Showing papers in "Physical Review D in 1981"

Inflationary universe: A possible solution to the horizon and flatness problems

Abstract: The standard model of hot big-bang cosmology requires initial conditions which are problematic in two ways: (1) The early universe is assumed to be highly homogeneous, in spite of the fact that separated regions were causally disconnected (horizon problem); and (2) the initial value of the Hubble constant must be fine tuned to extraordinary accuracy to produce a universe as flat (i.e., near critical mass density) as the one we see today (flatness problem). These problems would disappear if, in its early history, the universe supercooled to temperatures 28 or more orders of magnitude below the critical temperature for some phase transition. A huge expansion factor would then result from a period of exponential growth, and the entropy of the universe would be multiplied by a huge factor when the latent heat is released. Such a scenario is completely natural in the context of grand unified models of elementary-particle interactions. In such models, the supercooling is also relevant to the problem of monopole suppression. Unfortunately, the scenario seems to lead to some unacceptable consequences, so modifications must be sought.

Quantum Mechanical Noise in an Interferometer

Abstract: The interferometers now being developed to detect gravitational waves work by measuring the relative positions of widely separated masses. Two fundamental sources of quantum-mechanical noise determine the sensitivity of such an interferometer: (i) fluctuations in number of output photons (photon-counting error) and (ii) fluctuations in radiation pressure on the masses (radiation-pressure error). Because of the low power of available continuous-wave lasers, the sensitivity of currently planned interferometers will be limited by photon-counting error. This paper presents an analysis of the two types of quantum-mechanical noise, and it proposes a new technique---the "squeezed-state" technique---that allows one to decrease the photon-counting error while increasing the radiation-pressure error, or vice versa. The key requirement of the squeezed-state technique is that the state of the light entering the interferometer's normally unused input port must be not the vacuum, as in a standard interferometer, but rather a "squeezed state"---a state whose uncertainties in the two quadrature phases are unequal. Squeezed states can be generated by a variety of nonlinear optical processes, including degenerate parametric amplification.

Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation

Abstract: Unified electroweak gauge theories based on the gauge group $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{B\ensuremath{-}L}$, in which the breakdown of parity invariance is spontaneous, lead most naturally to a massive neutrino. Assuming the neutrino to be a Majorana particle, we show that smallness of its mass can be understood as a result of the observed maximality of parity violation in low-energy weak interactions. This result is shown to be independent of the number of generations and unaffected by renormalization effects. Phenomenological consequences of this model at low energies are studied. Observation of neutrinoless double-$\ensuremath{\beta}$ decay will provide a crucial test of this class of models. Implications for rare decays such as $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$, $\ensuremath{\mu}\ensuremath{\rightarrow}\mathrm{ee}\overline{e}$, etc. are also noted. It is pointed out that in the realm of neutral-current phenomena, departure from the predictions of the standard model for polarized-electron-hadron scattering, forward-backward asymmetry in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, and neutrino interactions has a universal character and may be therefore used as a test of the model.

Pointer Basis of Quantum Apparatus: Into What Mixture Does the Wave Packet Collapse?

Abstract: The form of the interaction Hamiltonian between the apparatus and its environment is sufficient to determine which observable of the measured quantum system can be considered "recorded" by the apparatus. The basis that contains this record---the pointer basis of the apparatus---consists of the eigenvectors of the operator which commutes with the apparatus-environment interaction Hamiltonian. Thus the environment can be said to perform a nondemolition measurement of an observable diagonal in the pointer basis.

Universal upper bound on the entropy-to-energy ratio for bounded systems

Abstract: We present evidence for the existence of a universal upper bound of magnitude $\frac{2\ensuremath{\pi}R}{\ensuremath{\hbar}c}$ to the entropy-to-energy ratio $\frac{S}{E}$ of an arbitrary system of effective radius $R$. For systems with negligible self-gravity, the bound follows from application of the second law of thermodynamics to a gedanken experiment involving a black hole. Direct statistical arguments are also discussed. A microcanonical approach of Gibbons illustrates for simple systems (gravitating and not) the reason behind the bound, and the connection of $R$ with the longest dimension of the system. A more general approach establishes the bound for a relativistic field system contained in a cavity of arbitrary shape, or in a closed universe. Black holes also comply with the bound; in fact they actually attain it. Thus, as long suspected, black holes have the maximum entropy for given mass and size which is allowed by quantum theory and general relativity.

