Julia-Diaz

Transcription

Julia-Diaz

Phenomenological N*
Analyses
B. Juliá-Díaz
Departament
p
d’Estructura i
Constituents de la Matèria
Universitat de Barcelona (Spain)
Summary
Brief motivation
Properties of reactions models
Dynamical coupled channels
Coupled channels K matrix
Unitary Isobar models
Tree level calculations
7. End
E d
1.
2
2.
3.
4.
5
5.
6.
qqq
B. Juliá-Díaz, MAMI and Beyond, April 1st, 2009
Motivation
Exciting the substructure we learn about the forces which keep the
quarks together
together, e.g.
e g using the quark model picture some of the
predicted states are:
J=1/2
J=3/2
0p
J=3/2
D33 (1700)
S11 (1535)
L=1, S=1/2, Jπ=1/2-
D13 (1520)
L=1, S=1/2, Jπ=3/2-
L=1, S=1/2, Jπ=3/2-
0s
P11 (939)
L=0, S=1/2, Jπ=1/2+
qqq
P33 Δ(1232)
L=0,
L
0, S
S=3/2,
3/2, Jπ=3/2
3/2+
J=1/2
S31 (1620)
L=1
L
1, S=1/2
S 1/2, Jπ=1/2
1/2-
N*s today
Cross section (mb)
10
N* : 1440,
1440 1520,
1520 1535,
1535 1650
1650, 1675
1675, 1680
1680, ...
2
Δ : 1600, 1620, 1700, 1750, 1900, …
π + p total
t t l
⇓
10
π + p elastic
Plab GeV/c
10
√s GeV
10
ross section (mb)
π+p Æ X, π+p
Δ (1232)
2
-1
πp
1
10
1.2
πd
2
2.2
3
3
4
4
5
6
10
5
7
6
7
8 9 10
2
8 9 10
20
20
30
30
40
40
50 60
9
The Delta (1232) resonance stands as a clear peak.
9
The region 1.4 GeV⇓– 2 GeV hosts ~ 20 resonances.
⇓
The current PDG values

π
(LIJ)
N
Are they all genuine quark/gluon
excitations?
|N*> =| qqq >
SAID does not
report eight N*s
GeV.
th
their
i origin
i i dynamical?
d belowi 2 GeV
l?

I
Is

E.g. some could be understood
as arising from meson-baryon
dynamics

|N*>= | MB >
Mostt off their
M
th i properties
ti are
extracted from
πN Æ π N
γN Æ π N
N*s above 1.6 GeV are still unsettled
Arndt, Briscoe, Strakovsky, Workman
PRC 74 045205 (2006)
N*s
B. Juliá-Díaz, E.m. NN* transition form factors, Oct 13th 2008, JLAB
Electromagnetic probes
Electrons are well suited
for baryon resonance
studies several facilities
studies,
have used them over the
last years:
y
•
•
•
•
•
•
e.m.
Jefferson LAB (USA)
GRAAL ((Grenoble))
MAMI (Mainz)
BATES (MIT)
ELSA (Bonn)
SPring 8 (Japan)
Courtesy of D. Leinweber
1.
Hard enough: structure needs to
be excited.
2.
Not too hard: we may find out
the constituents but not the way
y are g
glued together.
g
they
3.
However: A description of the
strong pieces will still be
y Strong
g coupled
p
necessary.
channels effects.
Desirable properties
for reaction models
Basic properties
1.
Basic
Unitarity contraint built in
Multi step (unitarity)
How do we produce
meson-baryon
b
states??
•
•
•
Î
γpÆ
σTOT (μb)
MS
Directly
Through MB states
Th
Through
h MMB states
t t
We need to incorporate
all the possibilities
Î Unitarity:
Coupled-channels
•
Basic properties
Basic
1.
2.
Simultaneous treatment of
•
Electromagnetic
•
Strong interactions
Basic properties | Consistency
e.g:
g γp ÆηΝ
π
N

