Showing papers in "Physical Review D in 1978"

Neutrino Oscillations in Matter

Abstract: The effect of coherent forward scattering must be taken into account when considering the oscillations of neutrinos traveling through matter. In particular, for the case of massless neutrinos for which vacuum oscillations cannot occur, oscillations can occur in matter if the neutral current has an off-diagonal piece connecting different neutrino types. Applications discussed are solar neutrinos and a proposed experiment involving transmission of neutrinos through 1000 km of rock.

Charmonium: The model

Abstract: A comprehensive treatment of the charmonium model of the ψ family is presented. The model's basic assumption is a flavor-symmetric instantaneous effective interaction between quark color densities. This interaction describes both quark-antiquark binding and pair creation, and thereby provides a unified approach for energies below and above the threshold for charmed-meson production. If coupling to decay channels is ignored, one obtains the “naive” model wherein the dynamics is completely described by a single charmed-quark pair. A detailed description of this “naive” model is presented for the case where the instantaneous potential is a superposition of a linear and Coulombic term. A far more realistic picture is attained by incorporating those terms in the interaction that couple charmed quarks to light quarks. The coupled-channel formalism needed for this purpose is fully described. Formulas are given for the inclusive e + e − cross section and for e + e − e annihilation into specific charmed-meson pairs. The influence of closed decay channels on ψ states below charm threshold is investigated, with particular attention to leptonic and radiative widths.

Massless Fields with Integer Spin

Abstract: The Fierz-Pauli Lagrangian for massive particles with arbitrary integral spin $s$, first obtained by Hagen and Singh, is examined in the limit of vanishing mass. Unexpectedly, a considerable simplification occurs. The potential $h$ is a symmetric tensor of rank $s$; the "trace" ${h}^{\ensuremath{'}}$, obtained by contraction of a pair of indices against the flat-space metric, does not vanish but the trace ${h}^{\ensuremath{'}\ensuremath{'}}$ of ${h}^{\ensuremath{'}}$ does. The wave equation admits a gauge group, and this implies conditions on the source. The divergence of the source need not vanish, only the traceless projection of the divergence must be zero; this is a major departure from the usual assumption and may bear on the question of the existence of a physically interesting source for fields with spin \ensuremath{\ge}3. This weaker condition on the source is sufficient to guarantee that only $\mathrm{helicities}\ifmmode\pm\else\textpm\fi{}s$ are transmitted between sources. A generalized Gupta program is proposed, that is, a search for a scheme for generating a theory of interacting, massless particles, consistent to all orders in the coupling constant.

Pattern of Symmetry Breaking with Two Higgs Doublets

Abstract: We analyze fully the pattern of symmetry breaking of an SU(2) \ifmmode\times\else\texttimes\fi{} U(1) gauge model with two Higgs doublets. We find the phenomenon of spin-zero leptons to be a very general one, and obtain a solution previously obtained by one of us as a limiting case.

Deep-inelastic scattering beyond the leading order in asymptotically free gauge theories

Abstract: We calculate the full order-${g}^{2}$ corrections to the coefficient functions which determine the ${Q}^{2}$ dependence of the moments of deep-inelastic structure functions. The calculation is performed in the minimal-subtraction scheme of 't Hooft. The results are combined with the recent two-loop calculations of anomalous dimensions by Floratos, Ross, and Sachrajda to give the full ${\overline{g}}^{2}$ corrections to the leading order of asymptotic freedom. We present results for ${C}_{n}(1,{\overline{g}}^{2})$ relevant for electroproduction and neutrino reactions for both nonsinglet and singlet combinations of the structure functions. Phenomenological consequences of the full ${\overline{g}}^{2}$ corrections to the nonsinglet structure function are discussed. The corrections to the Gross-Llewellyn Smith and Bjorken sum rules are estimated to be of the order of 15%.

P Wave Baryons in the Quark Model

Abstract: We discuss the spectrum and mixing angles of negative-parity baryons in a quark-model framework inspired by quantum chromodynamics. We take into account in zero order the removal of the degeneracy between the two $P$-wave states of the three-quark system in the $S=\ensuremath{-}1$ sector, as well as the hyperfine interaction between quarks, but neglect spin-orbit coupling. We find good agreement with experiment in the $S=0$ and $S=\ensuremath{-}1$ sectors where there are data and predict the $S=\ensuremath{-}2, \ensuremath{-}3$ sectors.

