Comments on the σ and κ

• Published in: Physics letters. B Vol. 572; no. 1-2; pp. 1 - 7
• Main Author: Bugg, D.V
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16-10-2003
• Subjects: 13.25.Gv; 13.40.Hq; 14.40.Gx
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2003.07.078

Evidence for the σ pole has been reported in production processes such as D+→π+π−π+; likewise evidence for the κ pole appears in D+→K−π+π+. Their effects in ππ and Kπ elastic scattering are much less conspicuous. However, consistent fits to both production data and elastic scattering may be obtained by including the Adler zero into an s-dependent width for each resonance. These zeros suppress strongly the effects of the σ and κ poles in elastic scattering; the zeros are absent from amplitudes for production data. With this prescription, data from ππ→ππ, Ke4 decays and CP violation in K0 decays give a σ pole position of (525±40)−i(247±25) MeV. A combined analysis with production data gives a better determination of (533±25)−i(249±25) MeV. The analysis of LASS data for Kπ elastic scattering, including the Adler zero, determines a κ pole at (722±60)−i(386±50) MeV.
The Fourier transform of the matrix element for σ→ππ reveals a compact interaction region with RMS radius ∼0.4 fm.