Key points:
•
•
Î
S11
π
Δ
e.m.
Couplings
p g of mesons to
baryons
Electromagnetic vertices
•
•
Coupling
C
li off resonances
to MB
Electromagnetic
structure of resonances
Basic properties
1.
2.
3.
Basic
•
Electromagnetic
•
Strong interactions
Simultaneous description of:
•
Hadroproduction observables ((πΝ
Ν Æ πN,
πN ηN,
ηN ΚΥ,
ΚΥ ππN,
N …))
•
Electroproduction observables (γΝ Æ πN, ηN, ΚΥ, ωΝ, ππN, …)
30
25
20
15
10
5
0
0
20
γpÆπ0p
πNÆMN
NÆMN
γpÆπ+n
1
40
W=1232 MeV
30
W=1232 MeV
0.5
10
60
120
180
W=1299 MeV
0
0
20
15
10
1
60
5
W=1299 MeV
60
60
120
180
W=1544 MeV
15
10
5
60
γpÆΚ+Λ
γp
120
180
0
0
60
5
W=1544 MeV
4
3
2
1
0
0
60
θ (deg.)
120
180
1
0
0
60
W=1209 MeV
0.5
180
60
120
180
1
60
120
180
180
1
-0.5
60
60
120
120
180
1
0.5
0
0
-0.5
-0.5
180
120
180
0
60
120
180
W=1544 MeV
0.5
180
0
60
W=1513 MeV
0
120-1
0
0
0
W=1496 MeV
0.5
180
0.5
0
120
120
W=1417 MeV
0.5
0
60
1
W=1299 MeV
180
0
60
0
0
W=1285 MeV
0.5
120
0
0.5
0
0
1
W=1232 MeV
0.5
0
1
120
W=1217 MeV
180
5
Basic
0.5
0
0
120
1
0
W=1178 MeV
0.5
0
10
0
0
20
1
W=1162 MeV
20
15
0
1
W=1154 MeV
Σ
dσ/dΩ (m
(mb/sr)
Basic properties | lots of data
-1
-1
0
60
120
180
0
θ (deg)
60
120
180
Basic properties | some data
γΝÆπΝ
πΝÆπΝ
From R. Arndt’s talk at Bad Honnef (2009)
Basic
Basic properties
1.
2.
3.
Basic
•
Electromagnetic
•
Strong interactions
Simultaneous description of:
•
Hadroproduction observables ((πΝ
Ν Æ πN,
πN ηN,
ηN ΚΥ,
ΚΥ ππN,
N …))
•
Electroproduction observables (γ*Ν Æ πN, ηN, ΚΥ, ωΝ, ππN, …)
4
4.
Chiral symmetry constraints built in
5.
Connection with quark gluon mechanisms at high
energies
Dynamical coupled
channels
h
l
Dynamical
y
Coupled-Channels
p
Full integration ?
Non-resonant + resonant
Effective lagrangians, quark
Dressed
vertex
models,resonant
…?
How
Resonance
self energies
many channels
?
E.m
ENon-resonant
andd hadronic
h d amplitude
i
simultaneously?
Dynamical CC | EBAC@JLAB
EBAC@JLAB
H. Kamano, , B. Julia-Diaz, J. Durand, T.S H
S.
H. Lee
Lee, A.
A Matsuyama,
Matsuyama B
B. Saghai
Saghai, T
T.
Sato, N. Suzuki,
πΝ, ηΝ, ππΝ, ωΝ,
σΝ,
Ν ρΝ,
Ν πΔ,
Δ (ΚΥ)
2009
16 PWA (J<9/2) | 16 explicit N*
Reactions studied:
γΝ Æ πΝ(fit DATA)(W<1.65 GeV)
γ*Ν Æ πΝ
(W<1650 MeV)
γΝ Æ ηΝ
(W< 2 GeV)
γΝ Æ ππΝ (W< 2 GeV)
γΝ Æ ωΝ
(W< 2 GeV)
D t il Matsuyama,
Details
M t
Sato,
S t Lee,
L
Phys.
Ph
Reports
R
t (2007)
∫vgt
Hadronic part: (effective lagrangians)
πΝ Æ πΝ (fit SAID+DATA),ηΝ
πΝ Æ ΚΛ,, ωN,, η
ηΝ,, ππΝ
Dynamical CC | EBAC@JLAB
Some properties:
Consistent study of several production reactions
Most relevant channels included
Unitarity
y fulfilled
Exact treatment of 3 body cut
Dynamical model solved for complex E
K-matrix version on the way
Parallel version working
∫vgt
/
U-channel resonances
/
Need to incorporate KY channels
γ
EBAC, πΝ scattering
EBAC
SAID06
J li Di
Julia
Diaz, L
Lee, M
Matsuyama,
t
S
Sato,
t Ph
Phys. Rev