Gravitational Field of Vacuum Domain Walls and Strings

Abstract: The gravitational properties of vacuum domain walls and strings are studied in the linear approximation of general relativity. These properties are shown to be very different from those of regular massive planes and rods. It is argued that the domain walls are gravitationally unstable and collapse at a certain time $\ensuremath{\sim}{t}_{c}$ after their creation. If the vacuum walls ever existed, they must have disappeared at $tl{t}_{c}$.

Optimized Perturbation Theory

Abstract: Conventional perturbation theory gives different results in different renormalization schemes, a problem which is especially serious in quantum chromodynamics (QCD). I propose a theoretical resolution of this ambiguity which uses the full renormalization-group invariance of the theory. The idea is that, in any kind of approximation scheme which does not respect the known invariances of the exact result, the "optimum" approximant is the one that is "most invariant," i.e., least sensitive to variations in the unphysical parameters. I discuss this principle in several examples, including the Halliday-Suranyi expansion for the anharmonic oscillator. Turning to massless field theories, I identify the unphysical variables which label a particular renormalization scheme as the renormalization point $\ensuremath{\mu}$, and the $\ensuremath{\beta}$-function coefficients. I describe how perturbative approximations depend on these unphysical variables, and show how to find the stationary point which represents the "optimum" result. Certain renormalization-scheme invariants, in one-to-one correspondence with the perturbation-series coefficients, arise naturally in the analysis. An application to the $e$,$\ensuremath{\mu}$ magnetic moments in QED provides a partial test of these ideas, with encouraging results. I suggest possible further theoretical developments, and advocate the method as a sound basis for quantitative QCD phenomenology.

Monte Carlo calculations of coupled boson-fermion systems. I

Abstract: We present a formalism for carrying out Monte Carlo calculations of field theories with both boson and fermion degrees of freedom. The basic approach is to integrate out the fermion degrees of freedom and obtain an effective action for the boson fields to which standard Monte Carlo techniques can be applied. We study the structure of the effective action for a wide class of theories. We develop a procedure for making rapid calculations of the variation in the effective action due to local changes in the boson fields, which is essential for practical numerical calculations.

Supersymmetry and the Scale of Unification

Abstract: Unified theories which are supersymmetric down to energies \ensuremath{\sim}${10}^{3}$-${10}^{5}$ GeV have been proposed as possible solutions to the gauge-hierarchy problem. The additional particles then required have significant effects on renormalization of coupling constants. The previous successful calculation of the weak mixing angle is only slightly changed, but the scale of unification is moved significantly higher, into the range of the Planck mass. This may be suggestive of an eventual unification including gravity, and markedly reduces the predicted rate of nucleon decay.

Statistical distance and Hilbert space

Abstract: A concept of "statistical distance" is defined between different preparations of the same quantum system, or in other words, between different rays in the same Hilbert space. Statistical distance is determined entirely by the size of statistical fluctuations occurring in measurements designed to distinguish one state from another. It is not related, a priori, to the usual distance (or angle) between rays. One finds, however, that these two kinds of distance are in fact the same, a result which depends on certain peculiarities of quantum mechanics.

How super-renormalizable interactions cure their infrared divergences

Abstract: Perturbative expansions in models which possess super-renormalizable interactions of massless fields are beset by severe infrared divergences We show that the complete theory is well defined and has no such divergences; rather the exact amplitudes are nonanalytic functions of the coupling constant and cannot be expanded in its powers Typically, logarithms of the coupling constant occur, as well as analytic pieces The analytic portions cannot be found in perturbation theory; they are determined by matrix elements of composite operators But the nonanalytic behavior is completely fixed in terms of the theory's other parameters The present investigation should be relevant to a study of physical quantum chromodynamics at its finite-temperature phase transitions

High-temperature Yang-Mills theories and three-dimensional quantum chromodynamics

