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Unformatted text preview: – 1– NOTE ON SCALAR MESONS Revised April 2010 by C. Amsler (University of Zurich), T. Gutsche (University of T¨ubingen), S. Spanier (University of Tennessee) and N.A. T¨ornqvist (University of Helsinki). I. Introduction: The scalar mesons are especially important to understand because they have the same quantum numbers as the vacuum ( J P C = 0 ++ ). Therefore they can condense into the vacuum and break a symmetry such as a global chiral U ( N f ) × U ( N f ). The details of how this symmetry breaking is implemented in Nature is one of the most profound problems in particle physics. In contrast to the vector and tensor mesons, the identifi- cation of the scalar mesons is a long-standing puzzle. Scalar resonances are diﬃcult to resolve because of their large decay widths which cause a strong overlap between resonances and background, and also because several decay channels open up within a short mass interval. In addition, the K ¯ K and ηη thresholds produce sharp cusps in the energy dependence of the resonant amplitude. Furthermore, one expects non- q ¯ q scalar objects, like glueballs and multiquark states in the mass range below 1800 MeV. For some recent reviews see Ref. [1–4]. Scalars are produced, for example, in πN scattering on polarized/unpolarized targets, p ¯ p annihilation, central hadronic production, J/ Ψ, B-, D- and K-meson decays, γγ formation, and φ radiative decays. Experiments are accompanied by the development of theoretical models for the reaction amplitudes, which are based on common fundamental principles of two- body unitarity, analyticity, Lorentz invariance, and chiral- and ﬂavor-symmetry using different techniques ( K-matrix formal- ism, N/D-method, Dalitz Tuan ansatz, unitarized quark models with coupled channels, effective chiral field theories such as the linear sigma model, etc. ). Dynamics near the lowest two-body thresholds in some analyses is described by crossed channel ( t , u ) meson exchange or with an effective range parameterization instead of or in addition to resonant features in the s-channel, only. Furthermore, elastic S-wave scattering amplitudes involv- ing soft pions have zeros close to threshold [5–6], which may be shifted or removed in associated production processes. CITATION: K. Nakamura et al. (Particle Data Group), JPG 37 , 075021 (2010) (URL: http://pdg.lbl.gov) July 30, 2010 14:34 – 2– The mass and width of a resonance are found from the position of the nearest pole in the process amplitude ( T- matrix or S-matrix) at an unphysical sheet of the complex energy plane: ( E − i Γ / 2). It is important to note that only in the case of narrow well-separated resonances, far away from the opening of decay channels, does the naive Breit-Wigner parameterization (or K-matrix pole parameterization) agree with this pole position....
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This note was uploaded on 06/07/2011 for the course PHYS 4132 taught by Professor Kutter during the Spring '11 term at University of Florida.
- Spring '11