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TRANSCRIPT
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!"#$!%"&'()*+,&$-#%."&'%/*
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1Tuesday, September 11, 2012
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C"+*:#E$^7::1$8-)'*7A3,-)$'-$!$!$*()!τ
ντ
d
u
WR
τντ
d
u
H
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! GGGV"78"$2*-8##E$'-$$((()!$+)E$(((()!7Tuesday, September 11, 2012
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Jµ ≡ �V (q1)π(q2)��dγµ
�1− γ5
�u�� 0�
= F1(Q2)�Q2�µ1 − �1 · q2Qµ
�
+F2(Q2)�1 · q2�
qµ1 − qµ2 −Qµ
Q · (q1 − q2)Q2
�
+iF3(Q2)�µαβγ�1αq1βq2γ + F4(Q2)�1 · q2Qµ
?X$e-*@$e+8'-*1$e-*$!$!$3()!$N3$g$24$%54$6O
๏ a"#"&)+$'/&78/7&"$L,&$NV$E)6&,#%8$87&&"#/Z^
! 9-'#c$$7M$71$#h2#8'#E$'-$A#$D#*6$1@+..
Qµ ≡ (q1 + q2)µ
2-.+*7\+,-)$'#)1-*$e-*$i
7%>7Mc$e-*@$e+8'-*1
!N3,+316'O:'?29&:'>'PD6'GQH'IRSQHKL'''N3,+31'A'=#1+3&6'O:'?29&:'>'FH6'GSF'IRSSPK:
8Tuesday, September 11, 2012
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JHiggs ≡ �V (q1)π(q2)��d
�a + bγ5
�u�� 0�
=�
bfH�1 · q2, V = vector,afH�1 · q2, V = axial-vector
95$e-*@$e+8'-*$e-*$!$!$3()!$N3$g$24$%54$6O
๏ N%B%+)&+*Z$E)6&,#%8$87&&"#/$L,&$_%FF'$8,#/&%C79,#Z
9:c$e-*@$e+8'-*%48c$2+*+@#'#*7\#$^7::1$8-32.7):1P$8+)$"+D#$C5>D7-.+,):$NV#+0O$2"+1#1
7%;7M$
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5+*,+.$L+'#$U16@@#'*6$e-*$!$!$3()!$N3$g$2;$%%;$6O
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ACP ≡Γ− ΓΓ + Γ
=∆Γ
Γ + Γ
∆Γ =�
g(Q2) |bfHF4| sin (δ4 − δH) sin (φb) dQ2
2+*+@#'#*7\#1$^7::1$8-32.7):1
e-*@$e+8'-*$e-*$95$j3+*0$83**#)'
1@+..$?X$e-*@$e+8'-*
1'*-):$2"+1#1V#+0$2"+1#
10Tuesday, September 11, 2012
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Jµ ≡ �V (q1)π(q2)��dγµ
�1− γ5
�u�� 0�
= F1(Q2)�Q2�µ1 − �1 · q2Qµ
�
+F2(Q2)�1 · q2�
qµ1 − qµ2 −Qµ
Q · (q1 − q2)Q2
�
+iF3(Q2)�µαβγ�1αq1βq2γ + F4(Q2)�1 · q2Qµ
JHiggs ≡ �V (q1)π(q2)��d
�a + bγ5
�u�� 0�
=�
bfH�1 · q2, V = vector,afH�1 · q2, V = axial-vector
๏ C($$e"'4$$f#"$A,''%C%+%/*$%'$/,$D"%FE/$/E"$%#/"F&)+$L,&$/E"$6%S"&"#9)+$D%6/E$%#$'78E$)$D)*$/E)/$'78E$/"&B'$)&"$"U/&)8/"6
๏ -'%#F$,#"$A)&987+)&$J%#"B)98)+$)#F+"$)++,D'$7'$/,$8,#'/&78/$)#$)'*BB"/&*$/E)/$6"A"#6'$,#$NVXO
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R +%$)#6$+&$"UA"8/"6$/,$C"$)AA&"8%)C+"$L,&$,$?$'%b$&"+)9."$'%Q"'$#,/$D"++$J#,D#
R I3-"$7&.80.%.8/'7'($$)'*BB"/&%"'$,L$7A$/,$3kl$8,#'%'/"#/$D%/E$"UA"&%B"#/)+$7#8"&/)%#9"'$%#$6"8)*$6%'/&%C79,#$L,&$,$?$'%$8)'"$='""$I"L4$i3j$L,&$L7&/E"&$6"/)%+'@
5-.+*7\+,-)>E#2#)E#)'$*+'#$+16@@#'*6$e-*$!$!$3()!
