Self-energy Contributions Research Articles

Light-meson orbital excitations in the QCD string approach

In the framework of the QCD string approach it is shown that the spin-averaged masses $\bar{M}(nL)$ of all low-lying light mesons are well described using the string tension $\sigma$ as the only parameter. The Regge slope $\alpha'_L$ and the intercept $\alpha_L(0)$ of the Regge L-trajectory for $\bar{M}(nL)$ are calculated analytically and turn out to be $\alpha'_L = 0.80$ GeV${}^{-2}$ (for $L \leq 4$) and $\alpha_L(0) = -0.34$, in good agreement with the experimental data: $\alpha'_{L {\rm exp}} = 0.81 \pm 0.01$ GeV${}^{-2}$, $\alpha_{L {\rm exp}}(0) = -0.30 \pm 0.02$. To obtain this strong agreement with the data the nonperturbative quark self-energy contributions to the meson masses must be taken into account, which appeared to be large and negative for small values of L, and are even for larger values of L important for a close fit. From the present analysis of the meson spectra the restriction $\alpha_s \leq 0.40$ on the strong coupling is required.

Singular structure and enhanced Friedel oscillations in the two-dimensional electron gas

We evaluate the leading-order corrections (in ${r}_{s})$ to the static polarization ${\mathrm{\ensuremath{\Pi}}}^{\mathrm{*}}$ $(q,0),$ of the two-dimensional electron gas with dynamically screened interactions. The corresponding diagrams all exhibit singular logarithmic behavior in their derivatives about ${q=2k}_{F}$ and provide significant enhancement of the proper polarization particularly at low densities. At a density of ${r}_{s}=3,$ the contribution from the leading-order fluctuational diagrams exceeds both the zeroth-order (Lindhard) response and the self-energy and exchange contributions. The importance of these diagrams in two-dimensions is demonstrated by comparison to those of an equivalent three-dimensional electron gas; we also consider the impact these findings have on ${\mathrm{\ensuremath{\Pi}}}^{\mathrm{*}}$ $(q,0)$ computed to all orders in perturbation theory.

Width and partial widths of unstable particles in the light of the Nielsen identities

Fundamental properties of unstable particles, including mass, width, and partial widths, are examined on the basis of the Nielsen identities (NI) that describe the gauge dependence of Green functions. In particular, we prove that the pole residues and associated definitions of branching ratios and partial widths are gauge independent to all orders. A simpler, previously discussed definition of branching ratios and partial widths is found to be gauge independent through next-to-next-to-leading order. It is then explained how it may be modified in order to extend the gauge independence to all orders. We also show that the physical scattering amplitude is the most general combination of self-energy, vertex, and box contributions that is gauge independent for arbitrary s, discuss the analytical properties of the NI functions, and exhibit explicitly their one-loop expressions in the Z-gamma sector of the Standard Model.

Nuclear matter spectral functions by transport theory

Quantum transport theory is used to calculate the nucleon spectral function in infinite nuclear matter. A self-consistent description is obtained by utilizing the relations between collision rates and correlation functions. Static and dynamical self-energies are taken into account in the single-particle propagators. The real parts of the nonstatic self-energy contributions are calculated by dispersion theory thus conserving the analyticity of momentum distributions. The transport theoretical spectral functions, momentum distributions, occupation probabilities and response functions are in close agreement with results of variational and other many-body theoretical calculations. The results indicate that the nucleon spectral functions are determined only by the average short-range correlation strength.

Relativistic pionic effects in quasielastic electron scattering

The impact of relativistic pionic correlations and meson-exchange currents on the response functions for electromagnetic quasielastic electron scattering from nuclei is studied in detail. Results in first-order perturbation theory are obtained for one-particle emission electronuclear reactions within the context of the relativistic Fermi gas model. Improving upon previous analyses where nonrelativistic reductions of the currents were performed, here a fully relativistic analysis in which both forces and currents are treated consistently is presented. Lorentz covariance is shown to play a crucial role in enforcing the gauge invariance of the theory. Effects stemming uniquely from relativity in the pionic correlations are identified and, in particular, a comprehensive study of the self-energy contributions and of the currents associated with the pion is presented. First- and second-kind scaling for high momentum transfer is investigated.

