unpublished).if there were a universal coupling for the electron and the muon, the suppression of the electron decay could be explained only in terms of a pseudoscalar meson decaying through an axial-vector coupling.
conspiracy has opposite parity Regge trajectories intersecting at t =0. For details on Lorentz pole theory, see M. Toller, Nuovo Cimento 53A, 671 (1967), and 54A, 295 (1968). 5 By cr we mean an S -wave state of two pions, of whatever isospin and energy. 6 H. Hogaasen and P. Salin, Nucl. Phys. B2, 657 (1967). 7An s a contribution to fi _i Q Q would require an M =0 trajectory {A t type) at J = a +1. Here we deal with M = 0 or M = 1 trajectories with leading J = a . ^t must, if M is to be defined from on-shell considerations. We might mention that our special results for the -KG and 7rp couplings are easily derivable without the explicit use of conspiracy conditions from the offshell invariant-amplitude approach given in R. F. Sawyer, Phys. Rev. 167, 1372. The argument given, leading to Eq. (4), is similar to one due to M. Le Bellac, Phys. Letters 25B, 524 (1967). Kinematic arguments leading to (2) and (3) can be found in L. Jones and H. K. Shepard (to be published). 9 This theorem is implicit in the general residue formula for the unequal-mass case given in the paper by Cosenza, Sciarrino, and Toller (to be published), Q Mtf^it-X + l+lM-Ui-Xgll] 10 This is true up to certain pole terms for the pion
The decay rate for the mode K + -^e + + v has been measured. There are ten events, which include an estimated 0.34 background event only, and the branching ratio relative to K + -*n + + v is found to be JR = 1.9l §;|x 10~5. This is in good agreement with the prediction of the V-A theory, which is i? = 2.10xlo~* 5 , including radiative corrections.The branching ratio for K*-~e + + v relative to K + -~ [i + + v is predicted to be 1 12 *0=l 9 9 2 KM^-M V K fi {M e /M K )fA +/P {M / M K )fA + fPneglecting radiative corrections and assuming (li,e) universality. The constants/^ and/^ are for axial vector and pseudoscalar coupling, respectively. They may be relatively complex if time-reversal invariance is violated. Some special cases of Eq. (1) are the following: /*o,/ p = 0, # 0 = 2.57xl0 -5
/'A o,f p ±o, R n = 1.10.It follows that measurement of R 0 is a sensitive test for a natural pseudoscalar coupling constant. For strangeness-conserving decays, such an investigation has been made 2 by measurement of the branching ratio for TT + ^e + + v. Radiative corrections have been calculated 3 for the case fP = 0. The branching ratio then becomes RJl.0-0.185 + 0.0273 ln(2£/M )].The second term gives a suppression of the rate owing to virtual photons. The third term results from inner bremsstrahlung over the electron energy interval (E max -e) to £ max . In this note we define the K e 2 branching ratio R to be given by the first two terms in expression (2), so that i? = 0.815# 0 . In normalizing our observed rate, we have made allowance for inner bremsstrahlung according to the third term. Thus our result is independent of the resolution of the apparatus.We have measured the K e 2 + branching ratio at NIMROD, the 7-GeV proton synchrotron at the Rutherford High Energy Laboratory. Our apparatus is shown in Fig. 1. K + mesons from a 700-MeV/c separated beam were brought to rest in the beryllium plates of a small spark chamber at an average rate of 1500 per machine 982
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