UNITARY SYMMETRY AND LEPTONIC DECAYS

UNITARY SYMMETRY AND LEPTONIC DECAYS

15 JUNE 1963 | Nicola Cabibbo
The position of the curve on the θ axis can be shifted to larger angles by increasing V₂ and R, maintaining the VR ambiguity in the optical model. It can be shifted to smaller angles by increasing V₁ and |η|, the energy difference between entrance and exit channels, which is experimentally determined. V₂ has a larger effect than V₁ because it determines two wave functions, while V₁ determines only one. A large difference between V₂ and V₁ is necessary to properly locate the curves. The quoted values are not unique. The overall width is mainly determined by R_b. Increasing R_b decreases the overall width and increases the cross-section magnitude at the curve's center. Using the best R_b value for each state automatically fits the relative magnitudes well. Increasing W₁, W₂, and a has small effects. Increasing W₁ and W₂ slightly decreases both curves. In fitting the p-state curve, V₂ and V₁ have opposite effects on the peak height ratio. Increasing V₂ increases the ratio, while increasing both V₁ and V₂ slightly reduces the minimum depth. From this calculation, we tentatively conclude that for finite potentials, there are no significant differences between single-particle wave functions with the same principal quantum number, angular momentum, binding energy, and rms radius. Thus, a distorted-wave analysis of (p,2p) experiments determines single-particle wave functions well. The rms radius of the charge distribution in C¹² from our empirical R_b value is 2.5 fm, close to the experimental value of 2.4 fm. The s-state proton rms radius is 1.7 fm, matching the α-particle value. Whether this holds for other light nuclei is under investigation. We thank Dr. M. A. Melkanoff, Dr. J. S. Nodvik, Dr. D. S. Saxon, and Dr. D. G. Cantor for their optical-model code SCAT 4, and Dr. C. A. Hurst and Mr. K. A. Amos for discussions. Nicola Cabibbo presents an analysis of leptonic decays based on unitary symmetry for strong interactions and the V-A theory for weak interactions. He assumes that the weak current J_μ transforms according to the eightfold representation of SU₃, neglecting currents with ΔS = -ΔQ or ΔI = 3/2. The vector part of J_μ is in the same octet as the electromagnetic current. An octet of axial currents is also assumed. From these assumptions, J_μ is expressed in terms of vector and axial currents. The parameter θ is determined from decay rates, yielding θ = 0.26. This parameter is used to predict branching ratios for baryon decays, showing agreement with experimental data. The vector-coupling constant for β decay is G cos θ, correcting FermThe position of the curve on the θ axis can be shifted to larger angles by increasing V₂ and R, maintaining the VR ambiguity in the optical model. It can be shifted to smaller angles by increasing V₁ and |η|, the energy difference between entrance and exit channels, which is experimentally determined. V₂ has a larger effect than V₁ because it determines two wave functions, while V₁ determines only one. A large difference between V₂ and V₁ is necessary to properly locate the curves. The quoted values are not unique. The overall width is mainly determined by R_b. Increasing R_b decreases the overall width and increases the cross-section magnitude at the curve's center. Using the best R_b value for each state automatically fits the relative magnitudes well. Increasing W₁, W₂, and a has small effects. Increasing W₁ and W₂ slightly decreases both curves. In fitting the p-state curve, V₂ and V₁ have opposite effects on the peak height ratio. Increasing V₂ increases the ratio, while increasing both V₁ and V₂ slightly reduces the minimum depth. From this calculation, we tentatively conclude that for finite potentials, there are no significant differences between single-particle wave functions with the same principal quantum number, angular momentum, binding energy, and rms radius. Thus, a distorted-wave analysis of (p,2p) experiments determines single-particle wave functions well. The rms radius of the charge distribution in C¹² from our empirical R_b value is 2.5 fm, close to the experimental value of 2.4 fm. The s-state proton rms radius is 1.7 fm, matching the α-particle value. Whether this holds for other light nuclei is under investigation. We thank Dr. M. A. Melkanoff, Dr. J. S. Nodvik, Dr. D. S. Saxon, and Dr. D. G. Cantor for their optical-model code SCAT 4, and Dr. C. A. Hurst and Mr. K. A. Amos for discussions. Nicola Cabibbo presents an analysis of leptonic decays based on unitary symmetry for strong interactions and the V-A theory for weak interactions. He assumes that the weak current J_μ transforms according to the eightfold representation of SU₃, neglecting currents with ΔS = -ΔQ or ΔI = 3/2. The vector part of J_μ is in the same octet as the electromagnetic current. An octet of axial currents is also assumed. From these assumptions, J_μ is expressed in terms of vector and axial currents. The parameter θ is determined from decay rates, yielding θ = 0.26. This parameter is used to predict branching ratios for baryon decays, showing agreement with experimental data. The vector-coupling constant for β decay is G cos θ, correcting Ferm
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