@misc{10481/57633,
year = {2018},
month = {10},
url = {http://hdl.handle.net/10481/57633},
abstract = {We carry out an analysis of ππ scattering in the
I J = 00, 11 and 20 channels in configuration space up to
a maximal center-of-mass energy
√
s = 1.4 GeV. We separate
the interaction into two regions marked by an elementarity
radius of the system; namely, a long distance region
above which pions can be assumed to interact as elementary
particles and a short distance region where many physical
effects cannot be disentangled. The long distance interaction
is described by chiral dynamics, where a two-pionexchange
potential is identified, computed and compared to
lattice calculations. The short distance piece corresponds to
a coarse grained description exemplified by a superposition
of delta-shell potentials sampling the interaction with the
minimal wavelength. We show how the so constructed nonperturbative
scattering amplitude complies with the proper
analytic structure, allowing for an explicit N/D type decomposition
in terms of the corresponding Jost functions and
fulfilling dispersion relations without subtractions. We also
address renormalization issues in coordinate space and investigate
the role of crossing when fitting the scattering amplitudes
above and below threshold to Roy-equation results. At
higher energies, we show how inelasticities can be described
by one single complex and energy dependent parameter. A
successful description of the data can be achieved with a
minimal number of fitting parameters, suggesting that coarse
graining is a viable approach to analyze hadronic processes.},
organization = {Work partially supported by Spanish MINEICO and European FEDER
funds (grants FIS2014-59386-P, FIS2017-85053-C2-1-P and FPA2015-
64041-C2-1-P), Junta de Andalucía (grant FQM-225) and the Swiss
National Science Foundation.},
publisher = {Springer Nature},
title = {Coarse graining ππ scattering},
doi = {10.1140/epjc/s10052-018-6342-7},
author = {Ruiz de Elvira, Jacobo and Ruiz Arriola, Enrique},
}