͯ͠Γ·͢ɻ࠷‫ʹޙ‬ɺ24 ೥ؒͰग़ձͬͨશͯͷօ༷ͱɺ͍ͭ΋ࢧ͍͍͑ͯͨͩͨՈ଒ʹ‫ँײ‬Λਃ্͛͠·͢ɻຊ౰ʹ͋Γ͕ͱ͏͍͟͝·ͨ͠ɻ

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