The potential for “complete” experiments in pseudoscalar ......History D 13(1895) -2000 ⇒ D...

N-N* Workshop Oct15’08

The potential for “The potential for “completecomplete” experiments” experiments in pseudoscalar meson productionin pseudoscalar meson production

A.M. Sandorfi (Jefferson Lab)

• missing (?) N* states of the quark model

• spin-observables in Jπ=0–photo-production

• γ N → Κ Λ JLab “complete” experiments

• Q: can such data provide total amplitudes, unique to a phase ?

• the mechanics of fitting out the amplitudes - potentials and limitations

• tests with mock data – work in progress ⇔ with S. Hoblit, UVa

3q,di-q options

All the excited states of the proton and neutron that we know about were determined from πN scattering qqq ⇔ conventional quark model

• predict many more resonances than have been observed (in πN) • g(πN) couplings predicted to decrease rapidly with mass in each oscillator band • “missing resonances” may have much larger couplings to lower cross section channels: ππN, ρN, ηN, ΚΛ or ΚΣ

q (qq) ⇔ di-quark models

• two quarks are quasi-bound • fewer degrees of freedom • there are no “missing” states

p and n KY-Mart&Bennhold-hst06

γp and γn KY reactions

Mart & Bennhold: including D13(1895)

without D13(1895) ⇔ subtle effects in σ History D13(1895) -2000 ⇒ D13(1895)+P13(1720) -2000 ⇒ D13(1900) -2002 ⇒ D13(1740) -2003 ⇒ D13(1870)=[D13(1520)]* -2005 ⇒ D13(1912) -2006 Problem: 20% Eγ -dependent normalization between SAPHIR and CLAS

⇔ channel separation ?

How do you find something thHow do you find something that at ““missingmissing”” ??

Issues:Issues: (1)(1) Res Res + + bkg bkg divisions ~ artificialdivisions ~ artificial +

s-ch resu-ch

all partial waves

(2)(2) Electromagnetic interaction is not Electromagnetic interaction is not isospin isospin invariantinvariantAA((γγ N N→→ ππ / /ηη / /ΚΚ))I=3/2I=3/2 ⇔⇔ ΔΔ∗∗ ; ; AA((γγ N N→→ ππ / /ηη / /ΚΚ))I=1/2I=1/2 ⇔⇔ NN∗∗ requires both n & p requires both n & p

(3)(3) CQM: CQM: ““ggππNN small for all but lowest in each oscillator bandsmall for all but lowest in each oscillator band”” ⇒⇒ need to look in need to look in ηηN, KY , N, KY , …… channels channels

(4)(4) large number of measurements needed to define amplitudelarge number of measurements needed to define amplitude

Suppose nothing isSuppose nothing is ““missingmissing”” ??

Pseudoscalar-meson Pseudoscalar-meson production:production: γγ + N + N →→ (J (Jππ = 0 = 0--)+N)+N

•• 2 2 XX 2 spin-states 2 spin-states →→ 4 complex amplitudes 4 complex amplitudes

Large number of spin observables needed to define amplitude: Large number of spin observables needed to define amplitude: •• 88 for A( for A(γγ N) N) for for bothboth N= n, p N= n, p •• 1212 for for A(A(γ γ * N)* N)

Proving Proving ““absenseabsense”” is much more difficult is much more difficult !! best hope is a compelling case

•• need to determine the full amplitude (never done) need to determine the full amplitude (never done)

Requirements from experimentsRequirements from experiments ??

POL gN-KL plane

Polarized Pseudoscalar meson photo-production:

!! +

!N " K +

!#

φ

PL

!

Pc

!

Pz

T

Px

T

PyT

!

!

