CVC test in e eKK cross section and data on tKK0t decay

1
CVC test in ee-?KK cross section and data on
t-?K-K0?t decay
International Workshop on ee- collisions from
Phi to Psi

Konstantin Beloborodov Budker Institute of
Nuclear Physics Novosibirsk, Russia
Laboratori Nazionali di Frascati, Italy, 7 - 10
April 2008
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Outline

• Introduction
• Experimental data
• VDM, relations, parameters
• Fit results
• CVC test
• Conclusions

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Introduction

• What is a goal of this work?
• Do simultaneous fit of ee?KK and ee?KSKL
  cross sections in wide energy region
  (2E01.032.2 GeV)
• Test and improve cross section description, based
  on Vector Dominance Model.
• Measure parameters of vector mesons
• As a result of the fit, extract isovector and
  isoscalar parts of the amplitude
• Compare the isovector part of K-meson form factor
  and spectral function, obtained from t decay

4
Experimental data

• DM2 data was corrected by a factor of
  1/0.71.4
• Correction parameter for DM2 cross section data
  was free and was obtained about 1.420.16
• Similar situation in the ppp0 channel In the
  paper hep-ex/0201040 v2

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Theoretical framework Vector Dominance Model
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Parameters
, not used in total width fixed from
PDG free parameters g??pg??p16.8 GeV1
V MV and GV fixed from PDG f(1020) Mf and
Gf free parameters V, V MV and GV free
parameters within errors from PDG
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Relations
Leptonic widths
SU(2)
phases for charge and neutral channels are the
same
SU(3)
LWSU(3)
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Problems in the approximation of cross sections

• Parameters of vector meson excitations are known
  very approximately
• Energy dependence of total widths is not well
  known
• SU(3) relations are not precise (violation 20)
• Quark model ratios between leptonic widths are
  not exact
• Mixing between vector mesons exists
• Additional amplitude exists due to rescattering
  in the final states
• Experimental data above 1.4 GeV have low
  precision
• Technical problem there are many solutions
  (local minima), up to 2N-1 in case of N
  resonances.

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Data approximations variants
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Data approximation results
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Data approximation results
Variant 1
Variant 1
Variant 2
Variant 2
Variant 3
Variant 3
Variant 4
Variant 4
Variant 5
Variant 5
Variant 6
Variant 6
Variant 7
Variant 7
Variant 8
Variant 8
Variant 9
Variant 9
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Data approximation systematic error
Data SND ee?KK ? DM2
ee?KK ? SND ee?KSKL ? DM1 ee?KSKL
Systematic ?2?5
?8?9 ?6,?7
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Data approximation cross section
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Data approximation summary

• In the charged channel there is a dip in the
  cross section in the energy range 1.05-1.15 GeV,
  which can be explained by an addition to the
  amplitude due to rescattering in the final state
• Amplitudes of radial excitations of vector mesons
  have opposite sign with respect to the amplitudes
  of ?, ? and f vector mesons, as expected
• Presence of ? mesons in the description is
  necessary
• Presence of orbital excitations of vector mesons
  in the description is necessary
• Experimental data above 1.7 GeV are not well
  described it is evident from the data that there
  is an interference structure
• Phases ?V, deviate from 0, showing that more
  sophisticated model taking into account mixing
  between vector mesons and rescattering effects in
  final state should be used

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CVC comparison of ee-??,?',?"?KK and
t-?K-K0?t
Data CLEO t-?K-K0?t
Fit variants ?2?5
?8?9 ?6 ?7
Hep-ph/0409080 v2
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Conclusions

• Simultaneous fit of ee?KK and ee?KSKL
  cross sections was performed in the framework of
  vector dominance model in a wide energy range
  (2E01.012.2 GeV)
• The following results were obtained
• dip in the ee?KK experimental cross section
  in the energy range from 1.05 to 1.15 GeV
• phases of radial excitations of light vector
  mesons are close to prediction
• Gf'eeGf'KK/Gf2(0.370.08)106
• G?"eeG?"KK/G?2(0.40.7)107
• Range parameter R2.00.2 GeV1
• Isovector and isoscalar parts of the K-meson
  form factor were obtained
• Comparison of isovector contribution and
  experimental data on spectral function, obtained
  from t-?K-K0?t decay, was done
• More sophisticated VMD model, including mixing
  between vector mesons and amplitude corrections
  due to rescattering in final state, should be used