ICHEP04 talk

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Semi-Inclusive Deep Inelastic Scattering
The cross section can be expressed as a
convolution of a distribution function and a
fragmentation function.
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Distribution Functions
Leading Twist

• 3 distribution functions survive the integration
  over transverse quark momentum

unpolarized DF
Helicity DF
Transversity DF
Transversity basis
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Virtual Photon Asymmetry - Path to Dq

• Virtual photon can only couple to quarks of
  opposite helicity
• Select quark helicity by changing target
  polarization direction
• Different targets give sensitivity to different
  quark flavors

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Quark Polarizations
Correlation between detected hadron and the
struck quark allows flavor separation
Inclusive DIS ?DS Semi-inclusive ?
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The HERMES Experiment

• 27.5 GeV polarized positron beam (ltPgt53)
• Longitudinally polarized H
• (ltPgt85)
• Transversely polarized H (ltPgt78)

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The Measured Hadron Asymmetries
PROTON
DEUTERIUM
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Polarized Quark Densities

• Polarized parallel to the proton

• Polarized anti-parallel to the proton

• Good agreement with LO-QCD fit

• No indication for
• 0.028 0.033 0.009 Measured range

Submitted Phys.Rev.D
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Properties of the Transversity DFs

• For non-relativistic quarks dq(x)Dq(x)
• dq(x) probes the relativistic nature of the
  quarks
• Due to Angular Momentum Conservation
• Different QCD evolution
• No gluon component
• Predominately sensitive to valence quarks
• Bounds
• Soffer Bound
• T-even
• Chiral odd
• Not measurable in inclusive DIS

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Measuring Transversity

• Need a chiral odd fragmentation function
  Collins FF

• Transverse quark polarization affects transverse
  hadron momentum
• Observed asymmetry in azimuthal angle about
  lepton scattering plane

• Collins Effect
• Artru string fragmentation model
• String break produces quark- antiquark pair
• pair must preserve vacuum quantum numbers
• angular momentum conservation gives the produced
  hadron transverse momentum

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Sivers Function f1T(x)

• Distribution function
• Naïve T-ODD
• Chiral even
• a remnant of the quark transverse momentum can
  survive the photo-absorption and the
  fragmentation process
• Can be inherited in the transverse momentum
  component
• influence azimuthal distribution
• Non-vanishing Sivers function requires quark
  orbital angular momentum
• Cross section depends on the angle between the
  target spin direction and the hadron production
  plane

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How to Measure Transversity
Collins azimuthal moment
Sivers azimuthal moment
Assuming gaussian distributions for initial an
final quark momentum
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RESULTS
Collins
Collins Moment

• Unexpected result

Sivers

• Possible interpretation

• Same Size

Sivers Moment

• More theoretical input needed to clarify
  interpretation
• f1T(x) DIS - f1T(x) DY UNIVERSALITY

Submitted to Phys.Rev.Lett.
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Summary and Conclusions

• Longitudinally Polarized Target Data
• First direct measurement of the helicity
  distributions
• Transversely Polarized Target Data
• Collins Disfavored fragmentation functions
  appear to be important and have opposite sign to
  the favored
• Sivers Amplitude is greater than zero

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Polarized Sea

• QSM expectation Eur.Phys.J.C14,147(2000)
• Meson cloud model Phys.Rev.D68,074002(2003)

• Unpolarized data on sea shows the Gottfried sum
  rule is broken

• Data favor symmertic ,but large
  uncertainties

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Purities
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