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CNRP

Qiang Zhao

Locality of quark-hadron duality and its manifestation in exclusive meson photoproduction reaction

above the resonance region

Qiang Zhao

Centre for Nuclear and Radiation Physics

Department of Physics, University of Surrey, Guildford, U.K.

In collaboration with F.E. Close (Oxford Univ.)

MeNu2004, IHEP, Beijing, Sept. 2, 2004

Outline

- What is quark-hadron duality?
- Physics in the interplay of pQCD and non-pQCD

-- above the resonance region

- Quark-hadron duality in the quark model
- Quark-hadron duality in exclusive photoproduction reaction
- Summary

Quark-hadron duality

- Bloom-Gilman Duality

The electroproduction of N* at low energies and momentum transfers empirically averages smoothly around the scaling curve for nucleon structure function F2(W2,Q2) measured at large momentum transfers for both proton and neutron targets.

- Low-energy resonance phenomena
- High-energy scaling behaviour

- Degrees-of-freedom duality
- Hadronic degrees of freedom
- Quark and gluon degrees of freedom

Bloom and Gilman, PRD4, 2901 (1971); Close, Gilman and Karliner, PRD6, 2533 (1972); I. Niculescu et al, Phys. Rev. Lett. 85, 1182 (2000); 85, 1186 (2000).

Nachtmann scaling variable:

=2x/[1+(1+4M2 x2 /Q2 )1/2], where x=Q2/2M2

Low-energy QCD phenomena: resonance production

M

N*,*

- Theory

QCD phenomenology:

quark model, hadronic model …

Lattice QCD ?

Strong

EM

N

N

- Experiment
- Jefferson Lab
- MAMI
- ELSA
- ESRF
- SPring-8
- BES

+ p

D13

F15

Quark counting rules (QCR)

For exclusive scattering processes at high energy and large transverse momentum, the differential cross section for a two-body reaction A + B C + D has a behaviour:

t =(pA–pC)2 =(pB–pD)2

A,

C, M

s =(pA+pB)2 =(pC+pD)2

p

n

B, N

D, N

Brodsky and Farrar, PRL31, 1153 (1973); PRD11, 1309 (1975).

Matveev, Muradian and Tavkhelidze, Nuovo Cim. Lett. 7, 719 (1973).

Lepage and Brodsky, PRD22, 2157 (1980).

Exclusive photoproduction reactions at fixed scattering angles

Other channels are also measured

Anderson et al., PRD14, 679 (1976)

Oscillatory deviations from the scaling behavior of dimensional quark-counting rules above the nucleon resonance region.

Scaled?

Oscillating?

Figure from JLab proposal PR94-104 , Gao and Holt (co-spokesperson)

Soft contribution dominant

- Dashed curves: Soft contributions
- Solid curves: Leading asymptotic contributions
- Dot-dashed: Bound on the leading asymptotic contributions

Isgur and Llewellyn Smiths, PRL52, 1080 (1984)

Theoretical explanations for the deviations

i) The channel-opening of new flavours

Brodsky, De Teramond, PRL 60, 1924 (1988).

ii) Interference between pQCD and sizeable long-range component.

Brodsky, Carlson, and Lipkin, PRD 20, 2278 (1979);

Miller, PRC 66, 032201(R) (2002);

Belitsky, Ji and Yuan, PRL 91, 092003 (2003).

iii) PQCD color transparency effects

Ralston and Pire, PRL 49, 1605 (1982); 61, 1823 (1988).

iv) Restricted locality of quark-hadron duality

Close and Zhao, PRD 66, 054001 (2002); PLB 553, 211(2003);

Zhao and Close, PRL 91, 022004 (2003); work in preparation.

Bloom-Gilman duality realized in the quark model

How does the square of sum become the sum of squares? --- Close and Isgur

F1n /F1p =2/3

F1p,n ~1/2 + 3/2

hadrons

g1 p /F1p =5/9

g1 p,n ~ 1/2 3/2

p,n

g1n /F1n =0

- For F1p,n and g1p , duality is recognized with the sum over both 56 and 70 states and negative parity ones.
- For g1n , the duality could be localized to 56 states alone.

Close, Gilman, and Karliner, PRD6, 2533 (1972); Close and Isgur, PLB 509, 81 (2001)

Manifestation of duality in exclusive reaction

q

, k

q

x

Pi

y

z

Pf

Pf

Pi

q1

Sum over intermediate states:

r

q2

R

r1

r2

Forward scattering (Close and Isgur’s duality) : 0

where the coherent term (~e1e2) is suppressed due to destructive interferences.

- Large angle scattering: = 90

i) At high energies, i.e. in the state degeneracy limit, all terms of N > 0 (L=0, …, N) vanish due to destructive cancellation: (–C22+C20) 0; (3C44–10C42+7C40) 0; …

R(t) : QCR-predicted scaling factor.

- At intermediate high energies, i.e. state degeneracy is broken, terms of N > 0 (L=0, …, N) will not vanish: (–C22+C20) 0; (3C44–10C42+7C40) 0; …

Deviation from QCR is expected !

Effective theory for pion photoproduction

Effective chiral Lagrangian for quark-pseudoscalar meson coupling:

where the vector and axial vector current are:

with the chiral transformation

The quark and meson field in the SU(3) symmetry:

and

The quark-meson pseudovector coupling:

Manohar and Georgi, NPB 234, 189 (1984); Li, PRD50, 5639 (1994);

Zhao, Al-Khlili, Li and Workman, PRC65, 065204 (2002)

Tree level diagrams

Internal quark correlations are separated out

M

N*,*

N*,*

s-channel

N

N

u-channel

N*,*

N*,*

t-channel

…

contact-channel

Sum of resonance excitations

c.m.-c.m. correlation

c.m.-int. correlation

int.-int. correlation

- In the SU(6)O(3) symmetry limit, resonances of n 2 are explicitly included via partial wave decomposition.
- At high energies, states of n > 2 (L=0, …, n) will be degenerate in n.
- The direct (incoherent) processes in the s- and u-channel are dominant over the coherent ones.

Pion () photoproduction in the resonance region

Resonances of n 2 included in the SU(6)O(3) quark model

Zhao, Al-Khalili, Li and Workman, PRC65, 065204 (2002)

Pion photoproduction above the resonance region

High energy degenerate limit:

- Mass-degeneracy breaking (L-depen.) is introduced into n=3, 4.
- For n=3, the L-dependent multiplets do not contribute at =90 since they are proportional to cos.
- For n=4, non-vanishing P, F, and H partial waves will contribute and produce deviations.
- At =90, destructive interferences occur within states of a given n, i.e., with the same parity.

The new data are from: Zhu et al., [Jlab Hall A Colla.], PRL91, 022003 (2003).

Further manifestations of Bloom-Gilman duality

- Onset of scaling with the local sum and average

Jeschonnek and Van Orden, PRD 69, 054006 (2004).

- Onset of scaling with the local sum and average

Dong and He, NPA720, 174 (2003).

Summary and discussion

Nonperturbative resonance excitations due to quark correlations, are an important source for deviations from QCR at 2 s1/2 3.5 GeV.

Features distinguishable from other models:

i) The deviations can be dominantly produced by “restrictedly localized” resonance excitations, i.e. the destructive cancellation occurs within states of the same parity.

ii) The deviation pattern need have no simple periodicity.

iii) The Q2 dependence of the deviations would exhibit significant shifts in both magnitude and position.

- Open questions ...

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