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Analysis of intermediate energy nucleon-deuteron elastic scattering
ANNALS
OF PHYSICS
81, 364-366 (1973)
Abstracts
of Papers
to Appear
in Future
Issues
Derivation of an Effective Lagrangian from a Generalized Scalar Curvature. T. A. BARNEBEY. Department of Physics, University of California, Los Angeles, California 90024. A spinor Lagrangian invariant under global coordinate, local Lorentz and local chiral SU(n) x SU(n) gauge transformations is presented. The invariance requirement necessitates the introduction of boson fields, and a theory for these fields is then developed by relating them to generalizations of the vector connections in general relativity and utilizing an expanded scalar curvature as a boson Lagrangian. In implimenting this plan, the local Lorentz group is found to greatly facilitate the correlation of the boson fields occurring in the spinor Lagrangian with the generalized vector connections. The independent boson fields of the theory are assumed to be the inhomogeneously transforming irreducible parts of the connections. It turns out that no homogeneously transforming parts are necessary to reproduce the chiral Lagrangian usually used as a basis for phenomenological field theories. The Lagrangian in question appears when the gravitational interaction is turned off. It includes pseudo-scalar, spinor, vector and axial vector fields, and the vector fields carry mass in spite of the fact that the theory is locally gauge invariant. On the High Energy Scattering of Protons by Nuclei and Triple Correlations. JOHN J. ULLO AND HERMAN FESHBACH. Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. The multiple scattering theory of Kerman, McManus, and Thaler is extended to include triple scattering effects. With a judicious choice of the propagator between scatterings, the triple scattering term is approximately proportional to the triple correlation function. The methods of Feshbach, Gal, and Hufner are generalized to provide a coupled channel description of the elastic scattering of fast particles including triple scattering. The coupling potentials depend directly on the pair and triple correlation functions. Numerical calculations are performed for protons of 1.69 BeV/c momentum on 4He. Centerof-mass correlations and phenomenological short-range dynamical correlations are tested using a spin isospin averaged nucleon-nucleon amplitude. The differential cross section around the second diffraction minimum and third diffraction peak is particularly sensitive to triple scattering effects. Present experimental accuracy around the third diffraction peak does not permit any definitive conclusions to be made. Analysis of Intermediate Energy Nucleon-Deuteron Elastic Scattering. E. A. REMLER AND R. A. MILLER. Department of Physics, College of William and Mary, Williamsburg, Virginia 23185. We present a theoretical analysis of a broad range of aspects of intermediate energy nucleondeuteron scattering. This analysis is based on a multiple scattering approach using knowledge of the deuteron’s structure and nucleon-nucleon interactions. Conversely, comparison of this theory with experiment can yield information about low and intermediate energy strong interactions. The relationship of this multiple scattering type of approach to the complementary Faddeev equation approach is discussed. Our program consists of calculating the single scattering and one nucleon exchange contributions in a realistic way then parametrizing the remaining contributions as an S-wave. We argue that the largest error in this analysis is the P-wave part of the double scattering and we give estimates of its size. The single scattering integral is evaluated 364 Copyright AU rights
0 1973 by Academic Press, Inc. of reproduction in any form reserved.
