Lattice calculation caveats and challenges
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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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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?

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


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.


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)


Lüscher formula


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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