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Challenges and Insights in Lattice QCD Calculations of Meson and Baryon Properties

This overview explores the intricacies and challenges associated with lattice quantum chromodynamics (QCD) calculations, particularly concerning meson masses, decay constants, matrix elements, and the study of multi-quark hadrons. It discusses the implications of the Charge-Hermiticity theorem, which assures the reality of observables, while acknowledging the absence of a direct S-matrix in lattice computations. Key issues such as the difficulties in fitting tetraquark candidates near threshold levels and the importance of finite volume dependence in discerning hadronic states are highlighted, drawing on lessons learned from pentaquark baryon calculations.

thomas-baxter
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Challenges and Insights in Lattice QCD Calculations of Meson and Baryon Properties

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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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