Duality in Unpolarized Structure Functions: Validation and Application

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Duality in Unpolarized Structure Functions
Validation and Application
Rolf Ent
First Workshop on Quark Hadron Duality and the
Transition to Perturbative QCD Frascati June 6-8,
2005 (Italy)
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Duality in the F2 Structure Function

• First observed 1970 by Bloom and Gilman at SLAC
  by comparing resonance production data with deep
  inelastic scattering data
• Integrated F2 strength in Nucleon Resonance
  region equals strength under scaling curve.
  Integrated strength (over all w) is called
  Bloom-Gilman integral
• Shortcomings
• Only a single scaling curve and no Q2 evolution
  (Theory inadequate in pre-QCD era)
• No sL/sT separation ? F2 data depend on
  assumption of R sL/sT
• Only moderate statistics

F2
Q2 0.5
Q2 0.9
F2
Q2 1.7
Q2 2.4
w 1W2/Q2
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Duality in the F2 Structure Function

• First observed 1970 by Bloom and Gilman at SLAC
• Now can truly obtain F2 structure function data,
  and compare with DIS fits or QCD
  calculations/fits (CTEQ/MRST/GRV)
• Use Bjorken x instead of Bloom-Gilmans w
• Bjorken Limit Q2, n ? ?
• Empirically, DIS region is where logarithmic
  scaling is observed Q2 gt 5 GeV2,
• W2 gt 4 GeV2
• Duality Averaged over W, logarithmic scaling
  observed to work also for Q2 gt 0.5 GeV2, W2 lt 4
  GeV2, resonance regime
• (note x Q2/(W2-M2Q2)
• JLab results Works quantitatively to better than
  10 at surprisingly low Q2

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Bloom-Gilman Duality in F2 Today
The scaling curve determines the Q2 behavior of
the resonances! or the resonances fix the
scaling curve!
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Low Q2 Too! Even Down to Photoproduction
Bodek and Yang duality-based model works at all
Q2 values tested DIS to photoproduction!
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Quantification Resonance Region F2 w.r.t.
Alekhin NNLO Scaling Curve
(Q2 1.5 GeV2)
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Quantification in a Fixed W2 Framework
(S. Liuti et al., PRL 2002)
F2exp/F2pQCDTMC 1 CHT(x)/Q2 DH(x,Q2)
Previous Extractions (DIS Only)
? Duality not only a leading-twist phenomenon
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If one integrates over all resonant and
non-resonant states, quark-hadron duality should
be shown by any model. This is simply
unitarity. However, quark-hadron duality works
also, for Q2 gt 0.5 (1.0) GeV2, to better than 10
(5) for the F2 structure function in both the
N-D and N-S11 region! (Obviously, duality does
not hold on top of a peak! -- One needs an
appropriate energy range)
One resonance non-resonant background
Few resonances non-resonant background
Why does local quark-hadron duality work so well,
at such low energies? quark-hadron transition
Confinement is local .
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Quark-Hadron Duality Theoretical Efforts
One heavy quark, Relativistic HO
N. Isgur et al Nc ? 8 qq infinitely
narrow resonances qqq only
resonances
Q2 1
Q2 5
u
Scaling occurs rapidly!

• F. Close et al SU(6) Quark Model
• How many resonances does one need
• to average over to obtain a complete
• set of states to mimic a parton model?
• 56 and 70 states o.k. for closure
• Similar arguments for e.g. DVCS
• and semi-inclusive reactions

• Distinction between Resonance and
• Scaling regions is spurious
• Bloom-Gilman Duality must be invoked
• even in the Bjorken Scaling region
• ? Bjorken Duality

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Quark-Hadron Duality - Applications

• CTEQ currently planning to use duality for large
  x parton distribution modeling
• Neutrino community using duality to predict low
  energy (1 GeV) regime
• Implications for exact neutrino mass
• Plans to extend JLab data required and to test
  duality with neutrino beams
• Duality provides extended access to large x
  regime
• Allows for direct comparison to QCD Moments
• Lattice QCD Calculations now available for u-d
  (valence only) moments at Q2 4 (GeV/c)2
• Higher Twist not directly comparable with Lattice
  QCD
• If Duality holds, comparison with Lattice QCD
  more robust

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E94-110/E00-116/E00-108 Experiments performed at
JLab-Hall C
HMS
SOS
G0
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E94-110 Precise Measurement of
Separated Structure Functions in Nucleon
Resonance Region

• The resonance region is, on average, well
  described by NNLO QCD fits.
• This implies that Higher-Twist (FSI)
  contributions cancel, and are on average small.
• The result is a smooth transition from Quark
  Model Excitations to a Parton Model description,
  or a smooth quark-hadron transition.
• This explains the success of the parton model at
  relatively low W2 (4 GeV2) and Q2 (1 GeV2).

