1127

˙ ‫঺ڀݚ‬հ

MEG ࣮‫ʹݧ‬ΑΔ µ+ → e+γ ୳ࡧ౦‫ژ‬େֶ ૉཻࢠ෺ཧࠃࡍ‫ڀݚ‬ηϯλʔ৿ ढ़ଇ
mori@icepp.s.u-tokyo.ac.jp
2017 ೥ (ฏ੒ 29 ೥) 12 ݄ 12 ೔

1

͸͡Ίʹ

ͱ͢ΔͱɺχϡʔτϦϊͷ୅ΘΓʹԿ͔ద౓ʹॏཻ͍ࢠ͕ഔհ͢Ε͹ʢਤ 1ʢbʣʣɺµ → eγ ่յ͸࣮‫؍Ͱݧ‬ଌ

MEGʢϝάɺMu-E-Gammaʣ࣮‫[ ݧ‬1] ͸ɺ1999 ೥ʹͰ͖Δେ͖ͳ෼‫ذ‬ൺͰ‫͜ى‬Δ͜ͱʹͳΔɻͭ·Γ͜ͷ่౦‫ژ‬େֶͱ KEKɺૣҴాେֶͷ‫͕ऀڀݚ‬ϩγΞͷ‫ڀݚ‬յ͸ɺՙిϨϓτϯͱ݁߹͢ΔͦͷΑ͏ͳॏཻ͍ࢠΛ൐ऀͱ‫ʹڞ‬εΠεࠃཱϙʔϧγΣϥʔ‫ॴڀݚ‬ʢPSIʣʹ࣮͏৽෺ཧʹରͯ͠ɺඇৗʹ‫౓ײ‬ͷߴ͍ϓϩʔϒʹͳΔɻ

‫ݧ‬ϓϩϙʔβϧ [2] Λఏग़͠ɺಉ೥ PSI ͷ‫ڀݚ‬ҕһձͰঝೝ͞Εͯ࢝·ͬͨ΋ͷͰ͋Δɻঝೝ‫·ޙ‬΋ͳ͘ PSI ͱΠλϦΞͷ‫ڀݚ‬άϧʔϓ͕ՃΘΓɺͦͷ‫ޙ‬ถࠃͷάϧʔϓ΋ࢀՃͯ͠ɺֶੜ΋‫ؚ‬Ί૯੎ 60ʙ70 ਓͷࠃࡍ‫ڞ‬ಉ࣮‫ͨͬͳͱݧ‬ɻ਺೥ʹΘͨΔଌఆ‫ث‬ͷ‫ڀݚ‬։ൃͷ‫ޙ‬ɺ2007೥ʹ࣮‫૷ݧ‬ஔ͕‫׬‬੒ɺ2008 ೥ΑΓຊ֨తʹ࣮‫ݧ‬Λ։࢝͠ɺͦͷ‫ޙ‬ຖ೥σʔλΛऔಘͯ͠ɺ2013 ೥ʹऴྃͨ͠ɻ
࢒೦ͳ͕Β໨ඪͱ͢Δ µ → eγ ʢϛϡʔΠʔΨϯϚʣ่յͷൃ‫ʹݟ‬͸ࢸΒͣɺ2016 ೥ʹൃදͨ͠࠷ऴ࿦จʹC

D

͓͍ͯͦͷ෼‫ذ‬ൺʹ 4.2 ×10−13 ͱ͍͏্‫ݶ‬஋Λ͚ͭͨਤ 1: ʢaʣχϡʔτϦϊৼಈɺʢbʣॏ͍৽ཻࢠΛ௨͠υ࣮‫ ݧ‬MEG II [4] Λ্ཱͪ͛ͭͭ͋Δɻ

ͨ µ → eγ ่յͷμΠΞάϥϜɻ[3]ɻ‫ࡏݱ‬͸࣮‫౓ײݧ‬Λ͞Βʹ 10 ഒ͋͛ͨΞοϓάϨʔ͜͜Ͱ͸ɺMEG ࣮‫ৼ͍ͯͭʹݧ‬Γฦͬͯ؆୯ʹ·ͱΊͯΈ͍ͨͱࢥ͏ɻ

2µ → eγ ͷ෺ཧµ → eγ ่յ͸ɺୈೋੈ୅ͷՙిϨϓτϯͰ͋ΔϛϡʔΦϯ͕ΨϯϚઢΛ์ग़ͯ͠ɺୈҰੈ୅ͷిࢠ΁ม‫͢׵‬Δ‫ݱ‬৅Ͱ͋Δɻ͜ͷ൓Ԡ͸Ͳͷ෺ཧ๏ଇʹ΋ҧ൓͠ͳ͍ͷͰ౰વ‫͜ى‬Δ͸ͣͰ͋Δ͕ɺ͜Ε·ͰҰ౓΋‫؍‬ଌ͞Εͨ͜ͱ͕ͳ͍ɻ͜ΕʹΑΓɺిࢠͱϛϡʔΦϯ͸ҟͳΔอ
ଘྔʮϑϨʔόʔʯΛ͍࣋ͬͯΔͱ͞Ε͖ͯͨɻ
ͱ͜Ζ͕χϡʔτϦϊৼಈ͕ൃ‫͞ݟ‬ΕɺϑϨʔόʔͷอଘͳͲͱ͍͏ͷ͸‫ݬ‬૝Ͱ͋Δ͜ͱ͕Θ͔ͬͨɻχϡʔτϦϊৼಈʹΑΓɺਤ 1ʢaʣͷμΠΞάϥϜΛ௨ͯ͠µ → eγ ่յ͸ඞͣ‫͜ى‬Δɻͱ͜Ζ͕χϡʔτϦϊͷ࣭ྔ͕ిऑεέʔϧʹൺ΂ͯ‫ۃ‬Ί͍ͯܰͨΊʹɺͦͷ่յ෼‫ذ‬ൺ͸ 10−54 ఔ౓·Ͱ཈੍͞Ε͍ͯΔɻͭ·Γɺµ → eγ่յ͕‫͔ͭݟ‬Βͳ͍ͷ͸ϑϨʔόʔ͕อଘ͢Δ͔ΒͰ͸ͳ͘ɺχϡʔτϦϊͷ࣭ྔ͕͍͍ܰͤͰ͋ͬͨɻ

2.1

௒ରশେ౷Ұཧ࿦ͱγʔιʔཧ࿦

1990 ೥୅ॳ಄ɺ౦‫ژ‬େֶͷάϧʔϓ͸ CERN ͷ LEPిࢠཅిࢠίϥΠμʔͰେྔͷ Z0 ཻࢠͷਫ਼ີଌఆΛߦͳ͍ͬͯͨɻͦͷ݁Ռ͔Βɺ௒ରশେ౷Ұཧ࿦Ͱ͸ࡾͭͷ૬‫ ͕༻࡞ޓ‬1016 GeV ͱ͍͏௒ߴΤωϧΪʔͰ౷Ұ͞
ΕΔ͜ͱ͕Θ͔ͬͨʢਤ 2ʣɻΧϛΦΧϯσ࣮‫͕ݧ‬໨ࢦ͍ͯͨ͠௒ରশੑͷͳ͍େ౷Ұཧ࿦Ͱ͸͏·͘౷Ұ͞Εͳ͍ɻ௒ରশେ౷Ұཧ࿦Ͱ͸େ౷ҰͷΤωϧΪʔ͕ΑΓߴ͍ͨΊɺΧϛΦΧϯσͰཅࢠ่յ͕‫͔ͭݟ‬Βͳ͔ͬͨͷ͸౰વͰɺ౰࣌·ͩ࢝·͍ͬͯͳ͔ͬͨεʔύʔΧϛΦΧϯσ࣮‫Ͱݧ‬΋ൃ‫ݟ‬͸ࠔ೉ͷΑ͏ʹࢥΘΕͨɻ

1995 ೥ʹ͸ LEP ࣮‫ݧ‬ͷ༧૝௨Γ໿ 175 GeV ͱ͍͏్ํ΋ͳ͍࣭ྔͰτοϓΫΥʔΫ͕ถࠃ Tevatron Ͱൃ‫͞ݟ‬Ε͕ͨɺಉ͡ࠒɺ௒ରশେ౷Ұཧ࿦Ͱ͸ µ → eγ ่յ͕ 10−11 ͔Β 10−14 ͱ͍͏ɺ‫؍ʹ࣮ݱ‬ଌͰ͖ͦ͏ͳ
෼‫ذ‬ൺͰ‫͜ى‬Δ͜ͱ͕ࣔ͞Εͨ [5]ɻ௒ରশཧ࿦ͳͲ৽෺ཧͷϞσϧͰ͸ɺµ → eγ ่յ͕‫͜ى‬Βͳ͍Α͏ʹɺ࠷ॳʹϑϨʔόʔීวੑͳͲΛԾఆ

2128µ → eγ ͕ O(10−12) ఔ౓ͷେ͖ͳ෼‫ذ‬ൺͰ‫͜ى‬Δ͜ͱ

͢Δͷ͕ৗ౟खஈͱͳ͍ͬͯΔɻͱ͜Ζ͕௒ରশେ౷Ұཧ࿦Ͱ͸ɺ࠷ॳʹͦͷΑ͏ͳԾఆΛ͓͍ͯͯ͠΋ɺ͘ΓΛࣔࠦ͢Δɻ

͜Έ‫ํ܈‬ఔࣜΛ௨ͯ͠ॏ͍τοϓΫΥʔΫͷޮՌʹΑΓҰํɺ2012 ೥ʹ LHC Ͱൃ‫͞ݟ‬Εͨώοάεཻࢠ͸ࣗવʹϑϨʔόʔͷࠞ߹͕‫͜ى‬Γɺµ → eγ ่յ͕େ͖

125 GeV ͱൺֱతܰ͘ɺେ౷Ұཧ࿦΍γʔιʔཧ࿦ͷͦͷ‫ޙ‬εʔύʔΧϛΦΧϯσʹΑͬͯχϡʔτϦϊৼিಥΤωϧΪʔΛ΄΅ഒ૿ͯ͠ӡస͍ͯ͠Δ͕ɺ͜Ε·ಈཱ͕͕֬ͨ͠ɺχϡʔτϦϊͷγʔιʔཧ࿦Ͱ΋ಉ༷Ͱ৽ཻࢠ͸‫͍ͳ͍͔ͯͬͭݟ‬ɻਤ 1ʢbʣͷμΠΞάϥ

ͷ͜ͱ͕‫͜ى‬Γɺେ͖ͳχϡʔτϦϊࠞ߹͕ΑΓେ͖ͳϜʹ͸ LHC Ͱͷൃ‫͕ݟ‬೉͍͠‫͍ڧ‬૬‫༻࡞ޓ‬Λ͠ͳ͍৽µ → eγ ่յΛಋ͘͜ͱ͕ࣔ͞Εͨ [6]ɻཻࢠ͕‫د‬༩͢ΔͨΊɺLHC ࣮‫ʹݧ‬ΑΔ੍‫ݶ‬͸·ͩ؇͍ɻµ → eγ ่յͷ୳ࡧ͸ɺLHC ࣮‫ͱݧ‬͸ҧͬͨ֯౓͔Β৽ͳ෼‫ذ‬ൺͰ‫͜ى‬ΔΑ͏ʹͳΔͷͰ͋Δɻ

γφϦΦͱ͸ໃ६͠ͳ͍ɻLHC ͸ͦͷ‫ ޙ‬2015 ೥͔Β‫ڭށંނ‬तͷൃҊͰ౦‫ژ‬େֶΛத৺ͱ͢Δάϧʔϓ͸µ → eγ ่յ୳ࡧ࣮‫ݧ‬ͷ‫ݕ‬౼Λ࢝Ί [7]ɺ1996 ೥ʹ͸༏͍͠෺ཧʹഭΔ΋ͷͰ͋ΔɻΕͨϛϡʔΦϯϏʔϜΛ࣋ͭ PSI Λ๚Εͯࠃࡍతͳٞ࿦ FLAVOR PHYSICS AT LARGE TAN % WITH A . . .

