A Hypergeometric Resummation Algorithm for the resummation of Divergent series in Quantum field Theory

In Phys. Rev. D 96, 025015 (2017), we used the effective potential to discuss the PT-symmetric if³ field theory. In PRL 115, 143001 (2015), a new precise as well as simple resummation technique has been introduced. We modified that resummation algorithm in arXiv:1811.10998 to extrapolate its accuracy to strong couplings. As the hypergeometric resummation and the effective potential are both non-perturbative techniques, in this talk we stress how can the results of the effective potential can predict the strong coupling behavior of the PT-symmetric if³ field theory and thus predict exactly the first two parameters of the hypergeomtric function ₂F₁ used to resum the divergent series of the ground state energy. This resummation algorithm is thus very suitable to rsum divergent series in quantum field theory as it uses only the first two terms in the perturbation series to predict the other two parameters. Accordingly, the algorithm results in accurate results for the whole range of the coupling space and expected to be suitable for problems where higher orders loop calculations are time consuming like QCD.