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? 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.

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

Atomic TF model basics

Some TF model quark equations

Unconfined NRTF Quark Model, f(x)

Unconfined NRTF Quark Model, density

Unconfined NRTF Quark Model, potential

Unconfined NRTF Quark Model, 2 degenerate flavors N 1 :N 2 =2:1 x 2 = ; x 1 =

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

Unconfined NRTF Quark Model, 2 different mass flavors Unequal mass case: N 1 :N 2 =2:1 m 2 :m 1 =2:1, x 2 = , x 1 =

Introduce a bag energy term ~ B V Realization

Confined NRTF Quark Model, f(x)

Confined NRTF Quark Model, f(x max ) vs. x max.

Confined ultraRTF Quark Model, w(x)

Confined ultraRTF Quark Model, density

Confined ultraRTF Quark Model, potential

Unconfined ultraRTF Massive Gluon Quark Model, w(r)

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)

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

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

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