Λ։࢝ͨ͠ɻ1997 ೥͔Β͸ µ → eγ ࣮‫ݧ‬ͷ࣮‫ݱ‬Λ໨ࢦ͢ࠃࡍ‫ڀݚ‬ձ͕ PSI Ͱఆ‫ظ‬తʹ։࠵͞ΕΔΑ͏ʹͳΓɺ

1998 ೥ͷ Letter of Intent [8]ɺ1999 ೥ͷ࣮‫ݧ‬ϓϩϙʔβϧ [2] ʹ‫͕ͨͬܨ‬ɻ

FIG. 6ਤ(color
Expectations for B"" ! e!$ and B"( ! "!$ vs !a" ! "g" #3: online).
ϛϡʔΦϯҟৗ࣓‫ؾ‬ೳ཰ͷඪ४ཧ࿦͔ΒͷͣΕ
10# 2 . The plots have been obtained employing the following ranges: 300 GeV * M‘~∆aµ* ͱ
eγGeV,
่յ෼‫ذ‬ൺͷ૬ؔʢจ‫ݙ‬[10] ΑΓసࡌʣ
ɻ M ! 1:5 T
500 GeV"µ* →1000
10 * tan% * 50, and setting
AU ! # 1 TeV,
q~
−10
−12
and M
'
6M
are
assumed.
The
inner
(red)
areas
correspondtopointswithin the∆aͰ͋Γ µ → eγ ͕ 10ఔ౓Ͱ
3 µ = 1(29 ± 8) × 10
8constraints listed in Sec. III B [B"Bs ! "% "# $ < 8 & 10# 12, 1:01 < R−4
Bs! < 1:24, 0:8 <‫͜ى‬Δ͜ͱΛࣔࠦ͢ΔɻϑϨʔόʔࠞ߹͸ |δLL | = 10

ਤ 2: LEP Ͱͷਫ਼ີଌఆʹΑΓɺ௒ରশੑΛೖΕͨϞσϧͱԾఆ͞Ε͍ͯΔɻ

tween the ‘i ! ‘j
Given that both ‘i ! ‘j ! and !a" ! "g" # gSM" $=2 aregeneratedbydipoleoperators,
itisnaturaltoestablishaillustrated
in Fig.
Ͱ‫͜ى‬Δ͜ͱ͕ࣔ͞ΕͨɻҰํɺ௒ରশੑΛೖΕͳ͍Ϟ
link between them. To this purpose, we recall the dominant
processes are notσϧʢ఺ઢʣͰ͸౷Ұ͞Εͳ͍ɻ
contribution
by the chargino
line; however, it" is
3 µto→!a3eͱalsoµNprovided→ eN
closely connectedexchange and can be written as
shown in Fig. 6µ → eγ ่յͱΑ͘ࣅͨϛϡʔΦϯͷ൓Ԡաఔʹɺϛ
!
" g "M2 =M2 ; "2 =M2 $#2 2 "M2 2c 2 ‘~mulas reported in
‘~
+
+
−
+
tan
%;
!aϡʔΦϯ͕ࡾͭͷిࢠʹ่յ͢Δ
!
#
m
"
"
→ e e e ่յ
2
2
2µ
4$
m
#
"
$
"M
tributions to bothL
2
2.2 ϛϡʔΦϯͷҟৗ࣓‫ؾ‬ೳ཰ͱ LHC
ʢµ → 3e ่յʣͱɺϛϡʔΦϯ‫ࢠݪ‬ͷதͷϛϡʔΦϯ͕
results in the mas(17)−−µ N → e (19)
N have been sਤ 1ʢbʣͰిࢠΛϛϡʔΦϯʹஔ͖‫͑׵‬Δͱɺϛϡʔ with ిࢠʹస‫͢׵‬ΔϛϡʔΦϯɾిࢠస‫׵‬൓Ԡ
gc2 "x; y$ defined as fc2 "x; y$ in terms of
inner dark-grayʢN ͸‫֩ࢠݪ‬ʣ͕͋Δɻ͜ΕΒͷ൓Ԡաఔ͸ɺਤ1 ͰޫࢠΦϯͷҟৗ࣓‫ؾ‬ೳ཰ aµ = (gµ −2)/2 ͷߴ࣍ޮՌΛද͢
B-physics constr"3 # 4a % a2 % 2 loga$
gc2 "a$
!
:
(18)
ͷ୺ʹిࢠ
ɾཅిࢠର·ͨ͸ΫΥʔΫରΛ଍͢͜ͱʹΑΓ
B-physics constraμΠΞάϥϜͱͳΔɻ2006 ೥ʹൃද͞Εͨถࠃϒϧο3"a # 1$fore,ಘΒΕɺ൓Ԡ֬཰͸ µ → eγ ่յͷ͓͓Αͦ α ∼1/100 through theΫϔϒϯ‫Ͱॴڀݚ‬ͷ aµ ଌఆͷ࠷ऴ݁Ռ [9] ͸ɺඪ४ཧIt is then straightforward to deduce the relation
Figs. 3 and 4). As
ͱߟ͑ΒΕΔɻ࿦͔Β໿ 3.5σ ͣΕ͓ͯΓɺ͜ͷΑ͏ͳॏ͍৽ཻࢠͷμ#$B"‘i ! ‘j !$ are3
2
B"‘i ! ‘j !$48$ # !a"ਖ਼֬ͳ‫ʹࢉܭ‬ΑΔͱҎԼͷؔ܎͕͋Δɿ
ΠΞάϥϜͰ͏·͘આ໌Ͱ͖Δɻ΋ͦ͠Ε͕ຊ౰ͩͱ͢
!
tary illustration o2
2
B"‘i ! ‘j &‘i &" ‘j $GFm"dark-matter const
Δͱɺ౰વ µ → eγ ่յʹ΋ಉ༷ͷμΠΞάϥϜΛ௨͠
+
+ −#+
+
2
2
2
2+$
scenario—is show
"M
=M
;
"
=M
$
2
f
B(µ → e e e 2c
) ≃0.006
× B(µ‘~ → eij γ)
2‘~ͯେ͖͘ޮ͍ͯ͘Δ͸ͣͰ͋Δɻਤ 3 ͸ɺ͋Δ௒ରশϞ&j'LL j2 :The normalizat2222"M2 =M‘~; ×" B(µ=M‘~+$ → e+ γ)
g2c≃0.0026
R(µ− Al → e− Al)σϧʹରͯ͠ aµ ͷඪ४ཧ࿦͔ΒͷͣΕ ∆aµ ͱ่յ෼corresponds to the(19)
M&R ! 1012 GeV‫ذ‬ൺ B(µ → eγ) ͷؔ܎Λࣔͨ͠΋ͷͰ͋Δ [10]ɻ͜ͷ
−
−
͜͜Ͱ
R(µ
N
→
e
N
)
͸ɺϛϡʔΦϯั֫൓Ԡʹର
rather natural (orΑ͏ͳ૬ؔ͸৽ཻࢠͷϞσϧͷৄࡉʹ͸͋·ΓґΒͣɺTo understand the relative size of the correlation, in thelimit ͢ΔϛϡʔΦϯɾిࢠస‫׵‬൓Ԡͷ‫͜ى‬Δׂ߹Λද͢ɻof degenerate SUSY spectrum we get
9$2#
For comparison,!a"dark-matter
constraB"‘i ! ‘j !$ '#10
20 & 10right-handed neutri
10%
For M&R , 101
2(" ! e);1 & 10# 4 j'12
LL jquark-induced term&
(20)
glected [43]. As a
2 & 10# 5 j'23 j2 (( ! "):ʢ࣮ઢʣͰ͸ࡾͭͷ૬‫༻࡞ޓ‬ͷେ౷Ұ͕͓Αͦ 1016 GeV

3129௒ରশϞσϧͰ͸ଟ͘ͷ৔߹ɺ͜ͷؔ܎ࣜ͸ਖ਼͍͠ɻҰํɺޫࢠҎ֎ͷཻࢠʹΑΔաఔ͕ µ → 3e ΍ µN → eNʹେ͖͘‫د‬༩͢ΔϞσϧͰ͸ɺ͜ͷؔ܎ࣜ͸ඞͣ͠΋੒4µ → eγ ่յ୳ࡧͷઓུµ → eγ ่յΛ‫͚ͭݟ‬Δʹ͸ɺ੩ࢭ͍ͯ͠ΔϛϡʔΦϯͷ่յΛଌఆͯ͠ɺిࢠͱΨϯϚઢ͕ͦΕͧΕϛϡʔΦΓཱͨͳ͍͜ͱʹ஫ҙ͢Δඞཁ͕͋Δɻ͜ΕΒࡾͭͷաఔͷ͜Ε·Ͱͷ୳ࡧͷྺ࢙Λɺ্‫ه‬ͷϯ࣭ྔͷͪΐ͏Ͳ൒෼ͷΤωϧΪʔʢ52.8 MeVʣΛ࣋ͬؔ܎ࣜΛ࢖ͬͯ µ → eγ ͷ่յ෼‫ذ‬ൺʹম͖௚ͯ͠ϓͯ൓ରํ޲΁ಉ࣌ʹඈͼग़͢ࣄ৅Λ୳ͤ͹Α͍ɻϛϡʔେ͖͘੾Γ։͍͖ͯͨ͜ͱ͕‫ͯݟ‬औΕΔɻ͜͜͠͹Β͘Φϯ͸ɺ‫ัʹ֩ࢠݪ‬Β͑ΒΕͯϛϡʔΦϯ‫ͳͱࢠݪ‬Γɺͳ͔ͬͨ µ → 3e ͱ µN → eN ͷ୳ࡧ͸ 2020 ೥୅ʹ่͔յͷࡍʹ‫͕֩ࢠݪ‬൓௓ͯ͠͠·͏ͨΊɺਖ਼ిՙϛϡʔϩοτͨ͠ͷ͕ਤ 4 Ͱ͋ΔɻMEG ࣮‫ྖͳͨ৽͕ݧ‬ҬΛ

−14͚࣮ͯࢪ͞ΕΔ༧ఆͰɺ͍Α͍Α O(10) ͷ࣌୅Λܴ͑Α͏ͱ͍ͯ͠Δɻ

Φϯ͸෺࣭தͰ‫ݮ‬଎ͯ͠੩ࢭͤ͞Δɻͨͩ͠ෛిՙϛϡʔΦϯΛ࢖Θͳ͍ͱ͍͚ͳ͍ɻ
ཅࢠϏʔϜΛੜ੒λʔήοτʹͿ͚ͭͯɺ͔ͦ͜Βग़

PHYSICAL REVIEW
D 75, 115019 (2007)͜ͷΑ͏ʹ͍ͭ͘΋ͷ୳ࡧ‫ܭ‬ը͕‫ٸࡏݱ‬଎ʹਐΜͰ͍ͯ͘Δਖ਼ిՙϛϡʔΦϯΛ࣓ੴͰूΊΔͱɺͦͷӡಈྔΔͷ͸ɺ΋ͪΖΜ৽෺ཧൃ‫ݟ‬ͷ‫ظ‬଴͕ߴ·͍ͬͯΔ͔Β෼෍ʹ͸ 28-29 MeV/c ෇ۙʹӶ͍ϐʔΫ͕͋Δɻ͜ΕͰ͋Δ͕ɺͦΕʹՃ͑ͯɺͦͷΑ͏ͳ‫౓ײ‬ͷߴ͍୳ࡧΛ͸ੜ੒λʔήοτͷද໘෇ۙͰ੩ࢭͨ͠ਖ਼ిՙύΠΦϯՄೳʹ͢Δ৽͍࣮͠‫ٕݧ‬ज़͕ɺ࣌‫ػ‬Λҳ͢Δ͜ͱͳ͘ߟ

ͷೋମ่յ͔ΒདྷΔϛϡʔΦϯͰɺʮද໘ϛϡʔΦϯʯͱҊɾ։ൃ͞Ε͖͔ͯͨΒͰ΋͋Δɻ

‫ݺ‬͹Εɺ100%ภ‫͍ͯ͠ۃ‬Δɻ௿ΤωϧΪʔͰӡಈྔ͕͜ͷ༧ఆ௨ΓਐΉͱɺ΋͠ µ → eγ ͕ൃ‫͞ݟ‬ΕΕ͹ɺΑ͘ଗ͍ͬͯΔͷͰɺബ͍੩ࢭλʔήοτͰ΄΅͢΂ͯͷͱͳΔɻҰํɺͨͱ͑ µ → eγ ͕ൃ‫͞ݟ‬Εͳͯ͘΋ɺ੩ࢭλʔήοτதͰͷଟॏࢄཚͱΤωϧΪʔଛ่ࣦ͕յ

