Nonperturbative strong coupling at timelike momenta
Jan Horak (Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany); Jan M. Pawlowski (Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany, ExtreMe Matter Institute EMMI, GSI, Planckstr. 1, D-64291 Darmstadt, Germany); Jonas Turnwald (Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany); Julian M. Urban (Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA, The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA); Nicolas Wink (Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany); et al - Show all 6 authors
We compute the strong coupling constant of Landau gauge QCD in the full complex momentum plane, both directly and via spectral reconstruction. In particular, we consider the Taylor coupling given by the product of ghost and gluon dressing functions. Assuming spectral representations for the latter, we first show that also the coupling obeys such a representation. The subsequent spectral reconstruction of the coupling data, obtained from flavor lattice QCD results for the ghost and gluon, is based on a probabilistic inversion of this representation using Gaussian process regression with analytically enforced asymptotics. In contradistinction, our direct calculation relies on earlier reconstruction results for the ghost and gluon spectral functions themselves, as well as data obtained in functional QCD. Apart from its relevance for studies of resonances or scattering processes, the calculation also serves as a nontrivial benchmark of our reconstruction approach. The results show remarkable agreement, testifying to the reliability of the method.