A�cos β�CP ≡∆Γ�cos β�
Γsum
∆Γ�cos β� =� �
g1(Q2) |F1| sin (δ1 − δH)
+g2(Q2) |F2| sin (δ2 − δH)�|afH | sin (φa) dQ2
V#+0$2"+1#
1'*-):$2"+1#1
#h2#*7@#)'+.$8"+..#):#c$$%%$71$+$A*-+E$*#1-)+)8#GGGG
13Tuesday, September 11, 2012
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Jµ ≡ �V (q1)π(q2)��dγµ
�1− γ5
�u�� 0�
= F1(Q2)�Q2�µ1 − �1 · q2Qµ
�
+F2(Q2)�1 · q2�
qµ1 − qµ2 −Qµ
Q · (q1 − q2)Q2
�
+iF3(Q2)�µαβγ�1αq1βq2γ + F4(Q2)�1 · q2Qµ
!*72.#>2*-E38'$+16@@#'*6$e-*$!$!$3()!
4#D7>C7D7'+$'#)1-*$.#+E1$'-$'*72.#$2*-E38'
ΓTP ∼ Im (bfHF ∗3 ) (��1 · �q1)��1 · (�pτ × �q1)
๏ I"8)++$/E"$NV$E)6&,#%8$87&&"#/Z
! (e$'"#$@-@#)'3@$-e$'"#$n$8+)$A#$@#+13*#E;$8+)$8-)1'*38'$+$'*72.#>2*-E38'$+16@@#'*6$'"+'$7)D-.D#1$'"#$N?XO$e-*@$e+8'-*$7`$+)E$'"#$N95O$e-*@$e+8'-*$9:$
! 8-)17E#*$'"#$8+1#$!0J0";$17)8#$7`$71$'"#$E-@7)+)'$e-*@$e+8'-*$7)$'"71$8+1#
! GGGe3*'"#*@-*#;$2$71$+$)+**-V$*#1-)+)8#
๏ P%#6$=)''7B%#F$!$7#A,+)&%Q"6@444
14Tuesday, September 11, 2012
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∆ΓTP = (��1 · �n1) (��1 · �n2)
�
gTP�Q2
�|bfHF3| cos (δ3 − δH) sin (φb) dQ2
!*72.#>2*-E38'$+16@@#'*6$e-*$!$!$2()!๏ P,&B$)$;
-
!*72.#>2*-E38'$+16@@#'*6$e-*$!$!$2()!
๏ O7B"&%8)+$"'9B)/"$A"&L,&B"6$%#$I"L4$i3j4444๏ TUA"&%B"#/)+$7#8"&/)%#9"'$%#$A)&9)+$D%6/E$)++,D$L,&$)#$)'*BB"/&*$,L$,&6"&$G2l$B7+9A+%"6$C*
ATPCP ≡∆ΓTPΓsum
(��1 · �n1) (��1 · �n2)
16Tuesday, September 11, 2012
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๏ N%B%+)&$/,$C+$?$2$8)'"Z$"U8"A/$D%/E$1$!$D
๏ f#8"$)F)%#Z$"U)B%#"$;
-
๏ a"#"&)+$'/&78/7&"$L,&$NV$E)6&,#%8$87&&"#/Z^
! 9-'#c$$7M$71$#h2#8'#E$'-$A#$D#*6$1@+..
?X$e-*@$e+8'-*1$e-*$!$!$'(()!
