Nuclear%20Duality%20(and%20related%20topics

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Nuclear Duality(and related topics)
Cynthia Keppel Hampton University / Jefferson Lab
First Workshop on Quark-Hadron Duality Frascati,
Italy June 2005
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A Program of Inclusive Structure Function
Measurements in Hall C at Jefferson Lab

• E94-110 L/T Hydrogen Resonance Region
• E99-118 L/T Low x, Q2 A-Dependence
• E00-002 L/T Low Q2 Deep Inelastic H, D
• E00-116 High Q2 H,D
• E04-001 L/T Nuclear Dependence, Neutrino
  Modeling
• E02-109 L/T Deuterium Resonance Region
• E02-109 xgt1, A-Dependence
• E03-103 EMC effect

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Inclusive e p ? e X Scattering
Rosenbluth
Where ? flux of transversely polarized
virtual photons ? relative longitudinal
polarization
Alternatively

Transverse
longitudinal
mIxEd
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High Precision Data E94-110 Example 180 L/Ts
ds/dWdE/G (nb/sr/GeV)
? 1.6
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Example Precision Proton Structure Function FL
Alekhin NNLO MRST NNLO MRST NNLO with Barbieri
Target Mass Corrections

• Smooth transition from DIS (solid squares) to
  resonance region
• Resonances oscillate about leading order curves
• Q2 dependence same for leading order scaling,
  resonances
• Target mass corrections large and important

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Duality in F2let the nucleus do the averaging
x 2x1 (1 4M2x2/Q2)1/2

• Data in resonance region, spanning Q2 range 0.7 -
  5 GeV2
• GRV curve
• The nucleus does the averaging
• For larger A, resonance region indistinguishable
  from DIS

p
d
Fe
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Duality and the EMC Effect
C/D
Red resonance region data Blue, purple, green
deep inelastic data from SLAC, EMC Medium
modifications to the structure functions are the
same in the resonance region as in the
DIS Cross-over can be studied with new data
Fe/D
Au/D
J. Arrington, et al., submitted
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Momentum Sum Rule M2(Q2) ?dx F2(x,Q2)
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Fe data data ) Fe curve 26p 30n d from
e-d data (sum 0.31) p from hydrogen n d-p
(sum rule 0.14)
0
.elastic contributions
I. Niculescu, et al, in preparation
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More quantitatively..
Momentum sum rule from iron agrees with simple
sum p,n to within 5 (not very sensitive to
neutron excess) EMC effect is a redistribution,
not additional, momentum of quarks
Where is the nuclear binding? 7 MeV / nucleon /
938 MeV expect 6 difference!
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Extraction of Nuclear Moments
JLab Hall C E89-009 E02-109 xgt1 (2004)
H,D,3He,4He,C,Cu,Au E03-103 EMC effect (2004)
H,D, 3He, 4He,C, Cu, Au

• 2

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Proton Momentum Sum Rule
For F2, QPM gives (1/3)2(0.17) (2/3)2(0.34)
0.17 50 of momentum carried by quarks - the
rest, assumably, by the glue FL gives a direct
measurement of the glue But, we get 0.70
(preliminary) - also different from pdfs

Preliminary
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n 2 Cornwall-Norton Proton Moments
F2, F1 in excellent agreement with NNLO TM
above Q2 2 GeV2 Very small (or canceling)
higher twists Yet, dominated by large x and
resonance region Remove known HT (a bit novel),
the elastic, and there is no more down to Q2
0.5 GeV2 The case looks different for FL (data or
curve?)
F2
2xF1
FL
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Neutron - Proton Moments Compare to Lattice
D. Dolgov, et al., Phys.Rev.D66034506, 2002
n-p reduces sea, higher twist effects
Need to wait for BONUS,,,,,,,
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Parton Distribution Functions not well known at
large x largely due to uncertainties associated
with neutron extraction from deuterium
CTEQ u,d(x) uncertainty bands
Similar for HERA, note also glue important still
at large x (scaled by factor of 20!)
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Being bold..
F2
Need to get scaling curves for p, n at large
x Duality implies nucleus averaging to scaling,
small higher twist Use duality-averaged curve to
get neutron Fix range in ?, average data, obtain
curve .lets see.
D
P
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A Prediction from Duality and Large x p,d Data
Helicity Conservation and d/u 1/5
Naïve SU(6) quark model, d/u 1/2 Helicity
conservation, d/u 1/5 1 gluon exchange. d/u 0
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Challenges / Issues / Physics at Low Q2

