The PartonHadron Transition in Structure Functions and Moments Rolf Ent Jefferson Lab

1
The Parton-Hadron Transition in Structure
Functions and MomentsRolf EntJefferson Lab
Science Technology Review June 2003

• Introduction QCD and the Strong Nuclear Force
• The Parton-Hadron Transition in Moments of
  Structure Functions
• Quark-Hadron Duality How Local is the
  Transition?
• Applications and Theoretical Understanding
• Summary

2
How are the Nucleons Made from Quarks and Gluons?
How do we understand QCD in the confinement
regime? A) What are the spatial
distributions of u, d, and s quarks in the
hadrons? B) What is the excited state
spectrum of the hadrons, and what does
it reveal about the underlying degrees of
freedom? C) What is the QCD basis
for the spin structure of the hadrons? Q2
evolution of structure functions and their
moments Extended GDH sum rule, Bjorken sum rule
D) What can other hadron properties
tell us about Strong QCD? Inclusive Resonance
Electroproduction and Quark-Hadron Duality Q2
evolution of structure functions and their
moments
3
QCD and the Strong Nuclear Force QCD has the
most bizarre properties of all the forces in
nature

• Confinement
• restoring force between quarks at large distances
  equivalent to 10 tons, no matter how far apart
• Asymptotic freedom
• quarks feel almost no strong force when closer
  together

• QCD ( electro-weak) in principle describes all
  of nuclear physics - at all distance scales -
  but how does it work?

4
QCD and the Parton-Hadron Transition
One parameter, LQCD, Mass Scale or Inverse
Distance Scale where as(Q) 1 Separates
Confinement and Perturbative Regions Mass and
Radius of the Proton are (almost) completely
governed by
Constituent Quarks Q L as(Q) large
Hadrons Q 1
?QCD?213 MeV
Asymptotically Free Quarks Q L as(Q)
small
L
5
QCD and the Parton-Hadron Transition
One parameter, LQCD, Mass Scale or Inverse
Distance Scale where as(Q) 1 Separates
Confinement and Perturbative Regions Mass and
Radius of the Proton are (almost) completely
governed by
?QCD?213 MeV
6
Inclusive Electron Scattering Formalism
Q2 Four-momentum transfer x Bjorken variable
(Q2/2Mn) n Energy transfer M Nucleon mass W
Final state hadronic mass
U

• Unpolarized structure functions F1(x,Q2) and
  F2(x,Q2), or FT(x,Q2) 2xF1(x,Q2) and FL(x,Q2),
  to separate by measuring R sL/sT
• Polarized structure functions g1(x,Q2) and
  g2(x,Q2)

L
T
7
The Parton-Hadron Transition in Structure
Functions and Moments

• Introduction QCD and the Strong Nuclear Force
• The Parton-Hadron Transition in Moments of
  Structure Functions
• Quark-Hadron Duality How Local is the
  Transition?
• Applications and Theoretical Understanding
• Summary

8
QCD and Moments
1

• Moments of the Structure Function Mn(Q2) dx
  xn-2F(x,Q2)

0
Let F(x,Q2) xf(x) be a probability density
distribution, describing the velocity
distribution in a dilute gas M1 1 M2
average velocity M3 variance e
tc.
In QCD also dependent on Q2 due to Q2 evolution
of probability density distributions ? ,
vary with Q2
9
QCD and the Operator-Product Expansion
1

• Moments of the Structure Function Mn(Q2)
  dx xn-2F(x,Q2)
• Operator Product Expansion
• Mn(Q2) ? (nM02/ Q2)k-1 Bnk(Q2)
• higher
  logarithmic
• twist dependence

