Cutoff effects of Wilson fermions in the absence of spontaneous chiral symmetry breaking.pdf

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Cutoff effects of Wilson fermions in the absence of spontaneous chiral symmetry breaking.pdf

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Cutoff effects of Wilson fermions in the absence of spontaneous chiral symmetry breaking

a r X i v : h e p - l a t / 0 5 1 0 0 9 2 v 2 1 4 N o v 2 0 0 5 HU-EP-05/67 SFB/CPP-05-71 Cutoff effects of Wilson fermions in the absence of spontaneous chiral symmetry breaking Michele Della Mortea and Magdalena Luza a Institut fu?r Physik, Humboldt Universita?t, Newtonstr. 15, 12489 Berlin, Germany Abstract We simulate two dimensional QED with two degenerate Wilson fermions and plaquette gauge action. As a consequence of the Mermin-Wagner theorem, in the continuum limit chiral symmetry is realized a? la Wigner. This property affects also the size of the cutoff effects. That can be understood in view of the fact that the leading lattice artifacts are described, in the continuum Symanzik effective theory, by chirality breaking terms. In particular, vacuum expectation values of non-chirality-breaking operators are expected to be O(a) improved in the chiral limit. We provide a numerical confirmation of this expectation by performing a scaling test. Key words: Lattice field theory; Schwinger model PACS: 11.10.Kk; 11.15.-q; 11.15.Ha October 2005 1. Cutoff effects in lattice (gauge) theories can be described using an effective continuum action, as proposed by Symanzik in refs. [1, 2]. In this approach the leading lattice artifacts (e.g. in the spectrum of the theory) can be removed by including a set of irrelevant operators in the action and by properly tuning their coefficients. For the case of the Wilson lattice regularization of QCD [3], the relevant coefficient can be tuned by requiring the restoration of chiral symmetry up to O(a2). This interplay between chiral symmetry and cutoff effects has been addressed in detail in ref. [4]. Further insights on this connection have been recently derived in ref. [5] by considering also so called spurionic lattice symmetries to classify the operators, which can appear in the Symanzik effective theory. Without reproducing the whole argument, here we will simply summarize the results relevant as premises for this work. Let’s