quark-hadron duality
DESCRIPTION
Quark-Hadron Duality. Cynthia Keppel Hampton University / Jefferson Lab. CIPANP 2003. Quark-Hadron Duality complementarity between quark and hadron descriptions of observables. At high energies: interactions between quarks and gluons become weak (“asymptotic freedom”) - PowerPoint PPT PresentationTRANSCRIPT
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