scadron70 page 1 Lattice Calculation: Caveats and Challenges What lattice can and cannot do What lattice can and cannot do Caveats of calculating meson masses Caveats of calculating meson masses Gluebal Gluebal How about the width? How about the width? Heavy-light mesons Heavy-light mesons Glueballs Glueballs

scadron70 page 2 What Can We Use Lattice to Calculate? Masses, decay constants, form factors, matrix elements, etc. Masses, decay constants, form factors, matrix elements, etc. Due to the Charge- Hermiticity (CH) theorem, all observables are real. Thus, there is no S-matrix. Due to the Charge- Hermiticity (CH) theorem, all observables are real. Thus, there is no S-matrix. However, one can calculate scattering length and phase shift for elastic scattering and discern multi-quark hadrons by exploring the finite volume dependence. However, one can calculate scattering length and phase shift for elastic scattering and discern multi-quark hadrons by exploring the finite volume dependence.

scadron70 page 3 Lessons Learned from Lattice Calculation of Pentaquark Baryons Hadron masses do not depend on interpolation fields. They only affect the spectral weights in the hadron correlators. Hadron masses do not depend on interpolation fields. They only affect the spectral weights in the hadron correlators. Since both the multi-quark hadron (e.g. ) and the muti-hadron state can be generated by the same interpolation field with a specific quantum number (e.g. a 0 and πη), one needs to identify both and discern their natures, e.g. through the volume dependence of the spectral weights. Since both the multi-quark hadron (e.g. ) and the muti-hadron state can be generated by the same interpolation field with a specific quantum number (e.g. a 0 and πη), one needs to identify both and discern their natures, e.g. through the volume dependence of the spectral weights.

scadron70 page 4 Challenges for calculation Except for σ(600), practically all the tetraquark mesonium candidates are near their respective two-meson thresholds, e.g. f 0 (980) and a 0 (980) Except for σ(600), practically all the tetraquark mesonium candidates are near their respective two-meson thresholds, e.g. f 0 (980) and a 0 (980) are near the threshold. So are are near the DK and DD (DD * ) thresholds. It is hard to fit both the mesonium and the two-meson state which are within are near the DK and DD (DD * ) thresholds. It is hard to fit both the mesonium and the two-meson state which are within ~ 100 MeV to each other. Heavy-light mesons: it is more desirable to have the same chiral fermion formalism. One needs to be concerned about the finite ma errors for the heavy quark which demands small lattice spacing a and thus large lattice volume. Heavy-light mesons: it is more desirable to have the same chiral fermion formalism. One needs to be concerned about the finite ma errors for the heavy quark which demands small lattice spacing a and thus large lattice volume.

Caltech 2008, page 5 Quenched Glueball Spectrum Y. Chen et al, PRD (2006); PDG (2006) Glueballs Quenched spectrum was calculated with ~ 100,000 configurations. Number of dynamical fermion configurations are typically in the hundreds.

chiral07 page 6 E |T| 2 in continuum E W on lattice E L E L ?

chiral07 page 7 K. Rummukainen and S. Gottlieb, NP B450, 397 (1995)

chiral07 page 8 Lüscher formula

Glasgow, 2005, page 9 Hadron Mass and Decay Constant The two-point Green’s function decays exponentially at large separation of time Mass M= E p (p=0), decay constant ~ Φ