Measurements of Longitudinal and Transverse Unpolarized Structure Functions and Their Impact on Spin

1
Measurements of Longitudinal and Transverse
Unpolarized Structure Functions and Their Impact
on Spin Asymmetry Measurements.
M. Eric Christy Hampton University

• Inclusive eP scattering and nucleon SFs
• Unpolarized SFs and spin asymmetry
  measurements
• E94-110 results resonance region unpolarized
  L-T SFs
• Resonance region fitting
• F2 at Low Q2
• Future outlook

2
Q2 Four-momentum transfer x Bjorken variable
(Q2/2M?) ? Energy transfer M Nucleon mass W
Final state hadronic mass
U
L
T
3
Moments of g1p (?1p)
30 of Spin carried by quarks (Ellis-Jaffe Sum
Rule)

• Elastic not included in
• Moment as shown ?
• With Elastic included
• no zero crossing, and
• Q2 dependence far
• smoother

CLAS EG1 Data
A

• SU(6) unbroken Mp M??
• ? ground state of ?3/2

Zero crossing mainly due to cancellation of ?
(negative) and S11 Resonances
In this scenario the ??is a ? function and all
higher twist ? it plays the same role as the
elastic in F2
? of proton (GDH Sum Rule)
4
Resonance Region L-Ts Needed For
Extracting spin structure functions from spin
asymmetries
With D 1-eE//E and h is a
1eR kinematic factor
A
DA1 h A2
s1/2 s3/2
s1/2 s3/2
A1


s1/2 s3/2
2sT
(2xF1 a s1/2 s3/2)
DA1 edR
From measurements of F1 and A1 extract s1/2 and
s3/2 ! (Get complete set of transverse helicity
amplitudes)
A1
F1(A1 gA2)
g1

1 g2
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Resonance Contribution to Moments (GDH)
Many new asymmetry measurements in the resonance
region.
At small Q2 most of the x range is in the
resonance region! Low Q2 moments require
resonance region measurements.
85 of x range at W2 lt 4.
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Misconceptions (addressed in this talk)
1) F2 is sometimes referred to as the
transverse SF. 2) F2 has been measured
in the resonance region independent of R
(i.e. SLAC fits to resonance cross section
data). 3) Behaviour of F2 at low
Q2 is 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 a s L s T

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

Knowledge of the small Q2 behaviour is important
for extending GDH measurements to the real photon
point.
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Resonance Region F2

• F2 a s L s T

Previous RR extractions of F2 at e lt 1depended
on assumption of R .
sL/ s T
Ratio of F2 extracted from RR cross
sections with R 0.2 to R 0.
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Experimental Status of Unpolarized Sfs
From Bodek (2000)

• Overall, F2 is well measured over 4 orders of
  magnitude, although large x, low Q2
  region is sparse!
• R is not so well measured (especially large x,
  low Q2 - )!

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World's Resonance Data on R

• Not able to study the Q2 dependence of individual
  resonance regions!
• No resonant behaviour can be observed!

(All data for Q2 lt 9 (GeV/c)2)
R

• E94 -110 proposed to survey RR longitudinal
  strength for 0.5 lt Q2 lt 4.0
• Requires Ds/s lt 2 pt-pt in e high
  statistics - systematic 'tour de
  force'

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Kinematic Coverage of Experiment
dsR (ds/G) sT(W2,Q2) esL(W2,Q2)
2 Methods employed for separating SFs

• Rosenbluth-type separations where possible
  (some small kinematic evolution is needed)
• Iteratively fit F2 and R over the entire
  kinematic range.

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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

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E94-110 Rosenbluth Extractions of R
lt
R
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E94-110 Rosenbluth Extractions of R

• Clear resonant behaviour is observed in R for the
  first time!
• ? Resonance longitudinal component NON-ZERO.
• ? Transition form factor extractions should be
  revisited.
• Longitudinal peak in second resonance region at
  lower mass than S11(1535 MeV)
• ? D13(1520 MeV) ? P11(1440 MeV)?
• R is large at low Q high W (low x)
• ? Was expected R ? 0 as Q2 ? 0
• ? R ? 0 also not seen in recent SLAC
• DIS analysis (R1998)
• ? Large longitudinal contribution from gluons?