Toward a Theory of the Strong Interactions

Abstract: A systematic study is made of the relevant degrees of freedom and the dynamics of quantum chromodynamics (QCD). We find that the dynamical properties of QCD are, to a large extent, a consequence of the structure of the vacuum arising from the tunneling between degenerate, classically stable, vacuums, and that the relevant degrees of freedom can be taken to be the Euclidean path histories that can be used to calculate the tunneling in the semiclassical approximation. This nonperturbative vacuum structure appears well suited to the major features of QCD, i.e., the dimensional transmutation that determines the size of the hadrons and the strong-interaction coupling constant, the source of dynamical chiral symmetry breaking, and the mechanism responsible for quark confinement.

Quantum field theory in anti-de Sitter space-time

Abstract: We consider the problem of quantizing scalar fields propagating in anti-de Sitter space-time. This space-time is static but not globally hyperbolic and hence the usual quantization procedures are inapplicable. Nevertheless, we show that a consistent quantization scheme can be devised by carefully controlling information entering and leaving the space-time through its timelike spatial infinity.

Massless fields with half-integral spin

Abstract: The Fierz-Pauli Lagrangian for massive particles with spin $s=n+\frac{1}{2}$, $n$ integer, is examined in the limit of vanishing mass. A considerable simplification occurs. The potential $h$ is a Rarita-Schwinger spinor-tensor of tensorial rank $n$. The "spinor-trace" ${h}^{\ensuremath{'}}$, defined by ${h}_{\ensuremath{ u}\ensuremath{\lambda}\dots{}}^{\ensuremath{'}}\ensuremath{\equiv}{\ensuremath{\gamma}}^{\ensuremath{\mu}}{h}_{\ensuremath{\mu}\ensuremath{ u}\ensuremath{\lambda}\dots{}}$ does not vanish, and neither does ${h}^{\ensuremath{'}\ensuremath{'}}\ensuremath{\equiv}{({h}^{\ensuremath{'}})}^{\ensuremath{'}}$; but ${h}^{\ensuremath{'}\ensuremath{'}\ensuremath{'}}$ does vanish. The wave equation admits a gauge group, $h\ensuremath{\rightarrow}h+\mathrm{sym}\mathrm{grad} \ensuremath{\xi}$, with ${\ensuremath{\xi}}^{\ensuremath{'}}=0$. The most interesting feature is that the source $t$ need not be divergence free, only the traceless part of ${p}^{\ensuremath{\mu}}{t}_{\ensuremath{\mu}\ensuremath{ u}\dots{}}$ must vanish. This weaker condition on $t$ turns out to be sufficient to guarantee that only $\mathrm{helicities}\ifmmode\pm\else\textpm\fi{}s$ are transmitted between sources.

Order and disorder in gauge systems and magnets

Abstract: We show how phase transitions in Abelian two-dimensional spin and four-dimensional gauge systems can be understood in terms of condensation of topological objects. In the spin systems these objects are kinks and in the gauge systems either magnetic monopoles or fluxoids (quantized lines of magnetic flux). Four models are studied: two-dimensional Ising and $\mathrm{XY}$ models and four-dimensional ${Z}_{2}$ and U(1) gauge systems.

Regularization, renormalization, and covariant geodesic point separation

Abstract: One of the techniques used in quantum field theory in curved space-times to eliminate divergences in the vacuum expectation value of the stress tensor for quantum fields propagating on a classical gravitational background is called covariant geodesic point separation. Beginning with the Schwinger-DeWitt proper-time method we show how to discard divergences in the effective action by renormalization of the coupling constants in a classical gravitational action functional. We then demonstrate how to determine which terms in the vacuum expectation value of the stress tensor vanish when this renormalization is carried out. This is done using the point-separation approach. We give the form of these terms for spin 0, 1/2, and 1 fields, massive or massless, on an arbitrary curved background. The procedure used is covariant and introduces no ambiguities beyond those inherent in any renormalization scheme. We note the appearance of trace anomalies which arise due to the breaking of conformal invariance by the renormalization process and give the form of the anomalies for arbitrary space-time dimension.

