Abstract
The spectrum of hadron is mainly composed as shortly-lived states (resonance) that decay onto two or more hadrons. These resonances play an important role in a variety of phenomenologically significant processes. In this talk, I give an overview on the present status of a rigorous program for studying of resonances and their properties using lattice QCD. I explain the formalism needed for extracting resonant amplitudes from the finite-volume spectra. From these one can extract the masses and widths of resonances. I present some recent examples that illustrate the power of these ideas. I then explain similar formalism that allows for the determination of resonant electroweak amplitudes from finite-volume matrix elements. I use the recent calculation of the πγ* → ππ amplitude as an example illustrating the power of this formalism. From such amplitudes one can determine transition form factors of resonances. I close by reviewing on-going efforts to generalize these ideas to increasingly complex reactions and I then give a outlook of the field.
Highlights
Hadronic resonances are ubiquitous in nature, and as a result play an essential role in a variety of phenomenologically significant processes
Lattice quantum chromodynamics (QCD) calculations are necessarily performed in a finite volume
In lattice QCD calculations, this ideas have been primarily been put into practice in determining elastic scattering amplitudes
Summary
Hadronic resonances are ubiquitous in nature, and as a result play an essential role in a variety of phenomenologically significant processes One such example is the famous ∆I = 1/2 rule in K → ππ weak decays. There is overwhelming evidence that without resonances most atomic nuclei would not be able to form This is seen for example in the essential role played by resonances, in particular the σ, ρ, and ω, in the construction of phenomenological potentials that accurately describe experimental data [1]. This is the motivation of a substantial experimental effort to precisely measure the basic properties of resonances (mass, decay widths, couplings, etc.) and explore the fringes of the hadronic spectrum, where these rules can be put to a test.
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