Partial flavor symmetry restoration for chiral staggered fermions

Abstract

We study the leading discretization errors for staggered fermions by first constructing the continuum effective Lagrangian including terms of O(a 2 ), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a 2 ) in the continuum effective Lagrangian completely break the SU (4) flavor symmetry down to the discrete subgroup respected by the lattice theory. We find, however, that the O(a 2 ) terms in the potential of the chiral Lagrangian maintain an SO(4) subgroup of SU (4). It follows that the leading discretization errors in the pion masses are SO(4) symmetric, implying three degeneracies within the seven lattice irreducible representations. These predictions hold also for perturbatively improved versions of the action. These degeneracies are observed, to a surprising degree of accuracy, in existing data. We argue that the SO(4) symmetry does not extend to the masses and interactions of other hadrons (vector mesons, baryons, etc), nor to higher order in a 2 . We show how it is possible that, for physical quark masses of O(a 2 ), the new SO(4) symmetry can be spontaneously broken, leading to a staggered analogue of the Aoki-phase of Wilson fermions. This does not, however, appear to happen for presently studied versions of the staggered action.

NeutralB-meson mixing from three-flavor lattice quantum chromodynamics: Determination of theSU(3)-breaking ratioξ<

“…To obtain information about the quark-mass dependence of the relevant matrix elements, which allows us to extrapolate our results to the physical masses, we perform our calculation at six sea × six valence quark masses, thus including numerous partially quenched data points. In addition, the leading-order taste violations, which arise at O(a 2 α s ), are included in the theory and then removed when the extrapolation is performed using rooted heavy-meson staggered chiral perturbation theory (rHMSχPT) [63,64,67]. The χPT expression for O q 1 , as well as for the matrix elements of all the other operators in the ∆B = 2 effective Hamiltonian was first described in Ref.…”

“…IV, we give the details of the procedure for the correlator fits. Section V is devoted to the chiralcontinuum extrapolation, which is performed within the framework of rooted staggered chiral perturbation theory [63][64][65][66][67]. We describe and discuss the choice of the functional form used in the extrapolation, the different fitting methods tested, and the choice of parameters and parametrization.…”

Next-to-Leading-Order Staggered Chiral Perturbation Theory

“…In practice it is easiest to first determine all allowed lattice operators of dimension ≤ 6, as in Refs. [15,6], and then map these onto continuum quark-level operators [6]. Next one maps the continuum quark-level operators onto chiral operators describing the PGB sector.…”

“…Thus the LO staggered potential is of O(a 2 ) [6,10], while the NLO taste-violating operators in the staggered chiral Lagrangian are of O(a 2 p 2 ), O(a 4 ), and O(a 2 m) [13].…”

“…Near the continuum limit, where there is a controlled expansion in powers of the lattice spacing, SχPT systematically describes taste violations in the PGB sector. Reference [6] determined the O(a 2 ) staggered potential for a single flavor and showed that even at tree-level it correctly predicts the mass degeneracy pattern observed among the different tastes of PGBs [7,8,9]. References [10] and [11] extended the potential to multiple staggered flavors and calculated the 1-loop mass and decay constant for the taste Goldstone (ξ 5 ) meson.…”