INFQCD10

Coupled-Channels Partial-WaveAnalysis of Kaon Photoproduction

Olaf ScholtenKVI / Univ. of Groningen

The Netherlands

NFQCD10, Kyoto

INFQCD10

Overview

Virtues of K-matrix model Importance of coupled channels effectsReproducing the data

– Determine Structure resonances

•Coupling to various decay branches•Input to QCD modeling

Outlook, dynamic generation resonances

Motivation: obtain a description of scattering data at moderate energies and have a dynamic description of some resonances

INFQCD10

The K-matrix model

Full coupled channels in large model space

Non-perturbativeUnitaryGauge invariantCovariantCrossing symmetric

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symmetry partial wave projected

INFQCD10

Recently added: (Λ(1520)+K)

INFQCD10

Photo-induced Φ-meson production

Tree-level calculation:

monotonically rising cross section

Data has structure

Resonance? probably not

S. Ozaki et al, PRC80(2009)035201

INFQCD10

(N+γ N+Φ) Coupled Channels I

Resonance in (K+Λ(1520) N+Φ) as pure hidden strangeness ½- resonance

> No direct coupling to entrance channel> Large interference effects

S. Ozaki, A. Hosaka, and O. S., Phys. Rev. C 80, 035201 (2009)

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(N+γ N+Φ) Coupled Channels II

Backward rise in differential cross sections

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Photo-induced η production I

CB-ELSA data

R. SHYAM AND O. S., PHYS REV C 78, 065201 (2008)

INFQCD10

Photo-induced η productionCB-ELSA data

R. SHYAM AND O. S., PHYS REV C 78, 065201 (2008)

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Photo-induced K+Λ & K+Σ

Decomposition of cross section in to resonance

contributions

Big difference between the two

R. Shyam, O. S., H. Lenske, arXiv:0911.3351 [hep-ph]

INFQCD10

Effects coupled channels

gNS11 -> - gNS11

No -meson

A.Usov, O.S., PRC72,25205

Invariant mass [GeV]

σtot [μb]

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Chi-square fitting in K-matrix

pion & photon sector fixedvary only ‘strange’ parameters

– How unique is fit?

Alexander Usov

Dave Iereland

> 3 fits with similar chi-square

Note:

Highly non-linear

~30 parameters

Observables at many energies

many iterations code optimization

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Cross sections&

Recoil polarizations

Data: SAPHIR

4 different fits plotted with 1.8 < Χ2/df < 2.0

K -

K-

K-

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Partial wave phase shifts

K - K- K-

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Summary

Coupled channels effects are large– Lambda photo-production – phi-meson photo-production

Good reproduction of data can be obtained in effective-Lagrangian approach, however partial wave decomposition is ambiguous– need complete set of polarization

observables– may help to implement causality in theory

• relate Real & Imaginary parts phase shifts•dynamic generation resonances

INFQCD10

Need to implement:

Driving terms consistent with chiral symmetry Low energy theorems

crossing symmetryUnitarity; consistency imaginary part

scattering amplitudenon perturbative at high energies

Causality=analyticity; consistency Real & Imaginary parts

amplitude –Self energies (molecular resonances)–Vertex correctionsDifferent aproaches:

•Dressed K-matrix•Renormalized loop corrections

INFQCD10

PRC64(2001)24005 Sergey Kondratyuk & O.S.

Non perturbative, Keeping Unitarity, Crossing

“Dressed K-matrix”

Use ‘Dressed’ - 3-point vertex - propagators

Crossing symm.Dressed From dispersion relation

From dispersion relationFrom K-matrix

INFQCD10

Restore analyticity

‘Dressed K-matrix’ PRC64(2001)24005 Sergey Kondratyuk & O.S.

Off Shell

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Results vertex functions

Bare form factor

Converged vertex function

N N

Soft vertex functions are generated through pion-loop correctionsNumerically very difficult

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Cusp in Compton Amplitude

Cusp due to analyticity

Bare

Dressed

Data

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Nucleon Polarizabilities

Proton NeutronModel data Model data

12.1 11.9±0.6 12.7 12.5±1.7

2.4 1.9±0.6 1.8 2.7±1.8

S. Kondratyuk & OS, PRC 64 (2001) 24005

Gellas, et al., Phys. Lett. 85, 14

Hemmert, et al.,PRD. 57, 5746

Full Bare

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Renormalized loops

Renormalization:– Pole position and residue

positive and negative E poleGuarantees correct value and derivative amplitude

at threshold

Aim: compare 2 approaches;

- Dyson loop

- Renormalized Analytic K-matrix

O.S, S. Tamenaga, H. Toki

PRC 75, 055203

S-type diagrams, only loop corrections:

Self-energy in Dyson approach

INFQCD10

Analytic K-matrix

Normal K-Matrix includes open channels only– Below 140 MeV: (+N)– Above : (+N) and (+N)

Discontinuous breaking analyticity

Analytic continuation K-matrix– Analytic continuation of momentum below thr.– Renormalize value and derivative at threshold

Finite renormalization constants

INFQCD10

Loop corrections through Dyson equation or Analytic continuation

Simple at s-level diagrams; problem: crossing is violated

with Setsuo Tamenaga and Hiroshi Toki

PRC75(2007) 55203

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Summary

Good progress in implementing unitaritycrossingcausality

However,

we are not there yet!

Motivation: obtain a description of scattering data and have a dynamic description of some resonances