Theory Of Weak Interactions Research Articles

Prabahan Kemal Kabir

Prabahan Kemal Kabir, a well-known theoretical physicist and retired professor at the University of Virginia in Charlottesville, died on 29 August 2004 near Berhampur, India, while swimming in the sea. He was an authority on charge conjugation–parity (CP) and time-reversal invariance (T) violation.Born in Calcutta, India, on 30 June 1933, Kabir was known to his family and friends as “Pasha.” His family was prominent in Indian politics: His father was the minister of education in the Nehru government. Kabir finished his undergraduate studies in physics at the University of Delhi at the age of 18 and spent two more years there on his MSc in physics under Ramesh Chandra Majumdar. Kabir came to the US to pursue his doctorate in theoretical physics at Cornell University, where his thesis advisers were Hans Bethe and Edwin Salpeter. His thesis work on the Lamb shift in helium, coauthored by Salpeter, is still widely quoted.Kabir completed his PhD in 1957 and spent a year at the Institute for Advanced Study in Princeton, New Jersey, followed by a year in the UK at the University of Birmingham with Rudolf Peierls, who was his mentor. Kabir left Birmingham for the University of Calcutta, where he briefly taught nuclear physics before joining the Carnegie Institute of Technology in Pittsburgh, Pennsylvania, as a research physicist and assistant professor of physics. He moved next to CERN, where he was a visiting scientist from 1963 to 1965, until he took a position as a principal scientific officer at the Rutherford High Energy Laboratory in the UK. He spent six years at Rutherford before returning to the US as a professor at the University of Virginia, his base for the remainder of his career while he still traveled extensively to Europe and India. He remained in Charlottesville following his retirement from the university in May 1998.Kabir’s most important work was on symmetry and symmetry violation. He formulated a description of T violation in the kaon system that does not assume CPT invariance. He realized that for T violation, detailed balance has to be broken, so in 1970, he introduced what became known as the Kabir parameter to quantify the imbalance. It would be another 30 years before that parameter was itself measured.An important idea in field theory was introduced in 1959, thanks to Kabir, Gerald Feinberg, and Steven Weinberg. Their theorem was the first example of the cancellation of a flavor-changing neutral current from muon to electron.Kabir suggested other new ideas that, like his T violation parameter, may take decades to be observed experimentally. He did not publish many of his ideas because he chose to help others tackle them. Not a follower of trends, Kabir concentrated on symmetries. He was fiercely independent and refused to accept new ideas if he found them at variance with his intuition. For example, he remained skeptical that the graviton would reach a limiting mass of zero discontinuously, as noted by Martinus J. G. Veltman in his 1999 Nobel lecture. Kabir edited the textbook Development of Weak Interaction Theory (Gordon & Breach, 1963), which reprints and translates to English important contributions to the field up to that time, and wrote The CP Puzzle (Academic Press, 1968), a still much quoted, detailed account of the neutral kaon system. He was editor of Physics Letters B (1978–81) and was on the board of trustees of Universities Research Association Inc (1979–85). Between 1984 and 1990, he chaired the Kilambi Ramavataram Fund Committee of the American Physical Society. The fund supports undergraduate physics teachers from India on short visits to the US.An exceptional and wonderful person, Kabir was also a warm and generous friend and a stimulating and provocative companion. He is deeply missed by his many friends and collaborators throughout the world. Prabahan Kemal Kabir PPT|High resolution© 2005 American Institute of Physics.

Tree level gravity?scalar matter interactions in analogy with Fermi theory of weak interactions using only a massive vector field

In this paper we work in perturbative quantum gravity coupled to scalar matter at tree level and we introduce a new effective model in analogy with the Fermi theory of weak interaction and in relation with a previous work where we have studied only the gravity and its self-interaction. This is an extension of the I.T.B. model (Intermediate-Tensor-Boson) for gravity also to gravitationally interacting scalar matter. We show that in a particular gauge the infinite series of interactions containing “n” gravitons and two scalars could be rewritten in terms of only two Lagrangians containing a massive field, the graviton and, obviously, the scalar field. Using the S-matrix we obtain that the low energy limit of the amplitude reproduces the local Lagrangian for the scalar coupled to gravity.