ͨͼൃ‫͞ݟ‬ΕΕ͹ɺͦΕͧΕͷ่յ෼‫ذ‬ൺͷ্‫ࣜ܎ؔه‬͹ബ͍ํ͕Α͍ɻଞͷೋͭ΋ଓ͚ͯൃ‫͞ݟ‬Εɺ৽෺ཧͷଘࡏ͕࣮֬ͳ΋Λ੩ࢭͰ͖ɺµ → eγ ่յ୳ࡧʹ͸΋͍ͬͯ͜Ͱ͋Δɻµ → 3e ͱ µN → eN ͕ൃ‫͞ݟ‬ΕΔՄೳੑ͕͋ΔɻͻͱཅిࢠͷଌఆΛ੍‫͢ݶ‬ΔͨΊɺ੩ࢭλʔήοτ͸ബ͚Ε͔ΒͷͣΕ͕ɺഎ‫͋ʹޙ‬Δ৽෺ཧΛ୳ΔώϯτͱͳΔɻ໓ଟʹ‫͜ى‬Βͳ͍ µ → eγ ่յΛ୳ͨ͢Ίʹ͸ɺେྔ͞Βʹɺµ → eγ ͱ µ → 3e ͷ֯౓෼෍ɺµN → eN ͷͷϛϡʔΦϯΛଌఆ͢Δඞཁ͕͋Δɻ10−13 ͷ่յ෼‫ذ‬֩छґଘੑΛௐ΂Δ͜ͱͰɺ৽෺ཧͷਖ਼ମʹ͍ͭͯ͞Βൺ·Ͱ୳ࡧ͢Δʹ͸࠷௿Ͱ΋ 1013 ‫ݸ‬ͷϛϡʔΦϯ่յʹ‫ͳྗڧ‬ख͕͔Γ͕ಘΒΕΔͩΖ͏ɻΛଌఆ͠ͳͯ͘͸ͳΒͣɺ‫࣮ݱ‬తʹྦྷੵ 1 ೥ఔ౓ͷϏʔ

12
# 4
gSM
j ! 10and/ Progress
j'23
T. Mori,
W. Ootaniin Particle and Nuclear Physics (" $=2, assuming j'LL
LL j !
*
600
GeV,
200
GeV
*
M
*
1000
GeV,
~
2
‘
TeV. Moreover, the GUT relations M2 ' 2M1
e funnel region which satisfy the B-physics< RB(& < 0:9, !MBs ! 17:35 + 0:25 ps# 1 ].

)–7ϜλΠϜͰ࣮‫ݧ‬ΛऴΘΒͤΔ͜ͱΛߟ͑Δͱɺ‫ݕ‬ग़ޮ཰Λ਺%ͱͯ͠ɺඞཁͱͳΔϛϡʔΦϯϏʔϜ‫౓ڧ‬͸ɺຖ
ඵ 107 Λ௒͑Δɻ͜ͷΑ͏ʹඇৗʹߴ͍‫཰਺ܭ‬ͷ࣮‫ͳݧ‬ͷͰɺ‫ൃۮ‬తͳόοΫάϥ΢ϯυ͕େ͖ͳ໰୊ͱͳΔɻ͜Ε͸ɺ͋Δ

j ! transitions and !a" in our scenario isϛϡʔΦϯͷ௨ৗͷ่յʢϛγΣϧ่յʣµ+ → e+ ν ν̄

. 6. Since the loop functions for the two͔ΒͷཅిࢠͱɺผͷϛϡʔΦϯͷ᫔่ࣹյ͔Βग़ͯ͘
identical, the correlation is not exactly aΔΨϯϚઢ͕ɺͨ·ͨ·൓ରํ޲΁ಉ࣌ʹඈͼग़ͯ͠t is clear that the two observables ared. We stress that the numerical resultsµ → eγ ่յʹ‫͏·ͯ͑͠ݟ‬΋ͷͰ͋ΔɻΨϯϚઢͱ͠have been obtained using the exact forͯ͸ɺཅిࢠ͕෺࣭தͰඈߦதʹফ໓ͯ͠ൃੜ͢Δ΋ͷn Ref. [41] for the supersymmetric conʢAIF: Annihilation in Flightʣ΋͋Δɻ
h B"‘i ! ‘j !$ and !a" (the simplified
ss-insertion approximations in Eqs. (15)–ϛϡʔΦϯͷ᫔่ࣹյ µ → eν ν̄γ ΋ɺχϡʔτϦϊͷMEG Final
shown only for the sake of clarity). The
ΤωϧΪʔ͕΄ͱΜͲθϩͷ΋ͷ͸ɺµ → eγ ่յͱ۠MEG II(red) areas are the regions where theผ͕͔ͭͳ͘ͳΔɻ͔͠͠᫔่ࣹյʹ͓͍ͯɺͨͱ͑͹raints are fulfilled. In our scenario theaints put a lower bound on MH and thereཅిࢠͱΨϯϚઢͷΤωϧΪʔ͕ͦΕͧΕ 52.8 MeV ͷ
funnel-region relation, also on M1;2 (see1%͓Αͼ 5%Ҏ಺ʹೖΔ֬཰͸ 10−14 ఔ౓Ͱ͋Γɺे෼s a result, the allowed!a" andਤ 4: µranges→ eγfor่յ෼‫ذ‬ൺͷ্‫ݶ‬஋ʢ
90%৴པ౓ʣͷྺ −mental upper limits (90% C.L.) on cLFV muon processes as a function of the year where the µ → 3e and µ Nྑ͍෼ղೳͰଌఆ͢Ε͹ɺ‫ൃۮ‬తόοΫάϥ΢ϯυʹൺ→ e−N bounds are converted
lowered.
complementcorrespondinglyµ → eγ bounds ࢙ɻby using
and(7).µNThe corresponding
new physics scale Λ for κ = 0, defined in Eqs. (9) and (10), is also indicated.
µ Eqs.
→(6)3eAͱ→ eN ʹ͍ͭͯ͸ຊจதͷؔ܎ࣜ
of the interplay of B-physics observables,΂ͯे෼খ͘͞཈͑Δ͜ͱ͕Ͱ͖Δɻµ →feweγyears่յ෼‫ذ‬ൺʹম͖௚ͯ͋͠Δɻനൈ͖Λ༻͍ͯ
13
ourdata taking (T ≈O (107 ) s), a DC muon rate of 10
traints,!a" , andction
efficiency
ϵ ≈LFVO (1%rates) in a—withinof/ϵ/T ≈107 –108 /s‫ൃۮ‬తόοΫάϥ΢ϯυ͸ϛϡʔΦϯͷ‫཰਺ܭ‬ͷೋ৐y.
Sucha highDC muon beam is currently only available at Paul Scherrer(PSI), Switzerland. PSI’s
MEG IIInstituteɺ‫߸ه‬͸ɺ‫ࡏݱ‬४උதͷ࣮‫ݧ‬ͷ͏ͪओཁͳ΋ͷʢ
wn
in Fig.
7.9rate# 4ochronous
ring cyclotron
mA proton beam with 50.6 MHzʹൺྫͯ͠૿͑ΔͷͰɺॠؒతͳϛϡʔΦϯ਺͕ଟ͍ύRF time structure. Sincetion j'12
used constantly
in Figs. 6ɺsupplies
and7 a 2.2
LL j ! 10
COMET-II/Mu2e
Mu3e-IIIʣɻ the muon decay rate becomes constant (DC) without any
fe
time
of
2
µ
s
is
much
longerthantheRF
structure,e central value in Eq. (14) for c& ! 1 andϧεϏʔϜΑΓ΋ɺৗʹಉ͡ස౓ͰϛϡʔΦϯ่͕յ͢ure.
Thenormalization
cyclotron is currently
upgraded
eventually to 3.0 mA,V.
This
can be being
regarded
as a and its beam current is planned to increaseΔ௚ྲྀϏʔϜͷํ͕ɺµ → eγ ่յͷ୳ࡧʹద͍ͯ͠Δɻ
g an unrivalled beam power of101.8 MW.
As
can
be
r
even
pessimistic)
choice.
xperimental challenges are (1) a good photon energy resolution to suppress background photons
from radiative‫ൃۮ‬తόοΫάϥ΢ϯυͷཅిࢠ͸ϛγΣϧ่յ͔Βys and annihilation of positrons in material, and (2) precise measurements of positrons in the high rate environ8͘ΔͷͰ 52.8 MeV ෇ۙͷ΋ͷ͕Ұ൪ଟ͍ɻ͕ͨͬͯ͠
positrons
second.
,–10
a detailed
studyperof LFVtransitions imposing
Gaintsexperiment
PSI,constrained
which finisheddata
taking in summer 2013, obtained the world’s best upper bounds on—within atthe
MSSM
with
13
inos—canbe−foundin Ref.
[42].
) < 5.7 × 10
at 90%
C.L. [7]using ∼1/2 of the data taken. The final result of MEG is expected during the year
12 GeV other sources of LFV, such as thently at PSI, preparations are underway for the MEG II experiment, an upgrade of MEG, which plans to start data
ms in
grand
unifiedtheoriesancannot
bemagnitude
ne016
with
a goalof achieving
order ofbetter sensitivity than MEG in three years’ data taking.

7

result, in many realistic scenarios it is not4130ཅిࢠͷӡಈྔ෼ղೳΛ͍͘Β‫ؤ‬ுͬͯ΋ɺը‫ظ‬తʹҎԼͰ͸ɺ͜ΕΒࡾͭͷ‫ͳͱݤ‬Δ࣮‫ٕݧ‬ज़Λத৺ʹɺόοΫάϥ΢ϯυΛམͱ͢͜ͱ͸೉͍͠ɻཅిࢠͷଌఆ

MEG ࣮‫૷ݧ‬ஔ [11]ʢਤ 5ʣʹ͍ͭͯղઆ͢ΔɻͰ͸ɺຖඵ 107 Λ௒͑ΔཅిࢠΛ͍͔ʹૉૣ͘͞͹͍ͯ࠶ߏ੒͢Δ͜ͱ͕Ͱ͖Δ͔͕Ұ൪ॏཁͳ՝୊Ͱ͋ΔɻҎલͷถࠃͷ࣮‫ݧ‬͸͜͜Ͱࣦഊͨ͠ɻ
Ұํɺ‫ൃۮ‬తόοΫάϥ΢ϯυͷΨϯϚઢ͸ओʹ᫔่ࣹ

