Symanzik improvement with dynamical charm: a 3+1 scheme for Wilson quarks
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Springer
Received: May 11, Revised: May 31, Accepted: May 31, Published: June 5,
2018 2018 2018 2018
ALPHA Collaboration
Patrick Fritzsch,a Rainer Sommer,b,c Felix Stollenwerkc and Ulli Wolffc a
CERN, Theoretical Physics Department, 1211 Geneva 23, Switzerland b John von Neumann Institute for Computing (NIC), DESY, Platanenallee 6, 15738 Zeuthen, Germany c Institut f¨ ur Physik, Humboldt-Universit¨ at zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We discuss the problem of lattice artefacts in QCD simulations enhanced by the introduction of dynamical charmed quarks. In particular, we advocate the use of a massive renormalization scheme with a close to realistic charm mass. To maintain O(a) improvement for Wilson type fermions in this case we define a finite size scheme and carry out a nonperturbative estimation of the clover coefficient csw . It is summarized in a fit formula csw (g02 ) that defines an improved action suitable for future dynamical charm simulations. Keywords: Lattice Quantum Field Theory, Nonperturbative Effects ArXiv ePrint: 1805.01661
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2018)025
JHEP06(2018)025
Symanzik improvement with dynamical charm: a 3+1 scheme for Wilson quarks
Contents 1
2 Symanzik improvement
3
3 Mass (in)dependent renormalization scheme and improvement 3.1 Mass independent case 3.2 Mass dependent case 3.3 A 3+1 flavor scheme
5 5 6 7
4 Scaling at constant finite volume physics 4.1 Finite size definition of the LCP 4.2 Values of Φ1,2,3 4.3 Lattice realization of the LCP
7 8 9 10
5 Determination of csw
12
6 Conclusion
15
1
Introduction
Physicists have been rather fortunate that perturbation theory in the form of low order Feynman diagrams has been largely sufficient to practically establish today’s highly successful Standard Model of elementary particles from experiment. Due to asymptotic freedom even the strongly interacting sector of confined quarks and gluons (QCD) could be pinned down in this way, based on high energy scattering of weakly interacting probes (e.g. e+ e− and e− p). The thus completely characterized theory is expected to also produce the hadronic bound states observed in nature. To extract these predictions — and thus ultimately validate the complete theory — nonperturbative techniques become indispensable. The only known nonperturbative definition of QCD is the regularization on a lattice which in particular provides a systematic way to extract nonperturbative information about hadrons from the theory by Monte Carlo simulations of QCD on sequences of finite computational lattices. This inflicts however several unavoidable distortions of the theory which need to be controlled. The lattice spacing a acts as an ultraviolet regulator that has to be extrapolated to zero up to tolerable errors. A finite system length L is introduced and has to be made effectively infinite in a s
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