Quark-Hadron Duality

Cynthia Keppel

Hampton University / Jefferson Lab

CIPANP 2003

At high energies: interactions between quarks and gluons

become weak(“asymptotic freedom”) efficient description of phenomena afforded in terms of quarks

At low energies: effects of confinement make strongly-coupled QCD highly non-perturbative collective degrees of freedom (mesons and baryons) more

efficient Duality between quark and hadron descriptions

reflects relationship between confinement and asymptotic freedom

intimately related to nature and transition from non-perturbative to perturbative QCD

Quark-Hadron Dualitycomplementarity between quark and hadron

descriptions of observables

Example: e+e- hadrons /

lim (e+e- X) = NC eq2

E (e+e- +-) q

Duality in Inclusive electron scatteringDuality in Inclusive electron scattering Single Photon Exchange

Elastic Resonance Deep Inelastic

In terms of coupling: d= [T(x,Q2) +

L(x,Q2)}

Where : flux of transversely polarized virtual photons : relative longitudinal polarization

Alternatively: d∝ [2xF(x,Q2) + FL(x,Q2)]

dW dE'

FL = F

2 – 2xF

1 + 2M

pF

2

dWdE'

F2 prop

L +

TR = L /

T =

F

L /

2xF

1

Duality in the F2 Structure Function

First observed ~1970 by Bloom and Gilman at SLAC

Bjorken Limit: Q2,

Empirically, DIS region is where logarithmic scaling is observed: Q2 > 5 GeV2, W2 > 4 GeV2

Duality: Averaged over W, logarithmic scaling observed to work also for Q2 > 0.5 GeV2, W2 < 4 GeV2, resonance regime

What about the other structure functions FWhat about the other structure functions FLL, F, F11, g, g11,….? ,….?

World's L/T Separated Resonance Data (before 2002):World's L/T Separated Resonance Data (before 2002):

Not able to study the Q2 dependence of individual resonance regions!

No resonant behaviour can be observed!

(All data for Q2 < 9 (GeV/c)2)

JLab E94-110: a global survey of longitudinal strength in the resonance region…...

R = L/T

JLab Hall C E94-110: Global Survey of Longitudinal JLab Hall C E94-110: Global Survey of Longitudinal Strength in Nucleon Resonance RegionStrength in Nucleon Resonance Region

Covers 0.4 < Q2 < 5.0 (GeV/c)2, Mp < W2 < 4.0 GeV2

Clear resonant behaviour can be observed!

Now able to study the Q2 dependence of individual resonance regions!

(All data for Q2 < 9 (GeV/c)2)

Now able to extract F2, F1, FL and study duality!...

R = L/T <

Rosenbluth Rosenbluth Separations Separations

180 L/T separations total (most with 4-5 points)

Spread of points about the linear fits is fairly Gaussian with ~ 1.6 %- consistent with the estimated pt-pt experimental uncertainty

a systematic “tour de force”

Duality now observed in all unpolarized structure functions

…and in Nuclei (F2)

p

Fe

d

= 2x[1 + (1 + 4M2x2/Q2)1/2]

GRV curve

Scaling (F2) in Nuclei

Duality and the EMC Effect

J. Arrington, et al., in preparation

Medium modifications to the pdfs are the same in the resonance region

Rather surprising (deltas in nuclei, etc.)

…and in Spin Structure Functions

A1p

g1

HERMES JLab Hall B

A1p

Qualitatively, duality is observed to hold in all unpolarized structure functions, in nuclei, and in tested spin structure functions down to surprisingly low Q2

Apparently a non-trivial property of nucleon structure

If we had used only scintillators, scaling would be thought to hold

down to low Q2!

QuantificationIntegral Ratio Res / Scaling

QuantificationThe available pdf-based parameterizations significantly undercut

the data at large x

SLAC data above W2 = 4 GeV2

Duality in QCD Moments of the Structure Function

Mn(Q2) = S dx xn-2F(x,Q2)

If n = 2, this is the Bloom-Gilman duality integral! Operator Product Expansion

Mn(Q2) = (nM02/ Q2)k-1 Bnk(Q2)

higher twist logarithmic dependence

(pQCD)

Duality is described in the Operator Product Expansion as higher twist effects being small or cancelling DeRujula, Georgi, Politzer (1977)

0

1

k=1

0

1

Mn(Q2) = S dx xn-2F(x,Q2)

+ elastics……

F2

n = 2 Moments of Fn = 2 Moments of F22, F, F

11 and F and FLL: : Mn(Q2) = S dx x2-2F(x,Q2)

Elastic Contributions

Flat Q2 dependence small higher twist! - not true for contributions from the elastic peak (bound quarks)

Elastic contribution excluded

DIS: SLAC fit to F2 and R

RES: E94-110 resonance fit

F1EL = G

M2 (x-1)

F2EL = (G

E2 + G

M2 )(x-1)

FL

EL = GE

2 (x-1)

1 +

= q2/4Mp

2

PreliminaryF2

F1

FL

0

1

n = 4 Moments of Fn = 4 Moments of F22, F, F

11 and F and FLL

Neglecting elastics, n = 4 moments have only a small Q2 dependence as well.

Momentum sum rule

This is only at leading twist and neglecting TM effects.⇒ Must remove TM effects from data to extract moment of xG…we’re working on it…..

Preliminary

ML

(n) = s(Q2){ 4M

2(n) + 2c∫dx xG(x,Q2)}

3(n+1) (n+1)(n+2)

Gluon distributions!

For the future….

Measuring Neutron Structure Functions: BONUS

Hall B CLAS spectrometer for electron detection

Thin deuterium target (7.5 atm)

Radial Time Projection Chamber (RTPC) for low momentum spectator proton detection

DVCS solenoid to contain Moller background

n

Electron detected in JLab Hall B CLAS

spectrometerp

Spectator proton detected in RTPC

e-

“Very Important Protons” Deuteron ~ free proton

+ free neutron at small nucleon momenta

Will target Tp ~ 2 – 5 MeV spectator protons

30% of momentum distribution is in

chosen ps range

Tp > 5 MeV spectators will also be detected

Duality in Meson Electroproduction

Duality and factorization possible for Q2,W2 3 GeV2

(Close and Isgur, Phys. Lett. B509, 81 (2001))

d/dz iei2qi(x,Q2)Dqi

m(z,Q2) + qi(x,Q2)Dqim(z,Q2)

Requires non-trivial cancellations of decay angular distributions

If duality is not observed, factorization is questionable

hadronic description quark-gluon description

(Semi-)Exclusive Meson Electroproduction

Large z = Eh/ to emphasize duality and factorization (Berger criterion)

Meson electroproduced along q, i.e. emphasize forward angles

Proposed SHMS in Hall C well suited to detect these mesons (cf. pion form factor)

If Berger criterion and duality factorization

MINER-A FermiLab proposal en route….. Can test duality in neutrino scattering!

(Melnitchouk and Close (2003), Beane (2001),….) Can also help with large x pdfs

Summary Quark-hadron duality is a non-trivial property of nucleon structure Duality has been shown to hold in all experimental tests thus far

All unpolarized structure functions Polarized structure functions Nuclei

More experiments are planned Neutron Semi-inclusive Neutrino scattering

Duality may provide a valuable tool to access high x regime Duality violations obscure comparison with lattice QCD through the

structure function moments

“It is fair to say that (short of the full solution of QCD) understanding and controlling the accuracy of quark-hadron duality is one of the most important and challenging problems for QCD practitioners today.”

M. Shifman, Handbook of QCD, Volume 3, 1451 (2001)

RTPC Design