Abstract: We demonstrate that for sufficiently high temperature $T$ the behavior of any four-dimensional gauge theory with small coupling constant $\ensuremath{\alpha}$, at distances beyond the electrical Debye screening length ${\ensuremath{\xi}}_{D}\ensuremath{\sim}\frac{1}{\sqrt{\ensuremath{\alpha}}T}$, is determined precisely by the corresponding three-dimensional theory. This is the magnetic sector of the original theory, and in the non-Abelian case it is a Yang-Mills theory like three-dimensional quantum chromodynamics (QC${\mathrm{D}}_{3}$). We study QC${\mathrm{D}}_{3}$ in the loop expansion, which is only valid for distances $\ensuremath{\ll}\frac{1}{\ensuremath{\alpha}T}$, in both covariant and Coulomb gauges. At a finite order in the loop expansion, the presence of logarithmic infrared divergences signals the appearance of new operators in the operator-product expansion. For example, in a covariant gauge, the gauge self-energy develops infrared divergences at two-loop order associated with the operator ${\overline{A}}^{2}$. Infrared divergences in the Wilson loop are also considered and shown to cancel below the order at which gauge-invariant local operators can appear in the operator-product expansion. The infrared structure of QC${\mathrm{D}}_{3}$ at distances $\ensuremath{\gtrsim}\frac{1}{\ensuremath{\alpha}T}$ cannot be directly probed in the loop expansion, however. We present a simpler model which is calculable in this infrared limit, and which might serve as a prototype for QC${\mathrm{D}}_{3}$. The model is massless scalar QE${\mathrm{D}}_{3}$, which with $N$ charged scalars is soluble in a $\frac{1}{N}$ expansion as $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Using the $\frac{1}{N}$ expansion, we demonstrate that infrared softening occurs: the long-range behavior of the photon propagator in massless scalar QE${\mathrm{D}}_{3}$ is less singular than that of free fields. Infrared softening might also occur in QC${\mathrm{D}}_{3}$, although it cannot be demonstrated to finite order in the loop expansion. The implications of an assumed infrared softening in QC${\mathrm{D}}_{3}$ for the magnetic sector of Yang-Mills theories at high temperatures are also discussed. In particular, we consider the possibility that, if the softening is sufficiently great, there is screening of hot non-Abelian magnetic fields and possible confinement of primordial magnetic monopoles.

Quarkonia and Quantum Chromodynamics

Abstract: The $\ensuremath{\psi}$ and $\ensuremath{\Upsilon}$ spectroscopies are analyzed in the framework of a recently proposed potential model which incorporates linear confinement and asymptotic freedom. Given the Regge slope ${\ensuremath{\alpha}}^{\ensuremath{'}}$ (${\ensuremath{\alpha}}^{\ensuremath{'}}$ taken to be 1 ${\mathrm{GeV}}^{\ensuremath{-}2}$) and the quantum-chromodynamics (QCD) scale parameter $\ensuremath{\Lambda}$ (${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}$ taken to be 0.5 GeV, where $\stackrel{-}{\mathrm{MS}}$ refers to the modified minimal-subtraction scheme) the potential is completely determined. Excellent agreement with experiment is found, including in particular leptonic widths and hyperfine splittings. This supports a short-distance behavior of the quark-antiquark potential as predicted by QCD. We also demonstrate in a model-independent way that the $\ensuremath{\Psi}$ and $\ensuremath{\Upsilon}$ spectra provide a lower bound on the QCD scale parameter $\ensuremath{\Lambda}$; we find ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}g0.1$ GeV. The properties of ($b\overline{c}$) and possible ($t\overline{t}$), ($t\overline{c}$), and ($t\overline{b}$) spectroscopies are studied, including weak-interaction effects. The implications of the $\ensuremath{\Psi}$, $\ensuremath{\Upsilon}$, and possible heavier quarkonium families for quantitative tests of QCD are discussed. It is shown that a ($t\overline{t}$) system with $m(t\overline{t})\ensuremath{\ge}40$ GeV would provide an accurate determination of ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}$.

