By Hasan-Uddin Khan, Sherban Cantacuzino, Charles Correa
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Forbidden semileptonic processes. (a) Neutral lepton currents. Q. S c = w+ W- -2. ---" e lie e e III I i= I 11> ::c ~ i= ~ 27 On Peratization Methods 3. UNCROSSED LADDER GRAPHS We will discuss the uncrossed ladder graphs for the process (Fig. 3) -- e e e Fig. 3. Ladder graphs for Vii Vii +e ---+ Ve + JL. L Ve Since we wish to sum the leading singularities of each graph, we have to know the maximum degree of divergence which occurs in each order. To this purpose, we proceed as follows: Of course, we have to introduce a cutoff A for virtual momenta in order to estimate the degree of divergence.
Cocconi for assistance prior to publication of this article. REFERENCES 1. D. , Nuovo Cimento 26:896 (1962). 2. T. Regge, Nuovo Cimento 14:951 (1959). 3. N. , Phys. Rev. J. , Phys. Rev. Letters 11 :425 (1963). 4. R. Hagedorn, Nuovo Cimento 15:455 (1960); Frtschr. Phys. 9:1 (1961). 5. G. Fast and R. Hagedorn, Nuovo Cimento 27:208 (1963). 6. G. Fast, R. W. Jones, Nuovo Cimento 27:856 (1963). 7. G. , Phys. Rev. Letters 11:499 (1963). Crossing Relations and Spin States M. JACOB* MATSCIENCE Madras, India It is well known that in any process involving two incoming and two outgoing particles there is a symmetry between the process obtained by replacing an incoming (outgoing) particle of momentum k by an outgoing (incoming) antiparticle of momentum -k, crossing symmetry.
Hereafter, we shall discuss only the W-field theory, although at the end we shall show that, even though the W-field theory and four-fermion field theory can be made equivalent in the second order, this is not necessarily true when we sum all the higher order graphs. By higher order graph we imply a graph in which a large number of vector mesons are exchanged between the fermions. Though it involves higher powers of g2, we do not neglect them. As is to be expected, higher order weak interactions will also raise the problems of renormalization of mass and charge, but this can be discussed as in renormalizable theory.