scholarly journals NEW DISPERSION RELATIONS IN THE DESCRIPTION OF ππ SCATTERING AMPLITUDES

2009 ◽  
Vol 24 (02n03) ◽  
pp. 402-409 ◽  
Author(s):  
R. KAMIŃSKI ◽  
R. GARCIA-MARTIN ◽  
P. GRYNKIEWICZ ◽  
J. R. PELAEZ ◽  
F. YNDURAIN
Keyword(s):  
Scattering Amplitudes ◽  
Partial Wave ◽  
Dispersion Relations ◽  
Crossing Symmetry ◽  
Stringent Test

We present a set of once subtracted dispersion relations which implement crossing symmetry conditions for the ππ scattering amplitudes below 1 GeV. We compare and discuss the results obtained for the once and twice subtracted dispersion relations, known as Roy's equations, for three ππ partial JI waves, S0, P and S2. We also show that once subtracted dispersion relations provide a stringent test of crossing and analyticity for ππ partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where the resulting uncertainties are significantly smaller than those coming from standard Roy's equations, given the same input.

Dispersion Relations for Three-Particle Scattering Amplitudes. I

1966 ◽  
Vol 146 (4) ◽  
pp. 1130-1149 ◽  
Author(s):  
Morton Rubin ◽  
Robert Sugar ◽  
George Tiktopoulos
Keyword(s):  
Scattering Amplitudes ◽  
Dispersion Relations ◽  
Particle Scattering

scholarly journals Global parameterization of $$\pi \pi $$ scattering up to 2 $${\mathrm {\,GeV}}$$

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
J. R. Pelaez ◽  
A. Rodas ◽  
J. Ruiz de Elvira
Keyword(s):  
Experimental Data ◽  
Partial Wave ◽  
Real Axis ◽  
Complex Plane ◽  
Dispersion Relations ◽  
The Real ◽  
Partial Waves

AbstractWe provide global parameterizations of $$\pi \pi \rightarrow \pi \pi $$ππ→ππ scattering S0 and P partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of $$\pi \pi \rightarrow \pi \pi $$ππ→ππ, both in the real axis up to 1.12 $${\mathrm {\,GeV}}$$GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 $${\mathrm {\,GeV}}$$GeV. Above that energy we just describe the available experimental data. Moreover, the analytic continuations of these global parameterizations also describe accurately the dispersive determinations of the $$\sigma /f_0(500)$$σ/f0(500), $$f_0(980)$$f0(980) and $$\rho (770)$$ρ(770) pole parameters.

DIFFERENTIAL OPERATORS FOR SCATTERING AMPLITUDES

2007 ◽  
Vol 16 (09) ◽  
pp. 2910-2914
Author(s):  
MÁRCIO JOSÉ MENON ◽  
REGINA FONSECA ÁVILA
Keyword(s):  
Elastic Scattering ◽  
Scattering Amplitudes ◽  
Cross Section ◽  
Differential Form ◽  
Differential Operators ◽  
Dispersion Relations ◽  
Proton Scattering ◽  
Cross Section Data ◽  
Proton Proton ◽  
Section Data

We discuss novel dispersion relations in differential form, connecting real and imaginary parts of elastic scattering amplitudes and formally valid at any energy above the physical threshold. By means of fits to total cross section data from proton-proton and antiproton-proton scattering, we evaluate the corresponding ratio ρ between the real and imaginary parts of the forward amplitudes. We show that the results are exactly the same as those obtained through standard integral dispersion relations.

Sign in / Sign up

Export Citation Format

Share Document