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Lattice Calculation: Caveats and Challenges

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- What lattice can and cannot do
- Caveats of calculating meson masses
- Gluebal
- How about the width?
- Heavy-light mesons
- Glueballs

- 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.

- 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.

- 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.

Glueballs

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)

|T|2 in continuum

W on lattice

E

E

?

L

L

E

E

Lüscher formula

The two-point Green’s function decays exponentially at large separation of time

Mass M= Ep(p=0), decay constant ~ Φ