Wednesday, September 21, 2011

Another W Boson v. Z Boson distinction

Only the charged weak force bosons, W+ and W-, give rise to inelastic neutrino scattering as well as to elastic scatter in electron neutrinos. Inelastic scattering is not created by the electrically neutral Z boson which produces only elastic neutrino scattering, continuing the basic picture in which the W bosons do all manner of things that nothing else does, while the Z boson's effects are pretty ordinary. Z bosons also manifest phenomenologically in electroweak interference and the proper calculation of anomalous magnetic moments.

Also on the subject of the weak force, it turns out to be horribly difficult to locate easy to understand descriptions of the "force", i.e. mass moving momentum, aspect of the weak force in layman's descriptions. With some real effort you can dig through some of the more techical literature to identify the charged and neutral current components of the electroweak Lagrangian, and with a bit more effort you kind dig up the potential function of the weak force field, which in practice, is a short range force that is approximately equal in strength to the electromagnetic force at 10^-18 m, "but at distances of around 3×10−17 m the weak interaction is 10,000 times weaker than the electromagnetic.", in general, the weak force is stronger at shorter ranges, and weaker at longer ranges. More generally:

Due to their large mass (approximately 90 GeV/c^2) these carrier particles, termed the W and Z bosons, are short-lived: they have a lifetime of under 1×10^−24 seconds. The weak interaction has a coupling constant (an indicator of interaction strength) of between 10^−7 and 10^−6, compared to the strong interaction's coupling constant of about 1; consequently the weak interaction is weak in terms of strength. The weak interaction has a very short range (around 10^−17–10^−16 m). . .

The weak interaction affects all the fermions of the Standard Model, as well as the hypothetical Higgs boson; neutrinos interact through the weak interaction only. The weak interaction does not produce bound states (nor does it involve binding energy) – something that gravity does on an astronomical scale, that the electromagnetic force does at the atomic level, and that the strong nuclear force does inside nuclei.

All told, the weak force has a rather modest impact on the way the universe behaves at the macrolevel.

It isn't clear to me if the lack of weak interaction bound states is a theoretical result, or an absence of empirical evidence, or both.

At the distance scale at which the nuclear binding force (mediated by pions and derivative of the strong force within protons and neutrons) operates, the weak force is a quantitatively negligable component factor, that is much weaker than either the strong force or the electromagentic force.

But, I have yet to see anything really credible that more than hints that the weak force is generally repulsive, and not attractive, based on the amateur authors assumption that it acts in opposition to the generally attractive strong force (although, of course, the strong force switches from a repulsive to an attractive regime with distance) and I don't have enough confidence that I understand the normal numerical values and sign conventions of the terms in the Lagrangian to say with confidence that I fully understand how they play out. It also seems from the neutral current portion of the Lagrangian that local electromagnetic field strength interacts to some extent with neutral current Z boson activity.

1 comment:

Andrew Oh-Willeke said...


"The simplest case is only one flavor of neutrino interacting with itself via the neutral
current. Since vector exchange produces repulsion among like particles, we intuitively expect
the ν−ν channel to be repulsive in this case. This is borne out by our explicit computation,
which we now describe. . . . if we confine ourselves to neutrinos alone, and to the dynamics of the standard model, we find no possibility of neutrino pairing. Among the ways to avoid this conclusion are

(a) extend the dynamics beyond the standard model (we shall discuss this possibility
in the conclusions);

(b) enlarge the dynamics to include the charged leptons (and possibly also the quarks). We have performed an analysis in which we consider not only neutrinos themselves but also electrons circulating in the loop. This generates an additional term in 􀀀eff , and hence an additional contribution to the gap equation for the neutrino condensate.
It does not, however, alter the result that there is no solution to the gap equation;

(c) Finally, we can consider condensates that are composed not of neutrinos alone, but that pair
neutrinos with charged leptons. Of course, since these condensates would be charged, their
phenomenological consequences would be much more drastic than those of purely neutrino
condensates. . . . Phenomenologically, therefore, it is unlikely that this type of condensate could occur, except maybe in the early universe when larger background densities of both electrons and neutrinos were present. . . .

One is led, therefore, to suggest the existence
of a new interaction, acting only on neutrinos, for which the effective G2 would have a scale
of approximately 1 eV instead of the 200 GeV characteristic of GF . An interaction of the
same form as eqs. (1) or (2) would serve nicely, provided only we change the sign, thereby
generating an attractive channel. The condensate would then produce Majorana neutrino
masses of the form m ∼ = G2hννi, and possibly a contribution to the cosmological constant ∼ G2 | hννi |2. Since both G and the fermi momentum pF are of order 1 eV, one
obtains neutrino masses and a cosmological constant that are likewise of this order.
Furthermore, if we generalize our earlier analysis and allow the chemical potentials for
the different neutrino species to vary, the condensates could depend non-trivially on flavor,
perhaps leading to an interesting spectrum of neutrino masses and mixings.

Our conclusions can be enumerated as follows:
(i) There is no attractive channel in the purely neutrino sector of the standard model;
(ii) The addition of charged leptons leads to attraction in the flavor off-diagonal channels,
but a pairing instability occurs only if the Fermi momenta of the neutrino and the charged
leptons are equal;
(iii) In the case of neutrino-charged lepton pairing, there may also be the possibility of
condensation in a Lorentz non-invariant channel. We have not looked at this in detail;
(iv) If a new interaction exists among neutrinos with characteristic scale 1 eV, neutrino
condensates could form with the right size to generate an interesting spectrum of masses
and mixings, as well as an appropriate contribution to the cosmological constant. This
possibility is currently under active investigation."