Scalar meson in dynamical and partially quenched two-flavor QCD: Lattice results and chiral loops

This is an exploratory study of the lightest nonsinglet scalar $q\overline{q}$ state on the lattice with two dynamical quarks. Domain wall fermions are used for both sea and valence quarks on a ${16}^3\times 32$ lattice with an inverse lattice spacing of 1.7 GeV. We extract the scalar meson mass $1.58\pm 0.34\mathrm{G}\mathrm{e}\mathrm{V}$ from the exponential time dependence of the dynamical correlators with $m_{\mathrm{v}\mathrm{a}\mathrm{l}}=m_{\mathrm{s}\mathrm{e}\mathrm{a}}$ and $N_f=2$. Since this statistical error bar from dynamical correlators is rather large, we analyze also the partially quenched lattice correlators with $m_{\mathrm{v}\mathrm{a}\mathrm{l}}\ne m_{\mathrm{s}\mathrm{e}\mathrm{a}}$. They are positive for $m_{\mathrm{v}\mathrm{a}\mathrm{l}}\ge m_{\mathrm{s}\mathrm{e}\mathrm{a}}$ and negative for $m_{\mathrm{v}\mathrm{a}\mathrm{l}}<m_{\mathrm{s}\mathrm{e}\mathrm{a}}$. In order to understand this striking effect of partial quenching, we derive the scalar correlator within the partially quenched chiral perturbation theory (ChPT) and find it describes lattice correlators well. The leading unphysical contribution in partially quenched ChPT comes from the exchange of the two pseudoscalar fields and is also positive for $m_{\mathrm{v}\mathrm{a}\mathrm{l}}\ge m_{\mathrm{s}\mathrm{e}\mathrm{a}}$ and negative for $m_{\mathrm{v}\mathrm{a}\mathrm{l}}<m_{\mathrm{s}\mathrm{e}\mathrm{a}}$ at large $t$. After the subtraction of this unphysical contribution from the partially quenched lattice correlators, the correlators are positive and exponentially falling. The resulting scalar meson mass $1.51\pm 0.19\mathrm{G}\mathrm{e}\mathrm{V}$ from the partially quenched correlators is consistent with the dynamical result and has an appreciably smaller error bar.