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Recent Research on the Thomas Fermi Quark Model

Recent Research on the Thomas Fermi Quark Model. Work with Andy Liu and Nate Larson!. Motivations. Where are the mesons, baryons or mixed states with more than the usual two or three quarks?

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Recent Research on the Thomas Fermi Quark Model

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  1. Recent Research on the Thomas Fermi Quark Model • Work with Andy Liu and Nate Larson!

  2. Motivations • Where are the mesons, baryons or mixed states with more than the usual two or three quarks? • There is a need for quark models which can help lead expensive lattice QCD calculations in the right direction in the search for high quark states.

  3. TF models: • Treats particles as a Fermi gas at T=0 • Builds in Fermi statistics, but not fully quantum mechanical. (“semi-classical”) • Gets more accurate for a larger number of particles • Gives accurate atomic binding energies • Relativistic versions can be formulated • TF model better than “bag models”, which do not include the Coulomb interactions, for large numbers of particles

  4. Atomic TF model basics

  5. Some TF model quark equations

  6. Unconfined NRTF Quark Model, f(x)

  7. Unconfined NRTF Quark Model, density

  8. Unconfined NRTF Quark Model, potential

  9. Unconfined NRTF Quark Model, 2 degenerate flavors N1:N2=2:1 x2=1.67188; x1=3.41003

  10. Unconfined NRTF Quark Model, 2 degenerate flavors, different number ratios

  11. Unconfined NRTF Quark Model, 2 different mass flavors Unequal mass case: N1:N2=2:1 m2:m1=2:1, x2=0.99430, x1=3.18200

  12. Realization Introduce a bag energy term ~ B V

  13. Confined NRTF Quark Model, f(x)

  14. Confined NRTF Quark Model, f(xmax) vs. xmax.

  15. Confined ultraRTF Quark Model, w(x)

  16. Confined ultraRTF Quark Model, density

  17. Confined ultraRTF Quark Model, potential

  18. Unconfined ultraRTF Massive Gluon Quark Model, w(r)

  19. Model can be extended: • To include nonzero mass quarks in relativistic case • To include anti-quarks • To include heavy quarks • To have spin-dependent forces • To look at exotic forms of matter (eg., “strange” matter, color-flavor locked quarks from Cooper pairs, or massive gluon models, or combinations)

  20. TF Quark Model Goals: • To survey the parameter space looking for relative stability and connections to known phenomenology • To shed light on the question: Are there states of many quarks and/or anti-quarks? • To prepare the way for detailed lattice calculations • First step: Confined NR model

  21. TF Quark Model Energies E Can show that E ~ A for large A. A

  22. Baylor paper: Thomas-Fermi quark model: Nucl.Phys.A826:49-73,2009.

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