Trace anomaly of a conformally invariant quantum field in curved spacetime

Abstract: We analyze a point-separation prescription for renormalizing the stress-energy operator ${T}_{\ensuremath{\mu}\ensuremath{ u}}$ of a quantum field in curved spacetime, based on the assumption that the expectation value $G(x, {x}^{\ensuremath{'}})=〈\ensuremath{\varphi}(x)\ensuremath{\varphi}({x}^{\ensuremath{'}})+\ensuremath{\varphi}({x}^{\ensuremath{'}})\ensuremath{\varphi}(x)〉$ has the form of a Hadamard elementary solution. An error is pointed out in the work of Adler, Lieberman, and Ng: The "locally determined" piece ${G}^{L}(x, {x}^{\ensuremath{'}})$ and "boundary-condition-dependent" piece ${G}^{B}(x, {x}^{\ensuremath{'}})$ of $G(x, {x}^{\ensuremath{'}})$ do not separately satisfy the wave equation in ${x}^{\ensuremath{'}}$, as required in their proof of the conservation of the boundary-condition-dependent contribution to ${T}_{\ensuremath{\mu}\ensuremath{ u}}$. This error affects the point-separation renormalization prescription given in my previous paper describing an axiomatic approach to stress-energy renormalization. It is now seen that this prescription yields a stress-energy tensor whose divergence is not zero but is the gradient of a local curvature term. However, this deficiency can be corrected by subtracting off this local curvature term times the metric tensor; as a direct consequence the trace of ${T}_{\ensuremath{\mu}\ensuremath{ u}}$ becomes nonvanishing. Given this result it is shown that any prescription for renormalizing ${T}_{\ensuremath{\mu}\ensuremath{ u}}$ which is consistent with conservation (axiom 3), causality (axiom 4), and agreement with the formal expression for the matrix element between orthogonal states (axiom 1) must yield precisely this trace, modulo the trace of a conserved local curvature term. Hence, for consistency with the first four axioms and dimensional considerations, we find that the trace of the stress tensor of the conformally invariant scalar field must be ${T}_{\ensuremath{\mu}}^{\ensuremath{\mu}}={(2880{\ensuremath{\pi}}^{2})}^{\ensuremath{-}1}({C}^{\ensuremath{\alpha}\ensuremath{\beta}\ensuremath{\delta}\ensuremath{\gamma}}{C}_{\ensuremath{\alpha}\ensuremath{\beta}\ensuremath{\delta}\ensuremath{\gamma}}+{R}^{\ensuremath{\alpha}\ensuremath{\beta}}{R}_{\ensuremath{\alpha}\ensuremath{\beta}}=\frac{1}{3}{R}^{2})$ plus an arbitrary constant times ${\ensuremath{ abla}}_{\ensuremath{\alpha}}{\ensuremath{ abla}}^{\ensuremath{\alpha}}R$. This confirms previous work of a number of authors on the existence of trace anomalies. For consistency with axiom 5 (no "local curvature terms containing third or higher derivatives of the matric"), the coefficient of the ${\ensuremath{ abla}}_{\ensuremath{\alpha}}{\ensuremath{ abla}}^{\ensuremath{\alpha}}R$ term must be zero. However, it is argued that if the expectation value $G(x, {x}^{\ensuremath{'}})$ is of the Hadamard form in the massless case, as assumed in defining the point-separation renormalization prescription, then axiom 5 cannot be satisfied and, indeed, a completely unambiguous prescription for ${T}_{\ensuremath{\mu}\ensuremath{ u}}$ cannot be given without introducing a length scale.

Properties of Conformal Supergravity

Abstract: We complete our program of constructing the gauge theory of the superconformal group, and show that the previously proposed action is completely invariant under both local supersymmetries. The gauge algebra closes off-shell as well as on-shell. A flat-space model with a local supersymmetry is also presented.