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L-T Separated Structure Functions
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Results for FT 2xF1 and FL

• Duality appears to hold in both transverse and
  longitudinal structure functions!
  (first observation of this)
• Resonance Region data links smoothly with DIS.

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F2p _at_ low Q2
Resonance region slides to lower x at low Q2,
but does not disappear like Q2 yet.
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R _at_ Low Q2 lt 0.5
Preliminary Still ?R 0.1 point-to-point (mainly
due to bin centering assumptions to x 0.1)
(The x lt 0.2, Low Q2 (0.1 GeV2) region pushed
the envelope of the E94-110 (and E99-118)
experiments. Dedicated data for this region were
taken last year.)
E99118
R shows surprisingly flat Q2 behaviour down to
very low Q2 (also shown by SLAC R1998
parameterisation) ? does not appear to follow
current conservation prescription yet R stays
rather constant
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Some issues with Existing SF Fits
Asymmetry measurements need good
parameterisations of all unpolarized structure
functions!
However,
1) R1990 / R1998 not in agreement at low
Q2. 2) R1998 not simultaneously fit with F2
(i.e. Will not reproduce
measured cross sections when combined.) 3)
No fit for R in the resonance region. 4)
PDF-based fits (CTEQ, MRS, GRV) disagree with
large x data. (currently working on this
with CTEQ) 5) Some data consistency studies
need to be done.
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Global Fits
Ansantz - Fit both sT and sL with 1)
Resonances Breit Wigners 2) Smooth NR
background polynomials in W-Wthesh(n1)/2 -
Allow prominent resonance position and width to
be different in different
channels. Note that this will allow R
sL/sT to have more wiggles than
resonances in each channel. - Try to link
smoothly with DIS L/T data. Currently, fit
psuedo-data generated from SLAC F2 R
parameterizations.
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Fits Comparisons
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E94-110 is continuing to provide new and
interesting physics results
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N2 CN Moments of F2, F1 and FL
DIS SLAC fit to F2 and R RES E94-110
resonance fit
Elastic Contributions
F1EL GM2 d(x-1)
F2EL (GE2 tGM2 )d(x-1)
1 t
t Q2/4Mp2
Preliminary
FLEL GE2 d(x-1)
Flat Q2 dependence small higher twist! -
not true for contributions from the elastic peak
(bound quarks)!
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Nachtmann Moments
n 4
n 2
F2
F2
F1
F1
FL
FL
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Measurement of the extended Baldin Sum Rule for
the proton(see talk by Y. Liang)
(PDG)
(a b) 14.2 /- 0.9
Q20
(D. Babusci et al. 1998)
(a b) 13.69 /- 0.14
Extended GDH Sum Rule
Q20
Extended Baldin Sum Rule
D. Drechsel, B. Pasquini, M. Vanderhaeghen
hep-ph/0212124 Dec 2002
Where ? anomalous magnetic moment of the
nucleon. a, ß electric and magnetic
polarizabilities respectively ?0
pion photoproduction threshold
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Summary

• Asymmetry measurements require knowledge of
  the
  
  unpolarized SFs.
  
• 
  
  
• Jlab E94-110 provides precision measurements of
  unpolarized
• SFs in RR for 0.2 lt Q2 lt 4.5.
• much more physics results to come
• E94-110 resonance region fit is ideal for spin
  structure function extractions from asymmetry
  measurements for 0.2 lt Q2 lt 4.5.
• Knowledge of unpolarized SFs at small Q2 and
  high x are needed for GDH
  extensions.
  
  
  

2003 Jlab HallC measurements.