P!y

"

P!z

"

P!x

"

xsc(Pg,Pt,Pr) general

Pseudoscalar meson photo-production

1

! 0

d! " ,#( ) = 1

+$ % PL&

cos(2# ) ' PyT %P (y

)*+ ,-

+T % PyT

' PL& %P (y

) cos(2# )*+ ,-

+P % P (y)

' PL& %Py

T cos(2# )*+ ,-

+E ! "Pc# !Pz

T " PL

# !PxT !P $y

% sin(2& )'( )*

+G ! PL# !Pz

T sin(2& ) + Pc

# !PxT !P $y

%'( )*

+F ! Pc# !Px

T + PL

# !PzT !P $y

% sin(2& )'( )*

+H ! "PL# !Px

T sin(2& ) " Pc

# !PzT !P $y

%'( )*

+C !x " Pc# "P !x

$ % PL

# "PyT "P !z

$ sin(2& )'( )*

+C !z " Pc# "P !z

$ + PL

# "PyT "P !x

$ sin(2& )'( )*

+O !x " PL# "P !x

$ sin(2& ) + Pc

# "PyT "P !z

$'( )*

+O !z " PL# "P !z

$ sin(2& ) % Pc

# "PyT "P !x

$'( )*

+L !x " PzT "P !x

# + P

L

$ "Px

T "P !z#

cos(2% )&' ()

+L !z " PzT "P !z

# * P

L

$ "Px

T "P !x#

cos(2% )&' ()

+T !x " Px

T "P !x#

* PL

$ "Pz

T "P !z#

cos(2% )&' ()

+T !z " Px

T "P !z#

+ PL

$ "Pz

T "P !x#

cos(2% )&' ()

Leading Pol dependence

Single Pol

beam+target

beam+recoil

target+recoil

16 possible observables

E & Tz asy planes

n γc

Rc

Lc

Λ

Κo

E asymmetry

n γL

Κo

p

π –

Λ Tz’ asymmetry

measured via

PL

! " Pz

T " P #x

$

leading Pol dependence Px

T! P

"z

#

leading Pol dependence Pc

!" P

z

T

0- N Pol table

Polarization observables in J π = 0– meson photo-production :

• single-pol observables measured from double-pol asy

• double-pol observables measured from triple-pol asy

Target Recoil Target - Recoil

x' y’ z’ x' x' x' y’ y’ y’ z’ z’ z'

Photon beam

x y z x y z x y z x y z

unpolarized σ0 T P Tx’ Lx’ Σ Tz’ Lz’

linearly Pγ Σ H P G Ox’ T Oz’ Lz’ Cz’ Tz’ E F Lx’ Cx’ Tx’

circular Pγ F E Cx’ Cz’ Oz’ G H Ox’

• not all are independent:

E2+ F

2+ G

2+ H

2= 1+ P

2! "

2! T

2

FG ! EH = P ! "T

Cx '

2+ C

z '

2+ O

x '

2+ O

z '

2= 1! P

2! "

2+ T

2

Cz 'Ox '! C

x 'Oz '= T ! "P

Tx '

2+ T

z '

2+ L

x '

2+ L

z '

2= 1! P

2+ "

2! T

2

Lz 'Tx '! L

x 'Tz '= !PT + "

gp-K+L Hall-B equip

! + p" K+# series of JLab experiments:

• hyperon weak-decays are self-analyzing

• Hall-B proton experiments: e-brem coherent e-brem

!e -brem

⇓

γ + p → K+ + Λ → K+ p π – ⇑ ⇑ H2 detect 2-3 charged C4H9OH particles in CLAS

gp-K+L JLab tbl

! + p" K+# series of JLab experiments:


x' y’ z’ x' x' x' y’ y’ y’ z’ z’ z'

Photon beam





status CLAS run period

beam target Coordinator/spokesman

complete g1 ! , !!c LH2 Miskimen/Schumacher

complete g8

!!L

LH2 Cole

complete g9a - PTz

!!L

, !!c FROST -

C4

!H9O!H Klein, Pasyuk

2010 g9b - PTx

!!L

, !!c FROST -

C4

!H9O!H Klein, Pasyuk

Full set of 16Full set of 16

gp-K0L Hall-B equip

φ

! + n(p)" K0#(p) measurements with

!H !!D

coherent e-brem !e -brem

⇓

γ + n(p) → K0 + Λ (p) → [π +π –] [ p π –](p) ⇑ ⇑ D⋅H detect 4 charged particles in CLAS • coplanarity ⇒ free neutron π-φ

