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The Lamb's Balance

  1. May 21, 2004 #1


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    I am calling "lamb balance" to the conjecture of recoil-lamb corrections to the energy levels between two particles of different mass M, m, when the small particle m has an additional coupling to a boson field of mass M' near to M. The link between M and m can be any coulombian or Yukawian field, in principle.

    One expects that when increasing M to be greater than M' the correction increases sharply and the corresponding loss of stability in the more external levels is noticeable.

    This way should let you to "weight" the mass of M'.

    The Lamb Balance is a conjecture because of two reasons:

    -People has not seen the utility of calculating Lamb+Recoil effects in this specific case of a massive field coupled only to one of the particles.

    -There are not, as far as I know, quantum experiments able to control the weight of the recoiling particle M.

    Lately I speculated that neutron skins (kind of populated halos) could be the appropriate experiment. There, the more external nucleons are far off from the rest of the nucleus, and the momenta exchanged is small. So in this very peculiar case the rest of the nucleus can be considered roughly as a single recoiling particle of mass M_A.

    These skins happen near the neutron dripline. So it is reasonable postulate that if the Lamb Balance works, we will notice a change in levels each time that the drip line crosses the value of a massive boson field. In a symmetrical way, and allthough the Coulomb barrier minimises the possibility of proton skins, it was also sensible to consider if the proton drip line presents the same effect.

    (Here, one should stop a moment to consider that meson-exchange models of force are not able yet to reproduce accurately the effects needed to calculate nuclear masses. Until ten years ago computational effort could be blamed, but today there are empirical models of force (Skirme etc) that are able to reproduce fairly the spectra of nuclear masses, so calculation is no more an excuse. Besides, these empirical models give us fairly confidence on the location of the drip lines)

    The first results of this research have been summarised in figures 1 and 8 of hep-ph/0405076 v2. Figure 8 is more complete, and some small progress could have occurred since I drawn it. Let me to go from the firm points to the more speculative ones:

    In the neutron dripline, the jump N=126 happens at a mass of about 175 Gev.
    In the proton dripline, the jump P=50 happens at the mass of Z0 boson, and the jump P=82 happens at a mass of about 175 GeV.

    In the neutron dripline, the jump N=82 happens at a mass of about 115 GeV, and the jump N=184 happens at the mass of 246 GeV.
    In the proton dripline, the jump P=114 happens at the mass of 246 GeV.

    First stop to identify these values. 175 GeV is singularised in the standard model as the mass of the Top quark. The very short lived mesons composed from it should also have masses in this range. Another possibility is a beyond standard model boson degenerated in mass with the mass of top.

    246 GeV is the vacuum expected value of the higgs *field* in the current electroweak model. No particle is expected there -except if the higgs coupling is unity- in the standard model, but anyway it is a known mass scale coming from the electroweak model.

    115 GeV is the mass scale at which an anomalous excess was detected in ALEPH, at CERN, some years ago, and expected to be a neutral boson.

    If you have followed me until here, you can have a couple of criticisms:
    Does the W particle has a role to play here? What happens with the Higgs at the proton dripline and, for the same token, with the Z0 at the neutron dripline?

    The second question seems to be answered by recalling the existence of semi-magic numbers. At the proton side of the Higgs, already Klinkenberg noticed a very strong competition between g7/2 and d5/2. At the neutron side of the Z, a semimagic n=64 could be researched. The small role of the Higgs could be simply a indication of a mass of the up quark lower than the one of the down, so the Higgs coupling to protons is weaker than to neutrons after all.

    As for the W, it is a peculiar particle because it is the responsible of beta decay, thus it is unclear if the Lamb Balance, as naively built, applies to it.

    One could also speculate if the W peculiarity lets it to contribute for magicities a bit below its natural scale, namely the ones of Z=40 (semimagic but very noticeable) and N=50. But for this scale the CERN has also a 2.5 sigma candidate in the closet, namely the 69 GeV excess of hep-ex/0105057, hep-ex/0309056, which has been discarded mainly because it does not decay to leptons as well as SUSY wants, and because it disagrees with current MSSM fashions. With a charged higgs like boson covering these two magic numbers, the role W could reduce simply to small perturbations in levels near its natural area, in hard competition with its usual beta decay; and perhaps some additional contribution to Z=50.

    To conclude:

    -At different speculation levels, the nuclear lamb balance is able to fit all the magic numbers beyond 28 in neutron and proton drip lines.

    -At his highest speculative level, the balance favours a THDM, not MSSM, model of symmetry breaking, where the mass of the charged higgs is smaller than mass of Z0, the mass of the top is degenerated with one of the extant bosons, and another one remains at exactly the value of the vacuum of the current minimal higgs mechanism.

    -at progressive speculation levels, the nuclear lamb balance favours both the 115 GeV excess and the 69 GeV excess measured by LEP.


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  3. May 28, 2004 #2


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