R C (2007)
πN
π
tγN→πN
N
Δ
N
EBAC, AC of πΝ scattering
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, in preparation (2009)
Two Bare N*
One Bare N*
EBAC, e.m. production
Q2 dependence FIXED
from γNN, γππ, and the
strong part
γ*N Æ N* helicity amplitudes
Before analyzing eN Æ e
e’ πN, e
e’ ππN, … , we need
1. Fix hadronicQamplitudes
(already
done)
2 dependence
p
can be
determined fitting
g to the
data of
2 =
ep Æ e’πN
, e’ππN ,at
…Qat
each
2. Good model to describe
γN reactions
0. Q2.
Æ Fix electromagnetic parameters independent of Q2
EBAC, pion photoproduction
300
γp
200
0
πp
1
30
25
20
15
10
5
0
0
20
1
W=1232 MeV
0.5
0
1
0
0
300
0.5
10
1
π
1
0
120
60
180
W=12990.5MeV
0.5
60
200
180
1
0
60
10
1
5
0.5
0
10060
180
0.5
0
120
180
1
0
60
W=1496 MeV
0.5
0
0
0
120
60
-0.5
-1
0
060
180
0
W=1217
0 MeV
20
5
1
0
60
-0.5
180
120
180
W=1232 MeV
120
60
180
W=1299 0.5
MeV
0
120
180
1
γp
0
+
60
W=1299 MeV
W=1285 MeV
120
60
0.5
120
0
120
10
0
0
10
15
W=1544 MeV
1100 1200 1300 1400 1500 1600
W (MeV)
180
0
5
0
120
W=1209 MeV
60
0
0
60
15
100
30
0.5
W=1178 MeV
W=1232 MeV
20
15
0
0
20
1
40
W=1162 MeV
W=1154 MeV
Σ
TOT
TσTOT (μb)
Comparison to data
– Total cross section
– Differential cross section
400
– Photon asymmetry
dσ/dΩ (m
(mb/sr)
Fitted up to W = 1.6 GeV.
π120n
180
W=1417 MeV
0
0
60
0.5
5
W=1544 MeV
4
0
3 120
180
0
2W=1513 MeV 1
0.5
1
0
0
0
60
-0.5
120
60
120
180
180
W=1544 MeV
120
-1
θ (deg.)
120
180
0
60
120
0
60
180
1100
1200
1300120 1400
1500
1600180
-1
θ (deg)
W (MeV)
Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008)
180
EBAC, in progress (e,e’)p
K. Joo et al. (CLAS Collaboration), Phys. Rev. Lett. 88, 122001 (2002).
Julia Diaz Kamano,
Julia-Diaz,
Kamano Lee,
Lee Matsuyama,
Matsuyama Sato,
Sato Suzuki,
Suzuki in prep (2009)
Dynamical CC | Juelich
Juelich
S. Krewald, J. Haidenbauer,
O. Krehl, A. Gasparian, C.
Hanhart Haberzettl , M.
Hanhart,
M
Doring, Meissner
πN, ηN, πΔ, σΝ, ρΝ
2009
Up to F waves| 8 explicit N*
Hadronic part: (Effective Lagrangians)
πΝ
Ν Æ πΝ
Ν (fit SAID) (~ 1.9 GeV)
πΝ Æ ηΝ
Reactions studied:
No e.m. yet
∫vgt
(expected progress from
Nakayama, Haberzettl, et al.)
DCC (πΝ)| Juelich (II)
Unitarity fulfilled
Most relevant channels included
Chiral constraints
/
U-channel resonances
No comparison to differential cross sections and
polarizations
/
∫vgt
Parallel version (useful for refitting the model)
DCC (πΝ)|Juelich (III)
M. Doring et al (2009)
W (GeV)
∫vgt
1.1
1.5
1.9
A. Gasparyan PhD thesis (2002)
Coupled channels kmatrix
Coupled-channels K-matrix
Key assumption:
E
Examples
l :
iπδ[]
o
SAID
o
Giessen
o
KVI
CC K-matrix |SAID
SAID
(R. A. Arndt, W. J. Briscoe, R. L. Workman, I. Strakovsky)
πN, γN, ηN
A and B are purely
phenomenological polynomials
Reactions studied:
iπδ[]
2008
008
Reference for many
other groups
Hadronic part:
γγ*Ν
Ν Æ πΝ
πΝ Æ πΝ
