Four-quark scatterings in QCD II
arxiv(2024)
摘要
In [1], we initiated a program for the quantitative investigation of
dynamical chiral symmetry breaking and resonant bound states in QCD with the
functional renormalisation group, concentrating on the full infrared dynamics
of four-quark scatterings. In the present work we extend this study and take
into account a three-momentum channel approximation (s,t,u-channel) for the
Fierz-complete four-quark vertices. We find that the four-quark vertex in this
approximation is quantitatively reliable. In particular, we have computed the
pion pole mass, pion decay constant, Bethe-Salpeter amplitudes, the quark mass
function and wave function. Our results confirm previous findings that low
energy effective theories only reproduce QCD quantitatively, if initiated with
a relatively low ultraviolet cutoff scale of the order of 500 MeV. The
quantitative description set up here paves the way for reliable quantitative
access to the resonance structure in QCD within the fRG approach to QCD.
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