MM2(K0L) HD,FROST

(Missing-Mass)2 distributions:

! n( p) "#0$

0( p) " #

0 + %! +( p)

" [&+

&'][ p&

'](! p)

! n( p) " #0 + $ +( p)

" [%+

%&][ p%

&]( p)

!! + H "

!D

!! +C

4"!D

9"O "!D

suppressed zero

MM2

(γ + D)

After cuts: - inv mass(K0 = π+π –) - < K0 - [pπ –] > coplanarity

MM2(γ + n)

gp-K0L HDice tbl

! + n(p)" K0# experiments at JLab with HDice:

• single-pol observables measured from double-pol asy • double-pol observables measured from triple-pol asy


x' y’ z’ x' x' x' y’ y’ y’ z’ z’ z'

Photon beam





⇑ simultaneous B-R with HD ⇔

schedule CLAS run period

beam target spokesmen

2010-2011 g14

!!L

, !!c

H !!D ice Sandorfi/Klein

Full set of 16Full set of 16

Chaing&Tabakin sets for K0L

Requirements for complete determination of the amplitude, free of ambiguities: ⇔ 8 observables - Chiang & Tabakin, PRC55,2054(97) (I) cross section and the three single-polarization observables: {σ , Σ , P, T}

(II) four double-polarization asymmetries:

Beam-Target Beam-Recoil Target-Recoil • 2 + 2 cases: (E , G) (Lx , Tx) or (Lz , Tz)

(E , G) (Cx , Ox) or (Cz , Oz)

(Cx , Cz) or (Ox , Oz) (Lx , Lz) or (Tx , Tz)

• 2 + 1 + 1 cases:

(E , G) 1 of {Cx , Cz , Ox , Oz} 1 of {Lx , Lz , Tx , Tz}

E (Cz , Ox) 1 of {Lx , Tz}

G (Cz , Ox) 1 of {Lz , Tx}

1 of {E , G} 1 of {Cx , Oz} (Lz , Tx)

G 1 of {Cx , Oz} (Lx , Tz)

⇒ huge redundancy in determining the γ n →Κ0 Λ amplitude !

N-N* Workshop Oct15’08

The potential for “The potential for “completecomplete” experiments” experiments in pseudoscalar meson productionin pseudoscalar meson production

A.M. Sandorfi (Jefferson Lab)

• missing (?) N* states of the quark model

• spin-observables in Jπ=0–photo-production

• γ N → Κ Λ JLab “complete” experiments

• Q: can such data provide total amplitudes, unique to a phase ?

• the mechanics of fitting out the amplitudes - potentials and limitations

• tests with mock data – work in progress ⇔ with S. Hoblit, UVa

Mechanics I multipoles->data

The mechanics of inferring amplitudes from data (I) theory ⇒ experiment: multipoles ⇒ observables

d!

d"=

P# ,$ ,KCM

E%cm & N(# ,$,K) F

i % N'

2

, CGLN, PR106(1957)

↑ (Cartesian) ⇔ (Spherical) Hi helicity amplitudes

•

E!±

, M!±{ }! P

! , "P

! , ""P

! { } ⇔ functions of W / E

!{ }" functions of #CM{ }

⇒ F1 , F2 , F3 , F4{ }CGLN

⇔ functions of (W / E! , "

CM){ }

⇒ ! 0 , " , T , P , E , ... L#z{ } ⇔ functions of (W / E

! , "

CM , # ){ }

-3.0

-2.0

-1.0

0.0

1.0

2.0

1.6 1.7 1.8 1.9 2 2.1 2.2 2.3

RE[E,M,O,1] K0L-m2soln

Re{E0+] K0L (mF)Re[E1+] K0L (mF)Re[E1-] K0L (mF)Re[M1+] K0L (mF)Re[M1-] K0L (mF)

Re{E/M](mF)

W (GeV)

γ n → Ko Λ

-1.0

-0.5

0.0

0.5

1.0

1.6 1.7 1.8 1.9 2 2.1 2.2 2.3

Im[E,M,O,1] K0L-m2soln

Im{E0+] K0L (mF)Im[E1+] K0L (mF)Im[E1-] K0L (mF)Im[M1+] K0L (mF)Im[M1-] K0L (mF)

Im{E/M](mF)

W (GeV)

Im[E0+] / 5

γ n → Ko Λ

multipoles from: B. Julia-Diaz, T-S. H. Lee - M2 (full) solution -

eg.

