Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction
-
Upload
dana-sutton -
Category
Documents
-
view
44 -
download
0
description
Transcript of Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction
![Page 1: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/1.jpg)
INFQCD10
Coupled-Channels Partial-WaveAnalysis of Kaon Photoproduction
Olaf ScholtenKVI / Univ. of Groningen
The Netherlands
NFQCD10, Kyoto
![Page 2: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/2.jpg)
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
![Page 3: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/3.jpg)
INFQCD10
The K-matrix model
Full coupled channels in large model space
Non-perturbativeUnitaryGauge invariantCovariantCrossing symmetric
![Page 4: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/4.jpg)
INFQCD10
symmetry partial wave projected
![Page 5: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/5.jpg)
INFQCD10
Recently added: (Λ(1520)+K)
![Page 6: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/6.jpg)
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
![Page 7: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/7.jpg)
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)
![Page 8: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/8.jpg)
INFQCD10
(N+γ N+Φ) Coupled Channels II
Backward rise in differential cross sections
![Page 9: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/9.jpg)
INFQCD10
Photo-induced η production I
CB-ELSA data
R. SHYAM AND O. S., PHYS REV C 78, 065201 (2008)
![Page 10: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/10.jpg)
INFQCD10
Photo-induced η productionCB-ELSA data
R. SHYAM AND O. S., PHYS REV C 78, 065201 (2008)
![Page 11: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/11.jpg)
INFQCD10
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]
![Page 12: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/12.jpg)
INFQCD10
Effects coupled channels
gNS11 -> - gNS11
No -meson
A.Usov, O.S., PRC72,25205
Invariant mass [GeV]
σtot [μb]
![Page 13: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/13.jpg)
INFQCD10
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
![Page 14: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/14.jpg)
INFQCD10
Cross sections&
Recoil polarizations
Data: SAPHIR
4 different fits plotted with 1.8 < Χ2/df < 2.0
K -
K-
K-
![Page 15: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/15.jpg)
INFQCD10
Partial wave phase shifts
K - K- K-
![Page 16: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/16.jpg)
INFQCD10
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
![Page 17: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/17.jpg)
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
![Page 18: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/18.jpg)
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
![Page 19: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/19.jpg)
INFQCD10
Restore analyticity
‘Dressed K-matrix’ PRC64(2001)24005 Sergey Kondratyuk & O.S.
Off Shell
![Page 20: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/20.jpg)
INFQCD10
Results vertex functions
Bare form factor
Converged vertex function
N N
Soft vertex functions are generated through pion-loop correctionsNumerically very difficult
![Page 21: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/21.jpg)
INFQCD10
Cusp in Compton Amplitude
Cusp due to analyticity
Bare
Dressed
Data
![Page 22: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/22.jpg)
INFQCD10
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
![Page 23: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/23.jpg)
INFQCD10
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
![Page 24: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/24.jpg)
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
![Page 25: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/25.jpg)
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
![Page 26: Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction](https://reader038.fdocuments.us/reader038/viewer/2022102909/5681378d550346895d9f2960/html5/thumbnails/26.jpg)
INFQCD10
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