2023/06/12 by R. Frezzotti, G. Gagliardi, Frezzotti, R. +9 · 2 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.2306.07228
openalex publication_date 2023/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present a novel method to determine on the lattice both the real and imaginary parts of complex electroweak amplitudes involving two external currents and a single hadron or the QCD vacuum in the external states. The method is based on the spectral representation of the relevant time-dependent correlation functions and, by extending the range of applicability of other recent proposals built on the same techniques, overcomes the difficulties related to the analytic continuation from Minkowskian to Euclidean time, arising when intermediate states with energies smaller than the external states contribute to the amplitude. In its simplest form, the method relies on the standard i ε prescription to regularize the Feynman integrals and at finite ε it requires to verify the condition 1/L ≪ ε ≪ Δ(E), where L is the spatial extent of the lattice and, for any given energy E, Δ(E) represents the typical size of the interval around E in which the hadronic amplitude is significantly varying. In order to illustrate the effectiveness of this approach in a realistic case, we apply the method to evaluate non-perturbatively the hadronic amplitude contributing to the radiative leptonic decay Ds →ℓν_ℓ γ^*, working for simplicity with a single lattice ensemble at fixed volume and lattice spacing.