ELECTROMAGNETIC CORRECTIONS TO WEAK INTERACTIONS. THE BETA DECAYS OF THE MUON, NEUTRON, AND O$sup 1$$sup 4$

Journal Article · Wed May 01 00:00:00 EDT 1963 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

OSTI ID:4707740

Durand, L III; Landovitz, L F; Marr, R B

The momentum-dependent radiative corrections to the beta decays of the Meson ( mu ), the neutron, and O/sup 14/ was calculated to order alpha using the techniques of dispersion theory. The transition matrix elements can be expressed to this order (neglecting some effects of strong interactions) in terms of sets of vertex functions that satisfy oncesubtracted dispersion relations. The absorptive parts of the vertex functions can be expressed to the appropriate order in terms of the vertex functions themselves and the amplitudes for electromagnetic scattering of the charged particles. It is a curious feature of the present calculation that the choice of the subtraction points is not arbitrary, but is determined uniquely by the requirement that such physically significant quantities as decay rates and the momentum spectra of the leptons should contain no infrared divergences when calculated including the contributions of processes in which soft photons are emitted STAinner bremsstrahlung!. The subtraction constants play the role of renormalized weak coupling constants. The significance of this electromagnetic renormalization, and the connection between the choice of the subtraction point and the infrared divergence is examined in detail in the case of the meson ( mu ). Two models for the beta decay of O/sup 14/ were considered. The results obtained from the two models differ only slightly. Because of the appearance in the absorptive parts of the vertex functions of the form factors of the charged particles, evaluated for the particles on the mass shell, the effects on the transition amplitude of the finite electromagnetic structure of the nuclei are studied. The effects of the finite spacial distribution of the decaying matter are treated using the usual multipole expansion of the nuclear matrix element. The leading electromagnetic structure correction is of the same form as the familiar Z alpha RW in the correction for finite nuclear structure (finite deBroglie wavelength effect), but is of a different origin, and leads to a near doubling of the total structure corrections. The known theoretical corrections to the decay rates for the 0+ min gave no sig 0+ transitions O/sup 14/( BETA /sup +/)N/sup 14*/, Al/ sup 26*/( BETA /sup +/)Mg/sup 26/, and Cl /sup 34/( BETA /sup +/))S/sup 34/ are summarized. Using the recent, very accurate data on the decays of the meson ( mu ), O/sup 14/, and Al/sup 26*/, we obtain the values G/sub mu / (1.436 ction in DDT-C/ 0.001) X 10 /sup -49/erg cm/sup 3/, G/sub BETA /(O/sup 14/) = (1.419 ction in DDT-C/ 0.002) x 10/sup -49/ erg cm/sup 3/, and G/sub BETA /(Al/sup 26*/ ) = (1.430 ction in DDT-C/ 0.002) x 10/ sup -49/ erg cm/sup 3/ for the renormalized vector coupling constants for these transitions. The less accurate data on the neutron yield G/sub V/ = (1.356 ction in DDT-C/ 0.068) x 10/sup -49/ erg cm/sup 3/. The results for G/sub mu / and G/sub BETA / are not directly comparable in the present theory, but the different values of G/sub BETA / should be. The discrepancy of (0.8 ction in DDT-C/ 0.5)% between the effective coupling constants for the decays of O/sup 14/ and Al/sup 26*/ could, therefore, be significant, and may yield information about the still uncertain Coulomb corrections to the nuclear matrix elements. If the validity of the cutoff- dependent results of perturbation theory is assumed, the renormalization constants can be evaluated, and one obtalns G/sub mu ,bare/ = (1.431 ction in DDT-C/ 0.001) x 10/sup -49/ erg cm/sup 3/ and G/sub BETA ,bare/ (O/sup 14/) = (1.404 ction in DDT-C/ 0.007) x 10/sup -49/erg cm /sup 3/. Those coupling constants differ by 1.9 ction in DDT-C/ 0.2%, but because of uncertainties regarding the nuclear matrix element O/sup 14/, the effects of strong interactions, and the possible existence of an intermediate vector meson which mediates the weak interactions, a direct comparison of these numbers may not be relevant to the possible universality of the Fermi interaction. (auth)

• Research Organization: Brookhaven National Lab., Upton, N.Y.; and Yale Univ., New Haven
• NSA Number: NSA-17-019141
• OSTI ID: 4707740
• Report Number(s): BNL-6539; 0031-899X
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Vol. Vol: 130; Other Information: BNL-6539. Orig. Receipt Date: 31-DEC-63
• Country of Publication: United States
• Language: English

Related Subjects

PHYSICS
ALUMINUM 26
BETA DECAY
CHLORINE 34
COUPLING CONSTANTS
DISPERSION THEORY
DISTRIBUTION
ELECTROMAGNETISM
ERRORS
FIELD THEORY
INTERACTIONS
MAGNESIUM 26
MATHEMATICS
MATRICES
MOMENTUM
MUONS
NEUTRONS
NITROGEN 14
NUCLEAR STRUCTURE
NUMERICALS
OXYGEN 14
PERTURBATION THEORY
SULFUR 34
VECTORS
VERTEX FUNCTIONS