1 / 16

Amplitude analysis for three-hadron states: Historical perspective

Amplitude analysis for three-hadron states: Historical perspective. Ian Aitchison INT-JLab Workshop, UW Nov 9 2009. Outline. The isobar model and 3-h analyses in the 1970s….and more recently But the isobar model doesn’t satisfy unitarity

lori
Télécharger la présentation

Amplitude analysis for three-hadron states: Historical perspective

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Amplitude analysis for three-hadron states:Historical perspective Ian Aitchison INT-JLab Workshop, UW Nov 9 2009 INT-JLab Workshop

  2. Outline • The isobar model and 3-h analyses in the 1970s….and more recently • But the isobar model doesn’t satisfy unitarity • Simplest implementation (“K-matrix –like”) of unitarity relation is wrong • Need also analyticity 3-h dynamics • Qualitative features of corrections to IM • Conclusions (as of mid-1980s) INT-JLab Workshop

  3. Illinois group(production density matrix) • “Partial-wave analysis of the 3 decay of the A2”, G.Ascoli et al., Phys. Rev.Lett. 25 (1970) 962-5 • “Spin-parity analysis of the A3”, G.Ascoli et al., Phys. Rev. D7 (1973) 669-686 • “The reaction at 25 and 40 GeV/c”, Yu. M. Antipov et al., Nucl. Phys. B63 (1973) 141-52, and 153-74 [A1, A2 and A3] P(event) e A2 INT-JLab Workshop

  4. isobar model amplitude factorization INT-JLab Workshop

  5. SLAC-Berkeley(fit coherent amplitudes) • “Generalized isobar model formalism” D.J.Herndon et al., Phys.Rev.D11(1975)3165 • “Partial wave analysis of the reaction in the c.m. energy range 1300-2000MeV” D.J. Herndon et al., Phys. Rev. D11(1975) 3183-3213 • “Amplitude analysis of production at 7 GeV/c” M.Tabak et al., Fourth Int. Conf. Exp. Meson Spectroscopy, 1974 AIP Conf Proc 21 46-58 P(event) INT-JLab Workshop

  6. “Improved measurement of the CKM angle in decays with a Dalitz plot analysis of decays to and ” B.Aubert et al. (BaBar) Phys. Rev. D78 (2008) 034023 The weak phase leads to different and decay rates (direct CPV) and is observable when and decay to common final states. About 0.5M events in the Dalitz plot. And more recently…… INT-JLab Workshop

  7. Unitarity (1) Two-body elastic unitarity Partial wave amplitude where power series in For example INT-JLab Workshop

  8. Unitarity(2)Two two-body f.s.i’sUnitarity: (U) Isobar modelwhere are independent ofBut this does not satisfy (U)Instead, setThen(U) is a linear function of Notfactorized INT-JLab Workshop

  9. Integration in unitarity relation INT-JLab Workshop

  10. So develops an imaginary part for due to rescattering from the other channel(s)Implementation(1) “ -matrix” (eg Ascoli and Wyld, PR D12(1975) 43-58) SetSpurious singularities(IJRA&Golding, Phys.Lett. 59B(1975)288) INT-JLab Workshop

  11. Implementation(2) add analyticity dispersionrelation uncorrected isobar model two-bodydata known function adds upallrescatterings IJRA P. R. 137(1965)B1970, R.Pasquier and J.Y.Pasquier, P.R. 170(1968)1294, IJRA and J J Brehm, P. R. D17(1978)3072 Integral equations for INT-JLab Workshop

  12. Integration for integral equation INT-JLab Workshop

  13. is essentially the partial wave projection of the OPE 3 3 process and has logarithmic singularities on the boundary of the Dalitz plot, when all particles in the OPE graph are on-shell. Inside the Dalitz plot, develops an imaginary part. INT-JLab Workshop

  14. The rescattering corrections to the IM uncorrected IM rescattering corrections where depends on final state interactions independent of production parameters Symbolically, And so Amplitude first rescattering correction provides reasonable approx. for dependence of full solution significant dependence can be generated in full solution INT-JLab Workshop

  15. Qualitative features of calculations • S-waves is complex “scattering length” Effects of “Triangle” singularities IJRA & JJBrehm, PR D 20(1979)1131; JJB, PR D21(1980)718, D23(1981) 1194, D25(1982)149 All depend on and INT-JLab Workshop

  16. Conclusions (as of mid-1980s)The corrections to the IM are unlikely to be larger than of order 20% in magnitudeSubenergy corrections can broadly be absorbed into either the two-body parametrizations or the barrier factors, at fixed But (a) there is a - dependence J.J.Brehm, P.R. D25(1982) [ -dependent modulation of ]Study of the heavy-lepton decay“We can summarize by asserting that rescattering can be a 20%effect relative to the resonance and should be included if the data are refined to that level of accuracy.”(b) the corrections are final-state dependent (eg versus ) Corrections might be needed to reconcile two-body amplitudes derived from different final states if data good enough. INT-JLab Workshop

More Related