ABSTRACTS OF PAPERS TO APPEAR IN FUTURE ISSUES
365
numerically. Coulomb effects are neglected. We derive the relativistic expressions for single scattering and nucleon exchange and discuss the approximations made, including the off-massshell extrapolation of the nucleon-nucleon scattering amplitude. Fits are made to experimental measurements of differential cross sections, nucleon polarizations, and total elastic cross sections. Unitarity is maintained. We tabulate the partial waves for J < 512, L < 2. They are consistent with recent Faddeev calculations. We argue that with the additional calculation of double scattering the deuteron D-state percentage can be determined to the same relative uncertainty as the differential cross section. Even without the calculation of double scattering, our results indicate a D-state percentage around 8%. In an effort to provide benchmarks for future work, we have tried to be conscientious in describing our techniques and in tabulating numerical results. Comparisons are also made with earlier analyses. Short-Distance Behaviour of Quantum Electrodynamics and the Callan-Symanzik Equation for the Photon Propagator. EDUARDO DE RAFAEL. Institute for Advanced Study, Princeton, New Jersey and Institut des Hautes etudes Scientifiques, Bures-sur-Yvette, France, and JONATHAN L. ROSNER. Institute for Advanced Study, Princeton, New Jersey and CERN, Geneva, Switzerland. The short-distance behaviour of the photon propagator is discussed within the context of the corresponding Callan-Symanzik equation. The Callan-Symanzik function ,8(a) is calculated in perturbation theory up to sixth order. We find
/3(a) =f(j +f(g)’- &yj8+o[Q4]. The simplicity of this result is to be contrasted with a corresponding perturbation theory calculation of the Gell-Mann-Low function #(z), whose sixth order coefficient contains the transcendental 5(3) (the Riemann zeta function of argument three). A mechanism of cancellations in the calculation of b(a) has been found, and we prove its validity to all orders in perturbation theory. Lower Bounds on Cross Sections Without Unknown Constants and Valid at All Energies. C. LOPEZ AND F. J. YNDURAIN. Departamento de Flsica-C-XI, Universidad Autonoma de Madrid, Canto Blanco, Madrid, Spain. We obtain lower bounds for cross sections (total and differential) which are of the form of integral constraints, and which contain no unknown constants and that are valid at fmite energies (and not only asymptotically). The information that we use to obtain the bounds may be of three different types (giving three different kinds of bounds): a few low energy parameters; a few low energy parameters plus experimental information on a given wave (the D-wave); or one unphysical parameter that may be obtained from other sources (field theoretical calculations with soft pion techniques). The comparison of the bounds with experiment is also discussed. A Relativistic Quark Model for Mesons Based on Numerical Solutions of the Bethe-Salpeter Equation. ALAN H. Guru. Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 and Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540. A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound spin-l/2 quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons. Numerical solutions to the Bethtialpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral
OF PHYSICS
81, 364-366 (1973)
Abstracts
of Papers
to Appear
in Future
Issues
Derivation of an Effective Lagrangian from a Generalized Scalar Curvature. T. A. BARNEBEY. Department of Physics, University of California, Los Angeles, California 90024. A spinor Lagrangian invariant under global coordinate, local Lorentz and local chiral SU(n) x SU(n) gauge transformations is presented. The invariance requirement necessitates the introduction of boson fields, and a theory for these fields is then developed by relating them to generalizations of the vector connections in general relativity and utilizing an expanded scalar curvature as a boson Lagrangian. In implimenting this plan, the local Lorentz group is found to greatly facilitate the correlation of the boson fields occurring in the spinor Lagrangian with the generalized vector connections. The independent boson fields of the theory are assumed to be the inhomogeneously transforming irreducible parts of the connections. It turns out that no homogeneously transforming parts are necessary to reproduce the chiral Lagrangian usually used as a basis for phenomenological field theories. The Lagrangian in question appears when the gravitational interaction is turned off. It includes pseudo-scalar, spinor, vector and axial vector fields, and the vector fields carry mass in spite of the fact that the theory is locally gauge invariant. On the High Energy Scattering of Protons by Nuclei and Triple Correlations. JOHN J. ULLO AND HERMAN FESHBACH. Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. The multiple scattering theory of Kerman, McManus, and Thaler is extended to include triple scattering effects. With a judicious choice of the propagator between scatterings, the triple scattering term is approximately proportional to the triple correlation function. The methods of Feshbach, Gal, and Hufner are generalized to provide a coupled channel description of the elastic scattering of fast particles including triple scattering. The coupling potentials depend directly on the pair and triple correlation functions. Numerical calculations are performed for protons of 1.69 BeV/c momentum on 4He. Centerof-mass correlations and phenomenological short-range dynamical correlations are tested using a spin isospin averaged nucleon-nucleon amplitude. The differential cross section around the second diffraction minimum and third diffraction peak is particularly sensitive to triple scattering effects. Present experimental accuracy around the third diffraction peak does not permit any definitive conclusions to be made. Analysis of Intermediate Energy Nucleon-Deuteron Elastic Scattering. E. A. REMLER AND R. A. MILLER. Department of Physics, College of William and Mary, Williamsburg, Virginia 23185. We present a theoretical analysis of a broad range of aspects of intermediate energy nucleondeuteron scattering. This analysis is based on a multiple scattering approach using knowledge of the deuteron’s structure and nucleon-nucleon interactions. Conversely, comparison of this theory with experiment can yield information about low and intermediate energy strong interactions. The relationship of this multiple scattering type of approach to the complementary Faddeev equation approach is discussed. Our program consists of calculating the single scattering and one nucleon exchange contributions in a realistic way then parametrizing the remaining contributions as an S-wave. We argue that the largest error in this analysis is the P-wave part of the double scattering and we give estimates of its size. The single scattering integral is evaluated 364 Copyright AU rights
0 1973 by Academic Press, Inc. of reproduction in any form reserved.
