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Lattice Calculation: Caveats and Challenges

Lattice Calculation: Caveats and Challenges. What lattice can and cannot do Caveats of calculating meson masses Gluebal How about the width? Heavy-light mesons Glueballs. What Can We Use Lattice to Calculate?.

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Lattice Calculation: Caveats and Challenges

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

  2. What Can We Use Lattice to Calculate? • 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. • However, one can calculate scattering length and phase shift for elastic scattering and discern multi-quark hadrons by exploring the finite volume dependence.

  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. • 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. a0 and πη), one needs to identify both and discern their natures, e.g. through the volume dependence of the spectral weights.

  4. Challenges for calculation • Except for σ(600), practically all the tetraquark mesonium candidates are near their respective two-meson thresholds, e.g. f0(980) and a0 (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 • ~ 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.

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

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

  7. K. Rummukainen andS. Gottlieb, NP B450, 397 (1995)

  8. Lüscher formula

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

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