5.1

PSI ͷେ‫౓ڧ‬ද໘ϛϡʔΦϯ௚ྲྀϏʔϜ

ຖඵ 107 −108 ΋ͷେ‫౓ڧ‬ͷ௚ྲྀϛϡʔΦϯϏʔϜ͸ɺյ͔Β͖͓ͯΓɺͦͷεϖΫτϧ͸ɺ࠷ߴ୺ͷ 52.8 MeVੈքதͰ།Ұ PSI ʹ͔͠ଘࡏ͠ͳ͍ɻPSI ͸ɺύΠΦϯʹ޲͔ͬͯ‫ʹܹٸ‬མ͍ͪͯ͘ɻ͕ͨͬͯ͠ΨϯϚઢͷΤ΍ϛϡʔΦϯͷੜ੒ʹదͨ͠ 590 MeV ͷཅࢠαΠΫϩωϧΪʔ෼ղೳΛ͋͛Ε͹ɺ‫ݪ‬ཧతʹ͸͍͘ΒͰ΋όοτϩϯΛ࣋ͪɺ2.2 - 2.4 mA ͷཅࢠϏʔϜ͸ 1.4 MW ͱΫάϥ΢ϯυΛ‫ݮ‬Β͢͜ͱ͕Ͱ͖Δɻੈք࠷‫ڧ‬ͷύϫʔΛ‫͍ͯͬތ‬ΔɻཅࢠϏʔϜ͸ 50.6 MHz
ͷ RF ύϧεߏ଄Λ͕࣋ͭɺϛϡʔΦϯͷण໋͸ 2 µsecͱ௕͘ɺ௚ྲྀϛϡʔΦϯϏʔϜͱߟ͑ͯΑ͍ɻPSI ͷαΠΫϩτϩϯ͸‫ࡏݱ‬΋গͣͭ͠૿‫͞ڧ‬Ε͓ͯΓɺকདྷతʹ͸ 3.0 mAɺ1.8 MW Λࢹ໺ʹೖΕ͍ͯΔɻྫྷ٫ͷͨΊճస͢Δंྠঢ়ͷ 4 cm ްάϥϑΝΠτλʔήοτʹཅࢠϏʔϜΛ౰ͯɺେྔͷද໘ϛϡʔΦϯΛੜ
੒͢ΔɻMEG ࣮‫ݧ‬Λ࣮ࢪ͢Δ πE5 ϏʔϜϥΠϯ͸ɺཅࢠϏʔϜʹରͯ͠ 166◦ ͷ‫͔ํޙ‬Βେཱମ֯ͰϛϡʔΦϯΛҾ͖ग़͢ɻӡಈྔબ୒ͯ͠Ҿ͖ग़͞ΕͨϏʔϜʹ͸ϛϡʔΦϯͷ 10 ഒ͍ۙཅిࢠ͕‫·ؚ‬Ε͍ͯΔͨΊɺ੩ిηύϨʔλͱ࢛ॏ‫࣓ిۃ‬ੴΛ࢖ͬͯऔΓআ͘ɻͦͷ‫ޙ‬ϏʔϜ༌ૹ༻ͷ௒఻ಋιϨϊΠυʢBTSʣʹΑͬͯ
COBRA ཅిࢠεϖΫτϩϝʔλʢ࣍અࢀরʣͷத৺ʹஔ͔ΕͨϛϡʔΦϯ੩ࢭλʔήοτ΁ಋ͘ɻBTS ͱCOBRA ͷ࡞Δ࣓৔͸λʔήοτʹ޲͔ͬͯ‫ͯͬͳ͘ڧ‬͓ΓɺϏʔϜ͕ߜΒΕͯɺλʔήοτͰͷϏʔϜαΠζ͸໿ 2.3 cmφ ͱͳΔɻ੩ࢭλʔήοτ͸‫౓ڧ‬΋ߟྀͯ͠ɺް͞ 205 µm ͷϙϦΤνϨϯʗϙϦΤεςϧͷ૚ঢ়ϑΟϧϜΛϏʔϜʹର
ͯ͠໿ 20 ౓ͷ֯౓ʹ܏͚ɺ‫ػ‬ցత‫ʹ౓ڧ‬༏Εͨൃ๐ࡐʢRohacellʣͷ࿮Ͱ௻ΓԼ͛ͨʢਤ 5ɺ6ʣɻλʔήοτͰ੩ࢭͤ͞ΔϛϡʔΦϯ਺͸ɺଌఆ‫ث‬ͷੑೳͱόοΫάϥ΢ϯυͷ݉Ͷ߹͍ʹΑΓɺ3 ×107 /sec ͱ͕ͨ͠ɺ࣮

ࡍʹ͸ͦΕΑΓ 2–3 ഒଟ͍ϛϡʔΦϯΛࢭΊΔ͜ͱ͕ՄೳͰ͋Δɻਤ 5: MEG ࣮‫૷ݧ‬ஔͷུ֓ਤɻµ → eγ ࣄ৅ͷγϛϡϨʔγϣϯ͕ॏͶΒΕ͍ͯΔɻ

5.2

COBRA ཅిࢠεϖΫτϩϝʔλຖඵ 3 ×107 ΋ͷϛϡʔΦϯ่յ͔Βग़ͯ͘ΔେྔͷཅిࢠΛਫ਼౓Α͘ଌఆ͢ΔͨΊɺCOBRAʢCOnstant5

MEG ࣮‫ݧ‬લઅͷߟ࡯ʹΑΓɺµ → eγ ่յ୳ࡧͷઓུ͸ҎԼͷࡾ఺ʹू໿͞ΕΔɿ

Bending RAdiusʣ௒఻ಋి࣓ੴΛߟҊͨ͠ɻ3 छྨͷҟͳΔ൒‫ܘ‬Λ࣋ͭ 5 ͭͷίΠϧ͔ΒͰ͖͓ͯΓʢਤ 5ɺ

7ʣɺͦΕʹΑͬͯத৺࣠ʹԊͬͯத৺Ͱ‫͘ڧ‬ʢ1.27 Tʣ྆୺Ͱऑ͍ʢ0.49 Tʣಛघͳޯ഑࣓৔Λ࡞͍ͬͯΔɻ͜ͷޯ഑࣓৔தͰ͸ɺಉ͡ӡಈྔΛ࣋ͭཅిࢠ͸ɺϏʔ• ຖඵ 107 −108 ΋ͷਖ਼ిՙϛϡʔΦϯͷ௚ྲྀϏʔϜϜ࣠ʹਨ௚ͳ໘಺Ͱͷ‫ي‬ಓ൒‫์͕ܘ‬ग़֯౓ʹΑΒͣҰఆ• େྔͷཅిࢠΛ͞͹͘εϖΫτϩϝʔλͱͳΔʢਤ 7ʢaʣʣɻ͜Ε͕ COBRA ͷ໊ͷ༝དྷͰ͋Δɻ• ΤωϧΪʔ෼ղೳͷ༏ΕͨΨϯϚઢଌఆ‫ث‬͜ͷ͓͔͛Ͱɺଌఆ‫ث‬ΛϏʔϜ͔࣠Β཭ͯ͠ઃஔ͢Δ͜

5
131

μ+

e+

(a)

μ+

e+

ਤ 6: Լྲྀଆ͔Β‫ ͨݟ‬COBRA ి࣓ੴ಺෦ɻத৺ʹϛϡʔΦϯ੩ࢭλʔήοτ͕௻Δ͞ΕɺԼ෦ʹ 16 ຕͷυϦϑτνΣϯόʔ͕ฒΜͰ͍Δɻશମ͸ϔϦ΢ϜΨεʹຬͨ͞Ε͍ͯΔɻ(b)ͱʹΑΓɺӡಈྔͷߴ͍ཅిࢠ͔͠ଌఆ‫ʹث‬ೖͬͯ͜ͳ
͍ɻ·ͨϏʔϜ࣠ʹ΄΅ਨ௚ʹ์ग़͞ΕͨཅిࢠͰ΋ɺεϖΫτϩϝʔλ಺ʹ௕͘ཹ·Δ͜ͱͳ͘ɺ͢͹΍͘૟͖ग़͞Εʢਤ 7ʢbʣʣɺଌఆ‫ث‬ͷ‫͕཰਺ܭ‬཈͑ΒΕΔɻਤ 7: COBRA ޯ഑࣓৔ͷ‫ݪ‬ཧɻʢaʣཅిࢠ͸์ग़֯ʹΑΒͣಉ͡ӡಈྔͷ΋ͷ͸ಉ͡൒‫ܘ‬ͷ‫ي‬ಓΛඳ͘ɻʢbʣϏʔϜ࣠ʹ΄΅ਨ௚ʹ์ग़͞Εͨཅిࢠ΋ૉૣ͘εϖΫτϩϝʔλ֎ʹ૟͖ग़͞ΕΔɻ

༷ʑͳ࣓৔഑ஔΛ‫ݕ‬౼͍ͯͨ࣌͠ʹɺ͋Δಛఆͷޯ഑࣓৔Ͱ͸ɺ‫ي‬ಓ൒‫࠷͕ܘ‬େ࣌ͷཅిࢠͷ෼෍͕λʔήοτ্ͷϛϡʔΦϯ෼෍ͦͷ··ͷ౤Өʹͳ͍ͬͯΔ͜ͱ

υϦϑτνΣϯόʔʢDCʣʹ‫͖෇ؾ‬ɺͦΕ͕ COBRA ͷσβΠϯʹͭͳ͕ͬͨɻ

52.8 MeV ͷཅిࢠͷଌఆਫ਼౓͸ଟॏࢄཚʹΑ੍ͬͯΨϯϚઢ͸ɺCOBRA Λಥ͖ൈ͚ͯͦͷ֎ଆʹஔ͔Ε‫͞ݶ‬Ε͓ͯΓɺཅిࢠΞΫηϓλϯε಺ͷ෺࣭ྔΛ‫ݮ‬ΒͨӷମΩηϊϯΨϯϚઢଌఆ‫Ͱث‬ଌఆ͞ΕΔɻͦͷͨΊɺ͢͜ͱ͸ඞਢͷ৚݅Ͱ͋Δɻ͜ΕʹΑͬͯ AIF ʹΑΔΨϯϚઢ͕௨ա͢Δத৺ίΠϧ෦෼͸᫔ࣹ௕Ͱ 0.2X0 ҎόοΫάϥ΢ϯυ΋‫ݮ‬ΔɻͦͷͨΊ COBRA ి࣓ੴ಺Լʹ෺࣭ྔ͕཈͑ΒΕ͓ͯΓɺµ → eγ ͷ 52.8 MeV Ψϯ͸ϔϦ΢ϜΨεͰຬͨ͞ΕɺνΣϯόʔΨεͱͯ͠ϔϦ௒఻ಋ௿Թ޻ֶηϯλʔ͕։ൃͨ͠ߴ‫౓ڧ‬Ξϧϛ҆ఆࡐDC ͸ 16 ຕͷಠཱͨ͠ϞδϡʔϧͰͰ͖͓ͯΓʢਤΛ༻͍ͨബ೑௒఻ಋίΠϧٕज़ʹΑͬͯՄೳͱͳͬͨɻ

6ʣɺ֤Ϟδϡʔϧ͸υϦϑτηϧʢ9×7 mm2 ʣΛ൒η

COBRA ͸ͦͷಛघͳޯ഑࣓৔Λ࣮‫͢ݱ‬ΔͨΊϦλʔϧͣΒͨ͠ 2 ૚͔Β੒͍ͬͯΔɻCOBRA ࣓৔ͷ͓͔͛ϯϤʔΫΛ࣋ͨͣɺ࿙Ε࣓৔͕େ͖͍ɻӷମΩηϊϯଌͰɺ࠷΋಺ଆͷηϧͰ΋ 10 kHz ఔ౓ͷ‫ʹ཰਺ܭ‬཈͑Βఆ‫͍ͯ͠༻࢖Ͱث‬Δޫిࢠ૿ഒ؅͸‫࣓ڧ‬৔தͰ͸ಈ࡞͠Εͨɻ྆ଆಡΈग़͠ʹΑΔిՙ෼഑ʢCharge Divisionʣͳ͍ͨΊɺCOBRA ͷपΓʹϔϧϜϗϧπίΠϧঢ়ʹͱΧιʔυύουʹΑͬͯϫΠϠʔํ޲ͷҐஔ͕ಘΒΕɺೋͭͷେ͖ͳৗ఻ಋίΠϧΛઃஔͯͦ͠ͷपลͷ࣓৔Λૉૣ͍ࡾ࣍‫يݩ‬ಓͷ࠶ߏ੒͕Մೳͱͳ͍ͬͯͨɻ

50 Ψ΢εҎԼʹ཈͍͑ͯΔɻ࿙Ε࣓৔͸ɺਅۭϙϯϓ΍ྫྷ٫ϑΝϯɺ͞Βʹ͸ྡͷ µSR ༻௿଎ϛϡʔΦϯϏʔDC ֎น͸ް͞ 12.5 µm ͷϑΟϧϜද໘ʹ໿ 250 nmͷΞϧϛͷύουΛΤονϯάͨ͠ɻബ͞ΛอͪͭͭϜϥΠϯͳͲʹӨ‫ڹ‬Λ‫͠΅ٴ‬ɺͦͷରࡦʹ͸ۤ࿑ͨ͠ɻ

