Analyzing photoproduction data on the proton

H. Haberzettl (GWU)K. Nakayama (UGA)

key references: PRC69, 065212 (’04), nucl-th/0507044

Outline of the talk Outline of the talk

Motivation.

Description of N N (in conjunction with NN→′NN): ● model for N→′N.

● analysis of the SAPHIR data (PLB444, ’98).

● analysis of the (preliminary) CLAS data (M. Dugger et al.).

Outlook.

MotivationMotivation

)0()0(2)0(2 2'

2' NNGNNFAN gmFgFNGm

Extract information on nucleon resonances in the less explored higher N* mass region: ● high-mass resonances in low partial-wave states. ● missing resonances. ● excitation mechanism of these resonances. Constrain the NN′ coupling constant (0≤ gNN′ ≤ 7.3): ● particular interest in connection to the “nucleon-spin crisis” (EMC collaboration, PLB206, ’88). NN′ coupling constant is related to the flavor-singlet axial charge GA through the U(1) Goldberger-Treiman relation:

quark contribution to the proton “spin”

gluon contributionto the proton “spin”

GA(0) ≈ 0.16±0.10(SMC collaboration,PRD56,’97)

Shore&Veneziano, NPB381, ’92.

Available photoproduction data & models Available photoproduction data & models ::

Experiment:

● total cross sections: ABBHHM, PR175, ’68. AHHM, NPB108, ’76. SAPHIR, PLB444, ’98.

● angular distributions: SAPHIR, PLB444, ’98. CLAS, (M. Dugger, this meeting)

● expected data: Crystal Barrel - ELSA, (I. Jaegle, this meeting).

Theory:

● quark models: Z. Li, JPG23, ’97. Q. Zhao, PRC63, ’01.

● (tree-level) effective Lagrangian: J. Zhang et al., PRC52, ’95. B. Borasoy, EPJA9, ’00. W. Chiang et al., PRC68, ’03. A. Sibirtsev et al., nucl-th/0303044.

● unitary approach: B. Borasoy et al., PRC66, ‘02. (s-wave coupled channel relativistic unitary approach )

Aim of the SAPHIR data analysis :Aim of the SAPHIR data analysis :

Shed light on the contradictory conclusions of existing model calculations:

origin of the shape of the observed angular distribution: interference among N* (S11 & P13) resonances. [Zhao,’01]

interference between N* (S11) and t-channel (Regge) currents. [Chiang et al., ‘03]

t-channel current (mec + exponential form factor). [Sibirtsev et al., ‘03]

t-channel current: ● Regge trajectory. [Chiang et al., ’03] ● meson-exchange [others]

Are we able to identify N* resonances from the (differential) cross section data ?

Can we constrain the NN coupling constant, gNN ? Combined analysis with hadronic induced reactions: NNNN.

N N (model):(model):

jnuc

j jnuc jmec

jres

jres

mecj

NN′ → (gNN′, NN′)

v′ → (v′) cutoff parameter

RN′ → (gRN′ , RN′ )

mass (mR) & width ( R)

RN → (fRN)

pp→→′′pp (SAPHIR data, (SAPHIR data, PLB444,’98PLB444,’98 ) )

mec+S11 mec+S11+nuc

mec+S11+P11

angular distribution & absolute normalization :due to an interference among different currents.

(a) (b)

(c)

pp→→′′pp (SAPHIR data, (SAPHIR data, PLB444,’98PLB444,’98 ) )

mec+S11+P11+ nuc

gNN′ cannot be much larger than 3

(d)

p→p→′p ′p ( insensitivity of the cross section to the( insensitivity of the cross section to the resonance mass ) resonance mass )

cross section: rather insensitive to the N* mass.

pp→→′′pp (mec x Regge trajectory)(mec x Regge trajectory)

mec regge

Regge trajectory. [Chiang et al., ’03] ,–exchange + (dip./exp.) form factor at v′.

v′

Some conclusions with the SAPHIR data :Some conclusions with the SAPHIR data :

On the shape of the angular distribution : Interference among different currents (especially, N* & t-channel) is

crucial (corroborates the Chiang et al.‘s findings).

,–exchange vrs. Regge trajectory: provided one introduces a form factor at the v′vertex (mec), they

describe the data equally well.

Cross sections alone are unable to pin down precisely the resonance mass values.gNN′ < 3. To improve, needs more accurate data at high-energy and large backward angles (more precise CLAS data will change this conclusion).

NN - NN - ′′NNNN (model)(model) ::

j

),( RNMRNMRNM g

RNM

,,M

RNM

DWBA:

)1()1( iiff TGJGTA

FSI ISI

transition current

pppp→→′′pp :pp :

)(nb

S11(1646)

P11(1873)

mec

total

(data: SPESIII,’98; COSY11,’98-’04; DISTO,’00)(data: SPESIII,’98; COSY11,’98-’04; DISTO,’00)

excitation mechanism of the S11 resonance can be studied

pp→→′′p p (preliminary CLAS data, M. Dugger et al. )(preliminary CLAS data, M. Dugger et al. )

pppp (M. Dugger et al., latest data set)(M. Dugger et al., latest data set)

● preliminary data● latest data

pp→→′′pp ( preliminary CLAS data, M. Dugger et al.) :( preliminary CLAS data, M. Dugger et al.) :

● resonances required: S11, P11, P13, D13

● curves correspond to different set of parameters with comparable 2.

● data at more forward and backward angles would constrain more the model parameters.