W = 1.95 GeV W = 1.95 GeV

-1.0

-0.5

0.0

0.5

1.0

-1 -0.5 0 0.5 1

Argand E2- K0LIm[E2-] K0Λ-M2soln (mF)

Im[E2-] K0Λ-M2soln-noD13 (mF)

Im[E2-](mF)

Re[E2-] (mF)

γ n → Κο Λ

W = 1.95 GeV

W

Constructing CGLN Fi amplitudes

Constructing the CGLN Fi amplitudes: F1 (x) = E0+ + M1+ + E1+( ) !P2

" (x)

+ 2M2+ + E2+( ) !P3" (x) + 3M2# + E2#( )

+ 3M3+ + E3+( ) !P4" (x) + 4M3# + E3#( ) !P2

" (x)

+ 4M4+ + E4+( ) !P5" (x) + 5M4# + E4#( ) !P3

" (x)

F3 (x) = + E1+ ! M1+( ) "P2## (x)

+ E2+ ! M2+( ) "P3## (x)

+ E3+ ! M3+( ) "P4## (x) + E3! + M3!( ) "P2

## (x)

+ E4+ ! M4+( ) "P5## (x) + E4! + M4!( ) "P3

## (x)

F2 (x) = 2M1+ + M1!( ) + 3M2+ + 2M2!( ) "P2

# (x)

+ 4M3+ + 3M3!( ) "P3# (x) + 5M4+ + 4M4!( ) "P4

# (x)

F4 (x) = M2+ ! E2+ ! E2! ! M2!( ) "P2## (x)

+ M3+ ! E3+ ! E3! ! M3!( ) "P3## (x)

+ M4+ ! E4+ ! E4! ! M4!( ) "P4## (x)

P! , P

!! , P

!!! " Legendre functions

x = cos(!CM)

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

0 30 60 90 120 150 180

Re[CGLN Fi] at Eg 1550

Re[F1] (mF)Re[F2] (mF)Re[F3] (mF)Re[F4] (mF)

Re F(i)(mF)

θCM

(deg)

γ n → Ko Λ

Eγ = 1.55 GeVW = 1.95 GeV

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

0 30 60 90 120 150 180

Im[CGLN Fi] at Eg 1550

Im[F1] (mF)Im[F2] (mF)Im[F3] (mF)Im[F4] (mF)

Im F(i)(mF)

θCM

(deg)

γ n → Ko Λ

Eγ = 1.55 GeVW = 1.95 GeV

CGLN amplitudes at W = 1.95 GeV- calculated from the multipoles of B. Julia-Diaz, T-S. H. Lee

eg.

hat notation

notation: Aasy = !o" Aasy

eg:

E = !Anti

" !Par

!Anti

+!Par

!o= 1

2!Anti

+!Par( )

# E = 1

2!Anti

" !Par( )

$

%

&&&&

'

&&&&

F1 , F2 , F3 , F4{ }CGLN

⇔ functions of (W / E! , "

CM){ }

⇒ ! 0 , " , T , P , E , ... L

#z{ } ⇔ functions of (W / E!

