Multichannel approach to studying scalar resonances

Parameters of scalar resonances from the combined analysis of data on processesππ→ππ,KK¯Surovtsev1, Bydžovský2, Kamiński3 et al. 2014Phys. Rev. D84110View full textAdd to dashboardCite

“…Sheets of the Riemann surface are numbered according to the signs of analytic continuations of the square roots √ s − s i as follows: Resonances are described on the Riemann surface using the formulas for analytic continuations of the S-matrix elements to all sheets. The formulas allow us to express the matrix elements on the unphysical sheets by means of the matrix elements on the physical sheet that have only the resonance zeros (aside the real axis), at least, around the physical region [2,11]. Assuming the resonance zeros on sheet I, we can obtain an arrangement of poles and zeros of the resonance on the whole Riemann surface which we denote as a resonance cluster.…”

“…It is also possible to distinguish, in a model-independent way [11,13], a bound state of colourless particles (e.g., KK molecule) from a qq bound state. Alike in the one-channel case, the existence of the particle bound state means presence of a pole on the real axis below the threshold on the physical sheet.…”

“…The formulas of the analytic continuations [2,11] prescribe that the resonance parameters (mass, total width, and coupling constants with the channels) must be calculated using the pole positions on sheets II, IV, and VIII because only on these sheets do the analytic continuations have the forms: ∝ 1/S I 11 , ∝ 1/S I 22 and ∝ 1/S I 33 , respectively, i.e., the positions of poles on these sheets are at the same points of the complex-energy plane as the resonance zeros on the physical sheet. The other pole positions are shifted due to the coupling of channels.…”

“…An optimal number of poles is the minimal number which guarantees a satisfactory description of the data and which contains only the poles significantly improving the fit. The poles are introduced according to the formulas for analytic continuations of the S-matrix elements to all sheets [2,11].…”

“…In this article, we describe the multichannel ππ scattering ( ππ → ππ, KK, ηη ) using the method based only on the first principles, analyticity and unitarity [11], which allows us to avoid any theoretical prejudice in extracting the resonance parameters. This we call "the model-independence" [2,6,12].…”