The $Dπ$ form factors from analyticity and unitarity
B. Ananthanarayan, I. Caprini, I. Sentitemsu Imsong
备注：
6 pages, 4 figures; Seminar given at DAE-BRNS Workshop on Hadron Physics Bhabha Atomic Research Centre, Mumbai, India, October 31-November 4, 2011, submitted to Proceedings
发表信息：
Journal of Physics: Conference Series 374 (2012) 012013
We study the shape parameters of the $Dπ$ scalar and vector form factors using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including $O(α_s^2)$ terms in perturbative QCD. For the scalar form factor, a low energy theorem and phase information on the unitarity cut are implemented to further constrain the shape parameters. We finally determine points on the real axis and isolate regions in the complex energy plane where zeros of the form factors are excluded.
I try to describe the extremely fruitful interaction I had with Harry Lehmann and the results which came out of the analyticity unitarity programme, especially the proof of the Froissart bound, which, with recent and future measurements of total cross-sections and real parts, remains topical.
We show how the combination of analyticity properties derived from local field theory and the unitarity condition (in particular positivity) leads to non-trivial physical results, including the proof of the "Froissart bound" from first principles and the existence of absolute bounds on the pion-pion scattering amplitude.
The experimental data on the processes $ππ\toππ,K\bar{K},ηη,ηη^\prime$ in the $I^GJ^{PC}=0^+0^{++}$ channel have been jointly analyzed to study the status and nature of the $f_0$. The method of analysis is based on analyticity and unitarity and uses an uniformization procedure. Some spectroscopic implications from results of the analysis are discussed.
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These notes are a fuller version of four lectures given at the 2015 International Summer Workshop in Reaction Theory held at Indiana University, Bloomington. The aim is to provide a simple introduction to how the tools of "the S-matrix era" - i.e. the constraints of unitarity, analyticity and crossing symmetry - can be incorporated into analyses of final state interactions in two- and three-hadron systems. The main focus is on corrections to the isobar model in three-hadron final states, which may be relevant once more as much larger data sets become available.
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