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SU(N) gauge theory couplings on asymmetric lattices

Authors
Journal
Nuclear Physics B
0550-3213
Publisher
Elsevier
Publication Date
Volume
205
Issue
2
Identifiers
DOI: 10.1016/0550-3213(82)90390-x

Abstract

Abstract The connection between euclidean and hamiltonian lattice QCD requires the use of asymmetric lattices, which in turn implies the necessity of two coupling parameters. We analyse the dependence of space- and time-like couplings g σ and g τ on the different lattice spacings a and a τ in space and time directions. Using the background field method we determine the derivatives of the couplings with respect to the asymmetry factor ξ= a a τ in the weak coupling limit, obtaining for ξ=1 the values. ( ag σ −2 aξ )ξ=1= 0.20161,N=3, 0.11403,N=2, ( ag τ − aξ )ξ=1= −0.13195,N=3, −0.06759,N=2, We argue that the sum of these derivatives has to be equal to b 0=11 N/48 π 2 and determine the Λ parameter for asymmetric lattices. In the limit ξ→∞ all our results agree with those of A. and P. Hasenfratz.

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