Form Of Effective Potential Research Articles

Correlation between confinement and chiral-symmetry breaking in the dual Higgs theory

We study the correlation between confinement and dynamical chiral-symmetry breaking (D$\chi$SB) in the dual Ginzburg-Landau (DGL) theory using the effective potential formalism. The DGL theory is an infrared effective theory based on the dual Higgs mechanism, and provides the nonperturbative gluon propagator, which leads to the linear quark potential. The screening effect for the confining potential can be obtained by introducing the infrared cutoff corresponding to the hadron size. We formulate the effective potential for D$\chi$SB in the DGL theory, and find the vacuum instability against quark condensation. To extract confinement effect, we separate the effective potential into the confinement part and others by dividing the confinement term from other terms in the gluon propagator in the DGL theory. The confinement part provides the dominant contribution to D$\chi$SB, which is regarded as monopole dominance for D$\chi$SB. The relevant energy for D$\chi$SB is found to be the infrared region below 1GeV. Monopole dominance for the DGL propagator is also found in the intermediate region, 0.2fm $\simle r \simle$ 1fm.

Light Hadrons at Finite Temperature in the Linear Sigma Model

The vacuum properties at finite temperature for the linear sigma model are studied by using the effective potential formalism. It is found that the light hadronic masses drop fast with increasing temperature. An extensive scaling behavior of light hadronic masses is observed and is found to follow the scaling law postulated in dense matter.

Chiral symmetry breaking in the gauged NJL model in curved spacetime.

Using the renormalization group (RG) approach and the equivalency between the class of gauge-Higgs-Yukawa models and the gauged Nambu--Jona-Lasinio (NJL) model, we study the gauged NJL model in curved space-time. The behavior of the scalar-gravitational coupling constant \ensuremath{\xi}(t) in both theories is discussed. The RG-improved effective potential of the gauged NJL model in curved spacetime is found. The curvature at which chiral symmetry in the gauged NJL model is broken is obtained explicitly in a remarkably simple form. The powerful RG-improved effective potential formalism leads to the same results as ladder Schwinger-Dyson equations which have not been formulated yet in curved spacetime. \textcopyright{} 1996 The American Physical Society.

Bound-state methods for low-energy electron-ion scattering.

An effective-potential formalism, previously developed for electron scattering by a neutral target, is extended to apply to electron-ion scattering, with the requirement of antisymmetrization now accounted for explicitly. A minimum principle for the effective potential is derived, valid for scattering below the ionization threshold and applicable when, as is usually the case, the target wave functions are imprecisely known. The basis for the minimum principle is the Rayleigh-Ritz property that is satisfied by the modified Hamiltonian in terms of which the effective potential is defined. An analysis of single-channel, zero-energy scattering for a particular partial wave is presented; it is based on the effective-potential formalism and leads to an absolute definition of the zero-energy phase shift \ensuremath{\delta}(0) of the form \ensuremath{\delta}(0)=\ensuremath{\mu}(\ensuremath{\infty})\ensuremath{\pi}, where \ensuremath{\mu}(n) is the quantum defect of the nth energy level. This result may be thought of as an extension of Levinson's theorem for scattering by short-range potentials. \textcopyright{} 1996 The American Physical Society.

Finite-temperature corrections in the dilated chiral quark model.

We calculate the finite-temperature corrections in the dilated chiral quark model using the effective potential formalism. Assuming that the dilaton limit is applicable at some short length scale, we interpret the results to represent the behavior of hadrons in dense and hot matter. We obtain the scaling law, ${\mathit{f}}_{\mathrm{\ensuremath{\pi}}}$(T)/${\mathit{f}}_{\mathrm{\ensuremath{\pi}}}$ =${\mathit{m}}_{\mathit{Q}}$(T)/${\mathit{m}}_{\mathit{Q}}$\ensuremath{\simeq}${\mathit{m}}_{\mathrm{\ensuremath{\sigma}}}$(T)/${\mathit{m}}_{\mathrm{\ensuremath{\sigma}}}$ while we argue, using partial conservation of axial-vector current, that pion mass does not scale within the temperature range involved in our Lagrangian. It is found that the hadron masses and the pion decay constant drop faster with temperature in the dilated chiral quark model than in the conventional linear \ensuremath{\sigma} model that does not take into account the QCD scale anomaly. We attribute the difference in scaling in heat bath to the effect of baryonic medium on thermal properties of the hadrons. Our finding would imply that the alternating-gradient synchrotron experiments (dense and hot matter) and the RHIC experiments (hot and dilute matter) will ``see'' different hadron properties in the hadronization phase.