Perturbative quantum gravity in analogy with Fermi theory of weak interactions using bosonic tensor fields

In this paper we work in perturbative quantum gravity and we introduce a new effective model for gravity. Expanding the Einstein-Hilbert Lagrangian in graviton field powers we have an infinite number of terms. In this paper we study the possibility of an interpretation of more than three graviton interacting vertices as effective vertices of a most fundamental theory that contain tensor fields. Here we introduce a Lagrangian model named I.T.B (Intermediate Tensor Boson) where four gravitational "pseudo-currents" that contain two gravitons couple to three massive tensorial fields of rank 1, 3, 5 respectively. We show that the exchange of those massive particles reproduces, at low energy, the interacting vertices for four or more gravitons. In a particular version, the model contains a dimensionless coupling constant "g" and the mass M of the intermediate bosons as free parameters. The universal gravitational constant G is shown to be proportional to the inverse of mass squared of mediator fields. A foresighting choice of the dimensionless coupling constant could lower the energy scale where quantum gravity aspects show up.

The Liouville Equation with Singular Data: A Concentration-Compactness Principle via a Local Representation Formula

For a bounded domain Ω⊂R2, we establish a concentration-compactness result for the following class of “singular” Liouville equations:−Δu=eu−4π∑j=1mαjδpj in Ω where pj∈Ω, αj>0 and δpj denotes the Dirac measure with pole at point pj, j=1,…,m. Our result extends Brezis–Merle's theorem (Comm. Partial Differential Equations16 (1991) 1223–1253) concerning solution sequences for the “regular” Liouville equation, where the Dirac measures are replaced by Lp(Ω)-data p>1. In some particular case, we also derive a mass-quantization principle in the same spirit of Li–Shafrir (Indiana Univ. Math. J.43 (1994) 1255–1270). Our analysis was motivated by the study of the Bogomol'nyi equations arising in several self-dual gauge field theories of interest in theoretical physics, such as the Chern–Simons theory (“Self-dual Chern–Simons Theories” Lecture Notes in Physics, Vol. 36, Springer-Verlag, Berlin, 1995) and the Electroweak theory (“Selected Papers on Gauge Theory of Weak and Electromagnetic Interactions,” World Scientific, Singapore).

A NEW THEORY OF ELECTROMAGNETIC, WEAK AND STRONG INTERACTIONS

The Higgs mechanism for imparting masses to gauge bosons and matter particles is obviated by showing that Yang–Mills gauge bosons have intrinsic nonzero masses (rest-frame energies) from self-interactions. Electroweak (EW) mixing is ruled out because it produces a photon field that is massive, carries EW charge, and does not satisfy Maxwell's equations. Other fundamental difficulties of the Standard Model are identified. A new gauge theory of electromagnetic, weak and strong interactions is derived from the Dirac equation with no other postulates and no free parameters. The three forces are intrinsically unified, the photon field is Maxwellian, weak interactions derive from spin (not isospin), and the weak and strong bosons are naturally massive and chiral. Charge is naturally quantized to integral values. Three generations of lepton pairs and elementary-hadron pairs, all with integral charges, are predicted, contradicting the phenomenology of fractional quark charges, but in full accord with experimental data on weak and strong processes and composite hadrons. Neutrinos are massive. The Dirac masses, the fine structure constant, neutrino oscillations and Cabibbo mixing are shown to have a common origin in the gravitational field. The new theory leads to a new interpretation of "negative energies" with cosmological implications. Finally, it is shown that key expressions of the EW formalism agree with those of the new theory and with experiments only if the mixing angle θ is given by sin 2 θ = 0.25, which accounts for the EW model's successes.

