Chiral Behaviour of the Rho Meson in Lattice QCD

In order to guide the extrapolation of the mass of the rho meson calculated in lattice QCD with dynamical fermions, we study the contributions to its self-energy which vary most rapidly as the quark mass approaches zero; from the processes $\rho \to \omega \pi$ and $\rho \to \pi \pi$. It turns out that in analysing the most recent data from CP-PACS it is crucial to estimate the self-energy from $\rho \to \pi \pi$ using the same grid of discrete momenta as included implicitly in the lattice simulation. The correction associated with the continuum, infinite volume limit can then be found by calculating the corresponding integrals exactly. Our error analysis suggests that a factor of 10 improvement in statistics at the lowest quark mass for which data currently exists would allow one to determine the physical rho mass to within 5%. Finally, our analysis throws new light on a long-standing problem with the J-parameter.