Quarkonium polarization with PHP data

1
QWG 07 _at_ DESY 16/10/07
Quarkonium polarization with PHP data A.
Bertolin

• Outlook
• (inelastic) quarkonium at HERA
• cross section measurements in PHP
• (new) polarization measurements in PHP
• conclusions and future prospects

2

• (inelastic) quarkonium at HERA

J/y

• PHP Û low Q2 Û electron escape undetected
• inelastic Û accompanying final state hadrons

3
z E(J/y) / E(g) p rest frame

• (inelastic) quarkonium at HERA

direct g, CS model 0.2 lt z lt 0.9
resolved g, CS model z lt 0.2

• direct g, CO model
• this particular diagram
• 0.2 lt z lt 0.9
• more typical ones
• z gt 0.9

diffractive contributions suppressed by cuts
on the main kinematic quantities
4

• cross section measurements in PHP

• no strong conclusion because of the large
  normalization uncertainties of the theoretical
  predictions

5

• polarization measurements (helicity parameters)

• study of the polar and azimuthal decay angular
  distribution of J/y mesons
• in general the m decay angular distribution in
  the J/? rest frame is parameterized as
• (M. Beneke, M. Kramer and M. Vanttinen, Phys.
  Rev. D 57, 4258 (1998))
• d2s/dWdy µ 1 ?(y) cos2 ? µ(y) sin 2? cos f
  ½ ?(y) sin2 ? cos 2f
• where y stands for a set of variables (z and
  pt(J/y) are good candidates)
• ?, µ, ? are related to the different color-octet
  matrix elements involved
• ?, µ, ? also depend on the definition of a
  coordinate system

main advantage Since the decay angular
distribution parameters are normalized, the
dependence on parameters that affect the absolute
normalization of cross sections, such as mc, as,
mR, mF and parton distribution, cancels to a
large extent and does not constitute a
significant uncertainty Þ main source of
theoretical uncertainties gone
main disadvantage for every y bin we have to fit
a distribution Þ unlikely requires large
statistics
6

• polarization measurements (helicity parameters)

• integrate the helicity master formula
• in f
• 1/s d2s/dcos ? dy µ 1 ?(y) cos2 ?
• in cos ?
• 1/s d2s/dcos ? dy µ 1 1/3 ?(y) 1/3 ?(y) cos
  2f
• which frame ? frame accessible experimentally
  using PHP events target frame
• z axis (quantization axis) along the opposite
  of the incoming proton direction in the J/y rest
  frame
• x and y axis chosen to complete a right-handed
  coordinate system in the J/y rest frame according
  to some conventions we were given by the
  theorists
• different helicity of the lepton beam does not
  matter as long as the proton beam is unpolarized
  (always true at HERA)
• q angle between the m vector in the J/y rest
  frame and the z axis
• f azimuthal angle in the x-y plane of the m
  vector in the J/y rest frame

7

• polarization measurements (helicity parameters)

• data NOT corrected for
• B J/y ( m m- ) anything
• very small contribution at HERA
• y(2S) J/y ( m m- ) anything

s(2S)/ s(1S) 0.33 0.10 (stat.) 0.01 0.02
(sys.) BR(2S 1S anything) (55.7 2.6)
PDG y(2S) J/y anything / J/y 15 dilute
the polarization
38 pb-1 lt 1/10 of what we have now

• experimentally it is very difficult to perform
  reliably these corrections

8

• (new) polarization measurements in PHP

• 0.4 lt z lt 1
• high pT region difficult to access at HERA

9

• (new) polarization measurements in PHP

• pT gt 1 GeV
• l good agreement between data and (degenerous)
  theory
• n do not see the positive values expected in
  the CS model

10

• conclusions

• the ZEUS helicity measurement has been updated
  with all the HERA available stat.
• n seems to be the more interesting parameter in
  order to access the size of the color octet
  matrix elements at HERA
• hopefully this measurement will be converted
  soon to a journal paper may try to improve the
  sys. with some more work
• ZEUS helicity data are compared to a LO
  prediction can the theory be improved in this
  respect ?
• can we have predictions also in the kt approach
  ?
• later on we plan a paper on J/y differential
  cross sections (PHP and DIS)