Density matrix functional theory of weak intermolecular interactions

The known asymptotic behavior of the total energy of two weakly interacting systems imposes stringent conditions on the exchange-correlation energy as a functional of the one-electron reduced density matrix. Although the first-order conditions that involve Coulomb-type two-electron integrals are relatively trivial to satisfy, the exact functional should also conform to two second-order expressions, and consequently to certain sum rules. The primitive natural spin-orbital functionals satisfy the first-order conditions but, lacking terms quadratic in two-electron integrals, are found to be incapable of recovering the dispersion component of the interaction energy. Violating the sum rules, the recently proposed Yasuda functional yields nonvanishing dispersion energy with spurious asymptotic terms that scale like inverse fourth and fifth powers of the intersystem distance.

A model comparison study to the imaging of submarine reefs with synthetic aperture radar

Signatures of submarine reefs near Heligoland in the North Sea were observed in airborne radar images recorded at L-, C- and X-bands on 14 November 1990 during rather high wind speed of 9 ms-1. Predictions from various models of the imaging mechanism were compared to these observations. One of the models is the so-called weak hydrodynamic interaction theory (WHIT) model. It is fully two-dimensional in position as well as wavenumber space, so any surface current variation can be handled. Also more sophisticated scattering models than first-order Bragg scattering can be included. The model contains a number of parameterizations for the roughness length, the equilibrium wave height spectrum and the relaxation rate as well as different forms for the local relaxation source term. In the model intercomparison, the WHIT model performed not very well. It is shown here that this is due to the choice of the radial relaxation rate. In a sensitivity analysis it is shown that also the form of the relaxation source ter...

Computational Cosmology: From the Early Universe to the Large Scale Structure.

In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations (and numerical methods applied to specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark-hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.

Structure beyond the Standard Model

We discuss ideas for extending present theory of strong, weak and electromagnetic interactions. String theory offers the hope that there is a fully unified theory of the fundamental interactions, including gravity. Such a ‘top–down’ approach is confronted with the ‘bottom–up’ approach, using current precision measurement to infer structure beyond the Standard Model. Implications for new measurable processes are discussed.

A model comparison study to the imaging of submarine reefs with synthetic aperture radar

Signatures of submarine reefs near Heligoland in the North Sea were observed in airborne radar images recorded at L-, C- and X-bands on 14 November 1990 during rather high wind speed of 9 ms-1. Predictions from various models of the imaging mechanism were compared to these observations. One of the models is the so-called weak hydrodynamic interaction theory (WHIT) model. It is fully two-dimensional in position as well as wavenumber space, so any surface current variation can be handled. Also more sophisticated scattering models than first-order Bragg scattering can be included. The model contains a number of parameterizations for the roughness length, the equilibrium wave height spectrum and the relaxation rate as well as different forms for the local relaxation source term. In the model intercomparison, the WHIT model performed not very well. It is shown here that this is due to the choice of the radial relaxation rate. In a sensitivity analysis it is shown that also the form of the relaxation source term is important. A linear source term may lead to unrealistically high positive hydrodynamic modulations (up to 50 dB) at some positions over the reefs for waves with a wavelength of about 0.6 m. Such effects do not occur in quadratic or cubic source terms, which are therefore to be preferred. The parameterizations chosen for the roughness length and the angular relaxation rate have little influence on the model results. Also shoaling may be neglected. A scattering model based on first iteration of the Stratton-Chu equation gives results similar to that of an improved two-scale model. When compared to the observations, good agreement is obtained at L-band, but at C- and X-bands the model underestimates the modulations. A number of possible causes is discussed, but additional data are needed to settle this question.