Kinematical conditions in the construction of spacetime

Abstract: We adopt the point of view that a solution of Einstein's equations is an evolution of given initial Cauchy data. Implementing the evolution equations necessarily requires a determination, not directly dictated by the field equations, of the kinematics of the observers in terms of which the evolution is represented. In this paper we study the observers' kinematics (velocities and accelerations) in terms of the geometry of their congruences of world lines relative to families of time slicings of spacetime, which contrasts with the more usual approach of imposing particular "gauge" or "coordinate conditions." The types of conditions we suggest are adapted to the exact Einstein equations for general strong-field, dynamic spacetimes that have to be calculated numerically. Typically, the equations are three-dimensionally covariant, elliptic, and linear in the kinematical functions (the lapse function and shift vector) that they determine. The gravitational field enters in nonlinear form through the presence of curvature in the equations. We present a flat-space model of such elliptic equations (e.g. for maximal slicing) which suggests that this curvature leads to an exponential decrease in the proper time between time slices at late times. We show how the use of maximal slicing with minimal-distortion observers generalizes the notion of a stationary rest frame to dynamical asymptotically flat spacetimes. In cosmological spacetimes the use of minimum-distortion observers is shown to differentiate between those universes which contain only kinematic time dependence (e.g. open Kasner universe) and those in which dynamical degrees of freedom are present (e.g. mixmaster universe). We examine many examples and construct new coordinate systems in both asymptotically flat and cosmological solutions to illustrate these properties.

Low-energy nucleon-nucleon potential from Regge-pole theory

Abstract: The results from a potential model for the low-energy $\mathrm{NN}$ interaction based on Regge-pole theory are presented. The forces are due to the dominant parts of the $\ensuremath{\pi}$, $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}$, $\ensuremath{\rho}$, $\ensuremath{\omega}$, $\ensuremath{\varphi}$, $\ensuremath{\delta}$, $\ensuremath{\epsilon}$, ${S}^{*}$ trajectories in the complex $J$ plane, which are the well-known one-boson-exchange forces. Novel features are the dominant $J=0$ parts of the Pomeron, $f$ ${f}^{\ensuremath{'}}$ and ${A}_{2}$ trajectories. At the Reggeon vertices we use exponential form factors, as suggested by high-energy fits. The Pomeron, $f$, and ${f}^{\ensuremath{'}}$ trajectories lead essentially to repulsive central Gaussian potentials. This soft-core, partially nonlocal potential model fits the $\mathrm{NN}$ data with $\frac{{\ensuremath{\chi}}^{2}}{\mathrm{data}}=2.09$, which is lower than any other model we know of. The $\mathrm{NN}$ coupling constants have reasonable values, and the contributions of the Pomeron and tensor trajectories agree with estimates from high-energy fits.

Low-Energy Manifestations of Heavy Particles: Application to the Neutral Current

Abstract: It is argued that in broken-symmetry theories the decoupling of heavy particles is incomplete. Some possible manifestations of this effect in neutral-current processes and the decay ${K}_{L}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\mu}$ are discussed. In the case of the neutral current, heavy-particle effects may be calculated accurately including strong-interaction corrections. A new method of making such calculations is explained and its application to the neutral-current process discussed in detail. The method is more efficient than previous ones and is especially useful in calculations involving several mass scales.

Periodic Euclidean Solutions and the Finite Temperature Yang-Mills Gas

Abstract: We present explicit periodic solutions for SU(2) Euclidean gauge theory and briefly consider the contribution of the corresponding finite-temperature configurations to the partition function of the Yang-Mills gas

Oscillations Among Three Neutrino Types and CP Violation

Abstract: If ${\ensuremath{ u}}_{e}$ ${\ensuremath{ u}}_{\ensuremath{\mu}}$ and ${\ensuremath{ u}}_{\ensuremath{\tau}}$ are treated symmetrically in a $\mathrm{CP}$-invariant theory, it is impossible to have vacuum neutrino oscillations in which on the average each of the three neutrino types becomes an equal mixture of all three. It is shown how this becomes possible for a $\mathrm{CP}$-noninvariant theory.

