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Subthreshold parameters of $ππ$ scattering revisited

Marián Kolesár, Jaroslav Říha

Abstract

Using a variety of experimental results and lattice QCD calculations of $ππ$ scattering lengths, while employing dispersive representations of the amplitude based on Roy equations, we compute the subthreshold parameters of this process. We use Monte Carlo sampling to numerically model the probability distribution of the results based on all uncertainties in the inputs. We also investigate the dependence of the results on a theoretical correlation between the $ππ$ scattering lengths $a^0_0$ and $a^2_0$, which was previously established in the framework of two-flavor chiral perturbation theory.

Subthreshold parameters of $ππ$ scattering revisited

Abstract

Using a variety of experimental results and lattice QCD calculations of scattering lengths, while employing dispersive representations of the amplitude based on Roy equations, we compute the subthreshold parameters of this process. We use Monte Carlo sampling to numerically model the probability distribution of the results based on all uncertainties in the inputs. We also investigate the dependence of the results on a theoretical correlation between the scattering lengths and , which was previously established in the framework of two-flavor chiral perturbation theory.

Paper Structure

This paper contains 10 sections, 51 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. $\pi\pi$ scattering amplitude
  3. Extraction of subthreshold parameters from scattering lengths
  4. Data on $\pi\pi$ scattering lengths
  5. Results
  6. Summary
  7. Unitarity corrections $\overline{K}(s|t,u)$
  8. Solutions of Roy equations
  9. $\overline{b}_{i}$ representation
  10. Relations between amplitude representations

Figures (2)

  • Figure 1: Illustration of reconstructed phase shifts and imaginary parts of the partial-wave amplitudes at $a_{0}^{0}=0.2196$, $a_{0}^{2}=-0.0444$, using the ACGL solution ACGL. Blue -- $t_0^0$, orange -- $t_1^1$, green -- $t_0^2$.
  • Figure 2: Moment $\overline{I}_0^1$: comparison of our numerical integration and CGL'sCGL quadratic interpolation as a function of the scattering lengths.