Internal Wave–Wave Interactions. Part I: The Role of Internal Wave Vertical Divergence

Abstract Small-scale internal waves are numerically ray-traced through random 3D Garrett and Munk internal wave backgrounds. Past ray-tracing investigations of the transfer of internal wave energy toward small scales have considered only interactions with background vertical shear Vz = (Uz, Vz). Here, scale analysis and numerical simulations indicate a nonnegligible role for vertical divergence Wz. Background low-frequency vertical shear Vz transfers high-frequency test waves toward small scales while background vertical divergence Wz transfers low-frequency test waves toward small scales. These ray-tracing results resemble those of weak resonant-triad interaction theory, although the interactions considered here are not limited to be weak or resonant.

Magnetoconductivity of AlPdRe quasicrystalline films

Magnetoconductivity (MC) and zero field conductivity have been measured at low temperatures in metallic and barely insulating AlPdRe quasicrystalline films. For a metallic film, both the magnetoconductivity and conductivity can be fitted well using the 3D weak localization (WL) and electron-electron interaction (EEI) theories. The AlPdRe films exhibit very strong spin-orbit scattering with . Therefore, the inelastic scattering times can be directly extracted from the low field magnetoconductivity data taken at various temperatures, yielding . Using the fitting parameters extracted from the MC data, the zero field conductivity as a function of temperature can be described nicely using the WL and EEI theories. MC data and conductivity data obtained on barely insulating films below the metal-insulator transition cannot be explained in the framework of the WL theory.

The influence of electrostatic and dispersion interactions on the NMR parameters of acetylene

The NMR shielding constants and the spin–spin coupling constants of acetylene in C 2H 2–H + and C 2H 2–He complexes are calculated as functions of the intermolecular geometry, using the supermolecular method on CAS SCF level. For the obtained surfaces a fit resulting from the perturbation theory of weak interactions is applied. The signs of the changes induced by the presence of He and H + are opposite for all the NMR parameters of acetylene. The R −3 and R −2 radial dependence is prevalent for the shielding constants in C 2H 2–H +, while for the shielding constants in C 2H 2–He the dispersion interactions and the influence of He shielding anisotropy are of similar magnitude. The changes in the coupling constants are dominated by the FC term. BSSE is large for the 13 C shielding, smaller for the coupling constants, and negligible for the 1 H shielding.

Degenerate symmetry-adapted perturbation theory of weak interactions between closed- and open-shell monomers: application to Rydberg states of helium hydride

Symmetry-adapted perturbation theory is extended to the (quasi) degenerate, open-shell case. The new formalism is tested in calculations of the interaction energies for a helium atom in the ground state interacting with an excited hydrogen atom. It is shown that the method gives satisfactory results if the coupling with higher Rydberg states of the dimer is small, as is the case for the A2Σ+,B2Π,E2Π,32Π, and 12Δ states of HeH. For the C2Σ+ state convergence of the method is very slow, but it can be improved by including the n=3 states in the model space.

Computational Cosmology: from the Early Universe to the Large Scale Structure.

In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations addressing specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark-hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.

Discussion on the lowest energy positron decay

Positrons (e +) from 59Ni decay have a maximum energy of 51 keV, the lowest known energy for a e + transition. The identifying signal is e +e − annihilation into two 511 keV γ-rays that can be readily observed. Modern Ge detector arrays offer the opportunity to accurately check the 59Ni result (to resolve an apparent error in the intensity) and, further, to search for even lower energy e + decays. The extremely small e + branching ratios associated with such decays: (1) require efficient detection and suppression of backgrounds and (2) limit the practical utility of low energy e + transitions. Branching ratio results for allowed low energy e + decays could be compared to atomic theory calculations and, at high precision, test weak interaction theory.

Physical and Relativistic Numerical Cosmology.

In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations addressing specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark-hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.

