Factorization and Transverse Momentum in SIDIS at JLab

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Factorization and Transverse Momentum in SIDIS at
JLab
P. Bosted, H. Avakian (JLab)
Trento, Italy, May 2007

• Semi-inclusive processes
• Factorization as a test of quark-hadron duality
• Factorization tests in unpolarized SIDIS
• Facorization tests in polarized SIDIS
• Tranverse momentum in fragmentation

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Semi-inclusive DIS
pion
Main focus of SIDIS studies
MX

• orbital motion of quarks (pt, f dependence)
• parton distributions (separate valence, sea)

X.Ji

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

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SIDIS kinematic plane and relevant variables
pion
MX
Pt is transverse momentum relative to virtual
photon W2M2Q2(1/x-1) is invariant mass of total
hadronic final state
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Factorzation in SIDIS
Basic idea hit a single quark in nucleon which
then hadronizes into a jet with negligible
interaction with remenant quarks.
s(x,z,pt) ? PDF(x,kt) x Frag.Fun.(z,pt)
Example, SIDIS p from u quark in proton
sp(x,z,ph) ? u(x,kt) x D(z,pt)
When integrated over transverse momenta of quarks
and hadrons
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Missing mass of pions in ep-gtepX with 6 GeV
electrons
p0
p-
p
n
D
D0
Duality question will factorization work if Mxlt2
GeV, even though D(1232) reonance visible? For
p-, guess need Mxgt1.4 GeV.
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EXPERIMENT E00-108 at JLAB Halll C

• Unpolarized electrons E6 GeV
• Scattered electrons E1.6 GeV, 25 to 40 deg.
  Average Q2 2.5 GeV2.
• W about 2.5 GeV, but Mxlt2 GeV.
• Detected positive and negative pions near 12
  degrees
• Proton and deuteron targets
• Made scans in x, z. ptlt0.2 GeV

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Z-Dependence of cross sections
Good agreement with prediction using CTEQ5M PDFs
and Binnewies fragmentation functions, except for
zgt0.7, or Mxgt1.4 GeV.
D or D,D-
X0.3, Q22.5 GeV2, W2.5 GeV
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In more detail, form super-ratios
Simple LO picture in valence region sp(p)
4u(x,pt)D(z,pt) d(x,pt)D-(z,pt) sp(p-)
4u(x,pt)D-(z,pt) d(x,pt)D(z,pt) sd(p)
u(x,pt)d(x,pt) 4D(z,pt) D-(z,pt) sd(p-)
u(x,pt)d(x,pt) 4D-(z,pt) D(z,pt) Rpd
sp(p) sp(p-) / sd(p) sd(p-)
4u(x,pt) d(x,pt) / 5u(x,pt)d(x,pt)
sp(x)/sd(x) for any z, x, pt (if d and u
have same pt depdendence)!
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In more detail, form super-ratios
Simple LO picture in valence region sp(p)
4u(x,pt)D(z,pt) d(x,pt)D-(z,pt) sp(p-)
4u(x,pt)D-(z,pt) d(x,pt)D(z,pt) sd(p)
u(x,pt)d(x,pt) 4D(z,pt) D-(z,pt) sd(p-)
u(x,pt)d(x,pt) 4D-(z,pt) D(z,pt) Rpd-
sp(p) - sp(p-) / sd(p) - sd(p-)
4uv(x,pt) - dv(x,pt) / 3uv(x,pt)dv(x,pt)
for any z, x!
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Rpd
Rpd-
Both ratios agree PDF models for zlt0.7 (Nxgt1.4
GeV)
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Rpd
Rpd-
Both ratios agree PDF models 0.2ltxlt0.5 for
z0.55 (possible complications xgt0.5)
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Another test D-/D from Deuteron p to p- ratio
sd(p) ud 4DD- sd(p-) ud 4D-D
Results agree HERMES (higher W, Mxgt2 GeV) up to
z0.7 (Mxgt1.4 at pt0), after rho correction
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Another test D-/D from Deuteron p to p- ratio
Results agree HERMES and EMC for z0.55 and
xgt0.35. Maybe some x depdendence xlt0.35 (sea
quark correction?)
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Now look at transverse momentum dependence

• Previous plots all for pion transverse momentum
  Ptplt0.1 GeV
• Looks like factorization works for 0.3ltzlt0.7,
  0.2ltxlt0.5, Q22.5 GeV2.
• Pulsihed in Phys. Rev. Lett. 98, 022001 (2007)
• Now look at Ptp dependence found need some
  Q2-dependence to model to get good overlap of
  spectrometer settings.
• Ptp probes combination of quark intrinsitc
  momentum kt and favored and unfavored
  fragmentation widths pt (not necessarily same)

