Summary
The differential cross-sections for the reactions
are discussed in the framework of Cabibbo’s theory, under the assumption that the ΔS=0 axial vector current is of the first class underG conjugation. It is pointed out that detailed studies of the differential cross-sections would permit, in principle, a test of the theory over a wide range of momentum transfers. Estimates for the probabilities of these reactions are given.
Riassunto
Si discutono, entro lo schema della teoria di Cabibbo, le sezioni d’urto differenziali delle reazioni
, nell’ipotesi che la corrente vettoriale assiale ΔS=0 sia della prima classe rispetto alla coniugazioneG. Si mette in rilievo che studi dettagliati della sezione d’urto differenziale permetterebbero, in linea di principio, una verifica della teoria in un grande intervallo di momenti trasferiti. Si dànno le stime delle probabilità di queste reazioni.
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Literatur
N. Cabibbo:Phys. Rev. Lett.,10, 531 (1963).
Several aspects of neutrino-induced reactions have been already discussed in the framework of Cabibbo’s theory byM. M. Block:Phys. Rev. Lett.,12, 262 (1964).
Identical relations have been derived in the literature: SeeN. Cabibbo andR. Gatto:Nuovo Cimento,21, 873 (1961). For the Wigner-Eckart theorem forSU 3 see, for example,J. J. de Swart:Rev. Mod. Phys.,35, 916 (1963).
S. Weinberg:Phys. Rev.,112, 1375 (1958). Alternatively, one can postulateT-invariance and the ΔI=1 rule.
L. Wolfenstein: (preprint).
S. L. Adler:Nuovo Cimento,30, 1020 (1963).
In eq. (5) we have assumed the validity ofT-invariance for the leptonic processes so that all the structure functions may be taken to be real.T-invariance is actually implied if one assumes that i) the complete vector currents belong to the same octet as the electromagnetic current and are, therefore, conserved in the limit of exact unitary symmetry and ii) the basic « unrenormalized » current of the strongly interacting particles is of theV — A type.
C. N. Yang:Proceedings of the International Conference on Fundamental Aspects of Weak Interactions, Brookhaven National Laboratory (1963), p. 249.
T. D. Lee andC. N. Yang:Phys. Rev.,126, 2239 (1962).
The estimates for dσ(0)/dq 2 andσ tot, based on eqs. (6), differ somewhat from the values indicated in Table Ib of ref. (2).
This reaction is allowed in theories in which the vector currents are assumed to be conserved under the symmetry groupG 2. See, for example,R. E. Behrends andA. Sirlin:Phys. Rev. Lett.,5, 476 (1960).
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Research Supported in part by the National Science Foundation.
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Sirlin, A. Cabibbo’s theory and neutrino-induced reactions. Nuovo Cim 37, 137–141 (1965). https://doi.org/10.1007/BF02734702
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DOI: https://doi.org/10.1007/BF02734702