barrelet zeros
DESCRIPTION
Barrelet zeros. PWA 2011 GWU May 2011. hadron states. 1. M 2 – s – iM . x. variables: E = s , . spinless particle scattering. cm. Spin analysis. M. 1. q. M. 2. Spectroscopy: interplay of poles & zeros. pp pp. t. u. r. f. 2. s. r. 3. u. s. t. 2. f m. p. - PowerPoint PPT PresentationTRANSCRIPT
Barrelet zerosBarrelet zeros
PWA 2011GWU May 2011
p h a s ec r o s s - s e c t i o n
p h asec ro ss -sec tio n
1M2 – s – iM
hadron states
s
x
s
x x
cm
variables: E = s ,
spinless particle scattering
-1 +10
cos
d/ds
W
J = 0
-1 +10
cos
d/ds
W
J = 1
-1 +10
cos
d/ds
W
J = 2
Spectroscopy: interplay of poles & zeros
M1
M2
Spin analysis
su
t
t
u s
f 2
3
f m 2A =
s + t + u = 4m2
u
tA
s
Adler zero makesthe - connection
f m 2A =Chiral symmetry
how to find the amplitudes
2JTruncate j < 2J
let z = cos
Barrelet ambiguity
2J amplitudes
how to find the amplitudes
exp (i )(s,z)
D
P
S
cos
Barrelet ambiguity
D
P
P´
S´
S
D´
cos
Barrelet ambiguity
Barrelet zeros
continuity
NN
NN d / ds W = | f | + | g |
2 2
P d / ds W = - 2 Im (f * g)
(1+P) d / ds W = | f + i g | _ _ 2
d / ds W = A P (z)nnn
P d / ds W B P (z)nn
n
-= sin
representingexperiment
NN
(1+P) d / ds W = | f + i g | _ _ 2
F (s, )
= =
Barrelet treatment
Barrelet treatment
= =
(1+P) d / ds W
s(1-P) d / dW
2J amplitudes
Barrelet treatment
exp (i (s,))
Barrelet treatment
m J, J+1=
cf. Omelaenko
2J amplitudes
= =
Barrelet treatment
.1
= =
Barrelet treatment
.1
1/1*
p p++ p p- - p n0-
dsdW
1234 MeV
1449 MeV
1678 MeV
1900 MeV
p p++ p p- - p n0-
P
1234 MeV
1449 MeV
1678 MeV
1900 MeV
pp++
a
1.75
2
2
2
2
2
2
2
1.11.1
1.45
1.45
c
d
b
SAIDEBAC Kamano
threshold behavio(u)r
pp++
a
b
1.11.1
2
2 2
2
2
c
d
SAIDEBAC Kamano
p p++ p p- -
u s
t
c
d
a
b
pp++SAIDEBAC
s
Lmax
L
continuum ambiguity
exp (i )(s,z)
PWA 2011GWU May 2011
END