Qiang Zhao

Theory Division Institute of High Energy Physics, CAS

Email: zhaoq@ihep.ac.cn

Update of quark model calculations for vector meson photoproduction

Update of quark model calculations for vector meson photoproduction

Oct. 06, 2008

Institute of High Energy Physics, CASInstitute of High Energy Physics, CAS

Outline

Effective Lagrangian approach for meson photoproduction

Updated results for , , and K* production

Summary

• The non-relativistic constituent quark model (NRCQM) makes great success in the description of hadron spectroscopy:

meson (qq), baryon (qqq).

• However, it also predicted a much richer baryon spectrum, where

some of those have not been seen in N scatterings.

– “Missing Resonances”.

, 0

N, ½+

N*, L2I,2J

P33(1232) P11(1440)S11(1535)D13(1520)…

1. Baryon spectroscopy and status of S11(1535)

Dilemma:

a) The NRCQM is WRONG: quark-diquark configuration? …

b) The NRCQM is CORRECT, but those missing states have only weak couplings to N, i.e. small gN*N. (Isgur, 1980)

Looking for “missing resonances” in N* N, K, K, N, N, N, N …

(Exotics …)

N* uud

d

du

ud

n

To pin down the underlying effective degrees of freedom and understand the property of QCD at low-energy limit

• Difficulties– Perturbative QCD cannot be

applied– A lot of resonances could be

present in a relatively narrow energy region

– Non-resonance background is almost equally complicated

• Experiment– Jefferson Lab (USA) – MAMI (Germany) – ELSA (Germany)– ESRF (France)– SPring-8 (Japan)– BES (China) ¶

M (,, , , , K …)

N N (N, , …)

EM StrongN*,*

+ p

Photo- & electroproductionPhoto- & electroproduction

D13

F15

¶ A unique way of studying baryon spectrum is via BES: J/ N N*,…

PDG2004: 22 nucleon resonances (uud, udd)

(**) not well-established

18 Lambda resonances (uds)

Kinematics for vector meson photoproductionKinematics for vector meson photoproduction

, k,

N, Pf , 2

N, Pi , 1

V, q,V

cmy

z

xy

zx

Spin observables: • Unpolarized cross sections• Polarized asymmetries

Invariant amplitudes:

See e.g. Pichowsky, Savkli, and Tabakin, PRC53, 593(1996)

Helicity amp. for an intermediate resonance excitation can be expressed as

i.e.

where the parity conservation gives

• Spin observables in terms of density matrix elements

, k,

N, Pi , 1

V, q,Vcm

y

z

x

Vector meson decay distribution:

N, Pf , 2

z

e.g. The polarized beam asymmetry:

Unpolarized decay distribution:

Linearly-polarized decay distribution:

Zhao, Al-Khalili & Cole, PRC71, 054004 (2005); Pichowsky, Savkli & Tabakin, PRC53, 593 (1996)

Two additional differential pol. beam asymmetries:

N.Pari. U.Pari.

0 0

A 1 1

B 1 1Zhao, PRC63, 025203 (2001)

0 180

d/

d

Scattering angle

1) Forward angle peaking is predominant due to the diffractive or t-channel light meson exchanges.

2) S-channel resonance excitations contribute to the cross sections at middle and backward angles.

3) Quark-hadron duality argument makes the s- and t-channel transitions obscure at some kinematics.

t-channel

s-channelu-channel

90

Kinematic features of the production mechanismKinematic features of the production mechanism

Interferences from different transition mechanisms

Three ingredients in our quark model approach:

1. s- and u-channel resonance excitationsVector meson production via an effective Lagrangian for quark-vector-meson interactions in the s- and u-channel;

2. t-channel natural parity exchangePomeron exchange for neutral vector meson (, 0, ) production in the t-channel, and t-channel scalar meson exchange;

3. t-channel unnatural parity exchangeLight meson exchanges in the t-channel, e.g. 0 exchange for production.

Refs.Z., Li, & Bennhold, PLB436, 42(1998); PRC58, 2393(1998);Z., Didelez, Guidal, & Saghai, NPA660, 323(1999); Z., PRC63, 025203(2001); Z., Saghai, Al-Khalili, PLB509, 231(2001); Z., Al-Khalili, & Bennhold, PRC64, 052201(R)(2001); PRC65, 032201(R) (2002);Z., Al-Khalili, & Cole, PRC71, 054004(2005); Z. and Close, PRD74, 094014(2006)

1. Effective Lagrangian for quark-vector-meson interactions:

Vector meson fields in the SU(3)-flavour symmetry:

V, q, k

N, Pi N, Pf

, k V, q

N, PfN, Pi

+N() ()

N() ()

s-channels-channel

, k

N, Pi N, Pf

V, q

+

V, q, k

N, Pi N, PfN() ()

N() ()

u-channelu-channel

, k V, q

N, Pi N, Pf

seagullseagull

Transition amplitude:

M=M(s) + M(u) + M(seagull) + M(t)

where

with

S-channel quark correlation operators

2. Pomeron exchange:

Donnachi & Landshoff’s Pomeron:Pomeron mediates the long range interactions between two confined quarks and behaves rather like a C=+1 isoscalar photon.