Infrared Behavior of Massive Scalar Matter Coupled to Gravity

In the framework of causal perturbation theory we consider a massive scalar field coupled to gravity. In the field theoretic approach to quantum gravity we start with a massless second-rank tensor field. This tensor field is then quantized in a covariant way in Minkowski space. This article deals with the adiabatic limit for graviton radiative corrections in a scattering process of two massive scalar particles. We compute the differential cross section for Bremsstrahlung processes in which one of the outgoing particles emits a graviton of low energy, a so-called soft graviton. Since the emitted graviton will not be detected we must integrate over the energy of all soft gravitons. Furthermore we discuss the infrared behavior of graviton and matter self-energy contributions.

QED self-energy contribution to highly excited atomic states

We present numerical values for the self-energy shifts predicted by QED for hydrogenlike ions (nuclear charge number $60<~Z<~110)$ with an electron in an $n=3,$ 4, or 5 level with high angular momentum $(5/2<~j<~9/2).$ Its applications include precise predictions of transition energies and studies of the outer-shell structure of atoms and ions.

Charge radius of the neutrino

Using the pinch technique we construct at one-loop order a neutrino charge radius, which is finite, depends neither on the gauge-fixing parameter nor on the gauge-fixing scheme employed, and is process independent. This definition stems solely from an effective proper photon-neutrino one-loop vertex, with no reference to box or self-energy contributions. The role of the $\mathrm{WW}$ box in this construction is critically examined. In particular it is shown that the exclusion of the effective $\mathrm{WW}$ box from the definition of the neutrino charge radius is not a matter of convention but is in fact dynamically realized when the target fermions are right-handedly polarized. In this way we obtain a unique decomposition of effective self-energies, vertices, and boxes, which separately respect electroweak gauge invariance. We elaborate on the tree-level origin of the mechanism which enforces at the one-loop level massive cancellations among the longitudinal momenta appearing in the Feynman diagrams, and in particular those associated with the non-Abelian character of the theory. Various issues related to the known connection between the pinch technique and the background field method are further clarified. Explicit closed expressions for the neutrino charge radius are reported.

Direct renormalization of two-electron self-energy contribution to energy of helium-like ions

A new practical approach to the calculation of two-electron self-energy corrections is presented for the energy of helium-like ions. The working formulas are derived within the modified adiabatic formalism. The direct renormalization procedure is used in terms of multiple commutator expansions. It is shown that the final expression does not contain ultraviolet and infrared divergences. This expression is used then to obtain numerical estimates for two-electron self-energy corrections in wide range of the nuclear charge Z.

Estimate of the second order electron self energy corrections in highly charged heavy ions

An estimate for the last unknown gauge-invariant set of QED corrections of order 2 ,t he second-order self-energy correction, is presented utilizing the so-called sign approximation. This is able to reduce the present uncertainties in Lamb-shift predictions considerably. Highly charged ions provide an ideal scenario to demonstrate the validity of QED in strong fields, e.g., by measurements of the Lamb shift at utmost precision. In this respect the recent experimental progress made in measurements in hydrogen-like uranium [1] indicates that calculations of higher-order radiative corrections become relevant. The set of second-order QED diagrams includes all various combinations of the first-order self-energy (SE) and vacuum polarization (VP) effects. The present status of theoretical predictions for the Lamb shift in different one-electron ions is presented in [2]. However, the calculations of the most difficult set of diagrams (see figure 1), the second-order self-energy correction (SESE) are yet uncomplete [3‐ 6], which remains as source for major theoretical uncertainties in present Lamb-shift predictions. To close this gap is a challenge for theory. As a step towards this, we present an estimate for the two-photon self-energy contribution. The graph SESE (a) consists of the irreducible and the reducible contributions. Utilizing Feynman gauge the first part can be renormalized and calculated separately since it does not contain infrared divergencies. The irreducible part has been calculated in [3] for large nuclear charge numbers Z and in [4,6] for arbitrary values of Z .F or high-Z systems all results obtained coincide, while for low- and intermediate-Z values a discrepancy between [4] and [6] has been found. In Feynman gauge, the remaining reducible part of the SESE (a) graph and the two diagrams SESE (b) and (c) have to be calculated simultaneously in order to cancel infrared and ultraviolet divergences arising from different diagrams [7]. The general renormalization scheme for all two-photon self-energy diagrams has

