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:+/3@)"$3\Ø/Ø4=Vƒ€ ì,+)-.#4D<1"2(/3)9¹=¿B4D¼)+)é 35"$%3@#"|yL6#"2+)3N74}"2<%4:yL3:%¢)<-T+/9$92+Œ…8<¦
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~ p = >@ƒ
…84*;IE"2<8#Š+/w3@;7—+)-²#4м)+/3¢"$35;Š92)Q5-T*;)!=¥]„"2(/7*1 p = > Ž )92<1+a"$929274<1#*;!#:<
;Nj*1+/Q92:Ÿ+!-Iw"2<1<;"$3(M#4N+/*1*;Yw`I]žQ47¼)Y6= BG%"2)(/+/3L!9†QL!3%<‡+)*;*;:<;j+/3%À#+
j4"2+/3<0…84+/<;D<1#)*1;"2wz"2<+)ÜhQ@RN<1+/wS79$;"2j9$z+)- ? = ‹/‹ p 3<:=
Ő:6)74<;8#8j*1+/Q92: +)-[+/3@#)"$3L!;"2+/3‡"$<²7a<1a!9292:*_-T+/*²j*1+)#+)3<²#L)3-T+/*²¼)+/34<¨
j4*;+);+/3<8)*1D"$%3@;"$yL:%G…8"|#5‡<;"2wj9$za!<;<7sI"$3N#&*#!3(/D‹4= ‚ UP)= ?¥Þ –5j šm S _ =
U)‹
β
1.2
1
ï
0.8
ï
0.6
ï
0.4
ï
0.2
ïï
0
0
ï
0.25
ï
0.5
ï
0.75
1
1.25
1.5
ð ð ð
ñMomentum
(GeV/c)
1.75
2
2.25
2.5
PMi æ¾)<}-T73Y#"$+/3G+)-_;&+/w3@;7Þ-T+/*0;SyL9$;*1%G%L!#<;)wj92!=
B4ˆ<1L)*;j\%4(/<}+)-.#&¼)+/3GQL)34%5*1:¸L::}#&<;:92::#"$+/3G74;<=
Counts
Us
ò
10 7
π
+
p
10 6
+
K
10 5
b
10 4
0
b0.2
b0.4
b0.6
b0.8
1
1.2
Mass (GeV)
PMi$ ó¥)%4*;+/3"$Sa!<;<-T+/*j+/<;"|#"$O)SjL)*t#"2:92:<)<
)92:79'#%N-T*1+/Þ;S#"2wY¤+)-'¤¸"2(/@)3%G#&w+/:3@#7\=
mass (GeV)
U?
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
momentum (GeV)
σmass (GeV)
(A) Mass vs. momentum for kaon candidates
0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0.4
0.6
0.8
ô
1
1.2
1.4
1.6
momentum(GeV)
(B) Dependence of σmass on momentum
T
.P¢i$A ±z:j[:3%34Š+!-„;&a)<1<0-T*;+/Þ#"2wY¤+)-'¤¸"2(/@†+/3G+/w3@;7 E=
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β
Up
1.2
1.1
2
2 1/2
p/(p +0.08 )
+ 0.02
1
b0.9
2
2 1/2
p/(p +0.3 )
b0.8
b0.7
b0.6
b0.5
b0.4 b
0
b0.25
b0.5
b0.75
1
1.25
1.5
1.75
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Momentum (GeV/c)
T
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Counts
U/U
x 10 2
1200
1000
Λ(1116)
d800
Σ (1193)
0
c600
°400
Λ(1405)
0
Σ (1385)
®200
b0
1
1.1
1.2
1.3
1.4
Λ(1520)
1.5
1.6
1.7
1.8
Mass (GeV)
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2000
1000
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Counts
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Counts
Counts
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Counts
x 10
40
35
30
25
20
15
10
5
-8
0.2
0.175
0.15
0.125
0.1
0.075
0.05
0.025
0
1
1.5
2
0
1
2.5
Em γ (GeV)
(A) Raw spectrum
2
2.5
Em γ (GeV)
(B) Normalized spectrum
-2
2.25
σ (µb)
Acceptance
x 10
1.5
0.45
0.4
2
1.75
0.35
0.3
1.5
0.25
1.25
0.2
1
0.15
0.75
0.1
0.5
0.05
0.25
0
1
1.5
2
nEm (GeV)2.5
γ
(C) Acceptance
0
1
1.5
2
nEm (GeV)2.5
γ
(D) Cross section
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Uncorrected yield (a.u.)
Counts
x 10
14
12
10
8
6
4
2
-9
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
1.5
2
0
1
2.5
Em γ (GeV)
(A) Raw spectrum
2
2.5
E² γ (GeV)
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σ (µb)
Acceptance
x 10
1.5
0.45
0.4
1.4
1.2
0.35
1
0.3
0.25
0.8
0.2
0.6
0.15
0.4
0.1
0.2
0.05
0
1
1.5
2
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γ
(C) Acceptance
0
1
1.5
2
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γ
(D) Cross section
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Acceptance
x 10
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0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-1.8
-1.6
-1.4
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-1
-0.8
-0.6
½t (GeV2¾)0
-0.4
-0.2
-0.4
-0.2
Yield (a.u.)
