2008/12/31 by Andrea Shindler · 1 citation
Mathematics · Physics and Astronomy · #Cutoff #Discretization #Fermion #Geometry #High-Energy Particle Collisions Research #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Quark #Scalar (mathematics) #Theoretical physics #Zero mode #hep-lat
paper · pdf · doi:10.1016/j.physletb.2008.12.061
published as Phys.Lett.B672:82-88,2009 · 17 pages, 1 figure. v2: few typos corrected. Published on PLB
openalex publication_date 2009/01/02 · arxiv created 2009/01/20 · arxiv updated 2009/12/01 · openalex created_date 2018/09/27 · openalex updated_date 2026/08/05
We make several observations concerning the low quark mass region with Wilson fermions and how this is connected with the ϵ regime in the continuum. A transition from tiny cutoff effects to rather large discretization errors would take place in general with Wilson fermions if we lower the quark mass at finite lattice spacing. We argue that these two regions exhibit rather different behaviours concerning the coupling between cutoff effects and zero-modes. We interpolate between these two regimes adding to the continuum ϵ regime formulae, in the spirit of the Symanzik expansion, the relevant operators parametrising the leading cutoff effects. We compute the partition function, the chiral condensate, scalar and pseudo-scalar correlation functions. The final formulae can be used to fit lattice data to extract physical low energy constants, and to estimate systematic uncertainties coming from discretization errors. Moreover they suggest ways on how to remove these cutoff effects, the core of which are captured by the continuum zero modes.