Variations on the Maiani-Testa approach and the inverse problem

Journal of High Energy Physics

M. T. Hansen¹  M. Bruno² 

[1] Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, EH9 3FD, Edinburgh, U.K.;Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland;

关键词: Lattice QCD;    Lattice Quantum Field Theory;    Scattering Amplitudes;   

DOI  :  10.1007/JHEP06(2021)043

来源: Springer

【 摘 要 】

We discuss a method to construct hadronic scattering and decay amplitudes from Euclidean correlators, by combining the approach of a regulated inverse Laplace transform with the work of Maiani and Testa [1]. Revisiting the original result of ref. [1], we observe that the key observation, i.e. that only threshold scattering information can be extracted at large separations, can be understood by interpreting the correlator as a spectral function, ρ(ω), convoluted with the Euclidean kernel, e−ωt, which is sharply peaked at threshold. We therefore consider a modification in which a smooth step function, equal to one above a target energy, is inserted in the spectral decomposition. This can be achieved either through Backus-Gilbert-like methods or more directly using the variational approach. The result is a shifted resolution function, such that the large t limit projects onto scattering or decay amplitudes above threshold. The utility of this method is highlighted through large t expansions of both three- and four-point functions that include leading terms proportional to the real and imaginary parts (separately) of the target observable. This work also presents new results relevant for the un-modified correlator at threshold, including expressions for extracting the Nπ scattering length from four-point functions and a new strategy to organize the large t expansion that exhibits better convergence than the expansion in powers of 1/t.

【 授权许可】

CC BY