, "CM

, # ){ }

n γc

Rc

Lc

Λ

Κo

Observables in terms of the CGLN Fi amplitudes: ! = P" ,# ,KCM

E$

cm

T = !m sin" F1

*F3# F

2

*F4+ cos" $ F

1

*F4# F

2

*F3( ) # sin2 " $ F

3

*F4

%& '({ } $ )

P = !m sin" #2F1

*F2# F

1

*F3+ F

2

*F4+ cos" $ F

2

*F3# F

1

*F4( ) + sin2 " $ F

3

*F4

%& '({ } $ )

Tx '= !e sin2 " #F

1

*F3# F

2

*F4# F

3

*F4# 1

2cos" $ F

3

2

+ F4

2( )%&

'({ } $ )

Lx '= !"e sin# F

1

2

! F2

2

+ 1

2sin

2 # $ F4

2

! F3

2( ) ! F2*F3 + F1*F4 + cos# F1

*F3! F

2

*F4( )%

&'({ } $ )

Tz '= !e sin" #F

2

*F3+ F

1

*F4+ cos" F

1

*F3# F

2

*F4( ) + 1

2sin

2 " $ F4

2

# F3

2( )%&

'({ } $ )

Lz '= !e

2F1

*F2" cos# F

1

2

+ F2

2( ) + sin2 # $ F1

*F3+ F

2

*F4+ F

3

*F4( )

+ 1

2cos# sin2 # $ F

3

2

+ F4

2( )

%

&'

('

)

*'

+'$ ,

! = " sin2 # $ 1

2F3

2

+ F4

2{ } +%e F2

*F3+ F

1

*F4+ cos# $ F

3

*F4( ){ }&

'()$ *

G = + sin2 ! " #m F

2

*F3+ F

1

*F4{ } " $

Ox '= sin! " #m F

2

*F3$ F

1

*F4+ cos! " F

2

*F4$ F

1

*F3( )%& '( " )

Oz '= ! sin2 " # $m F

1

*F3+ F

2

*F4

%& '( # )

E = F1

2

+ F2

2

+!e sin2 " # F2

*F3+ F

1

*F4( ) $ 2cos" # F

1

*F2( ){ }%

&'( # )

Cx '= ! sin" #$e ! F

1

2

+ F2

2

+ F2

*F3! F

1

*F4+ cos" # F

2

*F4! F

1

*F3( ){ } # %

Cz '= !"e !2F

1

*F2+ cos# F

1

2

+ F2

2( ) ! sin2 # $ F1

*F3+ F

2

*F4( ){ } $ %

!0=

F1

2

+ F2

2

+ 1

2sin

2 " # F3

2

+ F4

2( )+$e sin2 " # F

2

*F3+ F

1

*F4+ cos" # F

3

*F4( ) % 2cos" # F

1

*F2

&' ()

*

+,

-,

.

/,

0,# 1

EBAC gn->K0L [‘S’,BT]W1.95

γ n → Κ0Λ

Eγ = 1.55 GeV W = 1.95 GeV

expected data M2 solution

no π-cloud

no coupled-ch

no D13(1910)

Beam-Target

-B. Juliá-Díaz, T-S. H. Lee (preliminary)

σ

E

G

Σ

P

-T

EBAC gn->K0L [BR,TR]W1.95

γ n → K0 Λ Eγ = 1.55 GeV (W = 1.95 GeV)

Beam-Recoil Target-Recoil

M2 solution no π-cloud no D13(1910) no coupled-ch

-B. Juliá-Díaz, T-S. H. Lee (preliminary)

Cx

Cz

Ox

Oz

Lx

Lz

Tx

Tz

Mechanics IIA data->multipoles

Mechanics (II): experiment ⇒ multipoles

(a) (a) reverse the theoryreverse the theory→→ observable pathobservable path : ( & jump the F: ( & jump the F i i ))

measurements for sets of (E! , "CM

, # ) with different (Pc, L

! , Px ,y,z

T , Px ',y ',z '

")

⇓

• ! 0 , " , T , P , E , ... L#z{ } ⇔ tabluation vs (W / E

! , "

CM){ }

•

! 0 (Fi) , "(F

i) , T(F

i) , ... L #z (F

i){ }

F1(E

!±, M

!±) , F2 (E

!±, M

!±)

F3 (E!±

, M!±

) , F4 (E!±

, M!±

)

$%&

'()

*

fit ! 0 , " , T , P , E , ... L#z{ }

directly, varying E!±

, M!±

⇒ introduces an !max

dependence

note: A( bilinear combinations of E!±

, M!±

) ⇒ derivatives are linear

Multipole fits VS start pt

Fitting observables to multipoles - tests of uniqueness:

(1) create mock data:

- predict observables from Juliá-Días/Lee/Sato “M2” amplitudes in 10 deg steps from 100 to 1700 CM - assign each an error of 0.1% and Gaussian smear the predictions

(Note: no data set will ever be that good !)

