Abstract
Excited state contributions represent a formidable challenge for hadron structure calculations in lattice QCD. For physical systems that exhibit an exponential signal-to-noise problem they often hinder the extraction of ground state matrix elements, introducing a major source of systematic error in lattice calculations of such quantities. The development of methods to treat the contribution of excited states and the current status of related lattice studies are reviewed with focus on nucleon structure calculations that are notoriously affected by excited state contamination.
Highlights
Most notably affected by this kind of systematic effect are lattice quantum chromodynamics (QCD) calculations of nucleon structure, that cover a rich variety of observables
The selection comprises observables that can be computed with sufficiently good statistical precision and for which dedicated studies of excited state systematics and related methods can be found in the literature
While hadron masses can be readily obtained from two-point functions, the study of the structure of hadrons from lattice QCD relies on the computation of matrix elements
Summary
Most notably affected by this kind of systematic effect are lattice QCD calculations of nucleon structure, that cover a rich variety of observables. An important example is the nucleon axial charge guA−d = 1.2724(23) [1] which is experimentally measured in neutron β-decay and often serves as a benchmark observable for nucleon structure calculations in lattice QCD. The tensor charge plays a role in BSM searches for C Pviolation as it controls the contribution of quark electric dipole moments to the neutron electric dipole moment [4]. Another example for an observable of great phenomenological interest at zero momentum transfer is the average quark momentum fraction which contributes to the nucleon spin decomposition [5]. Axial form factors in turn are experimentally less well-known [15,16,17] but may provide critical input for future experiments
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