γΝ Æ ΚΛ, η(‘)Ν
π Ν Æ ηΝ, ππΝ
CC K-matrix |SAID (ii)
Physics:
N* properties from complex E plane
Single
g energy
gy and energy
gy dependent
p
fits
Q2 evolution of multipole amplitudes
Unitarity below ππΝ threshold
Unphysical parametrization of the amplitudes
Needs more channels coupled
/
K-matrix approximation
Accurate χ2
G t one and
Great
d two
t
meson database
d t b
handling
h dli
Updated regularly
Open access (ssh
Open-access
(ssh, web) (http://gwdac.phys.gwu.edu)
iπδ[]
Unitary
U
it
isobar
i b
model
Unitary Isobar Model
Reaction model
assumption:
E
Examples
l (up
(
and
d running):
i )
MAID, JLAB/Yerevan, CB-Elsa
MAID
D. Drechsel, S.S. Kamalov,
L. Tiator, Fix
Reactions studied:
γ N Æ πN
N
γ*N Æ πN
iπδ[]
πN, γγN
Up
N*
p to F waves,, 13 explicit
p
γN Æ η(‘)N (eta(‘)-MAID)
γN ÆππN (2pi-MAID)
(kaon-MAID)
γγ*N
N Æ ΚΛ (kaon-MAID),
2007
UIM|MAID
tπΝ from SAID
Full t matrix:
Non resonant part:
Resonant part:
The phase of the multipole
taken to:
Ensure Watson theorem is fulfilled
/
iπδ[]
But is an assumption above 2π threshold
UIM|MAID(ii)
Extract resonance structure (pion electroproduction)
Single energy and energy dependent fits
Unitary below ππ threshold
.
Mixture of PV and PS πΝΝ coupling
.
Hadronic information taken from GWU/SAID
/
Several
S
l relevant
l
t channels
h
l nott iincluded,
l d d e.g. πΔ, ηΝ,…
/
Principal value not included
Open-access (http://www.kph.uni-mainz.de/MAID)
Being updated regularly
iπδ[]
Tree diagram
Tree-diagram
Main motivation: Studies of reaction
mechanisms
Key assumption: Reactions assumed
to be dominated by a small number
of resonances
(e.g. specific kinematical regions)
T ≅ V = vbg +vR
Good for exploratory calculations
Chiral constraints (in some of them)
/
Not Unitary
/
Principal
p value not included
Tree-diagram (II)
Essentially:
o
o
Reactions studied:
Non-resonant usually
obtained from Efective
Lagrangians e
Lagrangians,
e.g.:
g:
The resonant part :
¾Effective
¾Quark
Lagrangians
models
¾Parametrizations
o
γ N Æ ΚΛ (Adelseck, Bennhold, Mart, Saghai,…)
o
γγ*N
N Æ ωN (Oh, Lee, Titov, Zhao)
o
γ N Æ πN (too many to be listed)
o
γ N Æ ππN (Oset,
(O t Nacher,
N h Roca,
R
A
Arenhoevel,…)
h
l )
o
γ*N Æ ππN (Mokeev et al.)
o
And many more of course
Concluding remarks

Experimental situation:
Lots of experimental data for πΝÆ to πΝ and single and double meson
electro/photo production reactions (MAMI, JLAB, GRAAL, Bonn).
polarization asymmetries
y
also measured.
Involved p
Not so many for πΝÆ ππΝ, necessary due to unitarity considerations.

O N*s
On
N*
Using electromagnetic probes helps greatly but DOES NOT remove a
great deal of the hadronic incertainty.
Dynamical models are needed to fully analyze the measured data.

Several theoretical efforts, which
hi h should
h ld eventually
t ll converge ((or
fade away), are currently on the market.
END