0
?
k1
At High Q2 ln(Q2) dependence of
moments one of first
proofs of QCD ? L(QCD) At Low Q2 Unique
regime for JLab to
determine (1/Q2)m ?
Higher Twist effects Lowest moments are
calculable in Lattice QCD (LQCD) least computer
intensive!
10
Moments of F2p _at_ Low Q2
50 of momentum carried by quarks (Momentum Sum
Rule)
n 2
n 4
n 6
n 8
11
Moments of F2p _at_ Low Q2
Proton Charge (Coulomb Sum Rule)
50 of momentum carried by quarks (Momentum Sum
Rule)
n 2
n 4
n 6
n 8
Elastic contribution
(A combination of Hall C CLAS data presented by
VB to constrain the Constituent Quark radius,
here only Hall C data are shown)
12
Moments of F2p _at_ Low Q2
Proton Charge (Coulomb Sum Rule)
_at_ Q2 2 (GeV/c)2 30 of M2 comes from the
resonance region
50 of momentum carried by quarks (Momentum Sum
Rule)
W2 4 GeV2 (DIS)
elastic
total
n 2
n 2
n 4
n 6
D-region
n 8
S11-region
Elastic contribution
13
n 2 Moments of F2, F1 and FL Mn(Q2) dx
xn-2F(x,Q2)
1
0
DIS SLAC fit to F2 and R Resonances E94-110
(Hall C) fit
Elastic Contributions
Preliminary
F2
F1EL GM2 d(x-1)
Elastic contribution excluded
F2EL (GE2 tGM2 )d(x-1)
1 t
F1
t Q2/4Mp2
FLEL GE2 d(x-1)
Flat Q2 dependence ? small higher twist! - not
true for contributions from the elastic peak
(bound quarks)
FL
14
n 4 Moments of F2, F1 and FL
Preliminary
Neglecting elastics, n 4 moments have only a
small Q2 dependence as well.
Elastic contribution excluded
Momentum sum rule
ML(n) as(Q2) 4M2(n) 2c?dx xG(x,Q2)
3(n1)
(n1)(n2)
Gluon distributions!
This is only at leading twist and for zero proton
mass ? Must remove non-zero proton mass effects
from data to extract moment of xG(x,Q2) ? Work
in progress
15
Moments of g1p (G1p)
30 of Spin carried by quarks (Ellis-Jaffe Sum
Rule)
CLAS EG1 Data

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

k of proton (GDH Sum Rule)
16
Moments of g1p (G1p)
30 of Spin carried by quarks (Ellis-Jaffe Sum
Rule)
CLAS EG1 Data

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

Zero crossing mainly due to cancellation of D
(negative) and S11 Resonances
k of proton (GDH Sum Rule)
17
Moments of g1p (G1p)
30 of Spin carried by quarks (Ellis-Jaffe Sum
Rule)
CLAS EG1 Data

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

s1/2 s3/2

• SU(6) unbroken Mp MD
• D ground state of s3/2

Zero crossing mainly due to cancellation of D
(negative) and S11 Resonances

• In this scenario the D is
• a d function and all higher
• twist ? it plays the same
• role as the elastic in F2

k of proton (GDH Sum Rule)
18
Moments of g1n and g1p-g1n

• Hall A 3He(e,e) to extract
• g1n and its moment G1n (E94-010)
• Similar ideas as with proton
• Here, whole region negative

G1n
19
Moments of g1n and g1p-g1n
Combine Hall A g1n with Hall B g1p data

• Hall A 3He(e,e) to extract
• g1n and its moment G1n
• Similar ideas as with proton
• Here, whole region negative

G1n
20
Moments of g1n and g1p-g1n
Combine Hall A g1n with Hall B g1p data

• Hall A 3He(e,e) to extract
• g1n and its moment G1n
• Similar ideas as with proton
• Here, whole region negative

Bjorken Sum Rule (Verification of QCD)
Chiral Perturbation Theory (cPT)
G1n
G1p - G1n
21
Summary I - Moments
Resonances are an integral part of the Structure
Function Moments at Low Q2 (Note QCD deals with
the Moments and does not care what contributes
to the moments!) The Structure Function Moments
have a smooth behavior as a function of Q2, and
in fact pick up almost uniquely the quark-quark
interactions in the SU(6) ground states This
seems to indicate that the parton-hadron
transition occurs in a local and small region,
with only few resonances ? Quark-Hadron
Duality ? Let us examine the structure
functions themselves rather than their
moments
22
The Parton-Hadron Transition in Structure
Functions and Moments

• Introduction QCD and the Strong Nuclear Force
• The Parton-Hadron Transition in Moments of
  Structure Functions
• Quark-Hadron Duality How Local is the
  Transition?
• Applications and Theoretical Understanding
• Summary

23
Quark-Hadron Dualitycomplementarity between
quark and hadron descriptions of observables
At high enough energy

• Hadronic Cross Sections
• averaged over appropriate energy range
• Shadrons

• Perturbative
• Quark-Gluon Theory

Squarksgluons

Can use either set of complete basis states to
describe physical phenomena But why also in
limited local energy ranges?
24
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
25
Rosenbluth Separations
Hall C E94-110 a global survey of longitudinal
strength in the resonance region...
sL sT
sT
sL sT
/
(polarization of virtual photon)
26
Rosenbluth Separations
Hall C E94-110 a global survey of longitudinal
strength in the resonance region...

• Spread of points about the
• linear fits is Gaussian with
• s 1.6 consistent with
• the estimated point-point
• experimental uncertainty
• (1.1-1.5)
• a systematic tour de force

27
World's L/T Separated Resonance Data
R sL/sT
R sL/sT
(All data for Q2 28
World's L/T Separated Resonance Data
R sL/sT

Now able to study the Q2 dependence of individual
resonance regions!