Quark liberation at high temperature: A Monte Carlo study of SU(2) gauge theory

Abstract: Quark confinement in a finite-temperature $\mathrm{SU}(N)$ gauge theory is formulated as the realization of a global ${Z}_{N}$ symmetry. Spontaneous breakdown corresponds to a transition to a nonconfining, plasma phase. The free energy of a single quark is an order parameter which probes the phase structure, and it may be calculated in the Euclidean theory in terms of a "Wilson line" running the length of the system along the (periodic) time axis. We present results of a Monte Carlo calculation in the SU(2) lattice theory which confirm the transition at a critical temperature computed in terms of the zero-temperature string tension; data for the quark-antiquark potential are presented as well. We discuss the implications of the finite-temperature transition for efforts to calculate zero-temperature quantities on finite-size lattices. Finally, we note that restoration of ${Z}_{N}$ symmetry as the temperature is lowered may be understood as a condensation of instantons and other topological objects.

Raising the sideways scale

Abstract: Extended hypercolor theories have been plagued with inherent flavor-changing effects occurring above experimental levels. The problem may be alleviated in a scenario in which hyper-color interactions are not asymptotically free. Then the scale of broken gauged family symmetry may be higher than before. The masses of the pseudo-Goldstone bosons of hypercolor may also be increased.

Inelastic Photoproduction of J/psi and Upsilon by Gluons

Abstract: Amplitudes are derived for the quantum-chromodynamic subprocess $\ensuremath{\gamma}g\ensuremath{\rightarrow}(\frac{J}{\ensuremath{\psi}})g$, with a specific wave function used to represent the $\frac{J}{\ensuremath{\psi}}$ as a $c\overline{c}$ system. The results are used to obtain the normalized total cross section ${\ensuremath{\sigma}}_{\ensuremath{\gamma}}$ for the inelastic process $\ensuremath{\gamma}N\ensuremath{\rightarrow}(\frac{J}{\ensuremath{\psi}})X$, predictions for the $z$ and ${p}_{T}$ dependence of inelastic $\frac{J}{\ensuremath{\psi}}$ photoproduction, and predictions for the $\frac{J}{\ensuremath{\psi}}$ helicity. The predictions apply as well to electroproduction at small ${Q}^{2}$.

Spin-dependent forces in quantum chromodynamics

Abstract: In a manifestly gauge-independent formalism, all relativistic corrections to the fermion propagation function are determined and the general form of the spin-dependent forces in quantum chromodynamics for heavy-quark-antiquark ( q q ¯ ) systems is derived. For example, the classical spin-orbit and Thomas-precession terms are found to be simple derivatives of the static potential. In addition to expressing the spin-dependent forces in terms of the minimal number of independent potentials, two new applications of this formulation are presented: (1) The effect of pseudoparticle solutions on the spin-dependent forces is analyzed, and (2) an electric-confinement assumption produces a zero-parameter spin-dependent potential. This potential determines the fine structure in heavy q q ¯ systems. Spin splittings in the ϒ system are predicted and the J /ψ system splittings are compared with the experimentally observed values.

Large-angle two-photon exclusive channels in quantum chromodynamics

Abstract: Detailed leading-order quantum-chromodynamics (QCD) predictions are given for the scaling, angular, and helicity dependence of the reactions $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}M\overline{M}$ ($M=\ensuremath{\pi},K,\ensuremath{\rho}$, etc) at large momentum transfer In addition to providing a basic test of QCD at short distances, measurements can be used to determine the process-independent meson distribution amplitudes ${\ensuremath{\varphi}}_{M}(x,Q)$ Other related two-photon channels such as $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\rho}$, ${\ensuremath{\gamma}}^{*}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0},{\ensuremath{\eta}}^{0},{\ensuremath{\eta}}^{\ensuremath{'}}$, and ${\ensuremath{\eta}}_{c}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ are also discussed We also prove the existence of a fixed Regge singularity at $J=0$ which couples to $\ensuremath{\gamma}\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\rho}$ in the $t$ channel but not to $\ensuremath{\gamma}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\pi}$

