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: 7(095)129-96-29, Fax: 7(095)883-96-01, E-mail : Dmitry.Svirida@itep.ru

Yu.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.

Dima Svirida (ITEP)

Light baryon resonances in the latest PDG are based mainlyon PWA’s 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.

Preface

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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.

Spin rotation parameter A at 1.43 GeV/c

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CM CM

Situation in +p is similar to 1.43 GeV/c, while in p the dataonly suggests slight continuous change to all PWAs

Spin rotation parameter A at 1.62 GeV/c

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CM CM

In +p the disagreement with KH80 is only essential, while in p the strong contradiction to CMB80 and SM90 is seen.

Spin rotation parameter A at 1.00 GeV/c

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CM CM

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

Transverse Amplitudes

ihgfihgfnihgM ,,

1

sinImcosRe

cosImsinRe

222

**

**

22

22

RAP

ffffR

ffffA

ffP

ff

labcmlabcm

labcmlabcm

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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

Transverse Amplitude Zeroes

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PBEAM

w-plane

CM

f +

f

A transformation of any zero of the form wi1/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.

Barellet Conjugation

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KH80Original

KH80reflected

VPI/GWU

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

fSPPPPcgPRPcbag

gPSPPPcfRPPcbafB

B

111

111

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

PWA Correction

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CM CM

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 widthR= EL/ 2 resonance circle radius on Argand plot pole residue phaseB background parameters

Pole parameters for all 7 -isobars in the second resonance region were determined

Resonance Parameter Fit

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2

11

1

112

2var 2/

)()8(

1

N

jl

j

i

jN

N fEiM

eREEEEBBB

N

2

12

2

2/)6(1

N

jl

j

i

const fEiM

eRBN

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

****F37(1950)

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CMB80 KH80

Though seen in many decay modes, the resonance is notstrongly pronounced in the elastic channel. The elasticity decreases after correction.

****P31(1910)

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CMB80 KH80

The elasticity sufficiently decreases after correction, yet doesn’t become vanishing. Strange that VPI/GWU group doesn’t see it as in their solutions the resonant behavior is well pronounced and was successfully fit by our technique.

***P33(1920)

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CMB80 KH80

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.

***S31(1900) **

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CMB80 KH80

The only evidence of *D33(1940) comes from the elastic channelin CMB80 analysis. After correction the behaviour of this partial wave becomes completely nonresonant.

*D33(1940) 0 ?

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CMB80 KH80

Acknowledgements

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

***D35(1930)

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CMB80 KH80