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Would baryons and their antiparticles interact via the strong interaction?

  1. Jun 11, 2008 #1
    And would the potential be equal in magnitude yet opposite in sign?

    If you were to approximate a yukawa potential for some baryon and had it "near" its antiparticle, what would the potential look like. The same for a baryon and another baryon but opposite?

    This would just be like a residual strong interaction right? A quick approximation maybe being a light meson exchange?
  2. jcsd
  3. Jun 11, 2008 #2
    It took me a while to realize what was the question about ! In hadronic physics, we are not used to considering particles vs antiparticles, but more in terms of multiplets of similar particles, where it so happens that the multiplets connect particles with their antiparticles. One of the reasons QCD was quickly realized to be an excellent candidate for strong interactions is that there is an attractive force in the quark-antiquark and three-quark sectors, but repulsive in the quark-quark sector. So things are not as simple as "if you turn a particle into its antiparticle, just reverse the force". However, particles and antiparticles do interact via strong interaction.
    The very notion of potential works only in non-relativistic physics, so bearing that in mind, we need to do something like fixing our baryons in static positions at a given distance from one another and the potential would be the resulting energy of the system. It may or may not be relevant to the dynamics, but we can do that. Then most likely the potential will remain essentially the same. Reason is partly answered
    we would indeed have meson exchanges between our static colorless sources. The quantum numbers of those mesons will determine whether the interaction is repulsive or attractive, their mass will determine the range of static interaction. So if you take one of your baryons and change it into another one in your multiplet (like its antibaryon) you will need to exchange other mesons but they will still be in the same multiplet of mesons (not the same multiplet as your baryons). Say at short distances you will have a similar more massive vector repulsion and at long distance you will have a less massive scalar attraction (masses are almost degenerate in a given multiplet).
    Last edited: Jun 11, 2008
  4. Jun 11, 2008 #3
    Well, I'm not sure how detailed I should be since I'm supposed to be researching this on my own, but I consider asking questions here part of research.

    Now, some of you may have the answer right away, but that not what I want, I really want to make sure I understand this and how to go about figuring it out. Heres the scenario:

    Non relativistic is fine.
    I'm trying calculate an oscillation suppression of a nnbar in the presence of other neutrons via the strong interaction with a very naive model. I've read a few articles that give a decent method of approximating the residual-strong interaction between nucleons in a nucleus by using a sum of a heavy and a light meson exchange. They have all the data fitted so I have actual values for the coupling contants + masses.
    While I'm not doing these calculations for nuclei, they are of the same interaction distance.
    I guess I'm asking, if I have this fit of a sum of two meson exchange potentials for a neutron-neutron interaction (approx), what can I do to it (the potential) to make it reflect the interaction (approx) of a neutron-antineutron?

    Is it equal in magnitude, yet opposite in sign? If so then I know what I have to do, just toss it in the Hamiltonian, and calculate he oscillation freq. {{E+V, dm},{dm,E-V}} or something similar.

    Or is it completely different?

    I'm trying to figure out how the strong interaction behaves for the antiparticle part of a nnbar state.
    Last edited: Jun 11, 2008
  5. Jun 11, 2008 #4
    I also thought about this question. I found a couple of references that might be useful:

    [1] M.-L. Yan, S. Li, B. Wu, B.-Q. Ma, Baryonium with a phenomenological
    skyrmion-type potential. http://www.arxiv.org/abs/hep-ph/0405087v4

    [2] J.M. Richard, Historical Survey of the Quasi-Nuclear Baryonium,

    For example, if you change the sign of the nucleon-antinucleon potential shown in fig 1. of [1] you'll get something similar to the nucleon-nucleon potential as usually drawn in textbooks. Experimental studies of baryon-antibaryon potentials are difficult, because they tend to annihilate.

    Another evidence for the opposite character of baryon-baryon and baryon-antibaryon potentials may come from the Sakata model, in which mesons are represented as nucleon-antinucleon bound states and baryons are composites of two nucleons and one antinucleon. This model was quite popular in the end of 1950's. Then it was replaced by the quark model and (almost) forgotten. In the paper

    K. Matumoto, S. Sawada, Y. Sumi, M. Yonezawa, "Mass formula in the
    Sakata model" Progr. Theor. Phys. Suppl. 19 (1961), 66

    masses of (then known) mesons and baryons were fitted in the Sakata model, and the conclusion was that interaction energy nucleon-antinucleon has equal magnitude but opposite sign wrt the interaction energy nucleon-nucleon.

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