6. Other Meson Decays

6.1. Photon and Dalitz Decays

In close analogy with , any net circular photon polarization in is a signal of violation or of final-state interactions (thought to be absent in Yang-Mills' theories). In the presence of P, S interactions, this could be as large as . In may well be 0.1%, and possibly detectable in the case , as [18] , although this decay has not yet been observed [8].

Perhaps the most interesting meson photon decay is . This is forbidden by (but not ) invariance, and its occurrence would be a signal of NWI or electromagnetic violation. The dominant diagram would probably be fig. 6. For V, A, NWI, Yang's theorem [26], which we generalize in subsect. 6.6, breaks down (11) since the virtual Z has a scalar component which can decay to , so long as NWI violate . In a Yang-Mills' theory, there is no direct coupling; the lowest-order process involves a virtual fermion loop, yielding (12). If, however, Z is pseudoscalar then the process is allowed (the coupling will probably be electromagnetic; c.f. ) and we expect (13).

[ Figure 6 ] Diagram for the process by NWI

6.2. Decays to Hadrons

The first form of decay which we consider here is pseudoscalar meson mesons. No decay of this type is fundamentally pure violating; [27], for example, violates . has been considered as a possible decay in which to detect electromagnetic -violation [19]; here we discuss its use as a signal for NWI. The conventional [28] diagram for is that of fig. 7; i.e. involving an electromagnetic tadpole. The NWI contribution would probably consist of a Z tadpole, so that either a or meson could occur in place of the virtual . However, a meson cannot decay to (c.f. the - paradox), and so we must assume that any NWI -violation is a result of an admixture of a , which is not allowed in quark models. Ignoring this suppression, we may make the naive estimate

Experimentally, [8].

[ Figure 7 ] Diagrams for in composite and constituent models.

Another possible form of decay is pseudoscalar meson mesons lepton pair. Examples of this are

The decay (6.2) occurs electromagnetically with [29] . For (6.3) we estimate , and for (6.4): and .

6.3. Charged Meson Decay

occurs primarily as an electromagnetic correction to the weak decay , with [30] and . Even weak-electromagnetic interference effects will occur only at the level, resulting in, for example, .

has been searched for [31] (as a test for strong interactions). One may estimate for charged-current weak interactions and for NWI.

6.4. Charmed Particle Decays

In the Weinberg-Salam-Glashow-Iliopoulos-Maiani model, charm-changing NWI are absent, simply in analogy with the absence of strangeness-changing NWI. Detection or failure to detect NWI at the level expected would thus put stringent constraints on weak interaction models. The best decay in which to achieve this appears to be

There is assumed to be no electromagnetic competition here.

6.5. Scalar Meson Decays

The only meson decay which is interesting from the point of view of NWI, and which differs significantly from the analogous meson decay is . Here only scalar NWI may contribute in the limit of invariance (14). In the Weinberg-Salam model, therefore, the only non-electromagnetic possible intermediate state is . One finds [32]

where is a fundamental fermion field whose mass arises from Higgs' mechanism, and is the trace of the stress-energy tensor. The may be either a quark field or a meson field. We find

leading to a contribution times the electromagnetic one, i.e. unobservably small. There do exist other models in which either the quark masses are very large or a second is introduced [33], which would lead to a larger weak component in but we deem these unlikely.

Experimentally, the existence of ordinary scalar mesons is still in doubt [34], but the state in may have a measurable branching ratio, since it probably contains rather heavy quarks.

6.6. Vector Meson Decays

There exist a number of vector meson decays which could furnish information on NWI. Isgur [35] has analysed , and we have nothing to add. has been discussed by Rich and Winn [36]. Using a free quark model, they obtain . Generally, , where is a dimensionless NWI coupling constant in the Weinberg-Salam model, and is the number of massless neutrino types. Rich and Winn conclude that

could be observed in colliding beams.

Yang [26] has shown that the decay of a particle to is forbidden by invariance. It is easy to show (15) , however, that this is also forbidden by gauge invariance and Bose statistics, and so we will never observe a decay such as even in the presence of violating NWI.

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