Abstract
Hadronic spectral densities are important quantities whose non-perturbative knowledge allows for calculating phenomenologically relevant observables, such as inclusive hadronic cross-sections and non-leptonic decay-rates. The extraction of spectral densities from lattice correlators is a notoriously difficult problem because lattice simulations are performed in Euclidean time and lattice data are unavoidably affected by statistical and systematic uncertainties. In this paper we present a new method for extracting hadronic spectral densities from lattice correlators. The method allows for choosing a smearing function at the beginning of the procedure and it provides results for the spectral densities smeared with this function together with reliable estimates of the associated uncertainties. The same smearing function can be used in the analysis of correlators obtained on different volumes, such that the infinite volume limit can be studied in a consistent way. While the method is described by using the language of lattice simulations, in reality it is completely general and can profitably be used to cope with inverse problems arising in different fields of research.
Highlights
Hadronic spectral densities are crucial ingredients in the calculation of physical observables associated with the continuum spectrum of the QCD Hamiltonian
In this paper we present a new method for extracting hadronic spectral densities from lattice correlators
While the method is described by using the language of lattice simulations, in reality it is completely general and can profitably be used to cope with inverse problems arising in different fields of research
Summary
The algorithm is designed in such a way that the width of the smearing function (having the properties of being peaked around E⋆ and of having unit area) is optimized on the basis of the number of observations and of their statistical uncertainties [in our case the number of discrete times t at which CðtÞ and the associated statistical errors are known] This feature of the algorithm may not represent a problem in experimental applications of the Backus-Gilbert method because, at the end of the procedure, the resulting smearing function is known and no infinite-volume limit has to be taken. Appendix B contains additional examples of applications of our method in the case of synthetic data
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