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?.

Download Presentation

Lattice Calculation: Caveats and Challenges

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

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.

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 Ï€Î·), one needs to identify both and discern their natures, e.g. through the volume dependence of the spectral weights.

Challenges for calculation

Except for Ïƒ(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 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)

|T|2 in continuum

W on lattice

E

E

?

L

L

E

E

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

LÃ¼scher formula

Hadron Mass and Decay Constant

The two-point Greenâ€™s function decays exponentially at large separation of time