Heavy quarkonium in extreme conditions

A novel proposal is outlined to determine scattering amplitudes from finite-volume spectral functions. The method requires extracting smeared spectral functions from finite-volume Euclidean correlation functions, with a particular complex smearing kernel of width $\ensuremath{\epsilon}$ which implements the standard $i\ensuremath{\epsilon}$ prescription. In the $L\ensuremath{\rightarrow}\ensuremath{\infty}$ limit these smeared spectral functions are therefore equivalent to Minkowskian correlators with a specific time ordering to which a modified Lehmann-Symanzik-Zimmermann reduction formalism can be applied. The approach is presented for general $m\ensuremath{\rightarrow}n$ scattering amplitudes (above arbitrary inelastic thresholds) for a single-species real scalar field, although generalization to arbitrary spins and multiple coupled channels is likely straightforward. Processes mediated by the single insertion of an external current are also considered. Numerical determination of the finite-volume smeared spectral function is discussed briefly and the interplay between the finite volume, Euclidean signature, and time-ordered $i\ensuremath{\epsilon}$ prescription is illustrated perturbatively in a toy example.

Scattering amplitudes from finite-volume spectral functions

We develop a method to compute the inclusive semileptonic decay rate of hadrons fully nonperturbatively using lattice QCD simulations. The sum over all possible final states is achieved by a calculation of the forward-scattering matrix elements on the lattice, and the phase-space integral is evaluated using their dependence on the time separation between two inserted currents. We perform a pilot lattice computation for the ${\overline{B}}_{s}\ensuremath{\rightarrow}{X}_{c}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ decay with an unphysical bottom quark mass and compare the results with the corresponding OPE calculation. The method to treat the inclusive processes on the lattice can be applied to other processes, such as the lepton-nucleon inelastic scattering.

Inclusive Semileptonic Decays from Lattice QCD.

We study the electromagnetic conductivity of QGP in a magnetic background by lattice simulations with ${N}_{f}=2+1$ dynamical rooted 2-stout smeared staggered fermions at the physical point. We study the correlation functions of the electromagnetic currents at $T=200$, 250 MeV and use the Tikhonov approach to extract the conductivity. The conductivity is found to rise with the magnetic field in the parallel direction and to decrease in the transverse direction, giving evidence for both the chiral magnetic effect and the magnetoresistance phenomenon in QGP. We also estimate the chiral charge relaxation time in QGP.

/pdf/lattice-study-of-the-electromagnetic-conductivity-of-the-1pkoclopsz.pdf

Lattice study of the electromagnetic conductivity of the quark-gluon plasma in an external magnetic field

https://link.springer.com/content/pdf/10.1007/JHEP07(2022)083.pdf

Lattice QCD study of inclusive semileptonic decays of heavy mesons

Hadronic spectral densities are important quantities whose nonperturbative knowledge allows for calculating phenomenologically relevant observables, such as inclusive hadronic cross sections and nonleptonic 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.

Extraction of spectral densities from lattice correlators

Abstract We present a lattice study of the SU (4) gauge theory with two Dirac fermions in the fundamental and two in the two-index antisymmetric representation, a model close to a theory of partial compositeness proposed by G. Ferretti. Focus of this work are the methodologies behind the computation of the spectrum and the extrapolation of the chiral point for a theory with matter in multiple representations. While being still technical, this study provides important steps towards a non-perturbative understanding of the spectrum of theories of partial compositeness, which present a richer dynamics compared to single-representation theories. The multi-representation features are studied first in perturbation theory, and then non-perturbatively by adopting a dual outlook on lattice data through a joint analysis of time-momentum correlation functions and smeared spectral densities. 

/pdf/multi-representation-dynamics-of-su-4-composite-higgs-models-huffn7ow.pdf

Multi-representation dynamics of SU(4) composite Higgs models: chiral limit and spectral reconstructions

The naturalness problem in the Higgs sector finds a popular solution in composite Higgs models. In such theories the Higgs boson emerges as the pseudo-Nambu-Goldstone boson associated with the breaking of a global symmetry realised in a new, strongly interacting sector. We address a model arising in this context, a SU(4) gauge theory with fermions in two distinct representations. We present a novel lattice study of this theory, in which we address the non-perturbative reconstruction of spectral densities from lattice correlators.

Spectral reconstruction in SU(4) gauge theory with fermions in multiple representations.

Motivated by recent progress in the numerical inversion of the Laplace transform, we investigate applications of finite-volume smeared spectral densities. These include the tuning of operator smearing, and the study of the finite-volume spectrum.

/pdf/fits-of-finite-volume-smeared-spectral-densities-2mqhytqp.pdf

Fits of finite-volume smeared spectral densities

Reservoir Computers (RC) are brain-inspired algorithms that use partially untrained recurrent neural networks where only output connections are tuned. RCs can perform signal-analysis tasks such as distortion compensation. We recently demonstrated a photonic RC in which neurons are encoded in a frequency comb, untrained interconnections are realized by phase modulation, and trained output connections are realized by spectral filters. Here, we present a further development of this scheme in which the same substrate is used to implement two RCs simultaneously. The two RCs can either be used in parallel on different tasks, or in series, thereby implementing a “deep” RC.

Alessandro Lupo

Papers

Extraction of spectral densities from lattice correlators

Multi-representation dynamics of SU(4) composite Higgs models: chiral limit and spectral reconstructions

Spectral reconstruction in SU(4) gauge theory with fermions in multiple representations.

Fits of finite-volume smeared spectral densities

Parallel and deep reservoir computing based on frequency multiplexing