Partially Quenched Qcd with Non-degenerate Dynamical Quarks * Lattice Simulations

We discuss the importance of using partially quenched theories with three degenerate quarks for extrapolating to QCD, and present some relevant results from chiral perturbation theory. Simulations of lattice QCD have, to date, largely used the quenched (Q), or partially quenched (PQ), approximations. These approximations introduce unphysical artifacts, some of which can be analyzed using chiral perturbation theory (ChPT) [1–3]. In particular, it has been found that the quenched theory has un-physical singularities in the chiral limit, and that these persist in the PQ theory, albeit in weakened form [3–5]. These results serve as a warning against relying on ChPT when straying too far from unquenched theories in which valence and dynamical masses coincide. In this talk we discuss a more constructive aspect of partially quenched QCD. We focus on PQ theories with three light dynamical quarks, where " light " means that the theory can be studied using ChPT. Such theories have the same quark complement as QCD, although with differing masses. When simulating such theories it is possible to push to much lighter valence quarks than dynamical quarks, and thus to map out a " rectangular " region in the space of theories as sketched in Fig. 1. Our aim is to make use of the extra information contained in the PQ data to learn about unquenched theories, and in particular about real QCD. The key point is that, as long as one stays far enough away from the m V = 0 axis, ChPT reliably predicts the functional dependence on valence and dynamical quark masses, and so provides a unified description of both the PQ and fully unquenched regions of the parameter space. m strange m m valence m sea =m valence strange m sea Figure 1. Schematic representation of the space of PQ theories. unknown coefficients appearing in the chiral La-grangian for PQ theories depend only on the number of light dynamical quarks, and not on their masses [4] 3. One way of viewing the extra input that PQ theories provide is that they allow a cleaner separation of the non-leading, O(p 4) coefficients 4. This is because some GL coefficients appear multiplied only by valence masses, others only by dynamical masses (see Eq. (2)). The picture that emerges is that, by simulating in a region of moderately light valence and dynamical quarks, and varying independently the masses of both, one can determine all the coefficients …