Renormalization of loop functions for all loops

Abstract: It is shown that the vacuum expectation values $W({C}_{1},\ensuremath{\cdots},{C}_{n})$ of products of the traces of the path-ordered phase factors $P\mathrm{exp}[ig\ensuremath{\oint}\ensuremath{\int}{{C}_{i}}^{}{\mathit{A}}_{\ensuremath{\mu}}(x)d{x}^{\ensuremath{\mu}}]$ are multiplicatively renormalizable in all orders of perturbation theory. Here ${\mathit{A}}_{\ensuremath{\mu}}(x)$ are the vector gauge field matrices in the non-Abelian gauge theory with gauge group $\mathrm{U}(N)$ or $\mathrm{SU}(N)$, and ${C}_{i}$ are loops (closed paths). When the loops are smooth (i.e., differentiable) and simple (i.e., non-self-intersecting), it has been shown that the generally divergent loop functions $W$ become finite functions $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$ when expressed in terms of the renormalized coupling constant and multiplied by the factors ${e}^{\ensuremath{-}KL({C}_{i})}$, where $K$ is linearly divergent and $L({C}_{i})$ is the length of ${C}_{i}$. It is proved here that the loop functions remain multiplicatively renormalizable even if the curves have any finite number of cusps (points of nondifferentiability) or cross points (points of self-intersection). If ${C}_{\ensuremath{\gamma}}$ is a loop which is smooth and simple except for a single cusp of angle $\ensuremath{\gamma}$, then ${W}_{R}({C}_{\ensuremath{\gamma}})=Z(\ensuremath{\gamma})\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}({C}_{\ensuremath{\gamma}})$ is finite for a suitable renormalization factor $Z(\ensuremath{\gamma})$ which depends on $\ensuremath{\gamma}$ but on no other characteristic of ${C}_{\ensuremath{\gamma}}$. This statement is made precise by introducing a regularization, or via a loop-integrand subtraction scheme specified by a normalization condition ${W}_{R}({\overline{C}}_{\ensuremath{\gamma}})=1$ for an arbitrary but fixed loop ${\overline{C}}_{\ensuremath{\gamma}}$. Next, if ${C}_{\ensuremath{\beta}}$ is a loop which is smooth and simple except for a cross point of angles $\ensuremath{\beta}$, then $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}({C}_{\ensuremath{\beta}})$ must be renormalized together with the loop functions of associated sets ${{S}^{i}}_{\ensuremath{\beta}}={{{C}^{i}}_{1},\ensuremath{\cdots},{{C}^{i}}_{\mathrm{pi}}}$ ($i=2,\ensuremath{\cdots},I$) of loops ${{C}^{i}}_{q}$ which coincide with certain parts of ${C}_{\ensuremath{\beta}}\ensuremath{\equiv}{{C}_{1}}^{1}$. Then ${W}_{R}({{S}^{i}}_{\ensuremath{\beta}})={Z}^{\mathrm{ij}}(\ensuremath{\beta})\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}({{S}^{j}}_{\ensuremath{\beta}})$ is finite for a suitable matrix ${Z}^{\mathrm{ij}}(\ensuremath{\beta})$. Finally, for a loop with $r$ cross points of angles ${\ensuremath{\beta}}_{1},\ensuremath{\cdots},{\ensuremath{\beta}}_{r}$ and $s$ cusps of angles ${\ensuremath{\gamma}}_{1},\ensuremath{\cdots},{\ensuremath{\gamma}}_{s}$, the corresponding renormalization matrices factorize locally as ${Z}^{{i}_{1}{j}_{1}}({\ensuremath{\beta}}_{1})\ensuremath{\cdots}{Z}^{{i}_{r}{j}_{r}}({\ensuremath{\beta}}_{r})Z({\ensuremath{\gamma}}_{1})\ensuremath{\cdots}Z({\ensuremath{\gamma}}_{s})$.

On the Quantum Mechanics of Neutrino Oscillation

Abstract: We try to understand and to develop some of the basic quantum mechanics of neutrino oscillation. First, we observe that measurements which identify the physical neutrino (mass eigenstate) involved in each event of an experiment destroy any oscillation pattern. We explain how these measurements do that. Then, we construct a wave-packet treatment of neutrino oscillation. We find that it gives the same results as the standard treatment. Next, we estimate the distance a beam must travel before its different physical neutrinos, which have different speeds, will stop interfering with each other. Finally, we consider the possibility of observing the difference in the arrival times of the various physical neutrinos at a given point.

