Spin of the proton and orbital motion of quarks

1
Spin of the protonand orbital motionof quarks

• Petr Závada
• Inst. of Physics, Prague

Workshop on Nucleon Form FactorsFrascati, 12-14
October, 2005
2
Introduction

• Presented results are based on the covariant QPM,
  in which quarks are considered as quasifree
  fermions on mass shell. Intrinsic quark motion,
  reflecting orbital momenta, is consistently taken
  into account. for details see P.Z. Phys.Rev.D65,
  054040(2002) and D67, 014019(2003).
• Recently, this model was generalized to include
  the transversity distribution A.Efremov,
  O.Teryaev and P.Z., Phys.Rev.D70, 054018(2004).
• In this talk the obtained spin functions
  will be discussed
• Sum rules for g1,g2.
• Calculation of the spin functions, comparison
  with experimental data, discussion on G1.

3
Model

• Input

4

Spin structure functions

• Output

5
Sum rules

• Basis

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Sum rules
7
Sum rules
8
Valence quarks
9
Valence quarks
E155
Calculation - solid line, data - dashed line
(left) and circles (right)
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g1 - analysis

• Integrating g1 gives

massless quarks
static quarks

• so, it seems more motionless spin?
• How to understand it?

11
Angular momentum

• Forget structure functions for a moment
• Remember, that angular momentum consists of
  jls.
• In relativistic case l,s are not conserved
  separately, only j is conserved. So, we can have
  pure states of j (j2,jz) only, which are
  represented by relativistic spherical waves

12
j1/2
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Spin and orbital motion
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Spin and orbital motion
j1/2
j1/2
jls 1s/j1/3 QM 1) For p0gtm there must be
some orbital momentum! 2) For localized
particles, there must be p0gtm!
o r b i t a l m o m e n t u m
spin
spin
mltp0
mp0
15
Recent experimental data

• Contribution of sea quarks is compatible with
  zero HERMES Phys.Rev.Lett. 92, 012005 (2004)
  Phys.Rev. D71, 012003 (2005).
• Contribution of gluons is compatible with zero,
  but with rather big errors HERMES, SMC, COMPASS
• Phys.Rev.Lett. 84, 2584 (2000) Phys.Rev. D70,
  012002 (2004) hep-ex/0501056

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Support for dominant role of the orbital
momentum

• Models, e.g.
• Casu, Sehgal, Phys.Rev.D58, 2644 (1996).
• Wakamatsu, Watabe, Phys.Rev.D62, 054009 (2000).
• Jefferson Lab Hall A Collaboration
• Experimental analysis suggests significant
  presence of the orbital momentum
  Phys.Rev.Lett.92, 012004 (2004) Phys.Rev.C70,
  065207 (2004).

17
PAX experiment

• Polarized Drell-Yan process in this reaction is
  very effective for measuring the transversity,
  which can be extracted from the double spin
  asymmetry in µµ- pair. This was discussed in the
  previous papers
• Efremov, Goeke, Schweitzer, Eur.Phys.J. C35
  (2004), 207
• Anselmino, Barone, Drago, Nikolaev, Phys. Lett. B
  594 (2004) 97
• We do the same, but as an input we use the
  transversity, which is calculated in the model.
  

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Useful relations
Double spin asymmetry defined as
can be calculated from the transversity
distributions
where
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Results

• Our calculation based on the 1st way - level of
  quark interference only (solid line)
• Calculation based on the 2nd way- interference
  effects at parton-hadron transition included
  (dashed line)
• Calculation based on the quark-soliton model
  Efremov (dotted line)
• s45GeV2, Q24-5GeV2

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Results

• Our calculation based on the 1st way -
  level of quark interference only (solid line)
• Calculation based on 2nd way- interference
  effects at parton-hadron transition included
  (dashed line)
• Calculation based on the estimation by Anselmino
  (dotted line)
• s45GeV2, Q24GeV2

21
Statistical errors

• How many events one needs for discriminating
  among the curves?
• If
• then
• which means roughly
• So for one needs at
  least 104 events in given subsample (bin,
  interval).

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Summary

• Covariant version of QPM involving intrinsic
  (orbital) motion was studied.
• Model reproduces the well known sum rules for
  g1,g2 WW, ELT, BC.
• Spin function g1 depend on intrinsic orbital
  motion rather significantly, this motion
  generates orbital angular momentum, which can
  represent as much as 2/3 j.
• Calculated g1,g2 from qval are well compatible
  with the experimental data.