Duality in SemiInclusive DIS

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Duality in Semi-Inclusive DIS
P. Bosted (JLab)
First Workshop on Quark-Hadron Duality and the
Transition to pQCD
June 6, 2005

• Semi-inclusive processes
• Factorization as a test of quark-hadron duality
• Factorization tests in unpolarized SIDIS
• Kinematic dependences of g1/f1
• PT dependence of spin and azimuthal asymmetries
• Summary Outlook

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Semi-inclusive DIS
Main focus of SIDIS studies

• orbital angular momentum of quarks
• parton distributions at large x

X.Ji

• Where region I/II boundary?
• Can useful information
• come from Region II?

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kT-dependent parton distributions
Semi-Inclusive Deep Inelastic Scattering (SIDIS)

• Probes orbital motion of quarks through quark
  transverse momentum distribution
• Access to new PDFs not accessible in inclusive
  DIS.

Off-diagonal PDFs vanish if quarks only in
s-state! In addition T-odd PDFs require FSI
(Brodsky et al., Collins, Ji et al. 2002)
Mulders, This talk
transversity
Sivers
This talk
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SIDIS kinematic plane and relevant variables
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Missing mass of pions in ep-gtepX
p0
p-
p
n
D
D0
Duality question is MXgt1.4 GeV (approximately
zlt0.7 for Q2-2.5 GeV2, W2.5 GeV) needed for
SIDIS factorization to work? Note absence of
Delta in p0!
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Factorization Test from Unpolarized Multiplicites

Multiplicity (proportional to D(z)) is
approximately independent of x for Wgt3 GeV,
Q22.5 GeV2, xlt0.5, and 0.25ltzlt0.6
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Factorization Test from Unpolarized Multiplicites

Dup KKP (LO)
Multiplicity (proportional to D(z)) is also
approximately independent of x for Wgt2 GeV, Q22
GeV2, 0.1ltxlt0.6, and 0.45ltzlt0.7 at E5.5 GeV
from CLAS at JLab
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Unpolarized SIDIS new test
Simple picture in valence region sp(p)
4u(x)D(z) d(x)D-(z) sp(p-) 4u(x)D-(z)
d(x)D(z) sd(p) u(x)d(x) 4D(z)
D-(z) sd(p-) u(x)d(x) 4D-(z)
D(z) Rpd sp(p) sp(p-) / sd(p)
sd(p-) 4u(x) d(x) / 5u(x)d(x)
sp(x)/sd(x)
Rpd should be independent of z and pt
x-dependence of Rpd should be same as inclusve
sp(x)/sd(x) in valence region
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Unpolarized SIDIS new test
Rpd is independent of z for 0.4ltzlt0.7 for W2.5
GeV, Q22.5 GeV2, x0.3, low pt Good
agreement GRV (using PEPSI MC, solid
histogram) 10 level deviations for
zgt0.7 (Mxgt1.4 GeV) Influence of Delta?
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Unpolarized SIDIS new test
Rpd is independent of pt for z0.55 W2.5 GeV,
Q22.5 GeV2, x0.3 Good agreement GRV (using
PEPSI MC, solid histogram)
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Unpolarized SIDIS new test
Rpd follows expected x-dependence for
z0.55 W2.5 GeV, Q22.5 GeV2, low pt Pretty
good agreement with GRV (using PEPSI MC, solid
histogram)
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CLAS Experiment Setup and Kinematics
Scattering of 5.7 GeV polarized electrons off
polarized NH3, ND3

• 8M p in SIDIS kinematics

x
x
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Determination of g1/F1 (approximately A1)

• Target polarization PT about 0.7 (0.3) for NH3
  (ND3)
• Beam polarization PB about 0.7
• Dilution factor f varies from 0.1 to 0.3 used
  Lund
• model for n/p ratio (agrees with Hall C data)
  and
• preliminary Hall B data for A-dependence
• Depolarization factor DLL(y) evaluated assuming
• RsL/sT same as for inclusive.
• Assumed Aperp0 (not measured)
• No radiative corrections applied
• p and p- include some K, K- for Pgt1.5 GeV
• p0 events cleanly identified with two photons

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x-depenence of SIDIS proton g1/F1
Wgt2 GeV, Q2gt1.1 GeV2, 0.4ltzlt0.7

• Good agreement with
• HERMES p data at
• higher W.
• x-dependence follows PEPSI
• (Lund) Monte Carlo using
• GRSV polarized PDFs (LO)
• Magnitude also in good
• agreement with simulation