Zitterbewegung and the internal geometry of the electron

Abstract: Schr\"odinger's work on the Zitterbewegung of the free electron is reexamined. His proposed "microscopic momentum" vector for the Zitterbewegung is rejected in favor of a "relative momentum" vector, with the value $\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}=mc\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\alpha}}$ in the rest frame of the center of mass. His oscillatory "microscopic coordinate" vector is retained. In the rest frame, it takes the form $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}=\ensuremath{-}i(\frac{\ensuremath{\hbar}}{2mc})\ensuremath{\beta}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\alpha}}$, and the Zitterbewegung is described in this frame in terms of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}$, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$, and the Hamiltonian $m{c}^{2}\ensuremath{\beta}$, as a finite three-dimensional harmonic oscillator with a compact phase space. The Lie algebra generated by $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}$ is that of SO(5), and in particular $[{Q}_{i},{P}_{j}]=\ensuremath{-}i\ensuremath{\hbar}{\ensuremath{\delta}}_{\mathrm{ij}}\ensuremath{\beta}$. It is argued that the simplest possible finite, three-dimensional, isotropic, quantum-mechanical system requires such an SO(5) structure, incorporates a fundamental length, and has harmonic-oscillator dynamics. Dirac's equation is derived as the wave equation appropriate to the description of such a finite quantum system in an arbitrary moving frame of reference, using a dynamical group SO(3,2) which can be extended to SO(4,2). Spin appears here as the orbital angular momentum associated with the internal system, and rest-mass energy appears as the internal energy in the rest frame. Possible generalizations of these ideas are indicated, in particular those involving higher-dimensional representations of SO(5).

Static spherically symmetric scalar fields in general relativity

Abstract: In 1957, Bergmann and Leipnik attempted to find static spherically symmetric solutions of a special form of the field equations of general relativity. They were not able to find explicit expressions for the gravitational potentials, and they did not realize that such expressions could be found by using a different coordinate system. Although Buchdahl developed an elegant procedure for finding, by inspection, the solutions sought by Bergmann and Leipnik, his procedure is severely limited when applied to the spherically symmetric case. Indeed, his procedure fails to identify one whole class of such static solutions. The object of this paper is to show that, under the assumptions of Bergmann and Leipnik, the integration of the field equations is almost trivial, and to identify the missing class of solutions.

Asymptotic behavior of the Sudakov form factor in quantum chromodynamics

Abstract: In this paper we give an algorithm to compute the asymptotic behavior of the on-shell quark form factor in the limit of large momentum transfer (Sudakov form factor) in Abelian and non-Abelian gauge theories. We ignore terms which are suppressed by a power of momentum transfer, but keep all nonleading logarithms of the momentum transfer and all powers of the coupling constant.

Majorana Neutrinos and Magnetic Fields

Abstract: It is stressed that if neutrinos are massive they are probably of "Majorana" type. This implies that their magnetic-moment form factor vanishes identically so that the previously discussed phenomenon of spin rotation in a magnetic field would not appear to take place. We point out that Majorana neutrinos can, however, have transition moments. This enables an inhomogeneous magnetic field to rotate both spin and "flavor" of a neutrino. In this case the spin rotation changes particle to antiparticle. The spin-flavor-rotation effect is worked out in detail. We also discuss the parametrization and calculation of the electromagnetic form factors of Majorana neutrinos. Our discussion takes into account the somewhat unusual quantum theory of massive Majorana particles.

Intrinsic heavy-quark states

Abstract: The postulate that ordinary hadrons contain intrinsic charm-quark states (such as Vertical Baruudcc-bar> in the proton) at the 1% level is shown to explain two sets of unexpected experimental results: (1) the copious diffractive production of charmed hadrons at large longitudinal momentum in high-energy proton-nucleon and pion-nucleon collisions, and (2) the anomalously large number of same-sign dimuon events observed in deep-inelastic neutrino reactions. We also predict cross sections for open b and t production for high-energy hadron-hadron collisions.