Vertices:

Pomeron trajectory:

Transition amplitude:

Thus,

Loop tensor: Lee and Pichowsky

3. Pseudoscalar meson exchange ():

, k V 0,, q

N, Pi N, Pf

0,

t-channelt-channel

Vertices:

Form factor:

Advantage: i) A complete set of NRCQM resonances is included with very few

parameters as leading contributions. ii) The same parameters for the production of SU(3) multiplets.

Disadvantage: Neither covariant nor unitary.

I. Theoretical results for production -- Data from SAPHIRI. Theoretical results for production -- Data from SAPHIR

Single polaration asymmetries

Theoretical results for production -- data from GRAAL Collaboration + …Theoretical results for production -- data from GRAAL Collaboration + …

GRAAL Collaboration, PRL96, 132003(2006)

• Total cross sections

p p

N 2Born terms +

N > 2degenerate in N

a = 3.67, b = 3.85

• Differential cross section

Full dot: GRAAL Empty circle: SAPHIR

p p

• Polarized beam asymmetry

• Without s- and u-channel, the asymmetry should be zero due to helicity conservation.

Effects without contributions from:D13(1520) [dashed];P13(1720) [dotted];F15(1680) [dot-dashed]

New data from CBELSA, 0807.0594[nucl-ex]

Consistent with the GRAAL results.

• Density matrix elements above resonance region

E = 2.8 GeV 4.7 GeV 9.3 GeV E = 2.8 GeV 4.7 GeV 9.3 GeV

Data from ABBHHM collaboration

Ambrozewicz et al., [JLab E91-016 Colla.], PRC70, 035203 (2004)

Diff. X-section at small Q2

Backward enhancement: Evidence for s-channel resonance excitations via N N* N

-- Data from Hall C (JLab)-- Data from Hall C (JLab)

e

e

Q2, *W

N N

a = 3.67, b = 3.85Same as extracted from GRAAL data

II. Theoretical results for productionII. Theoretical results for production

1) Diffractive pomeron exchange dominant.

2) t-channel unnatural exchange included.

3) s- and u-channel account for large angle cross sections. Nucleon Born term is important.

Parameter “a” can be related to the NN coupling and compared with the NN coupling extracted from production.

Predictions for the production on the neutron

The cross section difference at large angles is mainly due to the difference between p and n.

Prediction of A

Zhao, Al-Khalili and Bennhold, PRC64, 052201(R)(2001)

III. Theoretical results versus data from: K* production on the protonIII. Theoretical results versus data from: K* production on the proton

CLAS, PRC75, 042201(R)(2007), & erratum

Experimental data from JLab

Experimental data from CBELSA

Black dot: CBELSARed empty square: CLASSolid: a = 2.7 b = 1.7Dash-dotted: a = 2.2 b = 0.8

CBELSA/TAPS, Euro. Phys. J. A35, 333 (2008)

CBELSA/TAPS, Euro. Phys. J. A35, 333 (2008)

Total cross sections

Summary - ISummary - I

1. The forward peaking is dominated by the t-channel natural or unnatural exchanges. The measurement of the parity asymmetry is sensitive to their interferences at forward angles.

2. Resonance signals appear in vector meson productions. Polarized beam asymmetry at middle and large angles are essential for determining the underlying mechanisms.

3. Further coherent studies of all vector meson production channels as well as pseudoscalar meson productions are needed and they are in progress.

e.g. photoproduction of , , ; and N N; Kp Q. Z., PRC 63, 035205 (2001) ; Q. Z., J.S. Al-Khalili, Z.P. Li, and R.L. Workman, PRC 65, 065204 (2002); Q. Z., B. Saghai and Z.P. Li, JPG 28, 1293 (2002); X.H. Zhong, Q. Zhao, J. He, and B. Saghai, PRC 76, 065205 (2007)

Summary - IISummary - II

4. For the purpose of searching for individual resonance excitations, it is essential to have a quark model guidance for both known and “missing” states. And then allow the data to tell:

i) which state is favored;

ii) whether a state beyond quark model is needed;

iii) how quark model prescriptions for N*NM form factors complement with isobaric models;

5. Further questions and comments:

i) be aware of the collective effects arising from several closing states;

ii) how to recognize the mixture of t-channel and s-channel transitions due to the quark-hadron duality argument;

iii) how to introduce the relativistic effects;

iv) and more ……

Thanks for your attention !

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