ύουͷҐஔਫ਼౓ͱ໘఍߅ͷҰ༷ੑΛ࣮‫͢ݱ‬Δͷʹ͸ଟλʔήοτ͔ΒདྷΔ໿ 45 MeV/c Ҏ্ͷཅిࢠ͸υ͘ͷࢼߦࡨ‫͕ޡ‬ඞཁͰ͋ͬͨɻDC ಺֎ͷඍົͳѹྗࠩϦϑτνΣϯόʔʢDCʣʹΑͬͯଌఆ͞ΕɺӡಈྔͱͰΧιʔυ໘͕ม‫͍ͳ͠ܗ‬Α͏ɺѹྗࠩมಈΛ 0.005 PaϛϡʔΦϯͷ่յҐஔ͕‫ٻ‬ΊΒΕΔɻཅిࢠ͸ DC Λఔ౓ʹ཈͑ΔΨεγεςϜ΋։ൃͨ͠ɻ

Ϛઢ͸໿ 85%͕૬‫ʹͣͤ༻࡞ޓ‬௨ա͢Δɻ͜Ε͸ KEK΢ϜͱΤλϯΛ൒ʑࠞͥͨ΋ͷΛ࢖ͬͨɻൈ͚࣓ͯ৔தΛ͞ΒʹҰपͨ͠‫ޙ‬ɺλΠϛϯάΧ΢ϯ

͜ΕΒͷ౒ྗʹΑΓɺ52.8 MeV ཅిࢠͷ‫ي‬ಓʹԊͬλʔʢTCʣʹೖͬͯͦͷ͕࣌ؒଌఆ͞ΕΔʢਤ 5ʣɻཅͨશ෺࣭ྔ͸ɺ᫔ࣹ௕Ͱฏ‫ ۉ‬2 ×10−3 X0 ͱඇৗʹখ͞ిࢠͷதʹ͸ DC ͷϑϨʔϜ΍έʔϒϧͳͲʹিಥͯ͠TC ʹ౸ୡ͠ͳ͍΋ͷ΋গͳ͔Βͣ͋Γɺ୳ࡧޮ཰ʹӨ‫ͨ͠ڹ‬ɻ

ͳ஋Λ࣮‫͢ݱ‬Δ͜ͱ͕Ͱ͖ͨɻ

ཅిࢠӡಈྔͷֱਖ਼͸ɺϛογΣϧ่յεϖΫτϧͷ
࠷ߴ୺ΤοδΛ࢖ͬͯߦ͍ɺ52.8 MeV ͷཅిࢠʹରͯ͠
0.58%ʢσ ʣͷ෼ղೳ͕ಘΒΕͨʢਤ 8ʣɻϛϡʔΦϯ่6

Number of events /(0.080 nsec)

Number of events /(0.25 MeV)

132

15000

Relative efficiency

10000

5000

0
1

10000
8000
6000
4000

NRMD = 13700 ± 412
sigma = 123 ± 3 ps

2000
0.5
0
40

0
-2
45

50

-1

55
Ee (MeV)ਤ 8: ϛγΣϧ่յཅిࢠͷଌఆεϖΫτϧʢࠇ‫ؙ‬ʣɻϛγΣϧεϖΫτϧͷཧ࿦෼෍ʢҰ఺࠯ઢʣͱଌఆ‫ث‬ΞΫ012teγ (nsec)

ਤ 9: ཅిࢠͱΨϯϚઢͷ࣌ؒࠩʢteγ ʣͷ෼෍ʢαΠυόϯυʣɻϐʔΫ͸᫔่ࣹյࣄ৅ɺฏΒͳ෼෍͸‫ൃۮ‬తόοΫάϥ΢ϯυࣄ৅ɻηϓλϯεʢԼͷάϥϑʣΛϑΟοτͯ͠‫ٻ‬ΊͨυϦϑτνΣϯόʔͷ෼ղೳؔ਺ʢ੨఺ઢʣɻ

5.3

ӷମΩηϊϯΨϯϚઢଌఆ‫ث‬յҐஔʹ͍ͭͯ͸ɺ੩ࢭλʔήοτʹখ͞ͳ͕͍݀ͭ͘

༏Εͨ෼ղೳΛ࣋ͭΨϯϚઢଌఆ‫ͯ͠ͱث‬͸ɺओʹೋ͔։͚ͯ͋Γɺ͜ΕΒΛਖ਼͘͠࠶ߏ੒͢Δ͜ͱͰɺλʔͭͷλΠϓ͕ߟ͑ΒΕΔɿ
ʢ1ʣZ ͷେ͖ͳ෺࣭ʹΑͬͯήοτͷҐஔ΍܏͖ɺޯ഑࣓৔ʹର͢Δ DC ͷ഑ஔɺ‫ي‬ిࢠɾཅిࢠରੜ੒Λ‫͢͜ى‬ബ͍૚ͱɺͦΕʹଓ࣓͘৔੻࠶ߏ੒ΞϧΰϦζϜʹΑΔόΠΞε౳͕ௐ΂ΒΕͨɻεϖΫτϩϝʔλ͔Β੒Δʮରੜ੒εϖΫτϩϝʔλʯɺʢ2ʣޫྔ͕ଟ͘ɺ࣌ؒԠ౴ͷ଎͍݁থγϯνϨʔλɺͰ
͋ΔɻλΠϛϯάΧ΢ϯλʔʢTCʣ

TC ͸ɺϏʔϜ্ྲྀଆͱԼྲྀଆͷͦΕͧΕʹ 15 ຊઃஔ͞Εͨ 4 × 4 × 90 cm3 ͷϓϥεςΟοΫγϯνϨʔλͰ͋Δɻ࣌ؒ෼ղೳ͸γϯνϨʔγϣϯޫ͕ଟ͍΄ͲΑ͘ͳΔͷͰɺଠ͍γϯνϨʔλͰޫྔΛՔ͗ɺूޫޮ཰
Λ࠷దԽͨ͠ɻ‫࣓ڧ‬৔தͳͷͰɺಡΈग़͠ʹ͸ϑΝΠϯ
ϝογϡ‫ܕ‬ͷޫిࢠ૿ഒ؅Λ࢖ͬͨɻTC શମΛಛघͳϑΟϧϜͰ෴ͬͯ஠ૉΨεΛྲྀ͢͜ͱʹΑΓɺCOBRA
಺ͷϔϦ΢Ϝ͔Βޫిࢠ૿ഒ؅Λकͬͨɻਖ਼֬ͳཅిࢠͷλΠϛϯάΛಘΔͨΊʹ͸໿ 1 cm ͷਫ਼౓Ͱ TC ΁ͷೖࣹҐஔΛ஌Δඞཁ͕͋ΔɻTC ͷ྆୺ಡΈग़͠ʹΑΓ TC ͷ௕͞ํ޲ͷҐஔ͕Θ͔ΓɺDC ͔Βཅిࢠͷ‫੻ي‬Λ֎ૠͯ͠ೖࣹ֯ͳͲΛಘͨɻTC ୯ಠͷ࣌ؒ෼ղೳ͸ 50–70 ps Ͱ͕͋ͬͨɺDC ͱ TC ͷؒʹ͋Δ෺࣭ྔͷӨ‫ʹڹ‬ΑΓ࣮ޮతͳ෼ղೳ͸ 100 ps ʹͱͲ·ͬͨɻTC ͷ௚લʹઃஔͨ͠γϯνϨʔγϣϯϑΝ
Πόʔ͸ɺಠཱͳҐஔ৘ใΛఏ‫ؒ࣌ͯ͠ڙ‬ଌఆΛվળͰ͖Δ͸͕ͣͩͬͨɺ࢒೦ͳ͕Β·ͱ΋ʹಈ࡞͠ͳ͔ͬͨɻ
ਤ 9 ʹαΠυόϯυσʔλͷཅిࢠͱΨϯϚઢͷ࣌ؒࠩ෼෍Λࣔͨ͠ɻ᫔่ࣹյͷϐʔΫ͔ΒɺӷମΩηϊϯΨϯϚઢଌఆ‫ʹث‬ΑΔΨϯϚઢͷ࣌ؒଌఆͱ߹Θͤͯɺ122 ps ͷ࣌ؒ෼ղೳ͕ಘΒΕ͍ͯΔͷ͕Θ͔Δɻਤ 10: ӷମΩηϊϯΨϯϚઢଌఆ‫ث‬ͷ಺෦ɻ௿ԹͰ࡞ಈ
͠ਅۭࢵ֎ޫʹ‫౓ײ‬ͷ͋Δ 2 Πϯνޫిࢠ૿ഒ؅͕ 846ຊฒΜͰ͍Δɻରੜ੒εϖΫτϩϝʔλͷ໰୊఺͸ɺ‫ݕ‬ग़ޮ཰͕‫ۃ‬Ίͯ௿͍͜ͱͱɺ͞Βʹக໋తͳͷ͸ߴ‫཰਺ܭ‬ԼͰͷిࢠɾཅిࢠରͷ‫ي‬ಓ࠶ߏ੒͕େม೉͍͜͠ͱͰ͋ΔɻҰํͰ݁থγϯνϨʔλ͸ɺෆ७෺΍ෆ‫ۉ‬Ұ͞ɺ͞Βʹ͸ΨϯϚઢͷ൓ԠҐஔʹΑΔूޫޮ཰ͷҧ͍͕ɺ෼ղೳΛ੍‫͢ݶ‬Δɻ·ͨҰൠతʹҐஔ෼ղೳ͕ѱ͍ɻͦ͜Ͱ MEG ࣮‫Ͱݧ‬͸ɺӷମΩηϊϯΛ࢖ͬͨ͜Ε·7133Ͱʹͳ͍ΨϯϚઢଌఆ‫ث‬Λ৽ͨʹ։ൃͨ͠ɻӷମΩηϊγϣϯޫ͕ਅۭࢵ֎ޫͰ͋Δ͜ͱͱɺϚΠφε 110 ౓ʹϯ͸᫔ࣹ௕͕ 2.8 cm Ͱൃޫྔ͸ NaI ݁থͷ໿ 75 %΋ྫྷ΍͞ͳͯ͘͸͍͚ͳ͍͜ͱͰ͋Δɻ೾௕ม‫ࡎ׵‬Λ࢖͏͋ΓɺӷମͷͨΊҰ༷ੑʹ͸໰୊͕ͳ͍ɻ·ͨ݁থͱҧ͜ͱ΋ߟ͕͑ͨɺม‫ࡎ׵‬ͷҰ༷ੑͷ໰୊͕͋Δɻ·ͨ௿͍ɺ७Խ࡞‫ʹۀ‬Αͬͯඞཁͳ͚ͩෆ७෺Λམͱ͢͜ͱ͕

ԹͰ͸ޫిࢠ૿ഒ؅ͷޫి໘఍߅͕େ͖͘ͳͬͯɺޫి

Ͱ͖Δɻ࣌ؒԠ౴΋଎͘ɺΨϯϚઢʹର͢Δ৴߸ͷ‫ݮ‬ਰࢠ͕ग़ͳ͘ͳΔͱ͍͏໰୊͕͋ͬͨɻ

࣌ؒ͸໿ 45 nsec Ͱ͋Δɻ͕ͨͬͯ͠ߴ͍‫ʹ཰਺ܭ‬΋଱͑ΒΕɺ༏Εͨ࣌ؒ෼ղೳ͕‫ظ‬଴Ͱ͖Δɻ·ͨҰ༷ͳूޫޮ཰Λ࣮‫͢ݱ‬ΔͨΊɺ໿ 800 ℓ ͷӷମΩηϊϯͷ༗ޮମੵશମΛ 846 ຊͷ 2 Πϯνޫిࢠ૿ഒ؅ͰऔΓғΜͰ