(A) Acceptance in t
40000
35000
30000
25000
20000
15000
10000
5000
0
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
½t (GeV2¾)0
(B) Comparison of simulation with data
odprqtsuwv µyxÀ¿ ®Áƒ]¡tƒ]ˆ — ƒ]ˆ}WƒA‰ˆÂU“r~U„†žƒÁz¬– { }ªž¢’‰ˆˆšƒ]Ÿ¨Š‹rŒkŽUŒI}]}Wƒ]¡š„†’‰ˆ}]ƒA…‡ˆ&ÂÊ©‹”dŽ
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Counts
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20000
15000
10000
5000
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Ëcos(β*¾)1
0.8
Counts
(A) Thrown angular distribution
40
20
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Ëcos(β*¾)1
0.8
Ratio=B/A
(B) Accepted angular distribution
0.002
0.001
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Ëcos(β*¾)1
0.8
(C) Acceptance
odpqts)uvɵyx‡Ì zU– { ’‰ˆ ‰ŸÀ’‰~b’*}]}]ƒW¡š„ª’*ˆ}]ƒ*ÍUŒÁŽdίƒWˆƒ]~€’*„†ƒ — ’‰ˆ ‰ŸÀ’‰~ — …‡Æ„†~€…™˜š„€…‡ˆyŠ
”6ŽdŒI}]}Wƒ]¡š„€ƒ — ’*ˆ Ÿ‡’‰~ — …‡Æ„†~‚…‡˜š„€…‡ˆ§dŽdŒI}]}Wƒ]¡š„†’‰ˆ}]ƒ*Š"ÏdžƒA’‰ˆš Ÿ‡ƒkÐÑd…‡ — ƒÒ¢ˆƒ — …‡ˆ
„†žšƒ¯„€ƒÓj„¦Š
Counts
°‰Ô
10000
5000
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Õcos(β*Ö)1
0.8
Counts
(A) Thrown angular distribution
100
50
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Õcos(β*Ö)1
0.8
Ratio=B/A
(B) Accepted angular distribution
0.01
0.0075
0.005
0.0025
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Õcos(β*Ö)1
0.8
(C) Acceptance
odpqts)uwv8µyx™× ·6Ø´–fÙɒ‰ˆ šŸÀ’‰~d’*}]}]ƒW¡š„ª’*ˆ}]ƒ*ÍUŒÁŽdίƒWˆƒ]~€’*„†ƒ — ’‰ˆ ‰ŸÀ’‰~
— …‡‚„€~€…™˜š„†…™ˆyŠf”dŽ6Œ©}]}Wƒ]¡š„€ƒ — ’‰ˆ Ÿ‡’‰~ — …™‚„†~‚…‡˜¥„†…‡‰ˆyй§dŽ6Œ©}W}]ƒW¡š„ª’‰ˆš}]ƒ‰Š
Counts
° È
60
50
40
30
20
10
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Õcos(β*Ö)1
0.8
Intensity (arbitrary units)
(A) Raw angular distribution
70
60
50
40
30
20
10
0
-1
Õcos(β*Ö)1
(B) Acceptance-corrected angular distribution
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
odpqts)uwv8µyxÚjÛ zU– { ’‰ˆ ‰ŸÀ’‰~ — …‡‚„€~€…™˜š„†…™ˆyÍ܌kŽdÝI’¦Ä
— ’*„†’šŠ‹•”6ŽdŒI}]}Wƒ]¡š„†’‰ˆ}]ƒÃÅ}W~€~‚ƒ]}W„€ƒ —É— ’*„ª’šŠ
0.6
0.8
Counts
°Þ
80
70
60
50
40
30
20
10
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Õcos(β*Ö)1
0.8
Intensity (arbitrary units)
(A) Raw angular distribution
22.5
20
17.5
15
12.5
10
7.5
5
2.5
0
-1
Õcos(β*Ö)1
(B) Acceptance-corrected angular distribution
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
odpqts)uwv8µyxÚtÚ ·6Ø´–fÙɒ‰ˆ Ÿ‡’‰~ — …™‚„€~€…‡˜šš„†…™ˆyÍfŒÁŽ
ݒßÄ — ’*„†’šŠ‹•”dŽ"ŒI}]}Wƒ]¡š„†’‰ˆ}]ƒÃÅ}W~€~‚ƒ]}W„€ƒ —É— ’*„ª’šŠ
0.6
0.8
Counts
°‘à
100
80
å
60
ã
Σ(1385)→Λæ π events
ã
0
40
å 0æ
Λ(1405)→Σ π events
0
20
0
-0.02
0
0.02
0.04
0.06
á â 2 +ã ä
2Ö
MX (K ΛX) (GeV )
0.08
0.1
o prqtsuwv8µyxÚjç §"c¡¢’‰~‚…‡€‰ˆ‰“f‚…‡`šŸÀ’*„€…‡ˆ~‚ƒ]‚Ÿ™„€b“r‰~6„†žƒ¯}ªž¢’‰ˆšˆƒ]Ÿ™
d
· { ‹ ±ßʰ Ȏ¹è z¬– { ‹¡Ÿ‡’‰…‡ˆ~‚ƒ] …™ˆéŽ6’‰ˆ — zÁ‹ ±¦Ôê Ȏ¹è · { – { ‹rž¢’‰‚žƒ — ~€ƒ] ‰…‡ˆéŽÃŠeÏdžƒ
