Abstract
Multi-particle states with additional pions are expected to be a non-negligible source of the excited-state contamination in lattice simulations at the physical point. It is shown that baryon chiral perturbation theory (ChPT) can be employed to calculate the contamination due to two-particle nucleon-pion states in various nucleon observables. Results to leading order are presented for the nucleon axial, tensor and scalar charge and three Mellin moments of parton distribution functions: the average quark momentum fraction, the helicity and the transversity moment. Taking into account experimental and phenomenological results for the charges and moments the impact of the nucleon-pionstates on lattice estimates for these observables can be estimated. The nucleon-pion-state contribution leads to an overestimation of all charges and moments obtained with the plateau method. The overestimation is at the 5-10% level for source-sink separations of about 2 fm. Existing lattice data is not in conflict with the ChPT predictions, but the comparison suggests that significantly larger source-sink separations are needed to compute the charges and moments with few-percent precision.
Highlights
Chiral perturbation theory (ChPT) is a frequently used tool in the analysis of Lattice Quantum Chromodynamics (QCD) data
ChPT results for the quark mass dependence are commonly used in the chiral extrapolation to relate unphysical lattice results obtained at heavy quark masses to the physical point with quark masses as light as in nature
Constant progress in computer power as well as advances in simulation algorithms have made lattice simulations possible with the light quark masses set to their physical values
Summary
Chiral perturbation theory (ChPT) is a frequently used tool in the analysis of Lattice Quantum Chromodynamics (QCD) data. Excited states contributing to the nucleon 2-pt function: Multi-particle states become important for physical pion masses. We expect the multi-hadron states to be the dominant source for the excited-state contribution, since these have the smallest gap to the energy of the single nucleon state. Topic of this talk is that the correlation function ratios can be computed in ChPT. Such calculations provide the coefficients bA, j, b A, j, cA, j in (6) associated with multi-particle-state contributions.
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