Resonances :Resonances :

I 3.72 0.01 S11(1913), P11(1994), P13(1909), D13(1900+2084).

II 3.85 1.49 S11(1535+1626+2092), P11(1712+2094+2474), P13(1941), D13(1726+2092).

III 3.82 0.00 S11(1538+1846), P11(1710+2002), D13(1814+2090).

IV * 3.55 1.12 S11(1535+1650+2090), P11(1440+1710+2100), P13(1720+1900), D13(1520+1700+2080).

set 2/Ndata gNN′ resonances included

* masses fixed to the PDG values

p→p→′p′p (dynamical content)(dynamical content) : :

2/N=3.72 2/N=3.85 Set IISet I

2/N=3.82 2/N=3.55

p→p→′p′p (dynamical content)(dynamical content) : :

Set III Set IV

p→p→′p′p ( can nuc & mec be fixed ? )( can nuc & mec be fixed ? ) : :

would require data beyond the resonance region

p→p→′p′p ( prediction for the total cross section )( prediction for the total cross section ) : :

● sharp rise near threshold due to S11 resonance.

● bump around W=2.09 GeV due to D13 (and possibly P11) resonance. [ PDG: D13(2080) **, P11(2100) * ]

p→p→′p′p ( beam and target asymmetries )( beam and target asymmetries ) : :

much more sensitive to the model parameters than cross sections

Some conclusions with the CLAS data :Some conclusions with the CLAS data :

The CLAS data can be reproduced with the inclusion of spin-1/2 and -3/2 resonances, whose (resonance) parameters are consistent with those quoted in the PDG.

The existing cross section data, however, do not impose enough constraints to pin down the resonance parameters.

● data at more forward and backward angles would help constrain more those parameters.

● spin-observables (beam and target asymmetries) will impose much more stringent constraints.

We predict a bump in the total cross section around W=2.09 GeV. If this is confirmed (needs data), D13(2080) and/or P11(2100) resonance is likely to be responsible for this bump.

gNN′ should not be much larger than 2 (more exclusive data is needed and/or needs to go beyond the resonance region to pin it down).

Outlook :Outlook :

Experimentally: total cross section. differential cross section for more forward and backward angles. spin-observables: beam and target asymmetries. nn/dnp (CB at ELSA): shed light on t-channel mesonic current.

Theoretically: higher spin resonances [D15(1675),F15(1685)]. ● final state interaction (no realistic N FSI is currently available). coupled channel approach.

The End

Resonance widthsResonance widths

,

,

,qiR =qi (W=mR )

R→N

R→N

Phenomenological contact currentPhenomenological contact current

free parameters

free of any singularities

Resulting model parameters :Resulting model parameters :

R=150 MeV

R=150 MeV

Resulting model parameters :Resulting model parameters : 2/N=3.72 2/N=3.85 2/N=3.82 2/N=3.55

p→p→′p′p ( meson-exchange vrs. Regge trajectory )( meson-exchange vrs. Regge trajectory ) : :

High-precision CLAS data:

● Regge trajectory is, at best, comparable to the meson-exchange:

meson-exchange Regge trajectory

Set I 3.72 4.19

Set IV 3.55 3.82

2/N

Available data & models Available data & models ( pp( pppp )pp ) : :

Experiment:

● total cross sections: SPESIII, PLB438,’98. DISTO, PLB491,’00. COSY11, PRL80,’98; PLB474,’00; PLB482,’03; EPJA20,’04.

● angular distributions: DISTO, PLB491,’00. (Q = 144 MeV)

COSY11, EPJA20,’04. (Q = 47 MeV)

Theory:

● DWBA (meson-exchange models): Sibirtsev & Cassing, EPJA2, ’98. Bernard et al., EPJA4, ’99. Gedalin et al., NPA650, ’99. Baru et al., EPJA6, ’99. Nakayama et al., PRC61, ’99.

too many unknown parameters:(need independent reactions to fix some of those parameters)

pppp→→′′pp pp ((SPESIII,’98; COSY11,’98-’04; DISTO,’00 dataSPESIII,’98; COSY11,’98-’04; DISTO,’00 data) :) :

mec+S11 mec+S11+nuc mec+S11+P11 mec+S11+P11+nuc

pppp→→′′pp [pp [ang. distr. at Q=46.6 MeV (COSY11,’04) excluded from the fitang. distr. at Q=46.6 MeV (COSY11,’04) excluded from the fit ] :] :

mec+S11 mec+S11+nuc mec+S11+P11 mec+S11+P11+nuc

SS1111 resonace excitation mechanism(s) ? resonace excitation mechanism(s) ?

'** NNNN gg

'** NNNN gg

mec+S11 mec+S11+nuc mec+S11+P11

'** NNNN gg

3.62 16.34 11.11

-0.49 -2.25 11.25

0.24 7.75 -1.93

pp-pp-′′pppp (some conclusions)(some conclusions) : :

Dominant reaction mechanism: S11 resonance.

Existing data cannot constrain on the excitation mechanism(s) of the S11 resonance:

data on pn→′pn and/or pn→′d will impose more stringent

constraints (isoscalar vrs isovector meson-exchange).

and also spin-observables (e.g., Ay in -meson production can

disentangle pseudoscalar- and vector-meson exchanges; also

Axx ).

DISTO vrs. COSY11 data on the angular distribution: needs data for Q > 50 MeV.

pp→pp→′pp ′pp (based on the CLAS data results)(based on the CLAS data results) : :