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Register a new userChiral interpolation in a finite volume
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A simulation of lattice QCD at (or even below) the physical pion mass is feasible on a small lattice size of sim 2 fm. The results are, however, subject to large finite volume effects. In order to precisely understand the chiral behavior in a finite volume, we develop a new computational scheme to interpolate the conventional epsilon and p regimes within chiral perturbation theory. In this new scheme, we calculate the two-point function in the pseudoscalar channel, which is described by a set of Bessel functions in an infra-red finite way as in the epsilon regime, while chiral logarithmic effects are kept manifest as in the p regime. The new ChPT formula is compared to our 2+1- flavor lattice QCD data near the physical up and down quark mass, mud sim 3 MeV on an L sim 1.8 fm lattice. We extract the pion mass = 99(4) MeV, from which we attempt a chiral interpolation of the observables to the physical point.
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We report on the results of our calculation of meson correlators in a finite volume. The calculation is carried out in the quenched approximation near the chiral limit (down to Mq = 2.6 MeV) using the overlap fermion. For these small quark masses, the scalar and pseudo-scalar correlators are well approximated with a few hundred eigenmodes. The results for both connected and disconnected correlators are compared with the theoretical predictions of quenched chiral perturbation theory.
We perform an analysis of the QCD lattice data on the baryon octet and decuplet masses based on the relativistic chiral Lagrangian. The baryon self energies are computed in a finite volume at next-to-next-to-next-to leading order (N$^3$LO), where the dependence on the physical meson and baryon masses is kept. The number of free parameters is reduced significantly down to 12 by relying on large-$N_c$ sum rules. Altogether we describe accurately more than 220 data points from six different lattice groups, BMW, PACS-CS, HSC, LHPC, QCDSF-UKQCD and NPLQCD. Values for all counter terms relevant at N$^3$LO are predicted. In particular we extract a pion-nucleon sigma term of 39$_{-1}^{+2}$ MeV and a strangeness sigma term of the nucleon of $sigma_{sN} = 84^{+ 28}_{-;4}$ MeV. The flavour SU(3) chiral limit of the baryon octet and decuplet masses is determined with $(802 pm 4)$ MeV and $(1103 pm 6)$ MeV. Detailed predictions for the baryon masses as currently evaluated by the ETM lattice QCD group are made.
The volume-dependence of a shallow three-particle bound state in the cubic box with a size $L$ is studied. It is shown that, in the unitary limit, the energy-level shift from the infinite-volume position is given by $Delta E=c (kappa^2/m),(kappa L)^{-3/2}|A|^2 exp(-2kappa L/sqrt{3})$, where $kappa$ is the bound-state momentum and $|A|^2$ denotes the three-body analog of the asymptotic normalization constant, which encodes the information about the short-range interactions in the three-body system.
In the present paper we address the interaction of charmed mesons in hidden charm channels in a finite box. We use the interaction from a recent model based on heavy quark spin symmetry that predicts molecules of hidden charm in the infinite volume. The energy levels in the box are generated within this model, and several methods for the analysis of these levels (inverse problem) are investigated.
In this talk I present the formalism we have used to analyze Lattice data on two meson systems by means of effective field theories. In particular I present the results obtained from a reanalysis of the lattice data on the $KD^{(*)}$ systems, where the states $D^*_{s0}(2317)$ and $D^*_{s1}(2460)$ are found as bound states of $KD$ and $KD^*$, respectively. We confirm the presence of such states in the lattice data and determine the contribution of the $KD$ channel in the wave function of $D^*_{s0}(2317)$ and that of $KD^*$ in the wave function of $D^*_{s1}(2460)$. Our findings indicate a large meson-meson component in the two cases.
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