• NEED L/T separations to extract inclusive
  structure functions F1, FL, and F2
• Low Q2 behavior
• Photonuclear absorption resonances less apparent
  in nuclei than in the proton (beyond Fermi)
• Nuclear moment analyses indicate higher twist
  occur at smaller Q2

higher twists
current conservation
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At low Q2, L/T Separations are Crucial.
1) F2 is sometimes referred to as the
transverse SF. 2) F2 cant be obtained
precisely independent of R and L/T
separations 3) Behaviour of F2
at low Q2 is not actually well determined (F2
0 at Q2 0). 4) R must be small for Q2 lt 1
(R 0 at the photon point, Q2 0).

• In fact F2 ? s L s T

• Except at e 1 or Q2 large, F2 extracted from
  cross sections requires knowledge of R.

This has not yet been observed in the data - in
fact, quite the opposite..
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Just an example.
At W2 4 GeV2 and Q2 lt 1 GeV2, F2 will vary by
15 depending on the choice of R 0 or R 0.2.
At higher Q2, this can be as much as 20.
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R on the protonE99-118, E94-110 world
Note R still not small at low Q2 as
expected! Precious little nuclear data
available (E99-118 soon high W2, low Q2
H,D,C,Al,Cu,Au)
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E99-118 Ratio RD / RH
Very limited previous data RD 0.7 RH (within
large uncertainty)
V. Tvaskis, PhD Thesis, Vrije Universiteit, 2004
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LOTS of new, L/T separated, low Q2 nuclear data
en route
Very preliminary data (just obtained January
2005) H,D,C,Al,Cu,Fe,Au resonance region Models
D resonance - JLab n/p - d/u 1/5 EMC -
SLAC DIS - F2allm (NMC) R - JLab e99118
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Data will be used for Nuclear duality Neutrino
modeling Deuterium (neutron) moments R on
deuterium in resonance region A-dependence of
structure functions (and moments) at low
Q2 Search for nuclear pions (G. Miller
prediction)
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Summary

• Duality seems to hold even better in the nucleus,
  where Fermi motion naturally averages the
  structure function over resonances
• EMC effect in resonance region same as deep
  inelastic regime
• Fe momentum sum rule constructed from (d-p),p to
  within 5
• Use duality and the deuteron to extract
• n-p structure function moments (lattice
  comparison)
• n/p at large x (helicity conservation)
• Challenges at low Q2
• Need L/T separations
• When do R, F2 approach 0?
• Nuclear Effects
• LOTS of new data in the canexciting times

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

1
0
?
k1
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1
Mn(Q2) dx xn-2F(x,Q2)
0
F2
Need data covering wide range in x, at fixed
Q2 Large x increasingly important at large n
elastics
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Why is IGDH(Q2) interesting?
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Extended Baldin Sum Rule
Q2 0, photoproduction
Baldin Sum Rule
GDH Sum Rule
Q2 gt 0, electroproduction
Extended GDH Sum Rule
Extended Baldin Sum Rule
Where ? anomalous magnetic moment of the
nucleon. a, ß electric and magnetic
polarizabilities respectively ?0
pion photoproduction threshold
Need L/T separated data!
D. Drechsel, B. Pasquini, M. Vanderhaeghen
hep-ph/0212124 Dec 2002
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Multiply with Q4/2M to emphasize transition of
Baldin Sum Rule to Perturbative DIS Region
Again, smooth transition
2xF1 Moment
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Duality (F2) in Deuterium
Resonance region and DIS F2 same, with same Q2
dependence, other than at smallest W