Chiral Perturbation Theory for Staggered Sea Quarks and Ginsparg-Wilson Valence Quarks

Abstract

We study lattice QCD with staggered sea and Ginsparg-Wilson valence quarks. The Symanzik effective action for this mixed lattice theory, including the lattice spacing contributions of O(a^2), is derived. Using this effective theory we construct the leading order chiral Lagrangian. The masses and decay constants of pseudoscalars containing two Ginsparg-Wilson valence quarks are computed at one loop order.

Figures (5)

• Figure 1: Quark flow diagram for a connected meson propagator.
• Figure 2: Quark flow diagrams for the disconnected meson propagator.
• Figure 3: Meson graphs for the $P^+$ self energy. Graph (a) has a connected internal propagator (Fig. \ref{['fig:ConnProp']} in the quark flow picture); while graph (b) has a disconnected internal propagator (Fig. \ref{['fig:DiscProp']}).
• Figure 4: Quark flow graphs corresponding to the four meson vertices in the the $P^+$ self energy, Eqs. (\ref{['eq:VKE1']}), (\ref{['eq:VKE2']}), (\ref{['eq:VM']}) and (\ref{['eq:VUV']}). The horizontal $x$, $y$ lines produce the external $P^{\pm}$ fields. Graph (a) represents terms where the $P^+$ and $P^-$ are next to each other in the supertrace; an almost identical graph with $x\leftrightarrow y$ is not shown. The free index $i$ represents any quark type, but the numerical coefficient of the graph may depend on $i$. Graph (b) represents terms where $P^+$ and $P^-$ are not next to each other in the supertrace.
• Figure 5: Quark flow graphs corresponding to the $P^+$ self energy, Fig. \ref{['fig:MesonGraphs']}. Graphs (a) and (b) come from connected and disconnected contractions, respectively, of the internal meson lines in vertex Fig. \ref{['fig:Vertices']}(a); graph (c), from the disconnected contraction in vertex Fig. \ref{['fig:Vertices']}(b). Iterations of sea quark loops in the disconnected propagators, as in Fig. \ref{['fig:DiscProp']}, is implied in graphs (b) and (c).