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| Flatté parametrization | |
|---|---|
| Name | Flatté parametrization |
| Introduced | 1976 |
| Introduced by | S. M. Flatté |
| Used in | Particle physics, Scattering theory, Resonance analysis |
| Typical decay channels | K\bar{K}, \pi\pi, \eta\pi |
Flatté parametrization The Flatté parametrization is a model for describing near-threshold resonant line shapes in hadronic scattering and decay processes. It provides an amplitude form that incorporates coupled-channel effects and threshold singularities, enabling fits to data from facilities and collaborations such as CERN, Brookhaven National Laboratory, SLAC National Accelerator Laboratory, KEK, and DESY. The parametrization is widely used in analyses by experiments including LHCb, Belle, BaBar, BESIII, and CMD-3.
The Flatté parametrization was introduced to model resonances that overlap with thresholds for two-body channels, a situation encountered in studies of mesons like the a0(980), f0(980), and exotic candidates studied by Crystal Barrel (experiment), WA102, and E852. It modifies the Breit–Wigner resonance description used in analyses at LEP, Tevatron, and other facilities to account for coupled-channel dynamics relevant to experiments run by collaborations such as CMS, ATLAS, ALICE, and CDF.
The theoretical motivation draws on elements of S-matrix theory, unitarity, and analyticity employed in frameworks developed by researchers at institutions like Princeton University, Institute for Advanced Study, MIT, and Caltech. It complements effective field theory approaches used in work by groups at Harvard University, Stanford University, University of Cambridge, and University of Oxford. The model treats resonances as poles in the complex energy plane influenced by coupled channels explored in studies at Jefferson Lab, TRIUMF, and RIKEN.
Flatté's form replaces a simple Breit–Wigner denominator with one that includes channel-dependent, energy-dependent widths used in amplitude analyses by collaborations such as NA48/2 and KLOE. The amplitude A(s) is parameterized with real parameters related to a pole mass and coupling constants akin to treatments in publications from Physical Review Letters, Physics Letters B, and Nuclear Physics B. The formula encodes channel thresholds that appear in data sets from MINOS (experiment), OPAL, and ALEPH, and it is implemented in partial-wave analyses employed by SAID (analysis program), PWA (partial wave analysis), and groups at George Washington University.
The Flatté parametrization is applied in studies of scalar mesons in analyses from Belle II, GlueX, COMPASS, and legacy experiments like MARK II (detector). It is crucial in extracting resonance parameters for states that couple to K\bar{K}], ππ and ηπ channels, informing spectroscopy programs at IHEP, GSI Helmholtzzentrum, and J-PARC. Results feed into global amplitude analyses compiled by working groups at Particle Data Group and influence theoretical models from CERN Theory groups and university research centers such as Yale University and University of Tokyo.
Determinations of Flatté parameters arise from fits to invariant mass distributions measured by detectors including LHCb, Belle, BaBar, BESIII, CLEO, and fixed-target experiments like E791. Analyses often combine data sets from accelerator complexes such as RHIC, KEKB, and BEPCII and are reported in journals like Journal of High Energy Physics, European Physical Journal C, and Reviews of Modern Physics. Global fits incorporate systematic studies from collaborations including PDG, Heavy Flavor Averaging Group, and multinational consortia based at institutions such as CERN and Brookhaven.
Limitations of the Flatté parametrization are recognized in contexts requiring full coupled-channel unitary treatments developed in approaches by groups at Jefferson Lab, Institute for Nuclear Theory, Perimeter Institute, and SISSA. Extensions include multichannel K-matrix formalisms used by analyses at COMPASS, dispersive methods developed by theorists at IPPP, and effective field theory generalizations from research teams at University of California, Berkeley and Caltech. Alternative parameterizations employed by collaborations such as Belle II and LHCb may incorporate Blatt–Weisskopf barrier factors and channel-dependent form factors studied at SLAC and DESY.
The parametrization was proposed in 1976 by S. M. Flatté in the context of meson spectroscopy discussed at conferences organized by CERN, ICHEP, and EPS (European Physical Society). Subsequent adoption and refinement occurred through work by experimental groups at CERN ISR, theoretical contributions from researchers at Princeton, and phenomenological analyses published by teams at Moscow State University, Hamburg University, and University of Milan. Its continued relevance is reflected in analyses presented at workshops hosted by IHEP, JINR, KEK, and iterative updates summarized by the Particle Data Group.