Number of events /(0.50 MeV)ͦͷ௚઀ޫΛัΒ͑ΔσβΠϯͱͨ͠ʢਤ 10ʣɻ

Radiative decay &e+ annihilation

Pileup(a)100

w < 2 cm
Cosmic ray

50

0

(b)
200

ਤ 12: αΠυόϯυͷΨϯϚઢΤωϧΪʔ෼෍ɻ͜ͷw > 2 cm෼෍͔ΒΤωϧΪʔ෼ղೳͱεέʔϧ͕ಘΒΕɺ࣮‫ݧ‬தϞχλʔʹ࢖ΘΕͨɻ

100ͦ͜Ͱ඿দϗτχΫεͱͷ‫ڞ‬ಉ‫ʹڀݚ‬ΑΓɺӷମΩη

0
30

40

50

60

70
E γ (MeV)ϊϯதʹਁͯ͠࢖͑Δࢵ֎ޫʹ‫౓ײ‬ͷ͋Δޫిࢠ૿ഒ؅
Λ։ൃͨ͠ɻ͜Ε͸‫ࡏݱ‬ɺμʔΫϚλʔ୳ࡧͷӷମΩηϊϯ‫ݕ‬ग़‫࢖ʹͲͳث‬ΘΕΔඪ४తͳٕज़ͱͳ͍ͬͯΔɻਤ 11: ӷମΩηϊϯʹΑΔ 54.9 MeV ΨϯϚઢͷεϖ·ͨӷମΩηϊϯͷྫྷ٫ʹ͸ɺKEK ૉ֩‫ݚ‬௿ԹάϧʔΫτϧɻʢaʣΨϯϚઢͷ൓Ԡ͕ޫిࢠ૿ഒ؅ͷޫి໘͔ϓʹΑΓΩηϊϯʹ࠷దԽͨ͠ύϧε؅ྫྷౚ‫͕ػ‬։ൃ͞

Β 2 cm Ҏ಺Ͱ‫ͨͬ͜ى‬৔߹ɺʢbʣ2 cm ΑΓԕ͘Ͱ‫ى‬Εͨɻे෼ͳྫྷౚೳྗΛ࣋ͪɺৼಈϊΠζ͕গͳ͘อक

ͬͨ͜৔߹ɻ

͕༰қͱ͍͏͜ͱͰɺ͜Ε΋ӷମΩηϊϯΛ࢖͏ੈքத

࠷ऴతʹӷମΩηϊϯΛબΜܾͩΊखͱͳͬͨͷ͸ɺ͜ͷσβΠϯͰΨϯϚઢͷೖࣹҐஔ͕໿ 5 mm ͱ͍͏Α͍ਫ਼౓ͰಘΒΕͨ͜ͱͰ͋ͬͨɻ50 MeV ఔ౓ͷΨϯϚઢ͸ɺӷମΩηϊϯʹೖ͔ͬͯΒ਺ηϯνͰରੜ੒Λ‫͜͠ى‬ɺখ͞ͳి࣓γϟϫʔΛ࡞Δɻγϟϫʔ͸·͹ΒͰେ͖͘޿͕Γɺޫྔ෼෍શମ͔Βγϟϫʔͷॏ৺ҐஔΛ‫ٻ‬Ίͯ΋ɺΨϯϚઢͷҐஔ͸ਫ਼౓Αܾ͘·Βͳ͍ɻΨϯϚઢͷೖࣹҐஔͷपΓʹ͋Δޫిࢠ૿ഒ؅ʹ஫໨͢Δ
ͱɺೖࣹҐஔΛத৺ͱ͢ΔӶ͍ޫྔ෼෍͕ಘΒΕΔ͕ɺ
ͦΕ͸ରੜ੒ͷҐஔ͔Βͷཱମ֯Ͱ΄΅ܾ·Γɺͦͷ‫ޙ‬Ζʹ޿͕Δγϟϫʔ෼෍ʹ͸͋·ΓґΒͣʹɺରੜ੒ͷ‫ͨͬ͜ى‬ҐஔΛਖ਼֬ʹ‫ٻ‬ΊΔ͜ͱ͕Ͱ͖Δɻཁ͢ΔʹɺγϟϫʔશମͰ͸ͳ͘࠷ॳͷରੜ੒͔Βग़Δޫʹ஫໨͢ΔͷͰ͋Δɻಉ༷ʹΨϯϚઢͷ࣌ؒଌఆ΋ରੜ੒͔Βͷ௚઀ޫΛଌΔ͜ͱͰɺ65–70 psec ͱ͍͏༏Εͨ࣌ؒ෼ղ
ೳΛୡ੒Ͱ͖ͨɻ
ӷମΩηϊϯΛ࢖͏্Ͱ໽հͳ͜ͱ͸ɺγϯνϨʔͷ‫ऀڀݚ‬ͷؒͰ޿͘࢖ΘΕΔΑ͏ʹͳͬͨɻӷମΩηϊϯଌఆ‫ث‬͸ɺCOBRA ి࣓ੴΛғ͏Α͏ʹC ‫ܕ‬ͷਅۭஅ೤༰‫͔ث‬ΒͰ͖͓ͯΓɺΨϯϚઢͷೖࣹ໘͸෺࣭ྔΛ‫ݮྗۃ‬Βͨ͢ΊɺΞϧϛϋχΧϜͱΧʔϘϯϑΝΠόʔͷαϯυΠονύωϧΛ੡࡞ͯ͠࢖༻ͨ͠ɻ
ΠλϦΞ͔Β༧ࢉΛҾ͖ग़͢ͷʹ೔ຊ੡ͷޫిࢠ૿ഒ؅
Λങ͏͚ͩͰ͸೉͍͠ͱ͍͏ͷͰɺਅۭஅ೤༰‫ث‬ͷ੡࡞Λ೚͕ͤͨɺͦͷ͓͔͛Ͱࢄʑۤ࿑ͨ͠ɻࡾ‫ࢯݪ‬ͷ‫ࣄه‬[12] ʹ͸ͦͷลΓͷ࿩͕ਵ෼߇͑Ίʹॻ͔Ε͍ͯΔɻ
ߴ‫཰਺ܭ‬ͷ࣮‫Ͱݧ‬͸ɺෳ਺ͷΨϯϚઢ͕΄΅ಉ࣌ʹೖࣹ͢Δࣄ৅͕‫͜ى‬Δɻͦͷ৔߹ෳ਺ͷΨϯϚઢ͕ҰͭͷߴΤωϧΪʔΨϯϚઢʹ‫ ͱ͏·ͯ͑͠ݟ‬µ → eγ ่յͷόοΫάϥ΢ϯυͱͳΓಘΔʢύΠϧΞοϓʣɻӷମΩηϊϯଌఆ‫ث‬͸Ґஔͱ࣌ؒͷ෼ղೳ͕༏Ε͍ͯΔ
ͷͰɺෳ਺ͷΨϯϚઢΛ࠶ߏ੒ͯ͠෼཭͢Δ͜ͱ͕Ͱ͖
ΔɻͦͷͨΊʹߴ଎೾‫ܗ‬σδλϧճ࿏ʢDRS: Domino

Ring SamplerʣΛ։ൃͯ͠ɺ͢΂ͯͷޫిࢠ૿ഒ؅ͷ৴߸೾‫ܗ‬Λ‫ه‬࿥ͨ͠ɻ͜ͷ DRS ճ࿏͸ͦͷ‫༷ޙ‬ʑͳ࣮

8134‫࢖ʹݧ‬ΘΕ͍ͯΔΑ͏Ͱ͋Δɻଌఆ‫͕ث‬େ͖͍ͷͰγϯνϨʔγϣϯޫͷ‫ٵ‬ऩ͕໰୊
ͱͳΔ͕ɺΩηϊϯ͸ΤΩαΠϚʔʢXe∗2 ʣΛ௨ͯ͠ൃ
ޫ͢ΔͨΊɺΩηϊϯࣗ਎ʹΑΔ‫ٵ‬ऩ͸ͳ͍ɻ͕ͨͬ͠

Timing Counterͯਫ΍ࢎૉͳͲͷࢵ֎ޫΛ‫ٵ‬ऩ͢Δෆ७෺͕໰୊ͱͳ

targetΔɻಛʹਫ͸ 100 ppb ϨϕϧͰ΋ଌఆ‫ث‬ͷੑೳʹେ͖

Energy scale (arb. unit)ͳӨ‫ڹ‬Λ༩͑Δɻଌఆ‫ث‬ͷম͖͕ͩ͠Ͱ͖ͳ͍ͨΊɺਫͷআ‫ڈ‬͸େ͖ͳ՝୊Ͱ͋ͬͨɻͦͷͨΊΩηϊϯΛ॥‫؀‬
1.04ͤͯ͞७Խ͢ΔγεςϜΛ։ൃͨ͠ɻӷମͰͷ॥‫Ͱ؀‬ຖ
1.02
࣌1100 ϦοτϧΛ௒͑Δ७Խ͕Ͱ͖ɺ͜ΕʹΑͬͯଌఆ

3 m Λ௒͑Δ‫ٵ‬ऩ௕͕࣮‫Ͱݱ‬‫ث‬ͷେ͖͞ΑΓे෼௕͍
0.98
͖ͨɻ
0.96

31/12

Energy scale (arb. unit)

2009

01/09

2010

01/11

01/07

31/08

2011

31/10

31/08

31/10

2012

31/12

LXe Detector

02/07

2013

Drift Chamber

1.04

Muon Beam

1.02

1ਤ 14: ղੳྖҬ಺ͷࣄ৅ͷҰྫɻ

0.98

0.96

31/12

2009

01/09

2010

01/11

01/07

31/08

31/10

31/08

31/10

2011

31/12

2012

02/07

2013

ਤ 13: શ࣮‫ؒظݧ‬ͷΨϯϚઢΤωϧΪʔεέʔϧͷ҆ఆੑɻ͹Β͖ͭ͸ 0.2%ҎԼʢrmsʣɻ੺‫ؙ‬͸Ϧν΢Ϝͷ

17.6 MeV ΨϯϚઢɺࠇ‫ؙ‬͸όοΫάϥ΢ϯυͷΨϯϚ
ઢ෼෍ʢਤ 12ʣ͔ΒಘͨεέʔϧɻࠐΜͰ‫֩ࢠݪ‬λʔήοτʹཅࢠΛͿ͚ͭΔɻ‫֩ࢠݪ‬λʔήοτͱͯ͠Ϧν΢ϜΛ࢖͏ͱɺ17.6 MeV ͷ୯৭ΨϯϚઢ͕ಘΒΕΔɻ3-4 ೔ʹҰ౓ͷׂ߹Ͱ CW Ճ଎‫ʹث‬ΑΔֱਖ਼σʔλΛऔΓͳ͕Β࣮‫ݧ‬ΛਐΊͨɻ
·ͨɺ࣮‫ݧ‬தʹऔಘͨ͠αΠυόϯυͷΨϯϚઢΤωϧΪʔ෼෍͔Β΋ΨϯϚઢͷΤωϧΪʔεέʔϧ͕‫ٻ‬Ίଌఆ‫ث‬ͷֱਖ਼ʹ͸ɺෛύΠΦϯϏʔϜΛӷମਫૉλʔ−0ήοτʹ੩ࢭͤͯ͞ɺՙిަ‫׵‬൓Ԡ π p → π n Λ‫͜ى‬ΒΕΔʢਤ 12ʣɻઌ΄Ͳͷ 17.6 MeV ΨϯϚઢͷσʔλͱҰॹʹɺͦͷ݁ՌΛϓϩοτͨ͠ͷ͕ਤ 13 Ͱ͋Δɻͯ͠ɺதੑύΠΦϯͷ่յ͔Βग़ΔೋͭͷΨϯϚઢΛ༻σʔλͷ͹Β͖ͭ͸શ࣮‫ؒظݧ‬தͰ 0.2%ҎԼʢrmsʣͰ

͍ͨɻೋͭͷΨϯϚઢ͕ͪΐ͏Ͳ 180 ౓൓ରํ޲ʹग़Δ͋ΓɺΤωϧΪʔεέʔϧͷ҆ఆੑ͕֬ೝ͞Εͨɻͱ͍͏৚݅Λ՝͢ͱɺͦΕͧΕ 54.9 MeV ͱ 82.9 MeVͦͷଞʹ΋ɺଌఆ‫ʹ಺ث‬ுΒΕͨϫΠϠʔʹ෇͚ͨΞͷ୯৭ΨϯϚઢͱͳΔɻ54.9 MeV ͸ 52.8 MeV ʹۙ͘ɺϧϑΝઢ‫ݯ‬ʢ241 Amʣ΍ɺதੑࢠ‫ݯ‬Λ࢖ͬͯχοέϧͷ