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Polarized SIDIS factorization tests
Simple picture in valence region sp(p)
4u(x)D(z) d(x)D-(z) sp(p-) 4u(x)D-(z)
d(x)D(z) dsp(p) 4du(x)D(z)
dd(x)D-(z) dsp(p-) 4du(x)D-(z)
dd(x)D(z) (g1/F1)-dsp(p)dsp(p-)/sp(p)sp
(p-) 4du(x) dd(x) / 4u(x)
d(x) (g1/F1)inclusive Similarly for p0
(g1/F1)0 (g1/F1)inclusive
(g1/F1)- and (g1/F1)0 should be independent of
z and pt, and equal to inclusive (g1/F1)
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SIDIS factorization studies
Significant ?
GRVS
g1/F1 for inclusive, for the sum of p ,p- , and
for p0 are fairly consistent with each other in
the range 0.4ltzlt0.7, as expected in LO if
factorization works. Cuts used Mxgt1.4 GeV,
Q2gt1.1 GeV2, Wgt2 GeV
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z-depenence of SIDIS proton g1/F1
No significant z-dependence seen for p0 and
p p- for 0.3ltzlt0.7, as expected if
factorization holds Good agreement with
PEPSI predictions including dropoff at high z
for p-, due to increasing importance of
dd(x)
CLAS 5.7 GeV
PRELIMINARY
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pt-depenence of SIDIS proton g1/F1
No pt dependence for p0 (green), as expected if
factorization works p (red) and p- (blue)
individually show pt dependence, but the sum of
the two (not shown) is almost independent of pt,
as expected if factorization works Reasonable
agreement with PEPSI predictions.
CLAS 5.7 GeV
PRELIMINARY
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Q2-depenence of SIDIS proton g1/F1
PRELIMINARY
CLAS 5.7 GeV
No Q2 dependence for Q2gt1.1 GeV2. Evidence of HT
for Q2lt1.1 GeV2
Wgt2 GeV 0.4ltzlt0.7
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SIDIS g1/F1 for Deuteron
CLAS 5.7 GeV
PRELIMINARY
Results dont agree as well with PEPSI using
GRSV, more sensitive to un-favored fragmentation
function and NLO corrections than proton
(although errors are about a factor of two
larger) NLO QCD fits including new SIDIS CLAS
data can help constrain polarized PDFs in valence
region
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Longitudinally Polarized Target SSA

• Clear f dependence
• seen for proton
• target and p, p0
• Fit Asin(f) Bsin(2f)
• for Twist-3 and Twist-2
• respectively

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SSA x-dependence
Twist-2
Higher Twist
The hL functions depend on both x and pt, so no
simple factorization tests arent possible.
However, can check if (x,pt,z) dependence follows
model expectations
T
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SSA x-dependence
Twist-2
Higher Twist
Data in rough agreement with Efremov et
al. predictions, except for p0 sin(f)
term (evidence for terms not involving
Collins fragmentation?)
5.7 GeV
PRELIMINARY
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SSA PT-dependence of sinf moment
ssinfLU(UL) FLU(UL) 1/Q (Twist-3)
CLAS _at_4.3 GeV
CLAS _at_5.7 GeV
Beam and target SSA for p (not sensitive to
MX-cut) are consistent with increase with PT
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Summary

• Factorization tests with both unpolarized and
  polarized data work surprisingly well for Wgt2
  GeV, Q2gt1.1 GeV2, 0.3ltzlt0.7, ptlt1 GeV, even for
  Mxlt2 GeV (another evidence of quark-hadron
  duality)
• Breakdown of factorization at high z may be due
  to Delta excitation or diffraction vector meson
  production (ongoing analysis)
• Target fragmentation may come into play at lower
  z than naively expected (ongoing analysis)
• Data may be used even with 6 GeV electrons to
  study PDFs, at least in limited kinematic region
• More data planned all final states at 6 GeV and
  with 11 GeV at Jlab. High statistical accuracy
  tests will better quantify the useful kinematic
  range of SIDIS

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QUESTIONS

• Factorization Wlt2 GeV?
• Factorization for kaons at low energy?
• NLO tretment
• TM corrections
• Electroweak current?
• were just in the beginning!

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support slides..
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First glimpse of Twist-2 TMD h1L-
For Collins fragmentation function use HERMES data
Distribution functions from cQSM from Efremov et
al
PRELIMINARY
CLAS-5.7GeV
Systematic error only from unknown ratio of
favored and unfavored Collins functions (R
H1d?p/H1u?p), band correspond to -2.5ltRlt0

• More data required with p- p0
• Exclusive 2 pion background may be important

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SIDIS (gp-gtpX) x-section at leading twist
TMD PDFs
f1
h-1
g1
T-odd
h-1L
f-1T
g1T
h1
h-1T
kT-even
kT-odd
The structure functions depend on Q2, xB, z, PhT
1) Unpolarized target 2) Longitudinally pol.
target 3) Transversely pol. target
Studies of PDFs require three experiments
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Future more p0 data in SIDIS
advantages

• SIDIS p0 production is not contaminated by
  diffractive r
• HT effects and exclusive p0 suppressed
• Simple PID by p0-mass (no kaon contamination)
• Provides complementary to p/- information on PDFs

disadvantages reconstruction efficiency
(requires detection of 2g)
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CLASInner Calorimeter (IC)
424 PbWO4 ..crystals
IC
IC sE/E0.0034/E0.038/vE0.022
CLASIC
CLAS
Reconstruction efficiency of high energy p0 with
IC increases 4 times due to small angle coverage
CLAS
IC at CLAS opens new avenue for studies of spin
and azimuthal asymmetries of exclusive and
semi-inclusive g, p0,h,r
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Longitudinally polarized target SSA using CLASIC
50 days of CLASIC
curves, cQSM from Efremov et al
Hunf-5Hfav
Hunf-1.2Hfav
Hunf0

• Provide measurement of SSA for all 3 pions,
  extract the Mulders TMD and study Collins
  fragmentation with longitudinally polarized
  target
• Allows also measurements of 2 pion asymmetries

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SIDIS factorization
Structure functions FUU,FLL factorize into TMD
distribution and fragmentation
QCD Factorization (Ji and col.)
Naïve Factorization (Mulders and col.)
TMD FF
hard scattering
soft factor
TMD PDF
SIDIS Factorization proved for low PT !!!
P- has contributions from distribution,
fragmentation and soft gluon radiation
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ALU x-dependence CLAS _at_ 4.3 and 5.7 GeV
0.5ltzlt0.8
Beam SSA analyzed in terms of the Collins effect
by Schweitzer et al. using e(x) from cQSM
Separation of different HT contribution will
require independent measurements of separate
contributions
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double spin asymmetry A1p
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NH3 dilution
Dilution function extracted from PEPSI-MC is
consistent with data