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CP violation in gauge theories and the electric dipole moment of the neutron
ANNALS OF PHYSICS 126,
Abstracts
512-513 (1980)
of Papers
to Appear
in Future
Issues
Supergravity with and without Superspace. S. FERRARA, &ole Normale Superieure, Paris; AND P. VAN NIELWENHUIZEN, Institute for Theoretical Physics, State University of New York, Stony Brook, New York. We show that the superspace formalism follows from the component formalism. After constructing the supervielbeins and superconnections off-shell in second order formalism with the minimal set of auxiliary fields, we show that the resulting supertorsions satisfy the constraints of the various equivalent superspace approaches. Symmetries and Conservation Laws in Gauge Theories. R. JACKIW AND N. S. MANTON. Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. The relationship between conservation laws and symmetries of space-time is familiar. Here it is shown that in a symmetric background gauge field these conservation laws persist, but in modified form. A further contribution to the conserved quantity occurs. It is determined by the gauge transformation which, when acting together with some coordinate transformation, leaves the symmetric background gauge potential invariant. The addition to the constant of motion can also be interpreted as arising from the dynamical interaction of the gauge field with the system. A classical example is the angular momentum conservation law for a charged particle moving in the field of a magnetic monopole. Generalizations of this are here derived. ReIativistic Theory of Parity-Violation in Many-Electron Atoms. J. HILLER AND J. SUCHER, Department of Physics, University of Maryland, College Park, Maryland 20742; AND G. FEINBERG AND B. LYNN, Department of Physics, Columbia University, New York, New York 10027. We present a theoretical framework for the calculation of parity-mixing effects of the weak interaction in many-electron atoms which is based on first principles. The starting point is an extemalfield no-pair Hamiltonian H+ which allows for a consistent treatment of effects coming from virtual electron-positron pairs and can be used as a basis for a systematic program of calculations. We show that the matrix element & for parity-violating El transitions, given by quantum electrodynamics, gets an appreciable contribution 4 Pair from states involving an extra electron-positron pair. However, on eliminating the velocity operator a in favor of the length operator iwr, we find cancellations which result in an accurate formula for d involving only the positive-energy N-electron eigenstates of H+ as intermediate states and the length form, iwr . E, of the dipole operator. We discuss the implications of our results for calculations of amplitudes for parity-violating radiative El transitions in many-electron atoms. Our analysis includes a study of the effects coming from the weak electron+lectron interaction as well as those arising from the weak electron-nucleus interaction. CP Violation in Gauge Theories and the Electric Dipole Moment of the Neutron. D. V. NANOPOULOS AND AS~M YILDIZ, Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138; AND PAUL H. COX, Research Laboratory of Mechanics, University of New Hampshire, Durham, New Hampshire 03824. A nonvanishing contribution to the neutron electric dipole moment in CP-violating gauge theories of the weak interactions, arising from interaction of the photon with two-quark subsystems of the
512 Copyright All rights
0 1980 by Academic Press, Inc. of reproduction in any form reserved.
ABSTRACTS
OF
PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
513
three-bound-quark neutron system, is calculated. In the Kobayashi-Maskawa model the resulting value of the moment is estimated as 0(10m33) e cm; however, strong interaction corrections (gluonic radiative corrections) give quark moment contributions which may be numerically larger (possibly 10-80*1 e cm). Either case clearly distinguishes gauge-sector CP violation from Higgs-sector CP violation, which typically gives a neutron moment of order 10eZ4e cm. Variation of Parameters in Cosmology. ROBERT T. JANTZEN. Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27514. Parameters which appear in the solutions of the dynamical equations of spatially homogeneous cosmology or in the dynamical equations themselves are subject to algebraic relations imposed by the constraint equations, i.e., are confined to a constraint hypersurface in parameter space. Values of these parameters off the constraint hypersurface often correspond to solutions which have an additional stiff perfect fluid source that may or may not be flowing orthogonally to the spatially homogeneous foliation or to a related inhomogeneous but spatially self-similar solution or to a combination of the two. These possibilities are studied and explicitly illustrated, leading to a uniform derivation of most of the known exact anisotropic spatially homogeneous or spatially self-similar solutions as well as some new ones. Dynamics of the Crystallized One Component Plasma. H. R. GLYDE, Physics Department, University of Ottawa, Ottawa, Ontario KlN 6N5, Canada; AND G. H. KEECH, Chalk River Nuclear Laboratories, Atomic Energy of Canada Research, Co. Ltd., Chalk River, Ontario KOJ lJ0, Canada. The dynamics and energy of the crystallized one component plasma (OCP) is evaluated using the self-consistent phonon (SCP) theory of lattice dynamics. Melting of the crystal is also examined. The OCP crystal is harmonic for particle rms vibrational amplitudes as large as 25 % of the interparticle spacing. This is due to the soft (r-l) core of the Coulomb potential. Anharmonic effects are, however, entirely responsible for the eventual mechanical instability, identified here with melting, of the crystal at large enough rms amplitudes. This takes place at r, = 180 at T = 0 K for the most sophisticated SCP theory. In the classical limit, this SCP theory predicts the crystal to be more stable than does the “exact” Monte Carlo study of melting by Pollock and Hansen. This suggests that including further anharmonic terms in the SCP theory leads to melting at even larger rs at T = 0 K. However, comparison of crystal and fluid energies by Ceperley and Hansen and Mazighi suggest melting in the range rs = 65 to 135. Near melting the anharmonic contributions shift the phonon frequencies by a factor of 2 and the phonon lifetimes become very short.