Black-hole eddy currents

Abstract: We study dissipative test electromagnetic fields in a black-hole background. Quantities such as surface velocity, tangential electric field, normal magnetic induction, total surface current, and conduction surface current are introduced and are shown to satisfy Ohm's law with a surface resistivity of $4\ensuremath{\pi}\ensuremath{\simeq}377$ ohms. Associated with these currents there exists a "Joule heating". These currents can exist when the black hole is inserted in an external electric circuit, but they can exist even in the absence of external currents. In particular, we study the eddy currents induced by the rotation of a black hole in an oblique uniform magnetic field, and we show how the computation of the ohmic losses allows a very simple derivation of the torque exerted on the hole.

Electroproduction of single pions at low epsilon and a measurement of the pion form-factor up to $q^2$ = 10-GeV$^2$

Abstract: We report measurements of the electroproduction of single charged pions from hydrogen and deuterium targets for values of $\ensuremath{\epsilon}$ in the range $0.35l\ensuremath{\epsilon}l0.45$. Data were taken with a hydrogen target at the ($W, {Q}^{2}$) points (2.15 GeV, 1.2 ${\mathrm{GeV}}^{2}$), (2.65, 2.0), (2.65, 3.4), (2.65, 6.0), and (2.65, 10.0). Data were taken with a deuterium target at the ($W, {Q}^{2}$) points (2.15, 1.2) and (2.65, 2.0). The transverse cross section obtained by using these data in conjunction with earlier data at high $\ensuremath{\epsilon}$ to separate the longitudinal and transverse components is used in conjunction with the new data and the $t$-channel Born term to determine the pion form factor and to re-evaluate previously reported measurements. In the range $0.15 \mathrm{Ge}{\mathrm{V}}^{2}l{Q}^{2}l10.0 \mathrm{Ge}{\mathrm{V}}^{2}$ the pion form factor can be described by the simple pole form ${[1+\frac{{Q}^{2}}{(0.462\ifmmode\pm\else\textpm\fi{}0.024)}]}^{\ensuremath{-}1}$.

Absorption and emission spectra of a Schwarzschild black hole

Abstract: The absorption spectrum of a Schwarzschild black hole is studied in detail. Accurate and useful computational methods based on the analytical resolution of the wave equation are developed. In this way phase shifts and absorption cross sections are obtained for a wide range of energy and angular momentum. Comparison with the explicit results valid for low and high frequencies is made. The total absorption cross section of the black hole is obtained as a function of the energy. It presents behavior characteristic of a diffraction pattern. The constant geometric-optics limit [$(\frac{27}{4})\ensuremath{\pi}r_{s}^{}{}_{}{}^{2}$] is approached in an oscillatory fashion. The physical interpretation of these results is given and a simple model which describes qualitatively the absorption of waves by the black hole is presented. From these absorption parameters, the Hawking emission rates are calculated and their properties discussed.

Energy conditions and spacetime singularities

Abstract: In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete.

Baryon number of the universe

Abstract: We consider the possibility that the observed particle-antiparticle imbalance in the universe is due to baryon-numbers, C, and CP nonconservation. We make general observations and describe a framework for making quantitative estimates.

Wideband laser-interferometer gravitational-radiation experiment

Abstract: A wideband laser-interferometer gravitational-radiation antenna was constructed and used to search for gravitational radiation in the frequency band from 1 to 20 kHz. The antenna consisted of a Michelson interferometer with the beamsplitter and retroreflectors attached to masses on soft suspensions that allowed essentially free motion above the suspension frequencies. The strains in the gravitational radiation produce a differential path length change in the two arms of the interferometer which is detected by a pair of balanced photodetectors. The interferometer used a folded-path configuration with an effective length of 8.5 m. The sensitivity of the interferometer was calibrated with signals from a piezoelectric displacement transducer. The strain noise in a 1-Hz bandwidth was less than 0.3 fm/m from 1 to 3 kHz, and less than 0.1 fm/m above 3 kHz, where it was essentially photon-noise limited. (For comparison, the $\mathrm{kT}$ strain noise in a room-temperature, 2-m long, 1000-kg, elastic solid bar antenna is 0.14 fm/m.) The laser interferometer was operated as a detector for gravitational radiation for 150 h during the nights and weekends from the period 4 October through 3 December 1972. During the same period, bar antennas were operated by the Maryland, Glasgow, and Frascati groups, with 18 events reported by the Frascati group in their single bar, 22 single-bar events and no coincidences reported by the Glasgow group in their two bars, and 28 coincidences reported by the Maryland group between the Argonne bar and the Maryland bar and/or disk antennas. The various bar antenna systems were quite different but in general were sensitive to gravitational-radiation strain spectral components with an amplitude of the order of 0.1 fm/m in a narrow band of frequencies about the resonant frequency of the bar. The wideband interferometer data was analyzed by ear, with the detection sensitivity estimated to be of the order of 1-10 fm/m (depending upon the signature of the signal) for the total of the gravitational-radiation strain spectral components in the band from 1-20 kHz. No significant correlations between the Malibu interferometer output and any of the bar events or coincidences were observed.