The successful application of duality to extract
known quantities suggests that it should also be
possible to use it to extract quantities that
are otherwise kinematically inaccessible.
(CERN Courier, December 2004)
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Duality in FT and FL Structure Functions
Duality works well for both FT and FL above Q2
1.5 (GeV/c)2
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Quantification
Ratio Resonance Region / Scaling Curves
Large x Structure Functions
SLAC DIS data Q2 6 GeV2
x
Undershoot at large x
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E00-116 Experiment to Push to larger Q2 (larger
x)
Emphasis 1) With Duality Verified at Lower Q2,
Now Can Use Data to Extend Range in x 2) Need
Large x data to Constrain Higher Moments 3)
Quantify Q2 vs. Q2(1-x) Evolution
But show great numerical agreement compared to
(internal) scaling curve ? determines Q2 behavior
of the resonances
Preliminary data again do overshoot QCD
calculations
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E00-116 Experiment to Push to larger Q2 (larger
x)
Same behavior at largest Q2 of E00-116 analyzed
to date
Additional data (4 more resonance scans) at
higher Q2 for both proton and deuteron ? reach x
0.9. Data final in 1-2 months.
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Close and Isgur Approach to Duality
How many states does it take to approximate
closure? Proton W1.5 o.k.
Neutron W1.7 o.k.
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.
Scatter electrons off deuteron
The BONuS experiment will measure neutron
structure functions.
Detect 70 MeV/c spectator proton at backward
angles in BONuS detector
Commissioning Run in CLAS now!
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Neutron Quark-Hadron Duality Projected Results
(CLAS/BONUS)

• Sample neutron structure function spectra
• Plotted on proton structure function model for
  example only
• Neutron resonance structure function essentially
  unknown
• Smooth curve is NMC DIS parameterization

Systematics 5
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Duality in Meson Electroproduction
(predicted by Afanasev, Carlson, and Wahlquist,
Phys. Rev. D 62, 074011 (2000))
Hall C Experiment E00-108 Spokespersons Hamlet
Mkrtchyan (Yerevan) Gabriel Niculescu
(JMU) Rolf Ent (JLab)
H,D(e,ep/-)X
(e,e)
W2 M2 Q2 (1/x 1)
For Mm small, pm collinear with g, and Q2/n2 ltlt 1
(e,em)
W2 M2 Q2 (1/x 1)(1 - z)
z Em/n
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Duality in Meson Electroproduction
hadronic description quark-gluon description
Transition Form Factor
Decay Amplitude
Fragmentation Function
Requires non-trivial cancellations of decay
angular distributions If duality is not observed,
factorization is questionable
Duality and factorization possible for Q2,W2 ? 3
GeV2 (Close and Isgur, Phys. Lett. B509, 81
(2001))
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Factorization
P.J. Mulders, hep-ph/0010199 (EPIC Workshop, MIT,
2000)
At large z-values easier to separate current and
target fragmentation region ? for fast hadrons
factorization (Berger Criterion) works at lower
energies
At W 2.5 GeV z gt 0.4 At W 5 GeV z gt 0.2
(Typical JLab)
(Typical HERMES)
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E00-108 data

• Experiment ran in August 2003
• Close-to-final data analysis
• Small Q2 variation not corrected yet

x 0.32
W gt 1.4 GeV
W lt 2.0 GeV
x 0.32
No visual bumps and valleys in pion ratios off
deuterium
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From deuterium data D-/D (4
Np/Np-)/(4Np/Np- - 1)
z 0.55

• D-/D ratio should be independent of x
• but should depend on z
• Find similar slope versus z as HERMES, but
  slightly larger values for D-/D, and definitely
  not the values expected from Feynman-Field
  independent fragmentation at large z!

x 0.32
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W 2 GeV z 0.35 ? data predominantly in
resonance region What happened to the
resonances?
From deuterium data D-/D (4
Np/Np-)/(4Np/Np- - 1)
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The Origins of Quark-Hadron Duality
Semi-Inclusive Hadroproduction
F. Close et al SU(6) Quark Model How many
resonances does one need to average over to
obtain a complete set of states to mimic a parton
model? ?56 and 70 states o.k. for closure
Destructive interference leads to factorization
and duality
Predictions Duality obtained by end of second
resonance region Factorization
and approximate duality for Q2,W2 lt 3 GeV2
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How Can We Verify Factorization?

• Neglect sea quarks and assume no pt dependence to
  parton distribution functions
• Fragmentation function dependence drops out

sp(p) sp(p-)/sd(p) sd(p-) 4u(x)
d(x)/5(u(x) d(x)) sp/sd
independent of z and pt
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Dependence on z
Lund MC
Berger Criterion
W gt 1.4 GeV
Still to quantify (preliminary data only)
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Dependence on pt
Lund MC
but data not inconsistent with factorization
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Dependence on x
Lund MC
trend of expected x-dependence, but slightly
low?
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Duality in Unpolarized Structure Functions
Validation and Application
Duality was well established in the 70s in the
pre- and early-QCD era. The existence of
duality is well known, based on Regge theory, and
these ideas have not changed since that
time. Modern studies show that duality works
quantitatively better than expected, and works in
all observables tested to date. - Hence, duality
can be used as a tool for other studies. The
origin of duality is the subject of modern
theoretical research.
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)
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QCD and the Operator-Product Expansion
1

• Moments of the Structure Function Mn(Q2)
  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
• 
  
• Duality is described in the Operator Product
  Expansion
• as higher twist effects being small or
  canceling DeRujula, Georgi, Politzer
  (1977)

0
?
k1
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Example ee- hadrons
Textbook Example
R
Only evidence of hadrons produced is narrow
states oscillating around step function
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Factorization
Both Current and Target Fragmentation Processes
Possible. At Leading Order
Berger Criterion
Dh gt 2 Rapidity gap for
factorization
Separates Current and Target Fragmentation Region
in Rapidity