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Cross sections at x0.3, z0.55 versus Ptp
Cross sections drop exponentially to Ptp-0.4
slopes for all four cases are similar and about
4.5 GeV-2 (vaires from about 4 to 5 GeV-2
depending on Q2 correction)
p- from p
p from p
p from d
p- from d
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Super-ratios versus transverse momentum
Rpd
Rpd-
Both ratios independent of pt (to 0.3 GeV) for
z0.55
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Another test D-/D from Deuteron p to p- ratio
Ratio of fragmentation functions
appears independent of hadron transverse momentum
at these kinematics (x0.3, Q22.5, z0.55)
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Another test d/p ratios for p, p-
p
p-
Again, ratios appear constant at these
kinematics (x0.3, Q22.5, z0.55), although bit
higher than Lund MC predictions
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VERY preliminary d/p ratios from CLAS-
p0
For z0.55 and x0.3, CLAS results consistent
with Hall C, but when average over
wider kinematic range 0.3ltzlt0.7 and 0.15ltxlt0.45,
find d/p increases with ptp for p d/p
decreases with ptp for p- (for first bin, ratio
1.3, off plot!) d/p flat with ptp for p0 WHY?
(acceptance, kinematic effect, nuclear
effects, pr real physics?)
p
p-
Possible explanation unfavored D- Wider in pt
than favored D for zlt0.5
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Now to polarized SIDIS at JLAB using CLAS
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 about 0.7 (0.3) for NH3
  (ND3)
• Longitudinal 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)
• 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
Proton (g1/F1)- and (g1/F1)0 should be
independent of z and pt, and equal to inclusive
(g1/F1)
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Polarized SIDIS factorization test
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), in turn due to
increase of D/D- with increasing z
CLAS 5.7 GeV
PRELIMINARY
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pt-depenence of SIDIS proton g1/F1
First, need to account for LARGE pt-depenence of
dilution factor (ratio of counts from ptons to
counts from all materials in polarized target,
mainly nitrogen). Used CLAS measurements of C/d
averaged over our kinematics for SIDIS p .
Assumed N/d same as C/d and p- and p0 same as p
. Results on next page assume NO pt-depenence to
d/p ratio needed to obtain final dilution factor.
CLAS Preliminary
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pt-depenence of SIDIS proton A1
Signicant decrease of p A1 with increasing
pt! Can be explained in terms of broder kt
distributions for anti-aligned quarks compared to
quarks aligned with proton spin (blue curves).
CLAS Preliminary
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pt-depenence of SIDIS proton A1
IF we used very preliminary pt dependence of d/p
to correct dilution factor as shown on slide 19,
p lies almost on top of blue curve, and the
strange rise in the p- becomes less significant.
Essential to understand pt-dependence of
deuteron/proton for precision measurements using
polairzed NH3 target.
CLAS Preliminary
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pt-depenence of SIDIS proton g1/F1
dsp(p) 4du(x,pt)D(z,pt) dd(x,pt)D-(z,pt) dsp
(p-) 4du(x,pt)D-(z,pt) dd(x,pt)D(z,pt)
Another explanation for opposite slopes for p
and p- is that D-/D increases with pt (I.e.
unfavored fragmentation has a wider transverse
momentum dependence), as can be seen from
above. This effect magnified in g1 compared to
F1 due to dd negative while du positive
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In region where factorization tests hold, analyze
f depdendence of ALL, ALU, and AUL to learn about
orbital motion of quarks, polarized
fragmentation, and higher twist contributions.
CLAS 5.7 GeV PRELIMINARY
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Significant phi-dependence seen for proton p
sin(2f) in AUL of particular interest leading
twsit function Sensitive to L0 and L1
interference
sin(f) and sin(2f) in AUL
cos(f) in ALL
sin(f) in ALU
CLAS 5.7 GeV PRELIMINARY
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SSA measurements at CLAS
ep?epX
W2gt4 GeV2
CLAS PRELIMINARY
p1sinfp2sin2f
Q2gt1.1 GeV2
ylt0.85
0.4ltzlt0.7
MXgt1.4 GeV
PTlt1 GeV
0.12ltxlt0.48
p1 0.0590.010 p2-0.0410.010
p1-0.0420.015 p2-0.0520.016
p10.0820.018 p20.0120.019

• Significant SSA measured for pions with
  longitudinally polarized target
• Complete azimuthal coverage crucial separation
  of sinf, sin2f moments

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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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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
  analysis in progress.

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AULSSA PT-dependence
HT SSA significant for p and p 0
CLAS PRELIMINARY

• sinf SSA p increases with PT and is consistent
  with HERMES measurement.

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Future

• Full NLO, higher twist anlayses
• 20x more p, p -, 40x more p0 for g1/F1 at 6 GeV
  on proton (using CLAS)
• 3x more p and p- g1/F1 data on deuteron (Hall C)
• Jlab upgrade to 11 GeV electrons combined with
  major upgrade to CLAS will allow huge increase in
  kinematic coverage and statstical accuracy in
  SIDIS!

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Summary

• Factorization in SIDIS pion production seems to
  work for 0.3ltzlt0.7, Wgt2 GeV, Mxgt1.4 GeV,
  0.2ltxlt0.5, Q2gt1 GeV2.
• Opens opportunity for studies of transverse
  momentum in PDF, fragmentation
• Jlab upgrade will allow definitive measurements
  for xgt0.1
• Puzzling results for negative pions in both
  spin-average d/p, and proton g1/F1 versus pt.
  Could both be due to pt width of favored and
  unfavored fragmentation differing?

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In region where factorization tests hold, can use
data to constrain polarized PDFs in NLO
analysis(separate out polarized up, down valence
and sea quark parton distributions).
CLAS 5.7 GeV PRELIMINARY