Two mechanisms for the elimination of pinch singularities in out of equilibrium thermal field theories

We analyze ill-defined pinch singularities characteristic of out of equilibrium thermal field theories. We identify two mechanisms that eliminate pinching even at the single self-energy insertion approximation to the propagator: the first is based on the vanishing of phase space at the singular point (threshold effect). It is effective in QED with a massive electron and a massless photon. In massless QCD, this mechanism fails, but the pinches cancel owing to the second mechanism, i.e., owing to the spinor/tensor structure of the single self-energy insertion contribution to the propagator. The constraints imposed on distribution functions are very reasonable.

Effective energy function for proteins in solution.

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.

Damping of giant dipole resonances at finite temperature

The damping width γ ↓ GDR of the giant dipole resonance, due to its coupling to doorway states, is studied within the framework of the thermal Green's functions theory. It is found that γ ↓ GDR reflects the temperature dependence of the single-particle damping width but, as a consequence of the cancellation effects between self-energy and vertex contributions, the coefficient of such a dependence is so small that it can essentially be neglected, within the temperature range of physical interest.

Fourth-order self-energy contribution to the Lamb shift

Two-loop self-energy contributions to the fourth-order Lamb shift of ground-state hydrogenic ions are treated to all orders in $Z\ensuremath{\alpha}$ by using exact Dirac-Coulomb propagators. A rearrangement of the calculation into four ultraviolet finite parts, the $M, P, F$, and perturbed orbital (PO) terms, is made. Reference-state singularities present in the $M$ and $P$ terms are shown to cancel. The most computationally intensive part of the calculation, the $M$ term, is evaluated for hydrogenlike uranium and bismuth, the $F$ term is evaluated for a range of $Z$ values, but the $P$ term is left for a future calculation. For hydrogenlike uranium, previous calculations of the PO term give $\ensuremath{-}0.971$ eV: the contributions from the $M$ and $F$ terms calculated here sum to $\ensuremath{-}0.325$ eV.

Estimated valence-level Lamb shifts for group 1 and group 11 metal atoms

The leading Lamb-shift terms are evaluated for the valence electrons of neutral alkali-metal and coinage metal atoms (groups 1 and 11, respectively). The vacuum polarization (VP) contribution is treated using the Uehling potential and the self-energy (SE) contribution using either a density-based ${\ensuremath{\alpha}}^{3}$ expression or the ${E}_{\mathrm{SE}}{/E}_{\mathrm{VP}}$ ratios by Johnson and Soff [At. Data Nucl. Data Tables 33, 405 (1985)]. Both Dirac-Fock and model-potential wave functions are tested. The result for the valence $\mathrm{ns}$ electron is a destabilization, rising at moderate $Z$ values (30--80) as ${Z}^{2}$ and more steeply at high $Z.$ The $(n\ensuremath{-}1)d$ electrons suffer an indirect stabilization. The effects are opposite those of kinetic Dirac relativity and about 1--2% of them. They are roughly half of the valence Breit interaction and rise to about 0.5% of the ionization potential for $Z=111--119.$

First-principles approach to the calculation of electronic spectra in clusters

We discuss a method for first-principles calculations of photoemission spectra in small clusters, going well beyond a standard density functional theory-local density approximation (DFT-LDA) approach. Starting with a DFT-LDA calculation, we evaluate self-energy contributions to the quasiparticle energies of an electron or hole in the GW scheme, where the self-energy Σ = GW is constructed from the one-particle Green's function G and the RPA screened Coulomb interaction W. The contributions of structural relaxation are taken into account. We show the importance of these effects at the example of the photoemission spectrum of SiH4. We also briefly discuss results for longer hydrogenated silicon chains, and address the problem of optical absorption.