!N3,+31'A'=#1+3&6'O:'?29&:'>'FD6'DDR'IRSSEKL''DH6'PDGIZK'IRSSFKL''N3,+316'=#1+3&6'
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Jµ ≡ �K−(p1)π−(p2)π+(p3)��sγµ
�1− γ5
�u�� 0�
=�F1(s1, s2, Q2) (p1 − p3)ν
+F2(s1, s2, Q2) (p2 − p3)ν�Tµν
+iF3(s2, s2, Q2)�µνρσp1νp2ρp3σ + F4(s1, s2, Q2)Qµ
?X$e-*@$e+8'-*1$e-*$!$!$'(()!๏ NV$L,&B$L)8/,&'4444
๏ P,&B$L)8/,&'$8)#$)&%'"$)'$L,++,D'Z^
!N3,+316'=#1+3&6'
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C"+*:#E$^7::1$8-)'*7A3,-)$'-$!$!$'(()!
๏ ;E)&F"6$_%FF'$"S"89."$_)B%+/,#%)#Z
๏ m"c#"$A'"76,'8)+)&$L,&B$L)8/,&Z
๏ ;M$)#6$/E"$=O
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๏ 0#,/E"&$)AA&,)8E:R 7'"$W)'*BB"/&%8Y$%#/"F&)9,#'$,."&$AE)'"$'A)8"$/,$"U/&)8/$,/E"&$NVXO`
22Tuesday, September 11, 2012
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n!Τ
n!!
n!Lz'
z
y
y'y1"y2
x
x'
p3
x1
x2
Ψ
Α
Β
Β
Γ
!"*##$-'"#*$C5>-EE$+16@@#'*7#1$e-*$!$!$'(()!
E7*#8,-)$-e$.+A$7)$"+E*-)78$*#1'$e*+@#$
!
"+E*-)78$E#8+6$2.+)#
)-*@+.$'-$"+E*-)78$E#8+6$2.+)#
!
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!"*##$-'"#*$C5>-EE$+16@@#'*7#1$e-*$!$!$'(()!
dD+*7-31$e+8'-*1;$+1$V#..$+1$'"#$7)'#:*+,-)$-D#*$2"+1#$12+8#;$"+D#$A##)$-@7I#E$e-*$8.+*7'6P$$$2.#+1#$1##$L#eG$o&p$e-*$E#'+7.1G$
A(1)CP
∼ Im (F1 − F2) fHIm (ηP )
A(2)CP
∼ Im [F1 (p1 − p2)x + F2 (p2 − p3)x] fHIm (ηP )
A(3)CP
∼ Re (F3) fHIm (ηP )
J@-E7m#EK$*+'#$+16@@#'*7#1$E#2#)E$-)$'"#$NE-@7)+)'O$?X$
e-*@$e+8'-*1$7%$+)E$7&$
'*72.#>2*-E38'$+16@@#'*6$E#2#)E1$-)$'"#$N13AE-@7)+)'O$?X$e-*@$e+8'-*$7`
F@$2+*+@#'#*7\#1$^7::1$8-32.7):1
25Tuesday, September 11, 2012
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F1 : τ → K1ντ → (K∗π) ντ → KππντF2 : τ → K1ντ → (Kρ) ντ → KππντF3 : τ → K∗ντ → (Kρ,K∗π) ντ → Kππντ
A(1)CP
∼ Im (F1 − F2) fHIm (ηP )
A(2)CP
∼ Im [F1 (p1 − p2)x + F2 (p2 − p3)x] fHIm (ηP )
A(3)CP
∼ Re (F3) fHIm (ηP )
r-*@$e+8'-*1$e-*$!$!$'(()!
