The path from finite to infinite volume: Hadronic observables from lattice QCD

Abstract

Standard Model determinations of properties of strongly interacting systems of hadrons have become possible with the powerful method of lattice quantum chromodynamics (LQCD), a method with growing applicability and reliability. While growth in computational power and innovations in algorithmic and computational approaches have been essential in advancing the state of the field, conceptual and formal developments have played a crucial role in turning the output of LQCD computations to phenomenologically valuable results. From the invention of finitevolume technology to access physical observables by Martin Lüscher over three decades ago to date, this field has grown in scope and complexity, enabling studies of scattering amplitudes and reaction rates, as well as spectroscopy of excited states of quantum chromodynamics (QCD) and resonances. Further, LQCD studies are augmented with the inclusion of quantum electrodynamics (QED), and subtleties related to the finite volume of systems in presence of QED have been understood and largely controlled. In this talk, I focus on selected developments to give a taste of the status of the field concerning the mapping between the finite and infinite-volume physics and its state-of-the-art applications.

A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results

“…Apart from smearing of the operators, the essential ingredient is tadpole improvement. Recently, this approach has been revisited and exploratory numerical results were recently presented [202] We finalize by shortly discussing one more method of dealing with the power divergence related to the Wilson line in quasi-distributions. In 2016, H.-n. Li proposed [203] to modify the definition of such distributions by using "nondipolar" gauge links, i.e.…”

Prony methods for extracting excited states

“…Modeling the first excited state well helps produce a better variational estimate of the ground state, regardless of whether the excited states are the focus of the study. Additionally, the excited state spectrum encodes two particle scattering phase shifts through the Luscher method [1][2][3]. By extracting the spectrum of two particles in a box, this formalism provides a connection to the infinite volume continuum of two particle elastic scattering.…”

Automated label flows for excited states of correlation functions in lattice gauge theory

“…For example, lattice spectroscopy of nuclei requires a robust method for extracting excited states because their spectrum is dense compared to hadrons [1,2]. Additionally, the excited state spectrum may be of interest because it encodes two-particle scattering phase shifts through the Lüscher method [3,4]. Similarly, extracting excited states from confining gauge theories is crucial for beyond the Standard Model lattice spectroscopy in explorations such as composite Higgs [5,6].…”