Inelastic light scattering at high-energy excitations in doped cuprate superconductors

We present Raman spectra of low- and high-energy spin and charge excitations from Y{sub 1{minus}x}Pr{sub x}Ba{sub 2}Cu{sub 3}O{sub 7} and YBa{sub 2}Cu{sub 3}O{sub 6+x} thin films as well as from Y{sub 1{minus}x}Pr{sub x}Ba{sub 2}Cu{sub 3}O{sub 7} single crystals. We show that a rearrangement of spectral weight in B{sub 1g} and A{sub 1g} symmetry occurs below the respective critical temperatures T{sub c} of the samples at energies of about 5{endash}6 times 2{Delta}, where {Delta} is the magnitude of the superconducting order parameter. The redistribution of spectral weight shifts with doping towards lower energies. For optimally doped samples strong renormalization effects of the electronic and phononic structures occur. We discuss our results in terms of a simplified t-J model having magnetic and chargelike scattering channels. As far as the magnetic response is concerned, we apply the Heisenberg model of antiferromagnetism including self-energy contributions to the one-magnon states. This shows that the rearrangement at least partly results from an interaction between the remaining antiferromagnetism and the superconductivity. Moreover, the chargelike response at high energies seems to be influenced by the superconducting transition as well, indicating a strong interplay between holes and magnons in the normal and superconducting state. {copyright} {ital 1997} {ital Themore » American Physical Society}« less

Two-electron self-energy contribution to the ground-state energy of helium-like ions

The two-electron self-energy contribution to the ground-state energy of helium-like ions is calculated both for a point nucleus and an extended nucleus in a wide interval of Z. All the two-electron contributions are compiled to obtain most accurate values for the two-electron part of the ground-state energy of helium-like ions in the range Z = 20–100. The theoretical value of the ground-state energy of 238U 90+, based on currently available theory, is evaluated to be −261382.9(8) eV, without higher-order one-electron QED corrections.

Sum rules for asymptotic form factors in e+e− → W+W− scattering

At very large energies and in SU(2) L ⊗ U(1) Y gauge theories, the trilinear gauge boson vertices relevant for e + e − → W + W − scattering are related in a simple way to the gauge boson self-energies. We derive these relations, both from the requirement of perturbative unitarity and from the Ward identities of the theory. Our discussion shows that, in general, it is never possible to fully eliminate self-energy dependencies from all the different form factors that parametrize the e + e − → W + W − helicity amplitudes. The exclusion of the self-energy contributions would lead to estimates of the effects wrong by orders of magnitude. We propose a simple way of including the self-energy contributions in an appropriate definition of the form factors.

Comparison of perturbative and multiconfigurational electron propagator methods

Ionization energies below 20 eV of 10 molecules calculated with electron propagator techniques employing Hartree-Fock orbitals and multiconfigurational self-consistent field orbitals are compared. Diagonal and nondiagonal self-energy approximations are used in the perturbative formalism. Three diagonal methods based on second- and third-order self-energy terms, all known as the outer valence Green's function, are discussed. A procedure for selecting the most reliable of these three versions for a given calculation is tested. Results with a polarized, triple ζ basis produce root mean square errors with respect to experiment of approximately 0.3 eV. Use of the selection procedure has a slight influence on the quality of the results. A related, nondiagonal method, known as ADC(3), performs infinite-order summations on several types of self-energy contributions, is complete through third-order, and produces similar accuracy. These results are compared to ionization energies calculated with the multiconfigurational spin-tensor electron propagator method. Complete active space wave functions or close approximations constitute the reference states. Simple field operators and transfer operators pertaining to the active space define the operator manifold. With the same basis sets, these methods produce ionization energies with accuracy that is comparable to that of the perturbative techniques. © 1996 John Wiley & Sons, Inc.