Proceedings of RIKEN BNL Research Center Workshop: Multi-Hadron and Nonlocal Matrix Elements in Lattice QCD (Volume 120)
Nonperturbative QCD calculations of hadronic matrix elements are needed to understand the structure of the matter in our universe and to search for physics beyond the Standard Model. Numerical lattice gauge theory is uniquely suited for this task and has reached a remarkable level of precision. However, the types of observables that are accessible in a straightforward way are limited because lattice calculations are performed with imaginary time. Traditionally, lattice QCD determinations of hadronic matrix elements have been restricted to situations with at most one stable hadron in the initial and final states, and with a single insertion of a local current. This situation has been changing recently thanks to theoretical breakthroughs and pioneering numerical studies of new observables. At this workshop, the latest developments concerning multi-hadron systems and nonlocal matrix elements in lattice QCD were discussed: • Liischer's quantization condition relates the energy spectrum of two interacting particles in a finite volume to the scattering phase shifts. At this workshop, generalizations of Liischer's quantization condition to three-particle systems, and to two-particle systems with long-range QED interactions were presented. • Advanced numerical lattice QCD studies of hadronic resonances using the Liischer method were shown, including coupled-channel scattering and near-threshold resonances. • The Lellouch-Liischer formula relates two-hadron matrix elements computed in a finite volume to the infinite-volume matrix elements. This workshop included presentations of the latest numerical lattice QCD calculations ofthe nonleptonic weak decay K ® tl tl, as well as new theoretical results extending the Lellouch-Liischer formula to general multichannel 1 ® 2 transition matrix elements. • Novel methods allowing the direct calculation of parton distribution functions in lattice QCD were discussed, and a one-loop calculation of the lattice-to-continuum matching required for these methods was presented. • Lattice QCD calculations of nonlocal matrix elements relevant for rare kaon decays and for the Kl-Ks mass difference were shown. The inclusion of QED corrections in weak decays was discussed. Results from a new method for computing the hadronic light-by-light contribution to the muon anomalous magnetic moment were shown. • • Calculations of the binding energies and magnetic moments of light nuclei directly from lattice QCD were presented. The theoretical foundations of a potential-based method for studying multihadron interactions on the lattice were discussed, and an application of this method to charmed tetraquarks was shown.