Clear resonant behaviour can be observed!

Use R to extract

F2, F1, FL

R sL/sT
(All data for Q2
29
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)
• Use Bjorken x instead of Bloom-Gilmans w
• Bjorken Limit Q2, n ? ?
• 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 GeV2, resonance regime
• (note x Q2/(W2-M2Q2)
• JLab results Works quantitatively to better than
  10 at such low Q2

30
Duality in FT and FL Structure Functions
Duality works well for both FT and FL above Q2
1.5 (GeV/c)2
31
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
32
Duality easier established in Nuclei
EMC Effect Fe/D
Resonance Region Only
(s Fe/s D) IS
x
( x corrected for M ? 0)
Nucleons have Fermi motion in a nucleus

• The nucleus does the averaging for you!

33
but tougher in Spin Structure Functions
Pick up effects of both N and D (the D is not
negative enough.)
CLAS EG1
g1p
D

• CLAS N-D transition region turns positive at Q2
  1.5 (GeV/c)2
• Elastic and N-D transition cause most of the
  higher twist effects

34
The Parton-Hadron Transition in Structure
Functions and Moments

• Introduction QCD and the Strong Nuclear Force
• The Parton-Hadron Transition in Moments of
  Structure Functions
• Quark-Hadron Duality How Local is the
  Transition?
• Applications and Theoretical Understanding
• Summary

35
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

36
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

37
Summary
Despite the large value of as(Q2) at Q2 the transition from a QCD description in terms of
hadrons to a QCD description in terms of partons
occurs smoothly, in the region Q2 Quarks and the associated Gluons (the Partons)
are tightly bound in Hadrons due to
Confinement Still, they rely on camouflage as
their best defense a limited number of confined
states acts as if consisting of free quarks ?
Quark-Hadron Duality, which is a non-trivial
property of QCD, telling us that contrary to
naïve expectation quark-quark correlations tend
to cancel on average Integrating over all
confined states by forming a moment similarly
shows a smooth parton-hadron transition in both
spin-averaged and spin-dependent structure
functions, to compare with LQCD and cPT
38
Q2 Evolution of the F2 Structure Function
F2 Structure Function measured over impressive
range of x and Q2. Any QCD Theory has Q2
evolution.
W2 4 GeV2 (DIS) only
One can also start with the extracted Parton
Distribution Functions f(x,Q) and do the Q2
evolution
39
Moments of g2n (G2n)
Burkhardt-Cottingham Sum Rule
Hall A 3He(e,e) (E94-010)
Dispersion relation for forward spin-flip Compton
amplitude (similar assumption as GDH). Doesnt
follow from OPE and valid at all Q2 Many
scenarios of g2 low x behavior would invalidate
the sum rule. Here, the part of the integral
that comes from the nucleon resonance region is
shown. Its 0, mostly from a cancellation of the
large elastic and D contributions
Contribution beyond resonance region
as calculated from g1
40
Example ee- hadrons
Textbook Example
R
Only evidence of hadrons produced is narrow
states oscillating around step function
41
Example ee- hadrons
Textbook Example
Only evidence of hadrons produced is narrow
states oscillating around step function and steps
in the (partially) integrated spectrum reflecting
the quark mass difference
42
Local Duality in the F2 Structure Function
Define N-D region as 1.2

Obviously, duality

does not hold on top

of peak!

However, for F2 the

defined N-D region

mimics the DIS

parameterization

Note that one does

not expect much Q2

evolution at these

values of x (or x)

43
Duality easier in Nuclei
EMC Effect Fe/D
Resonance Region Only
Q23
J. Arrington et al., in preparation

• If we had used only large scintillators, QCD
  scaling would be thought to hold down to low Q2!

44
but tougher in Spin Structure Functions
HERMES
JLab Hall B
A1p
g1p
D

• HERMES at Q2 1.6 GeV2 agreement in A1
• CLAS N-D transition region turns positive at Q2
  2!

45
Moments of F2n
e
Electron detected in CLAS spectrometer, spectator
proton detected in RTPC
D
n
p
e

• Thin deuterium gas target (7.5 atm)
• Radial Time Projection Chamber (RTPC) for low
  momentum (60-100 MeV/c) spectator proton
  detection
• DVCS solenoid to contain Moller background

46
and easier again in Nuclei!
Hall A 3He(e,e)
g1n
Low Q2 (resemble DIS spectrum from SLAC Quantitative
Duality tests still to be done, additional
experiment ran January to extend these resonance
data to Q2 5 (GeV/c)2
D
?