dHGXG$U1)#*$"#$%&G$NC4RF$C-..+A-*+,-)O;$5"61G$L#DG$H$a&;$B=&BBa$N&BBBOG$ddH#80#*;$X7*0#1;$?+3#*$+)E$/+1;$sG$5"61G$C$Tb;$MMT$N%QQ`OG
9-'#c$C4RF$+)+.6171$1#'$7`$'-$\#*-P$V#$mh$7'1$)-*@+.7\+,-)$138"$'"+'$7'$$8-)'*7A3'#1$Tu$'-$
'"#$2+*,+.$V7E'"dddtG$U3A#*'$"#$%&G$NH>H>.$C-..+A-*+,-)O;$5"61G$L#DG$4#I$%BB;$B%%bB%$N&BBbOG
๏ 5#$,&6"&$/,$"'9B)/"$)'*BB"/&%"'$#7B"&%8)++*Z$#""6$/,$)''7B"$)$B,6"+$L,&$/E"$NV$L,&B$L)8/,&'
R F7%6"6$C*$;qTf$6)/)^$L,&$L,&B'$,L$+%$)#6$+&R 444)#6$C*$/E",&"98)+$8,#'%6"&)9,#'^^$L,&$+`R +M$'"/$/,$Q"&,b$0:$)''7B"6$/,$C"$8,#'/)#/$=L,&$'%BA+%8%/*@R ,."&)++$#,&B)+%Q)9,#$L&,B$12123$&"'7+/$L,&$[I^^^
R 4444'""$I"L4$i1j$L,&$6"/)%+'
26Tuesday, September 11, 2012
-
r-*@$e+8'-*1$e-*$!$!$'(()!
dHGXG$U1)#*$"#$%&G$NC4RF$C-..+A-*+,-)O;$5"61G$L#DG$H$a&;$B=&BBa$N&BBBOG$
TotalK1!1270"K1!1400"W!Z
0.8 1.0 1.2 1.4 1.6 1.80.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
MKΠΠ !GeV"
1 # tot
d#dM
KΠΠ!GeV!1 "
TotalΡ ReflectionK%W!Z
0.6 0.8 1.0 1.2 1.4 1.60.000
0.005
0.010
0.015
0.020
0.025
0.030
MKΠ !GeV"
1 # tot
d# dMKΠ!GeV!1 "
TotalΡK% ReflectionW!Z
0.2 0.4 0.6 0.8 1.0 1.20.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
MΠΠ !GeV"
1 # tot
d# dMΠΠ!GeV!1 "
C4RF$E+'+$+)E$m'd '"#-*#,8+.$E71'*7A3,-)1$:#)#*+'#E$317):$-3*$#h2*#117-)1$
e-*$e-*@$e+8'-*1
V#$7)8.3E#$+$8-)'*7A3,-)$E3#$'-$7`
dddXG
-
๏ I"8)++Z
๏ -A,#$%#/"F&)9,#$,."&$AE)'"$'A)8"Z$")8E$,L$/E"$)'*BB"/&%"'$=E$?$3Z$1$p$G@$E)'$/E"$L,&BZ
๏ 4448)#$)+',$L,&B$6%S"&"#9)+$]7)#99"'Z$
A(i)CP =1
Γ + Γ
� �dΓi
dQ2 ds1 ds2− dΓi
dQ2 ds1 ds2
�dQ2 ds1 ds2
93@#*78+.$*#13.'1$e-*$!$!$'(()!
A(i)CP
= a(i)CP
fHIm (ηP )
e-*@$e+8'-*$e-*$95$j3+*0$83**#)'$N+113@#E$8-)1'+)'O
)3@#*78+.$e+8'-*$-A'+7)#E$A6$7)'#:*+,-)$-D#*$2"+1#$12+8#
da(i)CPdX
$X = MKππ, MKπ, Mππ, cos θ
28Tuesday, September 11, 2012
-
๏ m%S"&"#9)+$)'*BB"/&%"':
93@#*78+.$*#13.'1$e-*$!$!$'(()!