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Counts
°°
20
18
16
14
12
10
8
6
4
2
0
1.08
1.1
1.12
1.14
1.16
1.18
1.2
1.22
Mass (GeV)
Counts
+í í (A) pπ invariant mass for Σ π events
5
4
3
2
1
0
-0.02
0
0.02
0.04
0.06
0.08
MX2 (K+ΛX) (GeV2)
î
(B) Mass squared of missing particle
o pqts)uvɵyx•Újï b
d
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Counts
°õ
30000
20000
10000
Counts
0
1.4
1.45
1.55
æ 1.5
Λπ mass (GeV)
ö í
(A) Generated Λπ mass distribution
1.25
1.3
1.35
1.25
1.3
1.35
60
40
20
0
1.4
1.45
æ
1.5
1.55
Λπ mass (GeV)
Acceptance
(B) Accepted mass distribution
0.01
0.0075
0.005
0.0025
0
1.25
1.3
1.35
1.4
1.45
1.55
ã æ 1.5
Λπ mass (GeV)
(C) Ratio of (B) to (A)
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Counts
õê
20000
15000
10000
5000
Counts
0
1.4
1.45
1.55
ú 1.5
Λγ mass (GeV)
ö ù
(A) Generated Λγ mass distribution
1.25
1.3
1.35
1.25
1.3
1.35
40
30
20
10
0
1.4
1.45
ú 1.5
1.55
Λγ mass (GeV)
Acceptance
(B) Accepted mass distribution
0.01
0.005
0
1.25
1.3
1.35
1.4
1.45
1.55
ã ú 1.5
Λγ mass (GeV)
(C) Ratio of (B) to (A)
odprq´s)uwv8µyxÚjµ Œ©}W}]ƒ]¡¥„ª’‰ˆ}WƒA“r‰~· { ‹ ±ßʰ Ȏ¹èôûtzüƒ£ƒ]ˆ‘„€Á’‰’`“rˆ}„†…‡‰ˆ ‰“„†žšƒ
· { ‹ ±ßʰ Ȏ¬’‰‚]ŠI‹ŒÁŽdίƒWˆƒ]~€’*„†ƒ — · { ‹ ±ßʰ ȉŽ"’‰‚ — …‡Æ„†~‚…‡˜š„€…‡ˆZŠb‹•”dŽ"ŒI}]}Wƒ]¡š„€ƒ —
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Counts
õš±
30000
20000
10000
Counts
0
1.25
1.3
1.25
1.3
1.4
1.45
1.55
æ 1.5
Σπ mass (GeV)
ý 0í 0
(A) Generated Σ π distribution
1.35
60
40
20
0
1.35
1.4
1.45
æ
1.5
1.55
Σπ mass (GeV)
Acceptance
(B) Accepted distribution
0.004
0.003
0.002
0.001
0
1.25
1.3
1.35
1.4
1.45
1.55
å æ 1.5
Σπ mass (GeV)
(C) Ratio of (B) to (A)
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h Ò m†m f$‹pg†l~ m f$h)‰ m†m hK‡H„ mœj<m lpf}$‘@}~${Uh m ƒ$h
‘@l~$ mœj Uh‰g “ hKg†l)‡Hf j\j f}U‹1‡k‰ j†jj Ç~$‰g†h@{3‰ j „W‰g m l € m ƒ$h m ‰f}…l€ m ƒ$h<—–˜ iA¯  m ƒ$f j ‘‰ j h7¥ ûYy
t
f j&m ƒUhÃh ӑKh j\j l€…‘Kl~$ mœj ‰|…lžh m ƒ$h m ‰f i þWl
g þ&f h Ό‰~ j\j f¢‰ »
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m Ê ÿl$I
l$h™€‚lg m ƒ$I
h û3„h‰ i σ$f j ‹f®h j ‰1‡Šw‰ ÓUf‡D~$‡»h j\m f‡Š‰ m h™€‚lg”¥ t ûYy"|…h@‘‰~ j h7f m ‰ j\j ~$‡Hh jm ƒW‰ m
h û±„h‰ i þ&f m†k
m ƒ$hn—x˜ m ‰fcf j ‡Hf}Uf}‡k‰xf} m ƒ$hDg\hK‹fl3l € m ƒ$A
j ¼ ‰U{ Ê {$f®Yh@g™f m ƒ$h1‘›ƒ$lf}‘@h j
l €5f}Uf m f}‰x‹~Uh j†j h j €‚lg m ƒ$h1„W‰ gœ‰‡Hh m hKg j@i¯ ?‰ m ƒ$g\hKh1‘K‰ j h j ÿ…¥ ·”˜œ—x˜Žd
y Ĕ‰ j h j\m f}‡k‰ m h@{­€‚g†l‡
t
m ƒ$hŒ~$‡D|hKgl€&‘Kl~$ m†j ²9f m ƒ$hŒgœ‰U‹h êUi ê‰Ê Å êUi êõŸµ•¶¸· q™‰ € m h@g j ~$| m gœ‰‘ m f$‹ m ƒ$h7—–˜ m ‰f¨ Í
¥
t
·
˜ — ˜ yA¼©½
t
²¿¾
¼*ÞÀ
yŽÁ
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tU
Counts
õ‰Ô
160
140
í π0
120
100
80
60
40
ùγ
20
0
-0.1
-0.075
-0.05
-0.025
0
0.025
0.05
0.075
Ö
0.1
Mâ X (K ΛX) (GeV )
2
+
2
ÂÃvÄŒÆvɶyx•Ú
ò­f j\j f}U‹H‡k‰ \j jj Ç~W‰g\hK{­€‚g\l‡ ë Ñ è w ìǀ‚lgƒ‘ñ„…h@g†l­‡Š‰ j†j h j f}
m ƒ$hŒg†‰$‹h ± i Ê‰Ô Å ±i ÔÊ ÎŒhŽ i σ$h•‘K~Ug\h•f jm ƒ$hŒg†h j ~$ m l€ m ƒ$hkÒ m {$h j ‘Kg\f}|hK{3f
j hK‘ m f}l ÞU¤i ±i
õ È
ħƒUhKg†h
À f jm ƒ$hD𐉠m |W‰‘›‹g\l~$${ m h@g†‡Èl| m ‰ f}$h@{3€‚g†l‡ m ƒUh`Ò m ÿ ¼*Þ f j`m ƒ$hD~$‡D|hKg7l€º|$f j
f m ƒ$h j „…h@‘Kf™Ò$hK{Égœ‰ $‹h‰ÿ§‰ ${ɽ_¼ ±'¤±±¦Ô) êU' ê°‰Ô f j ‰±‘Klg\g†hK‘ m flʀv‰‘ m lgH{$hKg\fhK{ˀ‚g†l‡
j f}‡D~U¢‰ m f}l m l1‰‘@‘Kl~U m €‚lg m ƒ$h§€‚gœ‰ ‘ m flHl€ m ƒ$hk·”˜†—x˜{$f jOm g\f}|$~ m f}l m ƒW‰ m Ĕl~$}{H€v‰}$l~ mœj f}{$h
y ĉ j ‘@lg†g\hK‘ m hK{R€‚lg m ƒUhG·”˜œ—x˜ m ‰f}Y‰‘K‘@lg†{$f$‹ m l
m ƒ$h j „hK‘@™f ÒWh@{­g†‰$‹h i σ$h• ‰~$h7l€¬¥ t —–˜ŽU
Ì ¥ — ˜ yͼÏÎ
t
½/¾
½
±
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Ð
t
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σUh•g\h j ~$ m†j l € m ƒ$h m ƒ$g\hKhkÒ mœj ‰g\h m ‰|$~U¢‰ m hK{Rf} m ‰ |$}h ÞUi¤±i
ÑfÓ m g†‰‘ m f}$‹ m ƒ$h¨~$‡D|hKgHl€
ÑH‘Kl~U m†j f j ‰|$f mŸm g†f‘›‘ñ iËҙjkj ƒ$lßħËf}4ÒW‹~$g\h Þi ¼ Ò ÿ
u
g\hK}‰ m f®hK¤k
ñ €‚hÄ u ѧ‘‰ ${$f}{$‰ m h jj ~$g\f®h m ƒ$h ±i Ê‰Ô Å ±i Ô‘Ê Î7h@Óƒ‘ñ„…h@g†l­‡Š‰ j\j ‘K~ mKi σ$h j lf}{
‘@~$g\hŸf j ‰&Ò m`m l m ƒ$hn{W‰ m ‰¡~ j f$‹p‰&ҚÓh@{z‡k‰ j\j l€ êUi °õ‘¼ ΌhŽ»‰${‰cҚÓhK{8ħf}{ m ƒ/l€ êUi ê È
Î h@Ô€‚lg m ƒ$h u Ñn‰${ˆ‰XΌ‰~ j\j f¢‰  m l3‰„U„$g†l¦Óf}‡k‰ m h m ƒ$hk|$‰‘›‹g†l~U${x¦ m ƒ$hk{$‰ j ƒ$h@{£‘K~Ug\h
7
f j1m ƒUhpg†h j ~$ m l €`‰ÉÒ m ~ j f}U‹kÕ\~ j\m)m ƒUhlΕ‰~ j†j f}‰ i σ$hp€‚lg†‡HhKgGÒ m ‹fh j ‰Öh jOm f‡Š‰ m h¡l
Ä f m ƒ¨‰H× q«Ø ¥xÙÚ/l€ êUi õ‰õõUi σ$h«Î•‰ ~ j†j f¢‰¥Å‰}l$h
m ƒ$hŒ~$‡D|hKg§l€ u Ñ ‘@l~$ mœj l€ ¼‰U
Ê '™
õ ±ßà ' à §
Ò m g\h m ~$g† j ‰ j }f‹ƒ m ¤£
ñ }lß"
Ä hKgH× q«Ø ¥xÙÚ t ê i õÊ È y i Ï ƒ$h m ”
Ä l:Ò mœj l€©$Ò ‹~$g†h UÞ i ¼ Ò ‰g†h¨$hK‰g†¤ñ
hW
Ç ~$f ‰hK miA¯ ¨lg†{UhKg m lH‰ j\j h j†j™m ƒ$hŒ‡kh@g†f m l€&‰{${$f$‹ m ƒ$h•Û”g\hKf m Å ÜÝf‹$h@g”€‚lg m ƒUh u Ñ „h‰éÿ
Ò $h
¯ „hKg\€‚lg†‡HhK{¨‰ þÅ m h j\mžÞ ʉõ ߪiº¯ {$hW$
àá¼ãâ
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גq tvä &
y ¾¤×’q ‚t ä ¹
× q tvä ¹ Ê y
y
å
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Þ iÊ y
tU
q
q
tvä y‘Klg†g†h j „l${ j§m l m ƒUhn{W‰ j ƒ$h@{3‘K~Ug\hnf}›ÒW‹~$g\h ÞUi ¼Ò ÿW× tvä ¹ Ê y‘Klg†g†h j „l${ j
m l m ƒ$h j l}f}{±‘K~$gOhpf ÒW‹~Ug†h ÞUi ¼ Ò ÿ&²9¾ ä ¾ Ê ¼ ¼ ç ‰${ ä ¼ ÊUi3¯ l| m ‰f êUi È Þ‘à ÿ m l
|h1‘@l‡H„W‰g†h@{ m l¡àéè Ê ÿ m ƒ$h•‰ }~$hnl€ÍàԋfhK m ƒ$h m Ä"lp{$hK‹g\hKh j l€A€‚g†h@hK{$l‡ãêë§¼ Ê ‰${
ê ¼ ¼ç €‚le
g ħƒ$f‘›ƒ m ƒ$h§„$g†l|$‰|$f}f m ñnl€…h ӑKh@hK{$f$‹1à©f jêUi ê È i σ$f j f}‡H„$f}h jcm ƒW‰ m ‰{${$f$‹ m ƒ$h
q
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h Ò m f j l €{$~$|$fl~ j ‡HhKg\f mKi5í l j ]h Ç~$h@ m ™ ñ‰ÿ m ƒ$h u Ñ Ø ‘@l m ‰‡Hf}$‰ m flAĔ‰ j
‰  j lkh jOm f}‡k‰ m hK{/f‰ j h@‘Kl$8
{ Ĕ¦‰ ñ i σ$h u Ø —–˜7‡k‰ j\j {$f jOm g\f}|$~ m f}l¨€‚lg m ƒ$h¡î i Ê‰Ô Åœî i Ô‘Ê Î7h@
‘ƒ ñ„hKg†ln‡k‰ j†j g†‰$‹¹
h Ĕ‰ j Ò m ħf m ƒn‰ j f}$‹
h Ό‰~ j†j f¢‰Œf m ƒ$hÍgœ‰U‹h êUi ༠śî i ¬
î Î7h@ i σ$ḧ́…hK‰
„l j f m flH‰${ j f}‹‡Š‰7l€ m ƒ$k
h Ό‰~ j\j f}‰c
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—–˜‡k‰ j†j {$f j\m g\f}|$~ m f}l j
Ø
u
€‚lg m ƒ$h j h m l€Œ‘
ƒ ñ„hKg†lɇЉ j\j f m hKgO‰  j î i Ê*Ô Å›î i È:ΌhŽ`
 ÿî i Ê*Ô Å›î i ÈÈ ÎŒhŽ`
 ÿî i Ê*Ô Å›î i Þ ÎŒhŽ`
 ÿ
 t ûYy
 t —x˜«y
 t ·”˜œ—x˜«y
|
× q«Ø ¥xÙÚ
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î ¼ i¼
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È
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çUi Ê
ççi à
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î iî ç È
j ~$ m†j l€ m ƒ$h m ƒ$g\hKhkÒ m†j l €ÜÒW‹~$g†h U
Þ i îŒ{$h j ‘Kg†f|…h@{3f m ƒ$h m hÃÓ mi
õÞ
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Ό‰~ j\j f}‰ j ƒ$‰„…h«Ä‰ j7j ~$| m gœ‰‘ m hK{?€‚g\l‡ÈhK‰‘›ƒ{$f jOm g\f}|$~ m f}l3‰${ m ƒ$hŸg†h j ~$ m Ĕ‰ j Ò m ħf m ƒ‰
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m ƒ$h)î i Ê‰Ô Å›î i Ô‘Ê Î7h@ð‡k‰ j†j f m hKgO‰ ¨ÿW‰ j§j ƒ$lßħ3f}ÒW‹~$g†h ÞUi ¼ Û i σ$h•‘K~Ug\hAĉ j g\h]Ç~$fg†hK{ m l
„$‰ j†jcm ƒ$g\l~$‹ƒ m ƒ$h t ê ÿ ê y’„lf mKi σUh<î i Ê‰Ô Å›î i Ô‘Ê Î7h@ñ‡Š‰ j\j f m hKgO‰ jĔ‰ j Ul m f$‘K~${$hK{nf} m ƒ$h
Ò m l€ m ƒ$h m g†h@${ i σ$h~$‡D|hKg¬l€ u Ñ Ø ‘@l~$ mœj l| m ‰ f}$h@{n€‚g†l‡ m ƒ$h”hÃÓ m gœ‰ „…l}‰ m fl m h@‘›ƒ$$f‡Ç~$h
Ĕ‰ j î õU' õ…&
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òh@hKg m ƒ$hKh j\j ÿ j f}$‘@h m ƒUhn‘
ƒ ñ„…h@g†l?‡k‰ j\j ‘@~ m l€î i Ê*Ô Å›î i Ô‘Ê ÎŒhŽ Ò mœj ħf m ƒ$f m ƒ$h1f$hK‡k‰ m f‘
g†‰$‹hŸl € m ƒUh
ѕ‰${ m ƒUhkhŽf{$hKU‘Kh)€‚g†l‡ Ò$‹~$g†&
h È i ¼ f j ‘Kh‰g m ƒW‰ m
ÑK´ j ‰ g†h j h@hKˆf m ƒ$h
u
u
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‰ ÿ m ƒ$h@g†hf j Ul7g†h‰ j l m l•‰ j\j ~$‡Hh m ƒ$‰ m5m ƒUh
A‘@l m ‰‡Hf}W‰ m f}l1f j&“ hKg\l$¦ƒ$hKU‘Kh m ƒ$h§g\h j ~U m
Ñ
u
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ôˆVÍbOX’õ7bV&S$Z\[<]ÔSWö<aø÷<TWVÍ[<Xö7Z\[<]ÔTWV&S$ZOù
۔h@‘‰~ j h1l € m ƒ$h•¢‰ g†‹hŒ|$g†‰$‘›ƒ3€‚lg m ƒ$h­· Ø m Š
l {UhK‘‰¦ñ m lAð$—–˜¦ÿ m ƒUh•—–˜™„…hK‰R‘‰­‘Kl m ‰f}
‘@l m g\f}|$~ m f}l j €‚g\l‡æ|l m ƒÉ· t î Êç Èy‰ ${ w t î ԑê Ȏy ¦W€‚~$g m ƒ$h@g†‡Hlg†h*ÿ u Ñ Ø „W‰g m f}‘@}h j „$g\l{$~U‘KhK{
f m ƒ$hÍg\h‰‘ m f}l¯ûðè u Ñ Ø…w {$hK‘K‰ßñ m l u Ø —–˜ºî¸ú Ê l € m ƒ$h m f‡kh i Ï&‰ f$‹ m ƒ$h j hº‘Kl m g†f}|U~ m fl j
f m l)‰‘@‘Kl~$ m ÿ
¥ t — ˜ yº¼r² t
· Ñ è
w — ˜ y¹/² t
· Ñ è
· Ø — Ù
Ñ è
· Ø — Ù
y¹3¥ t w u
ÑØ
y¹/² t
· Ø
ј
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t ÞUi Ô y
ħƒUhKg†h¨‰ m hKg†‡ j ‰g\h j ~$|Õ\h@‘ m)m l m ƒUh¨‘@l${$f m fl m ƒW‰ mŸm ƒ$h@g†hR|…hR‰ w f m ƒ$hRh@hK mi σ$h
· Ø u ј™‘@l m ‰‡Hf}W‰ m f}lpf j $h@‹}f‹f}|$h t j h@h j hK‘ m f}lXÈ i î i ¼ yÿ j lH² t · Ø u јŽy"ħf}Y|hŒf}‹Ulg†h@{ i
û f$‘Kh m ƒ$h&· î Êç Èy™f j f j l j „$f} ¯ ¼Dîÿ’f m ‘K‰$$l m {$hK‘K‰ßñ m lÉ·”˜œ—x˜¦ÿ|ħƒ$hKg\h‰ jŒm ƒ$h w î ԑê Èy
t
t
{Ulh j |hK‘‰ ~ j h<f m f j”¯ ¼ êUi σUf j €v‰‘ m ‘K‰p|h`hӄ$lf m hK{ m lDh j\m f‡Š‰ m h m ƒ$h<~$‡1|…h@g”l€ w t î ԑê Èy
„$‰g m f}‘Kh j „$g\l{U~$‘Kh@{ i σ$h±~$‡D|hKg¨² t w t î ԑê Èy\ypf j g†h@¢‰ m hK{ m l m ƒ$hz~$‡D|hKgRl€D‘@l~$ mœj
¥ t ·”˜œ—–˜›y‰|…lžh m ƒ$h7—–˜™„h‰ ¡f} ÞUi în‰‘K‘@lg†{$f$‹ m l
Ñ
y¹/² t w
u
¥ t ·”˜œ—–˜Žy
˜ — ˜ y t w
Á
t ÞUi Èy
wt Ñ è ·
Ñ è · ˜— ˜y
ħƒUhKg†hzü t w Ñ è · ˜ — ˜ ypf jŠm ƒUhz„Ug†l|W‰ |$f}f m ñ m ƒW‰ m¨m ƒ$h w t î ԑê Èycħf}`{$h@‘‰¦ñ m l · ˜ — ˜ ‰${
t w Ñ è · ˜ — ˜ y§f j™m ƒ$hD„$g\l|W‰|Uf}}f m ñ m ƒ$‰ m`m ƒ$f j {$hK‘K‰ßñ3‘›ƒW‰$UhKfħf}’|…h j hKh@‰ € m h@g m ƒ$h1 ‰g†f Å
l ~ j ‘K~ m†j ƒW‰hH|…h@hK±‰„$„$f}hK{ i σ$h í }h@| j ‘›ƒ¥Å Όlg†{$l m ‰|$}h j f}${Uf}‘‰ m h m ƒW‰ m h‰ ‘›ƒˆ‘›ƒW‰g\‹hK{
@‘ l‡D|$fW‰ m f}l¡l €¹·"—±ƒW‰ j h]Ç~W‰ –„$g†l|$‰|$f}f m ñtÍ5f i h*ÿ
² tw
ü tw
Ñ è
·
˜ — ˜ yͼ©ü w
t
Ñ è
yA¼
ü
· Ø — Ù
yA¼ýü t w
Ñ è
· Ù — Ø
yA¼
Ê
î
ü tw
Ñ è
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t ·"—cy
yÍè
Ê
î
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Þ iÞ y
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m ƒUf j †g h j ~$ m ‰­h j\m f}‡k‰ m h7l€ m ƒUh•~$‡1|…h@gl €&‘@l~$ mœj f} m ƒUh•— ˜ „h‰¡fÒW‹~$g\h Þ iî
‘@l‡Hf}$‹D€‚g\l‡ m $
ƒ hŒg†h‰ ‘ m fl w t î ԑê Èyfè · Ø — Ù ‘K‰­|hŒ‘‰‘K~$}‰ m h@y
{ Í
² tw
Ñ è
· Ø — Ù
yA¼ýü t w
Ñ è
· Ø — Ù
yO t w
Ñ è
· Ø — Ù
y\² t w
Ñ
yͼ
tw
w
t
Ñ¬è · Ø — Ù
Ñ è · ˜— ˜
y
y
¥ t
·
˜ — ˜ y
Þ ià y
tU
Counts
õ‘à
40
35
30
25
20
15
10
ÿ5
þ0
þ 0.5
þ 0.6
þ 0.7
þ 0.8
þ 0.9
1
*
K counts
1.1
+ 0
1.2
(A) Fits of K π mass for 1.34-1.43 GeV Y masses
+ 0
80
K π mass (GeV)
*
70
60
ÿ 50
40
30
20
10
þ0
þ0
þ 0.1
þ 0.2
þ 0.3
*
þ 0.4
mass window (GeV)
(B) Extrapolation of K contribution
ÂÂÄÅcÆwvɶ|x™ç
Ñ jOm f}‡k‰ m f}l¡l € u Ñ ‘Kl m g†f}|U~ m fl m l m ƒ$h7— ˜ „h‰¡f­o s q vt u Ø w ìzy i
y þ&f m l € m ƒ$h u ؅— ˜ ‡Š‰ j\j {$f jOm g†f|$~ m f}lŠ€‚lgh@h@ mœj ħf m ƒlë Ñ ‡Š‰ j†j f} m $
ƒ hŒgœ‰$‹h
Òt d
Ñ ‘@l m g\f}|$~ m f}lp€‚lg{UhK‘Kg\h‰ j f}$‹H‡k‰ j†j \g hK‹fl j
î i Ê*Ô Å›î i Ô‘Ê Î7h@ i ÛyA}l m l€ m ƒ$h
t
u
|h m Ä"hKh@£î i Ê‰Ô Åœî i ç Î7h@ø‰U{zî i Ê‰Ô Å›î i ȭΌhŽ i
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t Ê ç
² t
· Ñ
yA¼
ü t
· Ñ è
² t
·6Ñ6è
w —x˜«y
w — ˜ yO t
· Ñ è
w — ˜ y
Þ iïç y
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Ãh ӄ…h@g†f}‡HhK m ‰Ag†h j ~$ m ‡k¦‰ ñ?|hH‘@l j f}{$h@g†hK{z€‚lg m ~$f m l~ j ‘@l j f{$hKg\f}$‹ m ƒUhH‡Hl{$hK j ´Y€v‰f}~$g\h m l
l| m ‰f m ƒ$hpl| j h@g\h@{ w t î ԑê Èyn‡Š‰ j†jKi¤í }h‰ g†™ ñ‰ÿ m ƒ$h@g†hRf jŸj l‡khpf${$f‘‰ m f}l£l € j l‡Hh m ƒUf}$‹
ħg\l$‹)lg‡Hf j\j f}U‹Ÿf} m ƒ$hŒ‡Hl{UhK j@i
 ÿ ¯ ƒW‰hz„Ug†h j hK m h@{ýhŽf{$hKU‘Kh€‚lg m ƒUh?{$hK‘K߉ ñ ·”˜ t î Êç ÈÉ
y è
û w i σ$h
¯ ݑKl$‘K~ j fly
|Ugœ‰$‘›ƒUf}$‹Ÿg†‰ m flŸg†hK}‰ m f®h m l m ƒ$h w —–˜§‘›ƒW‰$UhK–f b
j ê' ꑼ î .
