Quark propagator with complex-valued momentum from Schwinger-Dyson equation in the Euclidean space
arxiv(2024)
摘要
In the Euclidean-space formulation of integral equations for the structure of
quantum chromodynamics (QCD) bound states, the quark propagators with
complex-valued momentum are densely sampled. We therefore propose an accurate
and efficient algorithm to compute these propagators. The quark propagator both
on the spacelike real axis and at complex-valued momenta is determined from its
Schwinger-Dyson equation (SDE). We first apply an iterative solver to determine
the quark propagator on the spacelike real axis. The propagator at
complex-valued momenta is then computed from its self-energy based on this
solution, where demanding integrals are encountered. In order to compute of
these integrals, we apply customized variable transformations for the radial
integral after subtracting the asymptotics. We subsequently apply an optional
compound of quadrature rules for the angular integral. The contribution from
the asymptotics is added at the last step. The accuracy and the performance of
this algorithm for the quark propagator at complex-valued momentum are tested
in comparison with an adaptive quadrature.
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