(2) fit the mock data, varying multipoles, with different starting pts

- as a starting point for a search, use M2 values randomly smeared by 0, 5%, 10%, 25%, 50%, 100%, …

- start search with Kaon-MAID, Born, … - repeat with more realistic data errors (~5 %)

-3.0

-2.0

-1.0

0.0

1.0

2.0

0 50 100

K0L(1950W) Im[L=0-1]deviat

Im[E0+]

Im[E1+]

Im[M1+]

Im[M1-]Im[AL±

]

(mF)

Starting Amplitudedeviation (%)

γ n → K0ΛW = 1950 MeV

100%

+ 107 MC-3.0

-2.0

-1.0

0.0

1.0

2.0

0 50 100

K0L(1950W) Im[L=2-3]deviat

Im[E2+]

Im[E2-]

Im[M2+]

Im[M2-]

Im[E3-]

Im[AL±

]

(mF)


γ n → K0ΛW = 1950 MeV

100%

+ 107 MC

0.0

1.0

K0L(1950W) chi^2 VS deviat

χ2/df0.0

1.0

K0L(1950W) chi^2 VS deviat

χ2/df

-3.0

-2.0

-1.0

0.0

1.0

2.0

0 50 100

K0L(1950W) Im[L=0-1]starts

Im[E0+]

Im[E1+]

Im[M1+]

Im[M1-]Im[AL±

]

(mF)


γ n → K0ΛW = 1950 MeV

-3.0

-2.0

-1.0

0.0

1.0

2.0

0 50 100

K0L(1950W) Im[L=2-3]starts

Im[E2+]

Im[E2-]

Im[M2+]

Im[M2-]

Im[E3-]

Im[AL±

]

(mF)


γ n → K0ΛW = 1950 MeV

0.0

1.0

K0L(1950W) chi^2 VS starts

χ2/df0.0

1.0

K0L(1950W) chi^2 VS starts

χ2/df

100% + 107 MC

KaonMAID

KaonMAID

Born

Born-steppedfrom threshold

100% + 107 MC

Born+109 MC

Born

Born-steppedfrom threshold

Born+109 MC

-2.0

-1.0

0.0

1.0

2.0

Re[A]

(mF)M1-

M1+

E1+E0+

M2 109+Grad

-1.0

0.0

1.0Re[A]

(mF)

M2-

M2+

E2-

E2+

M2 109+Grad-0.5

0.0

0.5

Re[A]

(mF)

M3-

M3+

E3-

E3+

M2 109+Grad

Re[A]

(mF)M

4-M

4+

E4-

E4+

M2 109+Grad

-2.0

-1.0

0.0

1.0

2.0

Im[A]

(mF)

M1-

M1+

E1+

E0+

M2 109+Grad

-1.0

0.0

1.0Im[A]

(mF)

M2-

M2+

E2-

E2+

M2 109+Grad-0.5

0.0

0.5

Im[A]

(mF)M

3-

M3+

E3-

E3+

M2 109+Grad

Im[A]

(mF)M

4-M

4+

E4-

E4+

M2 109+Grad

n(γ, ΚοΛ)→ → →

L = 0,1 L = 2 L = 3 L = 4

EBAC M2 vs Born + 109 MC + gradient search

Impossible to distinguishby any measurement

Mechanics IIB data->multipoles

Mechanics (II): experiment ⇒ multipoles

(b) (b) Stepwise pathStepwise path : : ⇔⇔ f i t f irst the F fi t f irst the F ii

measurements for sets of (E! , "CM

, # ) with different (Pc, L

! , Px ,y,z

T , Px ',y ',z '