ABSTRACTS OF PAPERS TO APPEAR IN FUTURE ISSUES
365
numerically. Coulomb effects are neglected. We derive the relativistic expressions for single scattering and nucleon exchange and discuss the approximations made, including the off-massshell extrapolation of the nucleon-nucleon scattering amplitude. Fits are made to experimental measurements of differential cross sections, nucleon polarizations, and total elastic cross sections. Unitarity is maintained. We tabulate the partial waves for J < 512, L < 2. They are consistent with recent Faddeev calculations. We argue that with the additional calculation of double scattering the deuteron D-state percentage can be determined to the same relative uncertainty as the differential cross section. Even without the calculation of double scattering, our results indicate a D-state percentage around 8%. In an effort to provide benchmarks for future work, we have tried to be conscientious in describing our techniques and in tabulating numerical results. Comparisons are also made with earlier analyses. Short-Distance Behaviour of Quantum Electrodynamics and the Callan-Symanzik Equation for the Photon Propagator. EDUARDO DE RAFAEL. Institute for Advanced Study, Princeton, New Jersey and Institut des Hautes etudes Scientifiques, Bures-sur-Yvette, France, and JONATHAN L. ROSNER. Institute for Advanced Study, Princeton, New Jersey and CERN, Geneva, Switzerland. The short-distance behaviour of the photon propagator is discussed within the context of the corresponding Callan-Symanzik equation. The Callan-Symanzik function ,8(a) is calculated in perturbation theory up to sixth order. We find
/3(a) =f(j +f(g)’- &yj8+o[Q4]. The simplicity of this result is to be contrasted with a corresponding perturbation theory calculation of the Gell-Mann-Low function #(z), whose sixth order coefficient contains the transcendental 5(3) (the Riemann zeta function of argument three). A mechanism of cancellations in the calculation of b(a) has been found, and we prove its validity to all orders in perturbation theory. Lower Bounds on Cross Sections Without Unknown Constants and Valid at All Energies. C. LOPEZ AND F. J. YNDURAIN. Departamento de Flsica-C-XI, Universidad Autonoma de Madrid, Canto Blanco, Madrid, Spain. We obtain lower bounds for cross sections (total and differential) which are of the form of integral constraints, and which contain no unknown constants and that are valid at fmite energies (and not only asymptotically). The information that we use to obtain the bounds may be of three different types (giving three different kinds of bounds): a few low energy parameters; a few low energy parameters plus experimental information on a given wave (the D-wave); or one unphysical parameter that may be obtained from other sources (field theoretical calculations with soft pion techniques). The comparison of the bounds with experiment is also discussed. A Relativistic Quark Model for Mesons Based on Numerical Solutions of the Bethe-Salpeter Equation. ALAN H. Guru. Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 and Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540. A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound spin-l/2 quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons. Numerical solutions to the Bethtialpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral