Quenched and Partially Quenched Chiral Perturbation Theory for Vector and Tensor Mesons

Quenched and partially quenched chiral perturbation theory for vector mesons is developed and is used to extract chiral loop correction to the ρ meson mass. Connections to fully quenched and totally unquenched chiral perturbation theory results are discussed. It is also shown that (partially) quenched perturbation theory for tensor mesons can be formulated analogously, and the chiral corrections for tensor meson masses are directly proportional to their counterparts in the vector meson sector. Utilizing this observation and non-relativistic quark model, we point out that mass difference (ma2− 3 2mρ) is “quenching-insensitive” in large-Nc limit. This quantity may be used for normalization of mass scale in lattice QCD calculations. 1 Work supported in part by NSF Grant, NSF-KOSEF Bilateral Grant, KOSEF Purpose-Oriented Research Grant 94-1400-04-01-3 and SRC-Program, Ministry of Education Grant BSRI 97-2410, the Monell Foundation and the Seoam Foundation Fellowships. Lattice QCD simulations have reached such an impressive stage of high precision that an accuracy up to a few percent error is expected to be within a reach. Amongst such results are spectroscopy of ground state hadrons including pseudo-Goldstone mesons, baryons as well as some of the vector mesons [1, 2, 3, 4, 5, 6]. More recently, the precision test of hadron spectroscopy on a lattice has gone beyond the ground state hadrons and has been extended, for example, to tensor or exotic mesons [8, 9, 10]. The tensor mesons are of particular interest since they are relatively clean states experimentally, much more so than scalar mesons. As such, one might hope that tensor mesons provide a good check-point on accuracy of lattice QCD simulations. Technically, the difficulty has been that gauge invariant lattice interpolating operator of tensor mesons is non-local. Dynamial evolution of such operator is far more computer-time consuming than low-lying mesons and baryons that require only local operators, hence, limits accuracy of lattice data. With the advent of recent results [9, 10], however, precision spectroscopy of the tensor mesons should become possible in the foreseeable future. Such an extension should be of importance in order to gain a more complete insight and better understanding of the nonperturbative aspects of QCD. Simulation of full QCD on a lattice has turned out to be both time consuming and costly. Most of the simulation time is to calculate changes in the determinant of the Dirac operator of light quarks. Because of this reason, so far, lattice QCD calculations on a large-scale volume have been mainly limited to quenched (valence-quark) approximation in which gauge field configurations are summed up with the determinant of NF light quarks det NF (D/(A) + m) is replaced by unity or, equivalently, NF → 0. While the approximation is well suited when quark masses are heavy enough [11], extrapolation of the masses to physical, light quark masses might results in potentially significant errors. It is therefore necessary to understand how reliable the quenched approximation is and where it begins to break down. Indeed, Sharpe [12, 13] and Bernard and Golterman [14, 15] have pointed out that the quenched approximation leads to sizable errors . If this is the case, then one needs to understand better the errors incurred by quenched approximation before a reliable hadron spectrum is extracted. In order to study the error introduced by the quenched approximation systematically, Sharpe has developed quenched chiral perturbation theory (QχPT) [12, 13], which is subsequently developed further by Bernard and Golterman [14] . In order to cancel the effect of internal quark loops, following the method proposed by Morel [21], Bernard and Golterman have introduced the ghost quarks, which have the same masses as the standard quarks, but with opposite for up-to-date review, see [7]. 3 Some relevant recent investigation includes [16, 17, 18]. For up-to-date review, see [19]. For a pedagogical review, see [20].