ITEP-PNPI Spin Rotation Parameters Measurements and Their Influence on Partial Wave Analyses. I.G. Alekseev, P.E. Budkovsky, V.P. Kanavets, L.I. Koroleva, B.V. Morozov, V.M. Nesterov, V.V. Ryltsov, D.N. Svirida, A.D. Sulimov, V.V. Zhurkin. Institute

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ITEP-PNPI Spin Rotation Parameters Measurements
and Their Influence on Partial Wave
Analyses.I.G. Alekseev, P.E. Budkovsky, V.P.
Kanavets, L.I. Koroleva, B.V. Morozov, V.M.
Nesterov, V.V. Ryltsov, D.N. Svirida, A.D.
Sulimov, V.V. Zhurkin.Institute for Theoretical
and Experimental Physics, B. Cheremushkinskaya
25, Moscow, 117218, Russia.Tel [phone],
Fax [phone], E-mail Dmitry.Svirida_at_itep
.ruYu.A. Beloglazov, A.I. Kovalev, S.P.
Kruglov, D.V. Novinsky, V.A. Shchedrov, V.V.
Sumachev, V.Yu. Trautman. Petersburg Nuclear
Physics Institute, Gatchina, Leningrad district,
188350, Russia.N.A. Bazhanov, E.I. Bunyatova
Joint Institute for Nuclear Research, Dubna,
Moscow district, 141980, Russia.
DUBNA-SPIN-03
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Preface
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• Light baryon resonances in the latest PDG are
  based mainlyon PWAs KH80 and CMB80, both
  performed more than two decades ago. More recent
  analyses by VPI/GWU group did not reveal
  D13(1700), S31(1900), P33(1920), D33(1940) in the
  resonance cluster at ?s 1.9 GeV/c2
• Latest A parameter measurement by ITEP-PNPI
  collaboration are in strong disagreement with
  either one of KH80 and CMB80 or both.
• The method of the transverse amplitude zero
  trajectories was applied to analyze the
  situation.
• The disagreements in most cases can be
  attributed to DISCREET AMBIGUITIES of Barellet
  type.
• Such ambiguities lead to COMPLETE INTERMIXING OF
  PARTIAL WAVES, which is extremely dangerous when
  analyzing resonance clusters.
• Correction to KH80 and CMB80 was introduced in a
  certain energy region, mainly affecting the
  resonance cluster at ?s 1.9 GeV/c2 .
• Fitting procedure was applied to the partial
  waves after correction to obtain resonance
  parameters.

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Spin rotation parameter A at 1.43 GeV/c
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Results agree well with FA02 and earlier versions
of GWU-VPIsolutions, and are in strong
contradiction to both KH80 and CMB80.
?CM
?CM
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Spin rotation parameter A at 1.62 GeV/c
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Situation in ?p is similar to 1.43 GeV/c, while
in ??p the dataonly suggests slight continuous
change to all PWAs
?CM
?CM
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Spin rotation parameter A at 1.00 GeV/c
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In ?p the disagreement with KH80 is only
essential, while in? ?p the strong contradiction
to CMB80 and SM90 is seen.
?CM
?CM
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Transverse Amplitudes
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• Transverse amplitudes f , f ? are the most
  suitable for the analysis
• Simple relation to the Pauli g and h amplitudes
  from scattering matrix
• Expression for observables ? ? differential
  crossection,
• P ? normal polarization,
• A, R ? spin rotation parameters.
• ? P ? ABSOLUTE VALUES of transverse
  amplitudes ONLY
• A (or R) ? RELATIVE PHASE of transverse
  amplitudes
• Conclusion older PWA do not correctly
  reconstruct the relative phase of the transverse
  amplitudes

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Transverse Amplitude Zeroes
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• Transverse amplitudes f (?), f ?(?) have
  finite number of complex zeroes, if Pauli
  amplitudes are represented as a finite sum of
  partial waves. Positions of these zeroes as
  functions of beam energy form trajectories in the
  complex plane of the angular variable w ei? .
  The unit circle is the physics region (at real ?
  the module of w is 1).
• Trajectories, close to the physics region
  determine the behaviour of the observables in
  corresponding kinematic ranges

PBEAM
f
?CM
f ?
w-plane
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Barellet Conjugation
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• A transformation of any zero of the form
  wi?1/wi changes only the relative phase of the
  transverse amplitude, not changing the values of
  differential cossection and asymmetry while
  affecting A and R.
• In the w-plane such transformation is equivalent
  to mirroring of a trajectory across the unit
  circle ? crossing points are critical for
  branching of PWA solutions.

• A correction is possible to a solution, provided
  the trajectory position relative to the unit
  circle is known from spin rotation parameter
  data.
• Important property of the Barellet conjugation
  ALL PARTIAL WAVES ARE LINEAR COMBINATIONS OF
  EACH OTHER
• a, b, c ? coefficients and R, S matrices, built
  from wj values
• P, P? ? matrices, built from Legandre polynomial
  coefficients

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PWA Correction
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In ? p such correction leads to the perfect
agreement of CMB80and KH80 with the A data and
VPI/GWU solutions in a wide energy range
?CM
?CM
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Resonance Parameter Fit
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• In order to make estimates of the influence of
  such correctionon the resonance pole parameters
  in the cluster near 1.9 GeV/c2, the partial waves
  were fit with using the Breight-Wigner function
  with constatnt or linearly varying background
• M ? resonance mass
• ? ? full width
• R ?EL/ 2? ? resonance circle radius on Argand
  plot
• ? ? pole residue phase
• B ? background parameters
• Pole parameters for all 7 ?-isobars in the
  second resonance region were determined

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F37(1950)
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• Elasticity of strong resonances grow, partial
  waves and resonanceparameters become closer to
  those from VPI/GWU solutions.
• Similar picture with F35(1905)

CMB80
KH80
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P31(1910)
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Though seen in many decay modes, the resonance is
notstrongly pronounced in the elastic channel.
The elasticity decreases after correction.
CMB80
KH80
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P33(1920)
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The elasticity sufficiently decreases after
correction, yet doesnt become vanishing.
Strange that VPI/GWU group doesnt see it as in
their solutions the resonant behavior is well
pronounced and was successfully fit by our
technique.
CMB80
KH80
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S31(1900) ?
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In all VPI/GWU solutions there is no resonant
behaviour, yetin both classic analyses the
correction does not kill the resonance
completely, though the elasticity becomes
comparable with 0.
CMB80
KH80
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D33(1940) ? 0 ?
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The only evidence of D33(1940) comes from the
elastic channelin CMB80 analysis. After
correction the behaviour of this partial wave
becomes completely nonresonant.
CMB80
KH80
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Acknowledgements
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• Our thanks to Professor G.Hoehler for very
  interesting and fruitful discussion on partial
  wave analysis procedures and perspectives.
• We are grateful to the ITEP accelerator team and
  cryogenic laboratory for creating excellent
  conditions for our experiments on measurements
  of polarization parameters.
• This work was partially supported by the Russian
  Fund for Basic Research grant 99-02-16635 and
  Russian State Scientific Program "Fundamental
  Nuclear Physics".
• GREAT THANKS to the organizers of this very
  interesting conference ! ! !

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F35(1905)
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CMB80
KH80
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D35(1930)
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CMB80
KH80
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