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