NUCLEON-NUCLEON INTERACTION?

The earliest efforts to understand the interaction potential between nucleons followed Yukawa by working in terms of meson exchange. In other words the various mesons were considered the bosons of the strong interaction.  The nucleon-nucleon interaction displays obvious physical analogies to the atom-atom interaction! Alas, as time went on it was found that the nucleon-nucleon interaction depends on everything it could possibly depend upon... in other words, it is as complex as is physically possible!   As a result, workers in medium-energy nuclear physics tended to work directly with a parametrized nucleon-nucleon scattering amplitude, fitted to cross section data as a function of center-of-momentum energy.

The big problem with this approach to the nucleon-nucleon interaction is that the potential energy turns out to depend on absolutely everything it could possibly depend upon!  Things quickly get insanely complex.  Efforts to find a simpler version of the interaction, based for example on QCD, have not been inspirational.

The tensor term breaks rotational symmetry!

Left: symmetric: TE, S = 1, T = 0 (d) and SE, S = 0, T = 1. Right: antisymmetric: SO, S = 0, T = 0, and TO, S = 1, T = 1.

Parametrized nucleon-nucleon potential, and state functions of the deuteron. [u(r) for s-state and w(r) for d-state].  Since the potential does not have spherical symmetry, the s and d states are mixed into the ground (and only) bound state.  Note most of the state is well outside the range of the potential!

Quarks come in three colors and gluons come in eight color-anticolor combinations (the green-antigreen plus red-anti-red plus blue-antiblue combination is symmetrically colorless, in other words neutral).  You won't be surprised to learn that Quantum Chromodynamics introduces color charge, color hypercharge, and color isospin!


Glueballs, predicted "bound" states consisting only of gluons, have been predicted using approximations to the Standard Model, but have never been observed. If they existed they would be very massive and have an extremely short lifetime.





CHIRAL PERTURBATION THEORY

In QCD, the gauge theory of strong interactions, the lowest mass quarks are nearly massless and an approximate chiral symmetry is present. In this case the left- and right-handed quarks are interchangeable in bound states of mesons and baryons, so an exact chiral symmetry of the quarks would imply "parity doubling", and every state should appear in a pair of equal mass particles, called "parity partners".  A 0+ meson would therefore have the same mass as a parity partner 0- meson. This suggested the use of the same mathematical apparatus as used in the Higgs case, to deal with this chiral symmetry breaking.


ASYMPTOTIC FREEDOM

Asymptotic freedom in QCD was discovered in 1973 by David Gross and Frank Wilczek, and independently by David Politzer in the same year. Quarks inside the baryons behave as if they were free particles, momentum eigenstates. Qualitatively, the closer you get to a quark, the fewer gluons are near it. Yet the binding energy of a quark in a baryon or meson is infinite. Note that it is essentially impossible to have a "free gluon." Gluons only exist as virtual particles, never real. Attempts to knock out quarks or gluons from a proton using very high energy electrons result in "jets" of hadrons... the quarks and gluons cease to exist as such, as they leave the proton interior.


The big problem with QCD is that exact formal solutions to the equations are impossible. There are of course many suggested approximations, for various applications, but the most generally accurate approach has proven over the years to be lattice gauge theory, a purely numerical method having its origins in condensed matter physics. We will discuss it later.

Bag Models of Baryons

Largely ignored by textbooks, there have been a huge number of different so-called “bag models,” of the nucleon and its excited states, proposed since the 1970s. All the models confine three free valence quarks inside a surface  or spherical box of some kind, with various different boundary conditions at, and couplings to, the surface. People are still working on various complex bag systems, but it is hard to see how any real basic physical insight can result, although various basic symmetry principles can be applied in creating a bag system.  All bag models stem from a very simple model originally suggested by Bogoliubov in 1967.  Research using bag models continues even today (2022), with the latest wrinkles being chiral bag models, and bag models for mesons. 





THE ENERGY DESERT???


The so-called Standard Model consists of Quantum Chromodynamics, the theory of the strong interaction, and the Electroweak Theory, the theory of electromagnetic and weak processes. No flaw in the model has yet shown up; experimental results support the Standard Model to high precision. However, one obvious problem is that it contains 26 parameters that must be put in "by hand," based on experimental results, with no justification from some deeper theory.  Parameters of the Standard Model.


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