Speaker
Description
Euclidean lattice correlators can be written as Laplace transforms of given spectral functions. Solving for the latter would thus simply amount to computing anti-transforms, which is unfortunately the prototype of an ill-posed problem. If one numerically approximates the integral transform via (e.g.) Gauss-Laguerre quadratures, the inverse problems is turned into a linear system, which is, not surprisingly, ill-conditioned, and thus asks for regularization. Our choice is a Tikhonov prescription. Once regularized, the system is manageable: most interestingly, given a value for the Tikhonov regulator, the anti-transform of an exponential decay is a given function, which turns out to be a legitimate regularization of a Dirac delta function. In this way, according to our prescription, the (numerical) inverse Laplace transform of a correlator can be fitted versus the superposition of transformed exponential templates. The method turns out to be successful, opening the way to multiple applications in lattice QCD. We present both the strategy of our approach and the numerics which go on top of it, discussing tests on mock (and actual) correlators, and stability of the method when applied to noisy signals.