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)

n At high energies: interactions between quarks and gluons become weak (“asymptotic freedom”) ä efficient description of phenomena afforded in terms of quarks n At low energies: effects of confinement make strongly-coupled QCD highly non-perturbative ä collective degrees of freedom (mesons and baryons) more efficient n Duality between quark and hadron descriptions u reflects relationship between confinement and asymptotic freedom u 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) = N C  e q 2 E  ( e + e -  +  - ) q

Duality in the F 2 Structure Function First observed ~1970 by Bloom and Gilman at SLAC  Bjorken Limit: Q 2,    u Empirically, DIS region is where logarithmic scaling is observed: Q 2 > 5 GeV 2, W 2 > 4 GeV 2 u Duality: Averaged over W, logarithmic scaling observed to work also for Q 2 > 0.5 GeV 2, W 2 < 4 GeV 2, resonance regime

What about the other structure functions FL, F1? World's L/T Separated Resonance Data (until 2002): n Not able to study the Q 2 dependence of individual resonance regions! n No resonant behaviour can be observed! (All data for Q 2 < 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? n Now able to study the Q 2 dependence of individual resonance regions! n Clear resonant behaviour can be observed! (All data for Q 2 < 9 (GeV/c) 2 ) Now able to extract F 2, F 1, F L and study duality!... R =  L /  T < R =   /  T

Rosenbluth Separations Rosenbluth 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 u a systematic “tour de force”

Duality now observed in all unpolarized structure functions

…and in Nuclei (F 2 ) p Fe d  = 2x [ 1 + (1 + 4M 2 x 2 /Q 2 ) 1/2 ]

Quark-Hadron Duality (F 2 ) 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 A1pA1p g1g1 HERMES JLab Hall B

n Experimentally, duality holds in all unpolarized structure functions, in tested spin structure functions, even better in nuclei, all down to surprisingly low Q 2 u Apparently a non-trivial property of nucleon structure If we had used only scintillators, scaling would be thought to hold down to low Q 2 !

Quantification Integral Ratio Res / Scaling For tomorrow

Quantification Large 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 n Hall B CLAS spectrometer for electron detection n Thin deuterium target (7.5 atm) n Radial Time Projection Chamber (RTPC) for spectator proton detection n DVCS solenoid to contain Moller background

“Very Important Protons” n Deuteron ~ free proton + free neutron at small nucleon momenta n Will target T p ~ 2 – 5 MeV spectator protons n 30% of momentum distribution is in chosen p s range n T p > 5 MeV spectators will also be detected

RTPC Design

F 2 n / F 2 p Ratio at Large x – Projected Results n Yellow shaded area represents current theoretical uncertainty n RR data begin the Resonance Region (W 2 > 3 GeV 2, Q 2 ~ 5) n Gray shaded areas represent systematic uncertainty u Light = total u Dark = normalized, point-to-point

Duality in QCD n Moments of the Structure Function M n (Q 2 ) = S dx x n-2 F(x,Q 2 ) If n = 2, this is the Bloom-Gilman duality integral! n Operator Product Expansion M n (Q 2 ) =  (nM 0 2 / Q 2 ) k-1 B nk (Q 2 ) higher twist logarithmic dependence (pQCD) n 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 M n (Q 2 ) = S dx x n-2 F(x,Q 2 ) For moments add elastics…… F2F2 Duality Above Q 2 =1 Below Q 2 =1, duality breaks Down (empirical fits shown)

n = 2 Moments of F 2, F 1 and F L : n = 2 Moments of F 2, F 1 and F L : M n (Q 2 ) = ∫ dx x 2-2 F(x,Q 2 ) Elastic Contributions Flat Q 2 dependence  small higher twist! - not true for contributions from the elastic peak (bound quarks) Elastic contribution excluded DIS: SLAC fit to F 2 and R RES: E resonance fit F 1 EL = G M 2  (x-1) F 2 EL = (G E 2 +  G M 2 )  (x-1) F L EL = G E 2  (x-1) 1 +   = q 2 /4M p 2 Preliminary F2F2 F1F1 FLFL 0 1

n = 4 Moments of F 2, F 1 and F L 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 M L (n) =  s (Q 2 ){ 4M 2 (n) + 2c∫dx xG(x,Q 2 )} 3(n+1) (n+1)(n+2) Gluon distributions!

X D. Dolgov et al., Phys. Rev. D 66:034506, 2002 X Data from JLab Hall C × Current (data) uncertainties are in nuclear extraction of F 2 n Moments are Calculated on the Lattice: F 2 n – F 2 p

n Another approach u 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 Q 2,W 2  3 GeV 2 (Close and Isgur, Phys. Lett. B509, 81 (2001)) d  /dz   i e i 2  q i (x,Q 2 )D qi m (z,Q 2 ) + q i (x,Q 2 )D qi m (z,Q 2 )  Requires non-trivial cancellations of decay angular distributions If duality is not observed, factorization is questionable hadronic descriptionquark-gluon description

(Semi-)Exclusive Meson Electroproduction Large z = E h / to emphasize duality and factorization (Berger criterion) n Meson electroproduced along q, i.e. emphasize forward angles n SHMS in Hall C well suited to detect these mesons (cf. pion form factor) n If Berger criterion and duality  factorization

n 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

  A 1 n from 3 He(e,e’) JLab Hall A 2

Summary n Quark-hadron duality is a non-trivial property of QCD  Soft-Hard Transition! n Duality has been shown to hold in all experimental tests thus far u All unpolarized structure functions u Polarized structure functions u Nuclei n More experiments are planned u Neutron u Polarized structure functions u Neutrino scattering n Duality may provide a valuable tool to access high x regime n Duality violations obscure comparison with lattice QCD through the structure function moments