Tensor representations of lattice vertices from hypercubic symmetry
Abstract
We present a symmetrybased method for obtaining suitable tensor descriptions of lattice vertex functions without spinor components. The approach is based on finding the polynomial functions of vertex momenta, which satisfy the appropriate tensor transformation laws under hypercubic symmetry transformations. We use the method to find the most general possible (up to finite volume effects) basis decompositions for lattice vectors and secondrank tensors. The leadingorder noncontinuum versions of these representations are then applied to the Landau gauge gluon propagator and ghostgluon vertex of Monte Carlo simulations, to reveal two interesting insights. First, it is demonstrated numerically and analytically that there exist special kinematic configurations where the basis descriptions of both functions reduce to their continuum analogues. Second, for the gluon twopoint correlator it is shown that the rate at which the function approaches its continuum form in the infrared is independent of the lattice gauge coupling $\beta$ (when working in lattice units): the said rate depends on kinematics alone and is ultimately dictated by the numerical gaugefixing procedure. We also comment on how this reflects on the lattice investigations of the anomalous magnetic moment of the muon. Finally, we argue how our findings can be used to directly test some of the continuum extrapolation methods.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.00651
 Bibcode:
 2019arXiv190500651V
 Keywords:

 High Energy Physics  Lattice
 EPrint:
 43 pages, 10 figures