")

⇓

• ! 0 , " , T , P , E , ... L#z{ } ⇔ tabluation vs (W / E

! , "

CM){ }

• fit ! 0 (F

i) , "(F

i) , T(F

i) , ... L

#z(Fi){ } ⇒ F1 , F2 , F3 , F4{ }

CGLN at each θ

note: A( bilinear combinations of Fi ) ⇒ derivatives !A!F

i

are linear

⇒ fits well behaved; rapid convergence ⇓ CGLN Fi functions of (W / E

! , "

CM){ }

Mechanics IIB INT[Fi]

• with {F1, F2, F3, F4}, vs W and x = cos(θ) in hand,

project out any desired multipole:

E!± =

1

2 !+1

0

!"#

$%&

dx

'1

+1

(P!F

1 ' P

!±1F

2

+!+

0

1

!"#

$%&

2!+1( ) P!"1 ' P!±1)* +,F3

+!+

1

0

!"#

$%&

2!+3

'1

!"#

$%&

P!' P

!±2[ ]F4

-

./

0/

1

2/

3/

M!± =

1

2 !+1

0

!"#

$%&

dx

'1

+1

( ±P!F

1 " P

!±1F

2 + 1

2!+1( ) P!±1' P

!"1)* +,F3{ }

potential

• independent of ambiguities associated with truncation of multipole expansions • smaller dimensional space for χ2 search limitation

• Fi cannot be determined near extreme angles (0,π) ⇒ some limitations on the accuracy of the integrals

S,E_hat limits at 0,180

Projection of multipoles from CGLN Fi amplitudes requires integration over all θ - but symmetries send all A observables → 0 or σ at extreme angles eg. 1 ! = " sin2 # $ 1

2F3

2

+ F4

2{ } +%e F2*F3 + F1*F4 + cos# $ F3*F4( ){ }&'

()$ *

→ 0 as θ → 0o or 180o

eg. 2 E = F1

2

+ F2

2

+!e sin2 " # F2

*F3+ F

1

*F4( )$ 2cos" # F1*F2( ){ }%

&'( # )

→

F1

2+ F2

2

!!e 2 "F1*F2#$ %&

'()

*)

+,)

-)" . = / 0 (0,180)

φ PL

!

!

!

Pc

!

!

!

0–

⇒ 1 eqn in 8 unknowns

Partial summary

Partial Summary – of a work in progress

• complete sets of spin-observables will soon be available for γ+p → Κ+Λ (and large partial sets for many other channels)

• complete sets of spin-observables for γ+n → Κ0Λ scheduled for 2010-2011 (and large partial sets for many other channels)

- using kinematic cuts on γ+D ⇒ γ+n observables, - checked by comparing γ+p(n)/γ+p and iterating with theory

• prospects for directly fitting out the full (Res+Bgk+cc+…) multipoles:

path (a) - 16 observables X N angles fitted to 32 parameters (L=0-4) at each W - χ2 space has a large number of valleys (even when the Chiang-Tabakin requirements are met) - valleys are not that narrow ⇔ spin data will force moderate variations in the amplitude to return to the “true” solution, but a quasi-reasonable approximation is needed to start the search.

Partial summary

- potential search strategy: start at threshold where L=0 (at most 1) and use solutions at E(i) to start the search at E(i+1), …

• difficult for KY channels; S11 at threshold ⇒ starting multipoles are very different from Born • may be able to start with a reasonable model at threshold, … The challenge: how to guide fits up the physically meaningful χ2(W) valley and still keep the exercise relatively model-independent !

• Alternate strategy - fit out the CGLN Fi amplitudes:

- 16 observables (with 6 inter-relations) to determine 4 complex Fi - must be done at each angle - conventional multipoles can be projected out of these Fi with integrals over angle, but 0 and 1800 will not be constrained

- stay tuned !

The potential for “complete” experiments in pseudoscalar ......History D 13(1895) -2000 ⇒ D...

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Transcript of The potential for “complete” experiments in pseudoscalar ......History D 13(1895) -2000 ⇒ D...