The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Asymptotic lattice spacing dependence of spectral quantities in lattice QCD with Wilson or Ginsparg-Wilson quarks

13 Aug 2022, 08:50

30m

CP1-HSZ/0.010 (CP1-HSZ) - HS2 (CP1-HSZ)

Plenary Theoretical Developments and Applications beyond Particle Physics Plenaries

Speaker

Nikolai Husung (University of Southampton)

Description

One major systematic uncertainty of lattice QCD results is due to the continuum extrapolation to extract the continuum limit at lattice spacing $a\searrow 0$. For an asymptotically free theory like QCD one finds corrections of the form $a^{n_{\min }}[2b_0{\overline{g}}^2(1/a){]}^{{\hat{\mathrm{\Gamma }}}_i}$, where $n_{\min }$ is a positive integer and $\overline{g}(1/a)$ is the running coupling at renormalisation scale $\mu =1/a$. ${\hat{\mathrm{\Gamma }}}_i$ can take any positive or negative value, which will impact convergence towards the continuum limit. How problematic such corrections can be has been first pointed out by Balog, Niedermayer and Weisz in their seminal work for the O(3) model.

I will present an analysis based on Symanzik Effective Theory for lattice QCD actions with Ginsparg-Wilson and Wilson quarks. This analysis yields various powers ${\hat{\mathrm{\Gamma }}}_i$ due to lattice artifacts from the discretised lattice action. Those powers are sufficient when describing lattice artifacts of spectral quantities, while non-spectral quantities will require additional powers originating from corrections to each of the discretised local fields involved. This new input should be incorporated into ansätze used for the continuum extrapolation.

Presentation materials

Nikolai Husung - LATTICE 2022.pdf