Physical Results from Unphysical Simulations

Abstract

We calculate various properties of pseudoscalar mesons in partially quenched QCD using chiral perturbation theory through next-to-leading order. Our results can be used to extrapolate to QCD from partially quenched simulations, as long as the latter use three light dynamical quarks. In other words, one can use unphysical simulations to extract physical quantities - in this case the quark masses, meson decay constants, and the Gasser-Leutwyler parameters L_4-L_8. Our proposal for determining L_7 makes explicit use of an unphysical (yet measurable) effect of partially quenched theories, namely the double-pole that appears in certain two-point correlation functions. Most of our calculations are done for sea quarks having up to three different masses, except for our result for L_7, which is derived for degenerate sea quarks.

Figures (12)

• Figure 1: Schematic representation of the space of PQ theories for "light" quarks (defined as lighter than the physical strange quark mass). The approximate range of present simulations is shown. The shape of this region is determined by the fact that critical slowing down is less severe for valence quarks than for sea quarks.
• Figure 2: Diagrams contributing to $M_{AB}$. The letters next to the lines denote the flavor indices of the propagating mesons. "VV" stands for Valence-Valence meson with $V=A,B$. "LO" and "NLO" describe the order of the vertex that makes the diagram contribute at 1 loop.
• Figure 3: diagrams contributing to $f_{AB}$. The wavy line represents the insertion of the axial current operator $j_{5AB}^\mu(p)$. "VS" stands for Valence-Sea mesons with $V=A,B$ and $S=1,2,3$.
• Figure 4: The dashed lines are rays in the $\pi$-plane or $K$-plane along which $\delta^f$ and $\delta^M$ are plotted in Figs. \ref{['fpirays']}-\ref{['MKrays']}.
• Figure 5: $\delta^f$ in the $\pi$-plane, $(y,y,x,1)$, is plotted along rays of angle $\theta$ with respect to the $x$-axis (see Fig. \ref{['thetas']}). The values of theta in degrees are indicated next to the corresponding curves. The point that corresponds to the "physical" pion, $(\chi _u ,\chi _u ,\chi _u ,\chi _s )$ is labeled "QCD".