Wigner and husimi partonic distributions of the pion in a chiral quark model
Metadatos
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Jagiellonian Univ Press
Date
2023-08-18Referencia bibliográfica
Broniowski, W., & Arriola, E. R. (2023). Wigner and Husimi partonic distributions of the pion in a chiral quark model. arXiv preprint arXiv:2307.14167[DOI:10.5506/APhysPolB.54.7-A4]
Patrocinador
National Science Centre, Poland 2018/31/B/ST2/01022; Junta de Andalucia; MCIN/AEI FQM-225 PID2020-114767GBI00Résumé
Generalized transverse momentum distributions (GTMDs), the Wigner
and the Husimi distributions of quarks in the pion are evaluated in a chiral
quark model at the one-loop level. Analytic expressions are obtained for
GTMDs, allowing for a qualitative discussion of their features, whereas the
Wigner and the Husimi distributions are obtained with numerical integration
of simple formulas. We explain the features of the Wigner distributions,
in particular their non-positivity. In our model, the Husimi distributions,
which are interpreted as coarse-grained Wigner distributions, are
not mathematically positive-definite, but the magnitude of their negative
values is tiny and occurs at large transverse momenta and impact parameters.
Hence, as expected, coarse graining leads to better-behaved functions
from the point of view of the probabilistic interpretation.