Abstracts
512-513 (1980)
of Papers
to Appear
in Future
Issues
Supergravity with and without Superspace. S. FERRARA, &ole Normale Superieure, Paris; AND P. VAN NIELWENHUIZEN, Institute for Theoretical Physics, State University of New York, Stony Brook, New York. We show that the superspace formalism follows from the component formalism. After constructing the supervielbeins and superconnections off-shell in second order formalism with the minimal set of auxiliary fields, we show that the resulting supertorsions satisfy the constraints of the various equivalent superspace approaches. Symmetries and Conservation Laws in Gauge Theories. R. JACKIW AND N. S. MANTON. Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. The relationship between conservation laws and symmetries of space-time is familiar. Here it is shown that in a symmetric background gauge field these conservation laws persist, but in modified form. A further contribution to the conserved quantity occurs. It is determined by the gauge transformation which, when acting together with some coordinate transformation, leaves the symmetric background gauge potential invariant. The addition to the constant of motion can also be interpreted as arising from the dynamical interaction of the gauge field with the system. A classical example is the angular momentum conservation law for a charged particle moving in the field of a magnetic monopole. Generalizations of this are here derived. ReIativistic Theory of Parity-Violation in Many-Electron Atoms. J. HILLER AND J. SUCHER, Department of Physics, University of Maryland, College Park, Maryland 20742; AND G. FEINBERG AND B. LYNN, Department of Physics, Columbia University, New York, New York 10027. We present a theoretical framework for the calculation of parity-mixing effects of the weak interaction in many-electron atoms which is based on first principles. The starting point is an extemalfield no-pair Hamiltonian H+ which allows for a consistent treatment of effects coming from virtual electron-positron pairs and can be used as a basis for a systematic program of calculations. We show that the matrix element & for parity-violating El transitions, given by quantum electrodynamics, gets an appreciable contribution 4 Pair from states involving an extra electron-positron pair. However, on eliminating the velocity operator a in favor of the length operator iwr, we find cancellations which result in an accurate formula for d involving only the positive-energy N-electron eigenstates of H+ as intermediate states and the length form, iwr . E, of the dipole operator. We discuss the implications of our results for calculations of amplitudes for parity-violating radiative El transitions in many-electron atoms. Our analysis includes a study of the effects coming from the weak electron+lectron interaction as well as those arising from the weak electron-nucleus interaction. CP Violation in Gauge Theories and the Electric Dipole Moment of the Neutron. D. V. NANOPOULOS AND AS~M YILDIZ, Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138; AND PAUL H. COX, Research Laboratory of Mechanics, University of New Hampshire, Durham, New Hampshire 03824. A nonvanishing contribution to the neutron electric dipole moment in CP-violating gauge theories of the weak interactions, arising from interaction of the photon with two-quark subsystems of the
512 Copyright All rights
0 1980 by Academic Press, Inc. of reproduction in any form reserved.
ABSTRACTS
OF
PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
513
three-bound-quark neutron system, is calculated. In the Kobayashi-Maskawa model the resulting value of the moment is estimated as 0(10m33) e cm; however, strong interaction corrections (gluonic radiative corrections) give quark moment contributions which may be numerically larger (possibly 10-80*1 e cm). Either case clearly distinguishes gauge-sector CP violation from Higgs-sector CP violation, which typically gives a neutron moment of order 10eZ4e cm. Variation of Parameters in Cosmology. ROBERT T. JANTZEN. Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27514. Parameters which appear in the solutions of the dynamical equations of spatially homogeneous cosmology or in the dynamical equations themselves are subject to algebraic relations imposed by the constraint equations, i.e., are confined to a constraint hypersurface in parameter space. Values of these parameters off the constraint hypersurface often correspond to solutions which have an additional stiff perfect fluid source that may or may not be flowing orthogonally to the spatially homogeneous foliation or to a related inhomogeneous but spatially self-similar solution or to a combination of the two. These possibilities are studied and explicitly illustrated, leading to a uniform derivation of most of the known exact anisotropic spatially homogeneous or spatially self-similar solutions as well as some new ones. Dynamics of the Crystallized One Component Plasma. H. R. GLYDE, Physics Department, University of Ottawa, Ottawa, Ontario KlN 6N5, Canada; AND G. H. KEECH, Chalk River Nuclear Laboratories, Atomic Energy of Canada Research, Co. Ltd., Chalk River, Ontario KOJ lJ0, Canada. The dynamics and energy of the crystallized one component plasma (OCP) is evaluated using the self-consistent phonon (SCP) theory of lattice dynamics. Melting of the crystal is also examined. The OCP crystal is harmonic for particle rms vibrational amplitudes as large as 25 % of the interparticle spacing. This is due to the soft (r-l) core of the Coulomb potential. Anharmonic effects are, however, entirely responsible for the eventual mechanical instability, identified here with melting, of the crystal at large enough rms amplitudes. This takes place at r, = 180 at T = 0 K for the most sophisticated SCP theory. In the classical limit, this SCP theory predicts the crystal to be more stable than does the “exact” Monte Carlo study of melting by Pollock and Hansen. This suggests that including further anharmonic terms in the SCP theory leads to melting at even larger rs at T = 0 K. However, comparison of crystal and fluid energies by Ceperley and Hansen and Mazighi suggest melting in the range rs = 65 to 135. Near melting the anharmonic contributions shift the phonon frequencies by a factor of 2 and the phonon lifetimes become very short.