êU' êêç Ø ˜ ˜˜ ÿ$‘Klg†g†h j „l${$f$‹ m lH‰
Ù ˜ ˜˜ ë
„$‰g m f¢‰
 ħf}{ m ƒzl € މÔê7 ¼à*ê Ø * ˜ h@ i σ$f j f j ‰ zÃh ӑKf m f}$‹Rg\h j ~U m |hK‘‰ ~ j h m ƒ$h)g†‰{$f¢‰ m fh
Ù qq˜
{UhK‘¦‰ ñpl € m ƒUG
h ·”˜ t î Êç Èy”ƒW‰ j $hŽhKg|hKhK¨l| j hKgOhK{3|…hŽ€‚lg†h i
θ (degrees)
î
180
160
140
120
100
80
60
40
20
0
0
50
100
150
200
250
300
θ (degrees)
ù
(A) Predicted γ angular distribution
350
φ (degrees)
180
160
140
120
100
80
60
40
20
0
0
50
100
150
200
250
300
350
φ (degrees)
(B) Counts surviving fiducial cut
ÂÃvÄŒÆwv8¶yx™ï
Ag†hK{Uf}‘ m hK{¨„$ƒ$l m lD8:9 ; h@g j ~ j < i t Ò y Ò x‘Kl~$ mœj ħf m ƒ­‡Hf j\j f}U‹
‡Š‰ j\j§j Ç~W‰g\hK{3|h m Ä"hKh@ Å êi êêàDµn¶¸· q`‰U{ êUi êêÊ È µ•¶¸· q i t Ûy6σ$l j h•‘@l~$ mœj
h ÒW{U~$‘Kf}‰–‘K~ m hÃÓU‘@}~${Uf}$‹ m ƒUh•‘@lf} j l€ m ƒ$hŒ‡k‰‹$h m ‰${ m ƒ$hŒƒ$l}h
j ‰ m f j œ€ ñf}U‹)‰H‘@g†~${$k
f} m ƒ$h7€‚l‚g Ĕ‰g†{¨{$fg†hK‘ m fl
Ft E çHG y i σ$h•ƒ$lg\f “ l m ‰x{$‰ j ƒ$h@{­f}$h`f}${$f‘‰ m h jm ƒ$h
‡Šw‰ ÓUf‡D~$‡-‰$‹h<l€¬‘Klžh@gœ‰‹h•l€ m ƒ$h7€‚lÆg ĉ g†{¨hK}h@‘ m g†l‡k‰‹$h m f‘<‘‰lg†f‡kh m h@g jKi
ꑼ
î
∆θ (degrees)
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-1
0
1
2
3
4
5
6
7
I∆φ (degrees)
Eγ, measured (GeV)
ù
(A) Measured-predicted γ angular differences
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.8
KEL ,0.6missing0.7mass (GeV)
γ
(B) Measured EJγ vs. predicted EJγ
0.2
0.3
0.4
0.5
ÂÂÄÅcwÆ v8¶yx ÷
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‘ ‰lg†f‡kh m h@g i t Ò y û ‘K‰ m†m hKg§„$}l m l€ m ƒ$h•‰$‹~U¢‰g{Uf…hKg†h@$‘Kh j fM8:9
‰${N<
;
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l€ m ƒ$hŒl| j hKgOhK{ û/hKUhKg†‹*ñphKg j ~ jm ƒ$hŒ„$g\hK{$f‘ m hK{›û/hKUhKg†‹*ñ t €‚g†l‡ m ƒUh•‡Hf j\j f$‹
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ÈÈ Ô t î õõÊ ydÈ õ‰Ê Å Þ î õUi
j l€ºÑfӑKf m h@{Cjbñ„…h@g†l j t ¯†¯ yÃÿT
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l Ng<h@‘‰¦ñ j l€
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Q ‰Óf}g†‰ j ÿÑ i ’ i ò­l$f “ ÿ ‰${Xò i û lßñh@~$g]ÿ•jñ„hKg\lX݉{$f}‰ m f®h{g<h@‘‰¦ñ j
Þ õß Ñ i Œ
acb\de[3b\fCg ʑ¼i Ê t î õç Èy Þõ ÈßÅ à‰êêi
Þ î ê ß
i ܈‰g\ j ÿ’Ü i 5€‚hKf}•ÿ’‰${–j i ݧl}$f}éÿc†ÑAhK‘ m g†l‡k‰‹Uh m f‘VAg†l„hKg m fh j l€jbñ„…h@g†l j
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g hßÎ7gœ‰${ZÿÝ i A˜ i ’‰ …h‰ÿQ i ’lƒ$ j lyÿW‰U{N’ i Q7f j f j ÿ“€ò3‰ j†j h j ‰${D1 m ƒUhKgc&‰ gœ‰‡­Å
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j ‰{$g†l j ÿ|”U$WYXeZ\[3]^`_acb\de[3b\fCgDî ¼i à t î õ‘à Èy ¼‰êÞê Å ¼‰ê‘à‰Þi
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î
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.
