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Quark-Hadron Duality. Cynthia Keppel Hampton University / Jefferson Lab.

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quark hadron duality
Quark-Hadron Duality

Cynthia Keppel

Hampton University / Jefferson Lab

slide2

“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)

slide3
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.

slide4

Example: e+e- hadrons / m+m-lim s(e+e- X) = NC S eq2 E  s(e+e- m+m-) q

duality in the f 2 structure function
Duality in the F2 Structure Function

First observed ~1970 by Bloom and Gilman at SLAC

  • Bjorken Limit: Q2, n 
  • 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 world s l t separated resonance data until 2002
What about the other structure functions FL, F1? World's L/T Separated Resonance Data (until 2002):

R = sL/sT

  • 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…...

what about the other structure functions fl f1
What about the other structure functions FL, F1?

R =  / T

R = sL/sT

<

  • 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!...

rosenbluth separations
Rosenbluth Separations
  • 180 L/T separations total (most with 4-5 e points)
  • Spread of points about the linear fits is fairly Gaussian with s ~ 1.6 %- consistent with the estimated pt-pt experimental uncertainty
    • a systematic “tour de force”
and in nuclei f 2
…and in Nuclei (F2)

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

p

d

Fe

duality and the emc effect
Duality and the EMC Effect

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

Rather surprising (deltas in nuclei, etc.)

J. Arrington, et al., in preparation

slide14
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!

quantification

For tomorrow

Quantification

Integral Ratio Res / Scaling

quantification1
Quantification

Large x Structure Functions

close and isgur approach
Close and Isgur Approach

How many states does it take to approximate closure?

Proton W~1.5

Neutron W ~ 1.7

Phys. Lett. B509, 81 (2001):

Sq = Sh

Relative photo/electroproduction strengths in SU(6)

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

To spectrometer

The BONUS experiment will measure neutron structure functions…….

p

n

e-

To recoil detector

experimental setup
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
“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
f 2 n f 2 p ratio at large x projected results
F2n / F2p 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
Duality in QCD

1

0

  • Moments of the Structure Function

Mn(Q2) = S dxxn-2F(x,Q2)

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

  • Operator Product Expansion

Mn(Q2) = (nM02/Q2)k-1Bnk(Q2)

higher twistlogarithmic dependence

(pQCD)

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

k=1

slide23

1

Mn(Q2) = Sdxxn-2F(x,Q2)

For moments add

elastics……

0

F2

Duality

Above Q2=1

Below Q2=1,

duality breaks

Down (empirical

fits shown)

n 2 moments of f 2 f 1 and f l m n q 2 dx x 2 2 f x q 2

1

0

n = 2 Moments of F2, F1 and FL: Mn(Q2) = ∫ dxx2-2F(x,Q2)

DIS: SLAC fit to F2 and R

RES: E94-110 resonance fit

Elastic Contributions

F1EL = GM2 d(x-1)

Preliminary

F2

F2EL = (GE2 +tGM2 )d(x-1)

Elastic contribution

excluded

1 +t

F1

t = q2/4Mp2

FLEL = GE2 d(x-1)

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

FL

n 4 moments of f 2 f 1 and f l
n = 4 Moments of F2, F1 and FL

Preliminary

Neglecting elastics, n = 4

moments have only a small

Q2 dependence as well.

Momentum sum rule

ML(n) = as(Q2){ 4M2(n) + 2c∫dx xG(x,Q2)}

(n+1)(n+2)

3(n+1)

Gluon distributions!

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…..

slide26

Moments are Calculated on the Lattice: F2n – F2p

  • D. Dolgov et al., Phys. Rev. D 66:034506, 2002
  • Data from JLab Hall C
  • Current (data) uncertainties are in nuclear extraction of F2n
slide27
Another approach

And some new experiments

close and isgur approach1
Close and Isgur Approach

How many states does it take to approximate closure?

Proton W~1.5

Neutron W ~ 1.7

Phys. Lett. B509, 81 (2001):

Sq = Sh

Relative photo/electroproduction strengths in SU(6)

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

slide29

Duality in Meson ElectroproductionDuality and factorization possible for Q2,W2  3 GeV2 (Close and Isgur, Phys. Lett. B509, 81 (2001))

hadronic description quark-gluon description

Requires non-trivial cancellations of decay angular distributions

If duality is not observed, factorization is questionable

ds/dz  iei2qi(x,Q2)Dqim(z,Q2) + qi(x,Q2)Dqim(z,Q2)

semi exclusive meson electroproduction
(Semi-)Exclusive Meson Electroproduction
  • Large z = Eh/n 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
separated unpolarized structure functions at 11 gev
Separated Unpolarized Structure Functions at 11 GeV

Hall C

x = 0.8

De > 0.3

SHMS

HMS

Also necessary for polarized structure function measurements...

summary
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