Källén-Lehmann spectroscopy for (un)physical degrees of freedom

Abstract

We consider the problem of "measuring" the Källén-Lehmann spectral density of a particle (be it elementary or bound state) propagator by means of 4d lattice data. As the latter are obtained from operations at (Euclidean momentum squared) p^2>=0, we are facing the generically ill-posed problem of converting a limited data set over the positive real axis to an integral representation, extending over the whole complex p^2-plane. We employ a linear regularization strategy, commonly known as the Tikhonov method with Morozov discrepancy principle, with suitable adaptations to realistic data, e.g. with unknown threshold. An important virtue over the (standard) maximum entropy method is the possibility to also probe unphysical spectral densities, as, for example, of a confined gluon. We apply our proposal here to "physical" mock spectral data as a litmus test and then to the lattice SU(3) Landau gauge gluon at zero temperature.

5 pages, 7 .pdf figures

References in corpus (10)

• Pinch Technique: Theory and Applications
• The Physics of Glueballs
• The Status of Glueballs
• A novel Bayesian approach to spectral function reconstruction
• Glueball masses from an infrared moment problem and nonperturbative Landau gauge
• Quark Spectral Function and Deconfinement at Nonzero Temperature
• On the analytic structure of scalar glueball operators at Born level
• Spin Zero Glueballs in the Bethe-Salpeter Formalism
• Examining the Analytic Structure of Green's Functions: Massive Parallel Complex Integration using GPUs
• From Euclidean to Minkowski space with the Cauchy-Riemann equations

Cited by in corpus (77)

• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• Spectral Functions for the Quark-Meson Model Phase Diagram from the Functional Renormalization Group
• Spectral functions of confined particles
• Reconstructing the gluon
• Heavy-flavor production and medium properties in high-energy nuclear collisions - What next?
• Numerical analytic continuation of Euclidean data
• High Precision Statistical Landau Gauge Lattice Gluon Propagator Computation vs. the Gribov-Zwanziger approach
• Gluon screening mass at finite temperature from Landau gauge gluon propagator in lattice QCD
• Analytic structure of QCD propagators in Minkowski space
• Spectral function for overoccupied gluodynamics from real-time lattice simulations
• Landau gauge Yang-Mills propagators in the complex momentum plane
• Ghost spectral function from the spectral Dyson-Schwinger equation
• Spectral representation of lattice gluon and ghost propagators at zero temperature
• Non-perturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST invariant two-point correlation function
• Spectrum of scalar and pseudoscalar glueballs from functional methods
• Functional renormalization group analysis of the soft mode at the QCD critical point
• Bayesian analysis of quark spectral properties from the Dyson-Schwinger equation
• The analytic structure of the lattice Landau gauge gluon and ghost propagators
• Spectral functions and critical dynamics of the $O(4)$ model from classical-statistical lattice simulations
• The gluon propagator in linear covariant $R_{\xi }$ gauges
• The non-perturbative structure of the photon and gluon propagators
• Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories
• Rethinking the ill-posedness of the spectral function reconstruction -- why is it fundamentally hard and how Artificial Neural Networks can help
• Quantum Gravity signatures in the Unruh effect
• Bayesian inference of non-positive spectral functions in quantum field theory
• Vector and Axial-Vector Mesons in Nuclear Matter
• Reconstructing confined particles with complex singularities
• Stochastic reconstructions of spectral functions: Application to lattice QCD
• Observing the Minkowskian dynamics of the pion on the null-plane
• Finite temperature gluon spectral functions from $N_f=2+1+1$ lattice QCD
• Fermionic spectral functions with the Functional Renormalization Group
• Conditions on the violation of the cluster decomposition property in QCD
• Padé approximation and glueball mass estimates in 3d and 4d with N_c = 2,3 colors
• Some more details of minimal-Landau-gauge Yang-Mills propagators
• Complex poles and spectral functions of Landau gauge QCD and QCD-like theories
• The (IR-)relevance of the Gribov ambiguity in SU(2) x U(1) gauge theories with fundamental Higgs matter
• Reflection positivity and complex analysis of the Yang-Mills theory from a viewpoint of gluon confinement
• Some remarks on the spectral functions of the Abelian Higgs Model
• Quasigluon lifetime and confinement from first principles
• A non-perturbative study of matter field propagators in Euclidean Yang-Mills theory in linear covariant, Curci-Ferrari and maximal Abelian gauges
• Dynamical mass generation in Minkowski space at QCD scale
• Non-perturbative constraints on the quark and ghost propagators
• The BRST-invariant vacuum state of the Gribov-Zwanziger theory
• A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations
• Calculation of the non-perturbative strong coupling from first principles
• Dyson-Schwinger equation constraints on the gluon propagator in BRST quantised QCD
• Bayesian inference of real-time dynamics from lattice QCD
• Dispersion relations for unphysical particles
• Spectral and transport properties from lattice QCD
• Spectral functions and in-medium properties of hadrons
• Fermionic excitations at finite temperature and density
• Spectral Functions from the Functional Renormalization Group
• $H(4)$ tensor representations for the lattice Landau gauge gluon propagator and the estimation of lattice artefacts
• Lattice pure gauge compact QED in the Landau gauge: the photon propagator, the phase structure and the presence of Dirac strings
• On the complex structure of Yang-Mills theory
• The analytic structure of three-point functions from contour deformations
• Thermal extension of the screened massive expansion in the Landau gauge
• Renormalizability of $\mathcal{N}=1$ super Yang-Mills theory in Landau gauge with a Stueckelberg-like field
• Gluon and Ghost Dynamics from Lattice QCD
• The Schwinger function, confinement and positivity violation in pure gauge QED
• Spectral density constraints in quantum field theory
• Källén-Lehmann Spectral Representation of the Scalar SU(2) Glueball
• Analytic continuation and physical content of the gluon propagator
• Study of a gauge invariant local composite fermionic field
• Gluons at finite temperature
• The chiral limit of a fermion-scalar $(1/2{)}^{+}$ system in covariant gauges
• The Dark Side of the Propagators: exploring their analytic properties by a massive expansion
• Quark mass function in Minkowski space
• Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
• Oscillators with imaginary coupling: spectral functions in quantum mechanics and quantum field theory
• Application of radial basis functions neutral networks in spectral functions
• Quark mass function at finite temperature in real-time formalism
• Compact QED: the photon propagator, confinement and positivity violation for the pure gauge theory
• Reconstructing propagators of confined particles in the presence of complex singularities
• Complex-mass definition and the structure of unstable particle's propagator
• Extracting topological information from momentum space propagators
• Transversal and longitudinal gluon spectral functions from twisted mass lattice QCD with $N_f=2+1+1$ flavors