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]\_ob^`pmU$WYXeZ\[3]rZ Ò È ¼‰õ t î õ‰õ î¸y à î Ê Å à¼*ÞUi
Þ îwÈ ß
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ò ~$}{$h@g j ÿc‚σ$h,<~W‰g\
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ò h‰ j ~$g\hK‡HhK m l€
i í`i ch m h@g j hKNb\sw^`_vu‡
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m ƒ$h û f}‹‡k‰ ê
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t
m l û m g†‰$‹h@$h j\j f}
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û m ‰ m h Ò „U„$g†l‰ ‘›ƒ m l û m gœ‰ $‹hKUh j†j f} m $
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ît õçç y ¼‰Þõ Å ¼à È i
Þ ¼‰ê ß
’
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ií`i ò™‰‘›ƒ$hKgWÿ$Ñ i 1 j h m ÿj i Ϭlf•ÿ‰${ Òni ™
l m ƒ$h&Íg\l m l­‰ ${3ò~$‘KhKf•ÿTŸ~$‘@¤Å m ƒú õç î ¼‰ê ÈÈ i
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m l„$g†l{$~$‘ m f}lHl € m ƒUh w t î
ԑê Èy
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kmln]\_ob^`pqU$WYXeZ\[3]rZÛ ¼ È Ê t î õç Èy à*Ô¼ Å à È ¼i
Þ ¼¼ß g i Ü i σ$l‡k‰ j ÿ Òni ÑA$‹}h@g]ÿŠj i Ñ i þ&f j éÿ"‰ ${;Ý i Ü i Q7g†‰hK‡HhKgWÿ& û m g†‰$‹h”¬‰g m f}‘@}h
g\l{$~U‘ m fllþWg†l‡_— Ù ð ¯  m hKg†‰‘ m f}l j ‰ m î i Þõ Î7h@7ú ‘‰ÿ|(kPln]\_ob^`pPU}WYXeZ\[3]rZÛdÈ Þ t î õ‘à*Ê y
A
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Ý
i
îßÈwÅ
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i
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Þ ¼‰Ê ß c
xb\s—sb\p0Z ¼ î i ¼ È t î õÞç y™î à îßÈwśî à î ài
Þ ¼*Ôß Ý‰f‡klU{$l۔h@g m f$f¨ÿ û m g†‰$‹h$¬‰g m f}‘KhÅ~U‘K}h@~ j f} m hKgœ‰ ‘ m fl j
t î õç‘à y ԑõ Å Þ*Ô$i
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ÿT{kPln]\_ob^`p„U}WYXeZ\[3]rZxÛ ¼à‰õ
’
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î ¼ î ê ŜîwÈ êê ò­h@ ò3‰ j†j ݉$‹hp‰ ${¤l€™ò™h@~ m g†‰bò­h j lÖf} m ƒ$h?îwÈ ê Å Þê‰ê ò­hŽ ò3‰ j†j
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Þ ¼‰Þ ßŒÒ ‰‘›ƒ$h@¥Å۔h@g†f}¥Å۔l$¥Åzj`‰‡1|$~$g†‹Åj™h@f}{$h@}|hKg ÅÆò­~$‘›ƒUhK
í l¢‰|lg†‰ m flyÿ kml€‚d`€ ƒ„[†…
‡ b\ˆnsz€ ԑõÒ t î õޑà |y È ê È`¦ g7Ñ û ..ݧhK„lg m މõ úî ê ¦ í ‰‡D|Ug†f}{U‹hÍ۔~$|$|U}h í ƒW‰‡D|hKgÜÎ7g†l~U„yÿ
U$WYXeZ\[3]^`_~acb\de[3b\fñßî È Þ t î õÞà y`î Ô¼‰Þi
Þ ¼àߌÒni ò i ۔ßl ñ‰g j f‰b\s^`_vu‡ÿ¡Aƒ$l m l„$g†l{$~$‘ m f}lËl€ u
g<h@~ m h@†g f~$‡¿‰ m î«
î Î7h@GÿT û ˜–Òí Å ³ ۬Šçê‰ÊUi
Ø Åƒ‘ñ„hKg†l݀‚g\l‡
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w t îwÈ ¼‰ê y۔h m Ä"hKh@ ¼i ç ‰${ Ô$i ç ΌhŽ`ÿ|N±™u™U$WYXZ\[o²Nƒ$¦tU-^`ps—[3]\_obrZž^`ˆ‰¨“[3b\_v‚Z¡³ t î õ‰ç ê y
î à Å ¼‰êi
Þ ¼‰õ ß
g
i
l |hKg)b\s•^`_vu‡ÿ“ÆÏƒ$h•Û”g†h@‡k‡ j\m gœ‰ƒ$~$$‹`Ϭ‰‹‹hK{MAƒ$l m l­Û"h‰‡Gf}”j`‰ }xÛ݉ ”
i ¯›i û m m ƒ$h
’hŽYh@g j l ˜ ‰|lgœ‰ m lg‚ñ‰ÿT&kPln]\_ob^`p“¯ˆZ\sypl ‡ b\ˆns?Z^`ˆm´Cb\s†Wn€µ‚Z ÒIÔԑê ú ¼ t ¼*êêê y ¼‰ÞÊ Å ¼ç‰ÔUi
Ï ‰¦ñ}lg)b\s•^`_vu‡ÿ$‚σUh í˜–Ò û¨û m ‰g m™í l~U m hKgWÿTkf}p„$g\hK„W‰g†‰ m fl i
ÞKÊê ß û i &
ò h jOm ‰¦ñh@gb\s•^`_vu‡ÿ$‚σ$h í˜–Ò û <
g g†f€ mí ƒW‰‡D|hKg û
i ­
ò
ÞKÊ î ß
ñ
jOm hK‡lÿ| j ~$|$‡Hf m†m hK{ m lkò ¯
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