ΤωϧΪʔઈର஋ͷֱਖ਼ʹ΋͍ͬͯ͜Ͱ͋Δɻ͜ͷͨΊதੑࢠั͔֫ΒͰΔ 9 MeV ΨϯϚઢɺ͞Βʹ͸ଌఆ‫ث‬ʹӷମΩηϊϯଌఆ‫ث‬ͷ൓ରଆʹ݁থγϯνϨʔλΛஔΛԣ੾ΔӉ஦ઢͳͲɺ༷ʑͳֱਖ਼σʔλΛ‫ͯ͠࢖ۦ‬ৗ͍࣌ͯಉ࣌‫ܭ‬ଌΛຖ೥Ұճߦͬͨɻ

ଌఆ‫ث‬ੑೳͷ҆ఆੑ͕͔֬ΊΒΕ͖ͯͨɻਤ 11 ʹ 54.9 MeV ୯৭ΨϯϚઢʹରͯ͠ಘΒΕͨεϖΫτϧͷྫΛࣔ͢ɻ௿͍ํͷ௕͍ςʔϧ͸ɺଌఆ‫ʹث‬ೖΔલʹ૬‫༻࡞ޓ‬Λͨ͠΋ͷͱɺి࣓γϟϫʔͷҰ෦͕ଌఆ‫ث‬ͷલ໘͔Β࿙Εͨ΋ͷͰ͋Δɻ͜ΕΒ͸෼ղೳͱ͍͏ΑΓ΋ଌఆޮ཰ͷҰ෦ͱߟ͑ΒΕΔɻµ → eγ ୳ࡧʹॏཁͳͷ͸ߴ͍ଆͷ෼ղೳͰɺ͜ΕʹΑͬͯόοΫάϥ΢ϯυΛམͱ͢ੑೳ͕ܾ·Δɻޫిࢠ૿ഒ؅ͷޫి໘͔Βԕ͘ͰΨϯϚઢ͕൓Ԡͨ͠ࣄ৅ʢਤ 11ʢbʣʣʹൺ΂ͯɺۙ͘Ͱ൓Ԡͨ͠ࣄ৅ʢਤ 11ʢa ʣʣ͸ɺूޫ཰͕ࣄ৅͝ͱʹ͹Β͍ͭͯ෼ղೳ͕ѱ͘ͳΔɻฏ‫ͯ͠ۉ‬ɺ

1.7–2.4%ͷΤωϧΪʔ෼ղೳ͕ಘΒΕͨɻ௕‫ʹظ‬ΘͨΔ࣮‫ݧ‬தɺଌఆ‫ث‬ੑೳΛϞχλʔֱͯ͠ਖ਼
͢ΔͨΊʹɺ‫֩ࢠݪ‬ͷྭ‫ى‬ঢ়ଶ͔Βग़ΔߴΤωϧΪʔͷ୯৭ΨϯϚઢΛ࢖ͬͨɻઐ༻ͷίοΫΫϩϑτɾ΢ΥϧτϯཅࢠՃ଎‫ث‬ʢCWʣΛϏʔϜϥΠϯԼྲྀʹઃஔ͠ɺऄෲঢ়ͷϏʔϜύΠϓΛԼྲྀଆ͔Β COBRA ಺ʹࠩ͠

6µ+ → e+ γ ୳ࡧղੳMEG ࣮‫ݧ‬͸ 2008 ೥ʹ෺ཧσʔλͷऔಘΛ։࢝͠ [13]ɺ

ຖ೥σʔλྔΛ΄΅ഒ૿͠ɺଌఆ‫ث‬ͷֱਖ਼ਫ਼౓΍όοΫάϥ΢ϯυͷཧղΛվળͯ͠୳ࡧ‫౓ײ‬Λ͞Βʹ্͛ɺͦͷ୳ࡧ݁ՌΛ߹‫ ܭ‬4 ճʹΘͨͬͯൃද͖ͯͨ͠ [3, 14]ɻ2009 ೥ͷσʔλʹ͸γάφϧͱόοΫάϥ΢ϯυͷ‫ڥ‬քྖҬʹࣄ৅ͷ௒ա͕͋ͬͯੈؒΛ૽͕͕ͤͨ [15]ɺͦͷ‫ͦޙ‬Ε͕੒௕͢Δ͜ͱ͸ͳ͘ɺ౷‫ܭ‬ͷ૿Ճͱͱ΋ʹόοΫάϥ΢ϯυͷ༧૝ͱҰக͢ΔΑ͏ʹͳͬͨɻσʔλதͷ µ → eγ ࣄ৅਺ͷࢉఆ͸ɺLikelihood ղੳʹΑͬͯߦͳͬͨɻղੳʹඞཁͳγάφϧͱ֤छόοΫάϥ΢ϯυͷ֬཰ີ౓ؔ਺ʢPDFʣ͸ɺ࣮ࡍͷϛϡʔΦϯ่յͷσʔλͱֱਖ਼σʔλ͔Β࡞ΒΕͨɻղੳͰ

9

1

400
350
300

0.5

250

0
−0.5

0

0.2

0.4

54

55
56
E e (MeV)

−2
−1

0.6

50

1

51

52

53

54

t e+ γ (ns)−0.9995−0.999−0.9985cosΘeγਤ 15: MEG ࣮‫ݧ‬શσʔλͷղੳྖҬۙลͷࣄ৅෼෍ɻ

µ → eγ ࣄ৅͕ 1σ ɺ1.64σ ɺ2σ Ͱ‫ظ‬଴͞ΕΔྖҬΛઢͰࣔͯ͋͠Δɻࠨਤʹ͸ teγ ͱ cos Θeγ ͷͦΕͧΕ 90%ޮ཰ͷΧοτʢcos Θeγ < −0.99963ɺ|teγ | < 0.24 nsʣɺ

400

(d)

350
300
250

55

56

400

300

150

150

100

100

0

20

52

54

56

58

E γ (MeV)

103

(f)

2

10

10

50

− 20

50

250
200

50

(e)

350

200

− 40

48

E e+ (MeV)
events / 3.0 (mrad)

53

102

10

100

50

events / 2.0 (mrad)

52

(c)

103

200

− 0.6 − 0.4 − 0.2

51

500

300

−1.5
48
50

600

400

100

−1

50

(b)

700

200
150

52

800

events / 0.6

54

(a)

450

events / 0.4 (MeV)

1.5

events / 0.24 (MeV)56

2
events / 56 (ps)58

t eγ (nsec)

E γ (MeV)

135

40

1

− 60 − 40 − 20020e+ γ (mrad)

40
e+ γ

60

(mrad)− 10 − 8

−6

−4

−2

0

2

4

Rsig

ӈਤʹ͸ Eγ ʹ 70%ɺEe ʹ 90%ޮ཰ͷΧοτʢ51.0 <ਤ 16: ʢaʣ– ʢeʣϑΟοτ͞Εͨ Likelihood ؔ਺ͱશEγ < 55.5 MeVɺ52.4 < Ee < 55.0 MeVʣ͕͔͚ΒΕMEG σʔλͱͷൺֱɻʢfʣRsig ʢຊจࢀরʣɻ‫ൃۮ‬త͍ͯΔɻΘeγ ͸ཅిࢠͱΨϯϚઢͷ։͖֯ɻόοΫάϥ΢ϯυʢ੺ഁઢʣͱ᫔่ࣹյόοΫάϥ΢ϯ
υʢ੺Ұ఺࠯ઢʣΛ଍͢ͱશόοΫάϥ΢ϯυʢ੨ઢʣ͸ɺΨϯϚઢͷ൓ԠҐஔʹΑΔ෼ղೳͷҧ͍΍ɺཅిࢠ

ͱͳΔɻγάφϧʢ྘ʣ͸ಘΒΕͨ 90%্‫ݶ‬஋Λ 100 ഒ‫ߏ࠶੻ي‬੒ͷ‫Ͳͳྻߦࠩޡ‬Λߟྀͯ͠ɺࣄ৅͝ͱʹҟͨ͠΋ͷɻ

ͳΔ PDF Λ࢖ͬͨɻ͜ͷࡍɺγάφϧࣄ৅͕‫ظ‬଴͞Ε
ΔྖҬͷσʔλʢϒϥΠϯυྖҬʣ͸‫͍ͳݟ‬Α͏ʹͯ͠ࠨਤͰγάφϧྖҬ಺ʹ͋Δࣄ৅͸ӈਤͰ͸֎Ε͍ͯ͢΂ͯͷղੳ͕ߦΘΕͨʢϒϥΠϯυղੳʣɻϒϥΠϯͨɻ͕ͨͬͯ͠ɺγάφϧྖҬ෇ۙʹࣄ৅਺ͷ௒ա͸ಛυྖҬ͸͔ͳΓ؇Ίʹઃఆͨ͠ʢ48 < Eγ < 58 MeVɺʹ‫ݟ‬ΒΕͳ͔ͬͨɻ

|teγ | < 1 nsʣɻµ → eγ ่յ୳ࡧ͸‫ൃۮ‬తόοΫάϥ΢

Likelihood ղੳͰ͸ϑΟοτʹΑΓɺղੳྖҬ಺ͷγάϯυ͕ࢧ഑తͳͷͰɺόοΫάϥ΢ϯυͷ෼෍Λγάφφϧ਺ͱόοΫάϥ΢ϯυ਺͕‫ٻ‬ΊΒΕΔɻਤ 16ʢaʣ–ϧྖҬͷ֎ଆʢαΠυόϯυʣ͔Βਖ਼֬ʹ‫ੵݟ‬΋Δ͜ͱʢeʣʹϑΟοτ͞Εͨ Likelihood ؔ਺ͱଌఆσʔλͷൺ͕Ͱ͖ɺ͜ͷΑ͏ͳϒϥΠϯυղੳʹ͸ద͍ͯ͠Δɻ
ͯ͞ɺϒϥΠϯυղੳʹ͍ͭͯগ͠ίϝϯτ͍ͨ͠ɻʮγάφϧΒ͠͞ʯRsig ≡ֱΛࣔͨ͠ɻਤ 16ʢfʣʹ͸ɺγάφϧྖҬʹࣄ৅͕ͳ͍ͷΛ‫͕ͳݟ‬Βղੳ͢ΔͷͱɺA ͸ͦΕͧΕγάφϧɺ᫔่ࣹյόοΫάϥ΢ϯυɺ‫ۮ‬ϒϥΠϯυͯ͠ղੳ͢ΔͷͱͰ͸ɺղੳʹ޲͔͏ଶ౓͕

ൃతόοΫάϥ΢ϯυͷ PDF ͰɺfR ͱ fA ͸ೋͭͷόοҧͬͯ͘Δ͜ͱ͸͋ΔͩΖ͏ɻ͔͠͠΄Μͷͪΐͬͱ͠Ϋάϥ΢ϯυͷׂ߹Ͱ͋ΔɻγάφϧΒ͠͞ͷߴ͍ྖҬͨؒҧ͍Ͱʢͨͱ͑͹ΤωϧΪʔεέʔϧΛΘ͔ͣʹؒ΋όοΫάϥ΢ϯυ͚ͩͷ෼෍ͱΑ͘߹͍ͬͯΔɻ

log10 (S/(fR R + fA A)) Λϓϩοτͨ͠ɻ͜͜Ͱ S ɺRɺҧ͑ͯʣγάφϧΛಀ͍ͯ͠Δ͚͔ͩ΋͠Εͳ͍ɻγάφϧΛܾͯ͠ಀ͞ͳ͍͜ͱɺ͜Ε͕୳ࡧ࣮‫ݧ‬ͷ͢΂ͯͰσʔλऔಘ೥

