News from bottomonium spectral functions in thermal QCD

Abstract

New results on bottomonium at nonzero temperature are presented, using the FASTSUM Generation 2L ensembles. Preliminary results for spectral function reconstruction using Kernel Ridge Regression, a machine learning technique, are shown as well and compared to results from the Maximum Entropy Method.

Reconstruction of bottomonium spectral functions in thermal QCD using Kernel Ridge Regression

“…Other mock functions can be constructed; in Ref. [8] the logarithm of the spectral function was expanded in an orthonormal set of incomplete basis functions. Continuing with the Gaussian peaks here, we generate a collection of peaks by sampling values for {𝑍 𝑝 , 𝑚 𝑝 , Γ 𝑝 } from a set of distributions.…”

“…In Ref. [8] Kernel Ridge Regression (KRR) was introduced to reconstruct bottomonium spectral functions from Euclidean lattice correlators. KRR is a machine learning method that requires training data and here we revisit intricacies of generating this data.…”

A comparison of spectral reconstruction methods applied to non-zero temperature NRQCD meson correlation functions

“…As is common in machine learning paradigms, kernel ridge regression (KRR) infers a prediction of a quantity based on previously observed training data. In the case of solving the Details of the KRR approach in the context of NRQCD can be found in [15]. Here we note that we modified our method how the input data, the set of correlators G i (τ) (where i = 1, 2, .…”

“…, N train ), is combined into the matrix (or kernel) C before the regression procedure. In contrast to [15], we use here the following encoding for the matrix elements of C,…”

“…Clearly then, the closer the training correlation functions are to the actual lattice correlation functions obtained via numerical simulations, the more relevant training spectral functions the KRR has to draw upon to infer a spectral function. Building on [15], work has been done to increase the overlap of the training data and the lattice data. The overlap between the new training data and the actual lattice correlators is shown in Fig.…”