Maximum entropy analysis of the spectral functions in lattice QCD

By M. Asakawa, Y. Nakahara, T. Hatsuda. 2000

384 citations recorded by the source corpus.

Abstract First principle calculation of the QCD spectral functions (SPFs) based on the lattice QCD simulations is reviewed. Special emphasis is placed on the Bayesian inference theory and the Maximum Entropy Method (MEM), which is a useful tool to extract SPFs from the imaginary-time correlation functions numerically obtained by the Monte Carlo method. Three important aspects of MEM are (i) it does not require a priori assumptions or parametrizations of SPFs, (ii) for given data, a unique solution is obtained if it exists, and (iii) the statistical significance of the solution can be quantitatively analyzed. The ability of MEM is explicitly demonstrated by using mock data as well as lattice QCD data. When applied to lattice data, MEM correctly reproduces the low-energy resonances and shows the existence of high-energy continuum in hadronic correlation functions. This opens up various possibilities for studying hadronic properties in QCD beyond the conventional way of analyzing the lattice data. Future problems to be studied by MEM in lattice QCD are also summarized.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/43ba94a7251fde4b066ab92b561f4f0b25630622

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Citations in the corpus

Electrical conductivity and charge diffusion in thermal QCD from the lattice (2014, methodology): “The MEM analysis indeed indicates a peak at this value below Tc, which becomes less pronounced and disappears as the temperature increases.”
Nonperturbative properties of Yang–Mills theories (2018, methodology): “Possible reconstruction methods are, for example, the maximum entropy method [134, 136, 459–469], fits motivated by analytic results or phenomenology [390, 470–472], Padé approximants [473], the Schlessinger point method [474, 475], the Tikonov regularization [384], or the Backus-Gilbert method [470”
Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, background): “Whether or not pre-formed q̄q pairs exist in in the QGP above Tc is still being investigated; see for example [198].”
Transport properties of the quark-gluon plasma (2011, methodology): “An argument for this form of S is given in [184].”
Gauge/String Duality, Hot QCD and Heavy Ion Collisions (2011, methodology): “The method that has been developed the furthest is called the Maximum Entropy Method (MEM) [240].”
Heavy-flavour and quarkonium production in the LHC era: from proton–proton to heavy-ion collisions (2015, methodology): “It has been mostly tackled by using the Maximum Entropy Method (MEM) [693], which has proven successful in a variety of applications.”
Spectral functions and dynamic critical behavior of relativistic Z2 theories (2020, neutral): “While different reconstruction schemes exist for different purposes, ranging from Maximum Entropy methods [10–12], the Bachus-Gilbert method [13], Tikhonov regularization [14] or the Schlessinger-Point (or Resonances-via-Padé) method [15, 16], all of these come with limited ranges of applicability (”
Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements (2007, neutral): “While different reconstruction schemes exist for different purposes, ranging from Maximum Entropy methods [10–12], the Bachus-Gilbert method [13], Tikhonov regularization [14] or the Schlessinger-Point (or Resonances-via-Pad) method [15, 16], all of these come with limited ranges of applicability (s”
Heavy quarkonium in extreme conditions (2019, methodology): “As long as the prior is convex it can be shown that if an extremum of the posterior exists it is unique (for a proof see [97]).”
Transport coefficients, spectral functions and the lattice (2002, neutral): “However, transport coefficients are determined by the small frequency limit of zero-momentum spectral functions of appropriate composite operators (such as components of the energy-momentum tensor) and spectral functions or other real-time correlators are not readily available on a euclidean lattice”