Helioseismology and p+p → d + e+ + νe in the sun

By using a phenomenological field theory of nucleon-nucleon interactions, Oberhummer et al. found a cross section of p+p → d + e + + �e about 2.9 times that given by the potential approach and adopted in Standard Solar Model calculations. We show that a solar model with S = 2.9SSSM is inconsistent with helioseismic data, the difference between model predictions and helioseismic determinations being typically a factor ten larger than estimated uncertainties. We also show that, according to helioseismology, S cannot differ from SSSM by more than 15%. The rate of the initial reaction in the pp chain is too low to be directly measured in the laboratory (even in the solar center this rate is extremely small, of the order of 10 −10 yr −1 consistently with the solar age) and it can be determined only by using the theory of low energy weak interactions, together with the measured properties of the deuteron and of the proton-proton scattering. In terms of the astrophysical factor, S(E), what really matters is its zero energy value, which for brevity will be indicated simply as S. While we refer to [1–3] for updated reviews, we remark that the calculated values are all in the range (3.89–4.21) 10 −25 MeV b, i.e. they differ from their mean by no more than 3%. In summary, as input of Standard Solar Model (SSM) calculations, one takes [2]: SSSM = 3.89 � 10 −25 (1 ± 0.01) MeV b .

An improved composite surface model for the radar backscattering cross section of the ocean surface: 2. Model response to surface roughness variations and the radar imaging of underwater bottom topography

In the companion paper we have presented an improved composite surface model for the calculation of normalized radar backscattering cross sections (NRCS) of the ocean surface. The proposed model accounts for the impact of the full two‐dimensional ocean wave spectrum on the radar backscatter and was shown to reproduce measured absolute NRCS values for a variety of radar configurations and wind speeds satisfactorily after some reasonable tuning of the input ocean wave spectrum. This paper focuses on the modulation of the NRCS in the presence of spatially varying surface currents. First, the sensitivity of the NRCS to intensity variations of different ocean wave spectral components is investigated. Then the hydrodynamic modulation of the wave spectrum over underwater bottom topography in tidal waters is computed in different ways, and the resulting radar signatures are discussed. The composite surface model yields comparable radar signatures at high (10 GHz, X band) and low (1 GHz, L band) radar frequencies, which is in much better agreement with experimental results than the predictions of a first‐order Bragg scattering model. On the other hand, measured variations of the NRCS at high radar frequencies appear to be still underestimated in some cases, which may be due to shortcomings of our description of the wave‐current interaction by conventional weak hydrodynamic interaction theory. Possible improvements of the theory are discussed, and requirements for future experiments are formulated.

Longitudinal Josephson-plasma excitation inBi2Sr2CaCu2O8+δ:Direct observation of the Nambu-Goldstone mode in a superconductor

Electromagnetic resonant absorption phenomena in a microwave frequency range have recently been studied in the single-crystalline high-temperature superconductor ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ in magnetic fields. Using a rectangular microwave cavity resonator technique with ${\mathrm{TE}}_{102}$ mode this absorption is unambiguously identified to be the collective longitudinal Josephson plasma excitation. Since the superconducting state is a state with a broken phase symmetry, the ordered state should be accompanied by the collective excitation (Nambu-Goldstone mode). This excitation has long been thought not to be observable, because of the formation of the large Coulomb gap (Anderson-Higgs-Kibble mechanism), above which strong damping mechanisms of excited plasma are presumably present. However, this Coulomb gap can be very small in the case of anisotropic layered system such as ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}},$ and the plasma mode may lie in a microwave frequency region. Using characteristic dispersion relations, which enables us to separate out the longitudinal mode from the transverse one, the microwave absorption observed in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ is unambiguously attributed to the longitudinal excitations. We believe that this is the first and the direct experimental evidence of the Nambu-Goldstone mode in a superconductor and provides a direct proof that the Anderson-Higgs-Kibble (AHK) mechanism within the concept of spontaneously breaking symmetry is indeed valid in the case of superconducting phase transition. Since the finite plasma frequency observed here signifies formation of the finite mass of the plasma (phason) due to the AHK mechanism in the relativistic sense, the above-mentioned scenario in a superconductor corresponds to a direct mapping from the unified gauge-field theory of weak interaction and electromagnetic interaction shown by Weinberg and Salam.