Abstract
AbstractThe chirally rotated Schrödinger functional (χSF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schrödinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O(a) improvement to be operational in the χSF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the χSF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O(a) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the χSF framework and prepares the ground for non-perturbative applications.
Highlights
The chirally rotated Schrodinger functional [1, 2] provides a new tool to address renormalization and O(a) improvement problems in lattice QCD and similar lattice gauge theories with Wilson type fermions
As the standard Schrodinger functional (SF) correlation functions are real-valued, their χSF counterparts must be either real or purely imaginary. While this dictionary is trivial in the formal continuum theory, it does lead to non-trivial consequences once the lattice regularization with Wilson-type fermions is in place, due to the additional symmetry breaking by the Wilson term
In this paper we have defined a complete set of boundary-to-bulk and boundary-toboundary correlation functions with both χSF and standard SF boundary conditions
Summary
The chirally rotated Schrodinger functional (χSF) [1, 2] provides a new tool to address renormalization and O(a) improvement problems in lattice QCD and similar lattice gauge theories with Wilson type fermions. With an even number of massless fermion flavours it is formally related to the standard Schrodinger functional (SF) [3,4,5] by a non-singlet chiral field rotation. We use one-loop perturbation theory to perform non-trivial tests of these expectations. For related nonperturbative applications of the χSF to quenched lattice QCD cf refs. The remainder of this paper discusses the perturbative expansion and one-loop results for the action parameters (section 5) and various ways to test and apply the theoretical expectations in perturbation theory (sections 6 and 7).
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