Effective potential for the order parameter of gauge theories at finite temperature

Abstract: $\mathrm{SU}(n)$ gauge theories at finite temperature $T={\ensuremath{\beta}}^{\ensuremath{-}1}$ are analyzed in terms of the spontaneous breakdown of a $Z(n)$ symmetry corresponding to the order parameter $L(\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}})=(\frac{1}{n})\mathrm{Tr}P\mathrm{exp}[ig\ensuremath{\int}{0}^{\ensuremath{\beta}}{A}_{0}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}},t)dt]$. An "effective potential" for $L$ is evaluated in the one-loop approximation for both the continuum and the lattice gauge theories. It is shown that the $Z(n)$ symmetry is broken, so that the continuum theory does not confine for high temperatures. Similarly the lattice theory does not confine for sufficiently weak coupling if the number of time sites ${N}_{t}$ is finite. It is argued that as ${N}_{t}\ensuremath{\rightarrow}\ensuremath{\infty}$ the $Z(n)$ symmetry is restored and the theory will confine for all values of the coupling.

Radiative corrections to Higgs-boson decays in the Weinberg-Salam model

Abstract: One-loop corrections to the Higgs-boson decays $H{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$, $H{W}^{+}{W}^{\ensuremath{-}}$, and $\mathrm{HZZ}$ are calculated up to Higgs-boson masses of about 1 TeV. The corrections are of the order of 10% for $200 \mathrm{GeV}\ensuremath{\lesssim}{m}_{H}\ensuremath{\lesssim}1 \mathrm{TeV}$ within the renormalization scheme adopted. Renormalization problems are discussed in detail. A complete set of one-loop counterterms in the 't Hooft gauge is presented.

Fermi-motion effects in deep-inelastic lepton scattering from nuclear targets

Abstract: The ratio of deep-inelastic structure functions of nuclear targets to the sum of free neutron and proton structure functions has been calculated using a modified form of the Atwood-West technique for deuterium. Fermi-gas momentum distributions were used with modifications to include high-momentum tails resulting from nucleon-nucleon correlations. Tables of smearing ratios for ${W}_{1}$, ${W}_{2}$, and ${W}_{3}$ are given as a function of $x$ and ${Q}^{2}$ for deuterium and several heavy nuclei. We find that for $xg0.5$ the scaling violations for heavy nuclei are smaller than those for free nucleons. The shapes of the antiquark distributions are also changed.

CP violation in B -meson decays

Abstract: The pattern of $\mathrm{CP}$ violation in the bottom sector is discussed. We introduce general techniques to expose new $\mathrm{CP}$-violating effects in the cascade decays of $B$ mesons. In the Kobayashi-Maskawa (KM) model, the $\mathrm{CP}$ asymmetries so obtained range from 2-20% for plausible values of the model parameters. This is to be compared with the small effects, of order ${10}^{\ensuremath{-}3}$-${10}^{\ensuremath{-}4}$, previously exhibited within this model. Effects of this size should be observable in upcoming experiments. Our approach stresses the on-shell transitions which make up the cascade decays of heavy mesons to ordinary hadrons, as opposed to the off-shell transitions which occur in the analogs of ${K}^{\ensuremath{\circ}}\ensuremath{-}{\overline{K}}^{\ensuremath{\circ}}$ mixing. The $\mathrm{CP}$ asymmetries generated by our techniques are of order $sin\ensuremath{\delta}$, where $\ensuremath{\delta}$ is the KM phase angle, and thus represent the maximum effects obtainable in this model.

Cloudy bag model of the nucleon

Abstract: A previously derived model in which a baryon is treated as a three-quark bag that is surrounded by a cloud of pions is used to compute the static properties of the nucleon. The only free parameter of the model is the bag radius which is fixed by a fit to pion-nucleon scattering in the (3,3)-resonance region to be about 0.8 fm. With the model so determined the computed values of the root-mean-square radii and magnetic moments of the neutron and proton, and ${g}_{A}$, are all in very good agreement with the experimental values. In addition, about one-third of the $\ensuremath{\Delta}$-nucleon mass splitting is found to come from pionic effects, so that our extracted value of ${\ensuremath{\alpha}}_{s}$ is smaller than that of the MIT bag model.