4. Decays Involving

4.1. Introduction

The system is thought to interact solely by NWI (except by couplings at the level), and thus it provides a good method for studying NWI. We find also, surprisingly, that the decays are often experimentally accessible.

4.2. Decays of the Form

In usual models, these decays cannot occur, since V, A and T couplings cannot contribute. There is no reason to believe, however, that is intrinsically left-handed [15]. The fact that it has appeared so in many experiments may simply be a manifestation of the fact that only charged-current weak interactions have been observed in detail, and it is known that contains which serves to project out a single helicity state. Let us assume that the apparent chirality of neutrinos is an accident arising from the form of the charged weak current. Thus P or S NWI would lead to .

By the very nature of the mass-generating terms associated with the Higgs' mechanism, at least in models similar to that of Weinberg and Salam, cannot contribute to since it couples to the trace of energy-momentum tensor of the fundamental fermion fields, i.e. to . This means that such a contribution would also be absent from X quasielastic scattering.

In the (somewhat unlikely) event that only pseudoscalar NWI exist,

where n is the number of massless types of neutrino coupling through NWI. Letting we obtain

There is, however, little reason to take such a small value for .

The process

has been suggested [15] as a possible one in which to detect helicity-flipping NWI. Another might be

The would be monochromatic and, with high hadron detection efficiency, this decay may be detectable (3). The process

is experimentally indistinguishable from , and it should occur in the Weinberg-Salam model---but with .

4.3. Decays of the Form

is very similar in structure to . In the latter, we take the photons to be dominated by vector mesons; in the former, the and virtual Z also to be dominated by mesons (fig. 2). The quantum numbers of M (which saturates the Z) depend on the model considered. In the Weinberg-Salam model, for example, M could be a vector meson (such as , or an axial vector one (4) (such as . It could not, however, be an isoscalar meson (such as D(1285)). In a pseudo-scalar model (5) , M could be any meson.

[ Figure 2 ] Diagram for the process . in a meson dominance approach.

In comparing with , which has been calculated by several authors [16] there is some difficulty associated with lepton mass singularities, but we obtain

In the Weinberg-Salam model, this yields (6) . A pseudoscalar model might give , a tensor one (taking ).

4.4. The Decay

The decay allows a rather clean study of the isovector NWI to be made. Regardless of its branching ratio, it will be difficult to detect experimentally, primarily because it is hard to know whether the initial particle was an without analysing most of its decay products. One method of circumventing this problem might be to use either in the N(1535) region, or near threshold, and to analyse the proton momentum to check that the recoiling mass was indeed . Then by increasing the photon detection efficiency, and decays could be rejected.

[ Figure 3 ] Graph of for various coupling types. The curves are normalised to the same .

We now write a general local matrix element for [17]:

where . This yields

with

and .

dd is given for various NWI in fig. 3. We have assumed that the coupling constants (form factors) are independent of . This appears to be roughly correct for most meson decays (7). We note the absence of interference terms in (4.9): these are all proportional to the lepton mass. Integrating (4.8), we obtain

We may take to proceed through the diagram of fig. 4. M must have , natural parity. In the Weinberg-Salam model, M must be (8) and preferentially . Such particles are not expected in quark models, and none are known to exist [8]. Removing the restriction and are candidates for M. Vector-meson dominance may not be a reasonable approximation in this decay (see subsect. 6.2). The largest alternative diagram contains an electromagnetic tadpole (exchange of a photon between quarks). In either of these models, we expect . For S, PS, , for T, PT, .

4.5. Decays of the Form

is structurally similar to ; the difference is simply that the is internally converted. The standard formulae [18] can thus be applied. The largest result is

yielding in the Weinberg-Salam model, and roughly the same for . The process will also be very difficult to detect experimentally: its only difference from is that the differential width is even more strongly at small values of the dilepton invariant mass.

previous  l   next