Quantum gravity and path integrals

Abstract: The path-integral method seems to be the most suitable for the quantization of gravity. One would expect the dominant contribution to the path integral to come from metrics which are near background metrics that are solutions of classical Einstein equations. The action of these background metrics gives rise to a new phenomenon in field theory, intrinsic quantum entropy. This is shown to be related to the scaling behavior of the gravitational action and to the topology of the gravitational field. The quadratic terms in the Taylor series of the action about the background metrics give the one-loop corrections. In a supersymmetric theory the quartic and quadratic but not the so-called logarithmic divergences cancel to give a one-loop term that is finite without regularization. From the one-loop term one can obtain the effective energy-momentum tensor on the background metric. In the case of an evaporating black hole, the energy-momentum tensor will be regular on the future horizon. The usual perturbation expansion breaks down for quantum gravity because the higher (interaction) terms in the Taylor series are not bounded by the quadratic (free) ones. To overcome this I suggest that one might replace the path integrals over the terms in the Taylor series by a discrete sum of the exponentials of the actions of all complex solutions of the Einstein equations, each solution being weighted by its one-loop term. This approach seems to give a picture of the gravitational vacuum as a sea of virtual Planck-mass black holes.

Two-dimensional Ising Field Theory in a Magnetic Field: Breakup of the Cut in the Two Point Function

Abstract: We demonstrate that the cut which is present as the leading singularity in the two-point function of the Ising field theory for $Tl{T}_{c}$ and $H=0$ breaks up into a sequence of poles for $H\ensuremath{ e}0$. Both the positions and the residues of the low-lying poles are calculated.

General self-dual Yang-Mills solutions

Abstract: The recent work of Atiyah, Hitchin, Drinfeld, and Manin is used to discuss self-dual Yang-Mills solutions for the compact gauge groups $O(n)$, $\mathrm{SU}(n)$, and $\mathrm{Sp}(n)$. It is shown that the resulting solutions contain the correct number of parameters for all values of the topological charge. Although explicit construction of a general self-dual field requires the solution of a finite-dimensional, nonlinear matrix equation, we show that for widely separated instantons this equation can be solved perturbatively, providing a systematic expansion about the dilute-gas limit and a physical interpretation of the independent parameters in this limit. Further, closed-form expressions can be obtained for the general SU(2) solutions with topological charge 2 or 3. Finally, explicit isospin-1/2 and isospin-1 propagators are derived for a massless scalar field in the presence of the general self-dual SU(2) solution.

Astrophysical bounds on the masses of axions and Higgs particles

Abstract: Lower bounds on the mass of a light scalar (Higgs) or pseudoscalar (axion) particle are found in three ways: (1) by requiring that their effect on primordial nucleosynthesis not yield a deuterium abundance outside present experimental limits, (2) by requiring that the photons from their decay thermalize and not distort the microwave background, and (3) by requiring that their emission from helium-burning stars (red giants) not disrupt stellar evolution. The best bound is from (3); it requires the axion or Higgs-particle mass to be greater than about 0.2 MeV.

Gluon contribution to hadronic J ψ production

Abstract: Using the recent CERN and Fermilab measurements for J/ψ production by π±, K±, p and p beams we show, within the framework of QCD, that only a combined version of light quark qq→cc fusion and gluon gg→cc fusion mechanisms can account for the various total cross section beam ratios as well as for the observed xF‐distributions.