2009-20112012-2013͢΂ͯ͋ΔɻΑ͍ϦϛοτΛಘΔ͜ͱͰ͸ͳ͍ɻࢲ͸ϒϥΠϯ

ϑΟοτ݁Ռ

-1.3

-5.5

-2.2

υղੳ৴๬ऀͰ͸ͳ͍͕ɺ࠷‫ޙ‬ͷॠؒ·Ͱଘ෼ʹؒҧ͍

90% CL ্‫ݶ‬஋

6.1

7.9

4.2

୳͠ʹྭΉ‫ۓ‬ு‫ײ‬Λ༩͑ͯ͘ΕΔͱ͍͏఺ͰɺϒϥΠϯ༧૝্‫ݶ‬஋

8.0

8.2

5.3

υղੳ͸ѱ͘ͳ͍ख๏ͩͱࢥ͏ɻ
αΠυόϯυσʔλΛ࢖ͬͨόοΫάϥ΢ϯυධՁ͕ऴΘΓɺղੳख๏͕࠷దԽ͞ΕΔͱɺ͍Α͍ΑϒϥΠϯ

ද 1: µ → eγ ่յ෼‫ذ‬ൺʢ×10 −13 ʣͷϑΟοτ݁Ռɺ

90% C.L. ্‫ݶ‬஋ͱͦͷ༧૝஋ɻυྖҬΛ։͚Δ͜ͱʹͳΔɻϒϥΠϯυྖҬͷ಺ଆʹɺγάφϧࣄ৅Λ‫׬‬શʹ‫ؚ‬Έɺ͞ΒʹόοΫάϥ΢ϯυࣄϑΟοτ݁Ռ͔Βɺ͍ΘΏΔ Profile Likelihood Ratio৅΋े෼࢒ΔྖҬΛղੳྖҬͱఆٛ͠ɺͦͷྖҬ಺ͷશΛ༻͍ͨස౓࿦తख๏ʢFrequentist ApproachʣʹΑͬࣄ৅Λ࢖ͬͯ Likelihood ղੳΛߦͳͬͨɻਤ 14 ʹղੳͯγάφϧ਺ͷ 90%৴པ͕۠ؒಘΒΕΔɻγάφϧ਺Λµ → eγ ่յ෼‫ذ‬ൺʹম͖௚͢ʹ͸ɺଌఆͨ͠૯ϛϡʔྖҬ಺ͷࣄ৅ͷҰྫΛࣔͨ͠ɻ·ͨɺਤ 15 ʹ͸ MEG ࣮‫ݧ‬શσʔλͷղੳྖҬۙลͷࣄ৅෼෍Λࣔͨ͠ɻ͜ͷਤΦϯ่յ਺Λ஌Δඞཁ͕͋ΔɻؒҾ͍ͨϛογΣϧ่յ͸֤ࣄ৅ʹରͯ͠ɺ࢛ͭͷଌఆྔʢEγ , Ee , teγ , cos Θeγ ʣτϦΨʔΛ࢖ͬͯϛϡʔΦϯ่յ਺͕ಘΒΕΔɻ·ͨɺͷ࢛࣍‫ݩ‬෼෍Λද͓ͯ͠Γɺͦͷղऍʹ͸஫ҙ͕ඞཁͰµ → eγ τϦΨʔʹೖ͍ͬͯΔ᫔่ࣹյͷ਺͔Β΋‫ࢉܭ‬

͋Δɻྫ͑͹ɺӈਤͰγάφϧྖҬ 1σ ಺ʹ͋Δࣄ৅͸͢΂ͯɺࠨਤͰ͸γάφϧྖҬ͔Β֎Ε͍ͯͨɻಉ༷ʹ

Ͱ͖Δɻ྆ऀ͸Α͘Ұக͓ͯ͠Γɺ݁‫ํ྆ہ‬ͷ݁ՌΛ߹ΘͤΔ͜ͱͰ 3.5%ͷਫ਼౓Ͱ૯ϛϡʔΦϯ਺͕‫ٻ‬ΊΒΕ

10
136

ͨɻ͜ΕʹΑͬͯಘΒΕ่ͨյ෼‫ذ‬ൺͷ্‫ݶ‬஋Λද 1 ʹࢀߟจ‫ݙ‬·ͱΊͨɻʢ2008 ೥ʹऔಘͨ͠σʔλ͸શମͷ 30 ෼ͷ

1 ҎԼͱΘ͔ͣͰ͋Γɺଌఆ‫ث‬ͷঢ়ଶ΋ෆ҆ఆͰ͋ͬͨ
ͨΊ࠷ऴ݁Ռʹ͸Ճ͍͑ͯͳ͍ɻʣ
݁‫ہ‬ɺશ MEG σʔλͷղੳ͔Β µ → eγ ่յ͸‫ͭݟ‬͚ΒΕͣɺͦͷ෼‫ذ‬ൺʹ 4.2 ×10−13 ͱ͍͏্‫ݶ‬஋Λ͚ͭΔ͜ͱʹͳͬͨʢ90% C.L.ʣɻ͜Ε͸ MEG ҎલΑΓ

໿ 30 ഒ‫͍݁͠ݫ‬ՌͰ͋Δɻ·ͨɺ͋ΒΏΔૉཻࢠͷ่յ෼‫ذ‬ൺͱͯ͠࠷΋খ͞ͳ஋ͱ΋ͳ͍ͬͯΔɻ

7

࠷‫ʹޙ‬
ੈ୅ɾϑϨʔόʔʹ͍ͭͯ͸Α͘Θ͔͍ͬͯͳ͍ɻྫ

͑͹ɺͳͥૉཻࢠʹ͸ 3 ੈ୅͋Δͷ͔ɻͨͩΑ͘Θ͔Βͳ͍ʹͯ͠΋ɺզʑͷӉ஦͕͜ͷΑ͏ʹෳࡶͰ๛͔ͳͷ͸ɺ͜ΕΒ 3 ੈ୅ͷૉཻࢠ͕Ұ‫ݟ‬டংͳ͘བྷ·͍ͬͯΔ͓͔͛Ͱ͋Δͷ͸͔֬Ͱ͋Δɻήʔδཧ࿦͸ඒ͍͕͠ɺ
ͦΕ͚ͩͰ͸͜ͷੈք͸ੜ·Εͳ͔ͬͨɻͨͱ͑ը‫ظ‬తͳ৽ཻࢠ͕Έ͔ͭΒͳ͘ͱ΋ɺඒ͍͠ରশੑΛͿͪյͨ͠ʮώοάεʯͷৄࡉ‫͕ͦڀݚ‬ͷ଍͕͔ΓΛ༩͑ͯ͘ΕΔͩΖ͏ɻILC ͷ࣮‫ظ͘ڧʹݱ‬଴͢ΔॴҎͰ͋Δɻ
ҰํͰɺͦͷΑ͘Θ͔͍ͬͯͳ͍ϑϨʔόʔͷ࣮‫ݚݧ‬[1] http://meg.icepp.s.u-tokyo.ac.jp/.
[2] T. Mori et al., Research Proposal to PSI, R99.05.01, May 1999.
[3] A.M. Baldini et al. (MEG Collaboration), Eur.
Phys. J. C, 76:434, 1-30 (2016).
[4] A.M. Baldini et al. (MEG II Collaboration),
arXiv:1301.7225 (2013); Ξοϓσʔτͨ͠ MEG
II Design Report Λ‫ࡏݱ‬४උத.
[5] R. Barbieri and L.J. Hall, Phys. Lett. B338
(1994) 212; R. Barbieri, L.J. Hall, and A. Strumia, Nucl. Phys. B445 (1995) 219.
[6] J. Hisano and D. Nomura, Phys. Rev. D 59
(1999) 116005.
[7] ୈ 2 ճૉཻࢠ෺ཧࠃࡍ‫ڀݚ‬ηϯλʔγϯϙδ΢Ϝ,τϥϯεϖΞϨϯγʔू, UT-ICEPP 96-02, April

1996. ʢ೔ຊͰͷϛϡʔΦϯϑϨʔόʔ‫ڀݚ‬ͷΤϙοΫͱͳͬͨγϯϙδ΢Ϝʣ‫͔ڀ‬Βɺ৽෺ཧͷώϯτ͕ಘΒΕͨ͜ͱ͕ɺ͜Ε·ͰԿ

[8] A.v.d.Schaaf et al., Letter of Intent for an exper-౓͔͋ͬͨɻྫ͑͹ɺϑϨʔόʔΛม͑ΔதੑΧϨϯτ

iment at PSI, R-98-05.0, May 1998. ʢLoI άϧʔͷෆࡏ͔ΒνϟʔϜΫΥʔΫͷଘࡏ͕༧‫͞ݴ‬Εɺதੑ Kϓ͸ͦͷ‫ܾޙ‬྾ɺཌ೥ͷ೔ຊͷϓϩϙʔβϧ͕ਖ਼தؒࢠͰൃ‫͞ݟ‬Εͨ CP ͷഁΕ͔Βɺখྛɾӹ઒྆ࢯ͸ࣜʹਐΉ͜ͱͱͳͬͨʣ

ΫΥʔΫ͕ 3 ੈ୅ଘࡏ͢ΔԾઆΛཱͯͨɻ·ͨதੑ BதؒࢠͰ‫؍‬ଌ͞Εͨ༧૝֎ʹେ͖ͳཻࢠɾ൓ཻࢠؒͷࠞ߹͸ɺτοϓΫΥʔΫ͕ඇৗʹॏ͍͜ͱΛ༧‫ͨ͠ݴ‬ɻ͞ΒʹɺχϡʔτϦϊ࣭ྔ͕ҟৗʹ͍ܰͷ΋ɺ௒ߴΤωϧΪʔʹଘࡏ͢Δ৽෺ཧͷώϯτ͔΋͠Εͳ͍ɻ[9] G.W. Bennett et al., Phys. Rev. D 73 (2006)
072003.
[10] G. Isidori, F. Mesia, P. Paradisi, D. Temes, Phys.
Rev. D 75 (2007) 115019.

࣍ʹૉཻࢠ෺ཧֶʹ‫͜ى‬Δେ͖ͳֵ໋తൃల͸ɺͦͷΑ͏ͳώϯτɺྫ͑͹ µ → eγ ่յͷൃ‫ݟ‬ͷΑ͏ͳ΋ͷ͔Β࢝·Δ͔΋͠Εͳ͍ɻۙ࢝͘·Δ MEG II ࣮‫ظ͝͏ޤʹݧ‬଴ɻ

[11] J. Adams et al. (MEG Collaboration), Eur. Phys.
J. C, 73, 2365 (2013).
[12] ࡾ‫ݪ‬ஐ, ߴΤωϧΪʔχϡʔε 26-1, 9 (2007).
[13] େ୩ߤ, ߴΤωϧΪʔχϡʔε 28-4, 227 (2010).

ँࣙ౦‫ژ‬େֶͱ KEK Λ͸͡Ίͱ͢Δ MEG ࣮‫ݧ‬Λࢧ͑Δ
֤‫ؔػڀݚ‬ͷαϙʔτʹ‫͍ͨ͠ँײ‬ɻMEG ࣮‫Ͱݧ‬ಘΒΕͨ͢΂ͯͷ੒Ռ͸ɺͲΜͳঢ়‫گ‬ԼͰ΋ৗʹ໌Δ͘લ޲͖ʹ࣮‫ݧ‬Λ‫ݗ‬Ҿ͖ͯͨ͠ྺ୅ͷֶੜॾࢯͷ΋ͷͰ͋Δɻຊ‫ڀݚ‬ͷҰ෦͸Պֶ‫ڀݚ‬අิॿۚʢಛผਪਐ‫ڀݚ‬

22000004 ͓Αͼ 26000004ʣͷॿ੒Λड͚ͨɻ࠷‫ʹޙ‬ɺ‫׬‬੒͢Δ౰ͯͷͳ͍‫ߘݪ‬Λࠜ‫ؾ‬Α͘଴͍͍ͬͯͨͩͨߴ
ΤωϧΪʔχϡʔεฤूҕһձͷօ͞·ʹ‫͢ँײ‬Δɻ

[14] J. Adams et al. (MEG Collaboration), Nucl.
Phys. B 834, 1-12 (2010); Phys. Rev. Lett. 107,
171801 (2011); Phys. Rev. Lett. 110, 201801(2013).
[15] ᖒాཾ, ‫ؠ‬ຊහ޾, ߴΤωϧΪʔχϡʔε 29-3, 133(2010); R. Sawada, Proceedings of ICHEP2010,
Paris, France, PoS (ICHEP 2010) 263. ʢ͜Ε͸༧උత݁ՌͰɺ࠷ऴ݁Ռ͸ 2010 ೥σʔλͱ߹Θͤͯཌ೥ PRL ʹग़൛ͨ͠ [14]ʣ