Quark-Hadron Duality

Cynthia Keppel

Hampton University / Jefferson Lab

“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)

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

Duality defines the transition from soft to hard QCD.

Example: e+e- hadrons /

lim (e+e- X) = NC eq2

E (e+e- +-) q

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 FL, F1? What about the other structure functions FL, F1? World's L/T Separated Resonance Data (until 2002):World's L/T Separated Resonance Data (until 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

What about the other structure functions FL, F1? What about the other structure functions FL, F1?

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

Clear resonant behaviour can be observed!

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

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

R = L/T <

R = / T

Rosenbluth Rosenbluth SeparationsSeparations

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]

Quark-Hadron Duality (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

Experimentally, duality holds in all unpolarized structure functions, in tested spin structure functions, even better in nuclei, all 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

For tomorrow

QuantificationLarge x Structure Functions

Close and Isgur Approach

Phys. Lett. B509, 81 (2001):

q = h

Relative photo/electroproduction strengths in SU(6)

“The proton – neutron difference is the acid test for quark-hadron duality.”

How many states does it take to approximate closure?

Proton W~1.5

Neutron W ~ 1.7

n p

e-

The BONUS experiment will measure neutron

structure functions…….

To spectrometer

To recoil detector

Experimental Setup

Hall B CLAS spectrometer for electron detection

Thin deuterium target (7.5 atm)

Radial Time Projection Chamber (RTPC) for spectator proton detection

DVCS solenoid to contain Moller background

“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

RTPC Design

F2n / F2

p Ratio at Large x – Projected Results

Yellow shaded area represents current theoretical uncertainty

RR data begin the Resonance Region

(W2 > 3 GeV2, Q2 ~ 5)

Gray shaded areas represent systematic uncertainty Light = total Dark = normalized,

point-to-point

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)For moments add

elastics……

F2

DualityAbove Q2=1

Below Q2=1,duality breaks

Down (empiricalfits shown)

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

11 and F and FLL: : Mn(Q2) = ∫ 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!

D. Dolgov et al., Phys. Rev. D 66:034506, 2002

X Data from JLab Hall C

× Current (data) uncertainties are in nuclear extraction of F2

n

Moments are Calculated on the Lattice: F2

n – F2p

Another approach And some new experiments

Close and Isgur Approach

Phys. Lett. B509, 81 (2001):

q = h

Relative photo/electroproduction strengths in SU(6)

“The proton – neutron difference is the acid test for quark-hadron duality.”

How many states does it take to approximate closure?

Proton W~1.5

Neutron W ~ 1.7

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

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

If Berger criterion and duality factorization

More of the experimental future

Separated Unpolarized Structure Functions at 11 GeV

Also necessary for polarized structure function measurements...

x = 0.8

HMS

SHMS

Hall C

Polarized Structure Functions at 11 GeV

Hall C

A1

n from 3He(e,e’) JLab Hall A

2

Summary Quark-hadron duality is a non-trivial property of QCD Soft-Hard Transition! 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 Polarized structure functions 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