A(i)CP
= a(i)CP
fHIm (ηP )
da(i)CPdX
daCP!1"#dM
daCP!2"#dM
daCP!3"#dM
0.8 1.0 1.2 1.4 1.6 1.8!0.001
0.000
0.001
0.002
0.003
0.004
0.005
MKΠΠ !GeV"
daCP
dMKΠΠ
!GeV!1 "
daCP!1"#dM
daCP!2"#dM
daCP!3"#dM
0.6 0.8 1.0 1.2 1.4 1.6!0.002
0.000
0.002
0.004
0.006
0.008
0.010
MKΠ !GeV"
daCP
dMKΠ
!GeV!1 "
daCP!1"#dM
daCP!2"#dM
daCP!3"#dM
0.2 0.4 0.6 0.8 1.0 1.2!0.002
!0.001
0.000
0.001
0.002
0.003
MΠΠ !GeV"
daCP
dMΠΠ
!GeV!1 "
daCP!1"#dcos!Θ"
daCP!2"#dcos!Θ"
daCP!3"#dcos!Θ"
!1.0 !0.5 0.0 0.5 1.0!0.0010
!0.0005
0.0000
0.0005
0.0010
cos!Θ"
daCP
dcos$!Θ"
w$71$E#m)#E$7)$'"#$n$*#1'$e*+@#$N1##$L#eG$o&pO$
'"*##$+16@@#'*7#1$NE$g$%;$&$Z$`O
9-'#c$$R+8"$+16@@#'*6$13x#*1$1-@#$+@-3)'$-e$8+)8#..+,-)$32-)$7)'#:*+,-)$-D#*$2"+1#$12+8#GGGG$
29Tuesday, September 11, 2012
-
93@#*78+.$*#13.'1$e-*$!$!$'(()!
A(i)CP
= a(i)CP
fHIm (ηP )
daCP!1"#dM
daCP!2"#dM
daCP!3"#dM
0.8 1.0 1.2 1.4 1.6 1.8!0.001
0.000
0.001
0.002
0.003
0.004
0.005
MKΠΠ !GeV"
daCP
dMKΠΠ
!GeV!1 "
daCP!1"#dM
daCP!2"#dM
daCP!3"#dM
0.6 0.8 1.0 1.2 1.4 1.6!0.002
0.000
0.002
0.004
0.006
0.008
0.010
MKΠ !GeV"
daCP
dMKΠ
!GeV!1 "
daCP!1"#dM
daCP!2"#dM
daCP!3"#dM
0.2 0.4 0.6 0.8 1.0 1.2!0.002
!0.001
0.000
0.001
0.002
0.003
MΠΠ !GeV"
daCP
dMΠΠ
!GeV!1 "
daCP!1"#dcos!Θ"
daCP!2"#dcos!Θ"
daCP!3"#dcos!Θ"
!1.0 !0.5 0.0 0.5 1.0!0.0010
!0.0005
0.0000
0.0005
0.0010
cos!Θ"
daCP
dcos$!Θ"
๏ 0'*BB"/&%"'$'7S"&$',B"$)B,7#/$,L$8)#8"++)9,#$7A,#$%#/"F&)9,#$,."&$AE)'"$'A)8"$
๏ ;)#$/&*$/,$B%9F)/"$/E"$A&,C+"B$C*$B7+9A+*%#F$C*$r3$%#$.)&%,7'$&"F%,#'$,L$AE)'"$'A)8"4444
)-$#h'*+$V#7:",): 8-1NyO$!z8-1NyOz @+h7@3@$2-117A.#
30Tuesday, September 11, 2012
-
93@#*78+.$*#13.'1$e-*$!$!$'(()!
๏ 0''7B%#F$s9:F@s$%'$'78E$/E)/$/E"$O
-
MG$C-)8.3E7):$L#@+*01๏ (E"$A&"'"#/`#")&$L7/7&"$)&"$"U8%9#F$9B"'
R E)6&,#%8$!$6"8)*'$A&,.%6"$)$A&,B%'%#F$)."#7"$/,$'")&8E$L,&$450'7;%.8'0.$"0?2''7N8"
๏ P7&/E"&$&"c#"B"#/$,L$6"8)*$6%'/&%C79,#'$)#6$6"/"&B%#)9,#$,L$L,&B$L)8/,&'$D%++$)++,D$L,&$B,&"$A&"8%'"$)#)+*'%'$,L$;
-
t+80>32$1.7E#1GGGG
33Tuesday, September 11, 2012
-
C5>D7-.+,):$+16@@#'*7#1
๏ 5#$F"#"&)+Z$#,#XQ"&,$;-EEO$+)E$1'*-):$NC5>#D#)O$2"+1#1;$*#12#8,D#.6
๏ P7++$&)/":$$8,BA7/"$s>s&b$'7B$,."&$'A%#'Z$%#/"F&)/"$,."&$AE)'"$'A)8"
A = A1 + A2eiφeiδ
34Tuesday, September 11, 2012
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