Volume 317 - The 9th International workshop on Chiral Dynamics (CD2018) - Session: Goldstone-Boson Dynamics
E. Ruiz Arriola* and R.d.E. Jacobo
Full text: pdf
Published on: February 28, 2020
Abstract
We show that it makes sense to coarse grain hadronic
interactions such as $\pi\pi$ and $\pi N$ reactions following
previous work on NN scattering. Moreover, if the interaction is
taken to be given by chiral dynamics at long distances above a given
value $r > r_c$ larger than the elementary radii of the interaction
hadrons the unknown short distance region $r< r_c$ is charecterized
by a {\it finite} number of fitting parameters. This number of
independent parameters needed for a presumably complete description
of scattering data for a CM energy below $\sqrt{s}$ has been found
to be given by $N_{\rm Par} = N_S \times N_I \times (p r_c )^2 /2$
with $N_S$ and $N_I$ the number of spin and isospin channels, and
$p$ the CM momentum respectively. Therefore, for an experiment (or
sets of experiments) with a total number of data $N_{\rm Dat}$ the
number of degrees of freedom involved in a $\chi^2$-fit is given by
$\nu = N_{\rm Dat}-N_{\rm Par}$ and confidence levels can be
obtained accordingly by standard means. Namely a $1 \sigma$
confidence level corresponds to $\chi_{\rm min}^2/\nu \in (1- \sqrt{2/\nu},1+\sqrt{2/\nu})$. We discuss the approach for $\pi\pi$
and $\pi N$ with an eye put on a data selection program and the
eventual validation of chiral symmetry.
DOI: https://doi.org/10.22323/1.317.0082
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