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Mu Capture, Beta Decay, and Pi-Meson Decay

M. L. GOLDBERGER

1959
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Reviews of Modern Physics
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I N the original Yukawa formulation of meson theory, the r meson (as we now believe Yukawa's particle to be) was to provide a natural explanation for fJ decay. The process r -e+ ii was regarded as an elementary interaction and nuclear fJ decay was imagined to proceed by the route n -p+r -µ+e+ ii. There are a variety of reasons why this scheme fails. Just the opposite point of view is now generally adopted, namely, that the nuclear {3 decay is fundamental and that the observed decay of the r
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... decay of the r meson is to be explained in terms of it. We do not exclude the possibility that {3 decay be described in terms of an as yet unknown heavy intermediate. Nevertheless, the nuclear {3 decay is to be regarded as essentially primary. In order to describe the actual dominant r-meson decay mode r -µ+ii it is necessary to assume the existence of another {3 decay like process, µ-meson capture. The elementary process may be described as µ+p-n+v, or equally well as n+p -µ+ii; the first is the experimentally observed µ-meson absorption reaction, whereas, the second, the annihilation of a neutron and an antiproton, plays an important role in r-meson decay. Since this is a conference on weak interactions, I shall not be able to say that one of the r mesons, the neutral one, decays into two gamma rays; electromagnetic interactions are too strong to be mentioned [ Furthermore, I will not be able to point out that a theory of the r 0 decay can be given which is very similar to what we describe for charged pions. During the past year or two the field of weak interactions has become a surprisingly orderly one. The twocomponent theory of the neutrino, as well as the principle of lepton conservation now both seem to be well established. Both nuclear {3 decay and µ-meson decay seem to be describable in terms of a vector ( V) and axial vector (A) coupling. This statement has to be qualified somewhat in the case of nuclear {3 decay. There is the additional fact that in both {3 decay andµ decay the vector coupling constants are almost identical. Rather less is known of the coupling types for the µ-meson capture reaction, but the dominant couplings seem to have about the same strength as in {3 decay. This is discussed by Primakoff. We tentatively assume that the apparently universal (V,A) interaction extends also to this Fermi process. Precisely what do we mean by a universal interaction? This can mean only that the basic interaction Lagrangian contains only these two coupling types. Given this basic definition let us see whether there is anything surprising in the observed decays. First, in µ decay the V and A couplings are forced to be equal if we adopt the two component neutrino theory. In {3 decay, gA = 1.25 gv, which need not be disturbing. The amazing thing is, with {3 decay and µ capture involving strongly interacting particles and µ decay involving only weakly interacting ones, that there is any kind of universality whatsoever. One would expect the existence of pions and other strongly interacting particles to modify greatly the effective matrix element for transitions between physical nucleons as compared to the µ-decay process. Insofar as the vector coupling is concerned, Gerstein and Zel'dorich and Feynman and Gell-Mann have made a very attractive suggestion: They propose that there may be a principle analogous to gauge invariance in electrodynamics which would insure that the vector coupling constant in {3 decay be the same even when the strong interactions are turned on. Recall that as a result of current conservation, or, if you prefer, gauge invariance, the charge of a bare and physical proton is the same. In order to achieve this goal the {3 decay "vector current density" gvi/r(µl/I [1/1 is a nucleon field operator] must be augmented by terms which ultimately couple leptons directly to pions, etc., and such that the total "current density" jµV satisfies ojµV /OXµ. The difference between vector and axial vector couplings in {3 decay is attributed to renormalization of the axial vector interaction. One troublesome point in connection with this proposal has been raised by Wightman, Telegdi, and Michel. When one computes the electromagnetic radiative corrections forµ decay and {3 decay, one finds that to lowest order in all couplings not a finite correction for µ decay, but a logarithmic divergence in {3 decay. One may argue that if the nucleons are "dressed" properly and the radiative corrections are then computed (something no one knows how to do exactly) the result will be convergent. Nevertheless, it is not clear why, even if the {3-decay effect is made finite, the two radiativelycorrected vector coupling constants should continue to be equal. Let us discuss in a systematic way the role of strong interactions in Fermi processes. The work to be reviewed was carried out by Treiman and me and has been, for the most part, published elsewhere. I apologize for this, but in order to talk about something new, I would have to make an obviously wrong new theorythe correct one already having been given. We suppose that {3 decay andµ capture are described by the Lagrangian density, £1= Z2J A1{;.(l-75)i'YA"Y61/11 (1/lni"fA'Y51/I p) +Z2fv{t.(l-75)'YA1/;1( {Jn' YA1/I p) +Hermitian conjugate, (1) 797

doi:10.1103/revmodphys.31.797
fatcat:bmp5g2rj6nc6hd6sq5u6uslgaa