Precision scale setting in Lattice QCD
Loading...
Date issued
Authors
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Reuse License
Abstract
We investigate the prospects of setting the lattice scale via the mass of one of the SU(3)-octet or -decuplet baryons including isospin-breaking effects in Lattice Quantum Chromodynamics and discuss first, but incomplete results on the topic. To determine values for the lattice scale, we compute the correlation functions for SU(3)-octet and -decuplet baryons as well as pseudoscalar octet mesons on ten of the (2+1)-flavor QCD gauge ensembles of the Coordinated Lattice Simulations (CLS) collaboration at five different lattice spacings on a trajectory of constant average quark mass. As these ensembles are simulated in the isospin-symmetric limit, i.e. with two identical light quarks instead of distinct up and down quarks, we also compute corrections to the above mentioned correlation functions to account for a difference in mass of these two light quarks and for electromagnetic interactions of the quarks to leading order following a perturbative approach by the RM123 collaboration. We compute masses and their corrections for the baryons that are stable in isospin-symmetric QCD as well as the pion and kaon from correlation functions using the model averages of single and two-state fits to an effective mass based on the Akaike information criterion. We use the isospin-symmetric masses as well as available values for the Wilson flow scale $t_0$ to extrapolate the combinations $\sqrt{8t_0}m_B$ for all stable baryons $B$ to the physical point following a procedure by the RQCD collaboration. At the physical point, we match the extrapolated data to modified experimental baryon masses that account for isospin-symmetry in order to determine a physical value $\sqrt{8t_0^\phys}$ for the Wilson flow scale. We use this physical value to determine values of the five different lattice spacings at which we have gathered data which we use to compute the isospin-breaking expansion coefficients for each ensembles by matching the differences of squared pion and kaon masses in the isospin-broken theory to experimental data. From these data and the corrections to the baryonic masses in lattice units, we compute masses for the baryons in the isospin-broken theory. We furthermore discuss a method we developed to substantially reduce the computational effort for the computation of electromagnetic corrections of the investigated correlation functions and the generalization of the isospin-symmetric scale-setting procedure to include isospin-breaking corrections. Finally, we discuss the results with with regards to the precision achievable for the lattice scale and the different baryonic candidates to use as intermediate scales.