Effective-potential method for relativistic electron-ion scattering.

The problem of electron scattering by a heavy hydrogenic ion is formulated relativistically by using a simplified version of hole theory in which the effects of virtual-pair creation and exchange of transverse photons are ignored. An effective-potential formalism is developed and a minimum principle for the effective potential is derived, which is valid in a range of energies below the ionization threshold, through a generalization of the projection-operator procedure developed some time ago in the context of the nonrelativistic scattering problem. A version of the minimum principle is shown to hold, even in cases in which an infinite Rydberg series of autoionizing resonances lies below the scattering energy. Concepts derived from quantum-defect theory are used, in conjuction with the effective-potential formalism, to describe the effect of these resonances on the scattering. Positive-energy projection operators appear naturally in the theory. Their presence ensures that ``variational-collapse`` difficulties are avoided, as required for the validity of the minimum principle. Some care is given to the analysis of different features of the scattering theory associated with the appearance of these projection operators.

Dual Higgs Mechanism for Quarks in Hadrons

We study nonperturbative features of QCD using the dual Ginzburg-Landau (DGL) theory, where the color confinement is realized through the dual Higgs mechanism brought by QCD-monopole condensation. The linear confinement potential appears in the QCD-monopole condensed vacuum. We study the infrared screening effect to the confinement potential by the light-quark pair creation, and derive a compact formula for the screened quark potential. We study the dynamical chiral-symmetry breaking (D$\chi $SB) in the DGL theory by solving the Schwinger-Dyson equation. QCD-monopole condensation plays an essential role to D$\chi $SB. The QCD phase transition at finite temperature is studied using the effective potential formalism in the DGL theory. We find the reduction of QCD-monopole condensation and the string tension at high temperatures. The surface tension is calculated using the effective potential at the critical temperature. The DGL theory predicts a large mass reduction of glueballs near the critical temperature. We apply the DGL theory to the quark-gluon-plasma (QGP) physics in the ultrarelativistic heavy-ion collisions. We propose a new scenario of the QGP formation via the annihilation of color-electric flux tubes based on the attractive force between them.

Chiral symmetry breaking in a finite volume.

In the context of the $N$-component four-fermion model in 2+1 dimensions we investigate the effects of a finite volume and boundary conditions on chiral-symmetry restoration in the large-$N$ limit using the effective potential formalism. We obtain the critical lines, which separate the chirally symmetric phase from the broken phase, in terms of an infinite-volume fermion mass and system size for three types of boundary conditions.

Squark contributions to Higgs boson masses in the next-to-minimal supersymmetric standard model

Within the context of an effective potential formalism we calculate the contribution to Higgs boson masses in the next-to-minimal supersymmetric standard model from squark loops. We then supplement a previously performed renormalisation group analysis of the Higgs sector of this model with these results in order to determine the shift in the bound on the lightest CP-even Higgs boson mass as a result of squark effects. The improved bound on the lightest neutral CP-even Higgs boson mass, including squark contributions, is m h ⩽ 146 (139, 149) GeV for m t = 90 (140, 190) GeV. For m t = 190 GeV squark effects contribute 23 GeV to the bound, with smaller contributions for small m t values.

Gauge independence of interelectronic potentials

It has been shown that recently by Lindgren (1990) that gauge independent energy shifts in the effective potential formalism can only be obtained when all the diagrams to the same order of perturbation are taken into account. In this work, the authors extends Lindgren's proof in two generalized gauge conditions. It is shown explicitly that in the generalized Landau gauge and axial gauge, by neglecting radiative corrections, the energy shifts calculated in these gauges equal the Feynman gauge results to the leading relativistic order.

Study of a simple model ferroelectric using the effective potential method

Abstract We have applied the effective potential formalism to a simple one-dimensional model of a ferroelectric crystal. The method incorporates quantum effects into a partition function of classical form, which greatly simplifies the calculation. Our results for the nature of the phase transitions, the transition temperatures, and the temperature dependence of the ordering parameter, are all in very good agreement with a full quantum mechanical calculation. Pacs 63.70, 77.80, 64.60.C

Effects of transverse photon exchange in helium Rydberg states: Corrections beyond the Coulomb-Breit interaction.

The Breit correction only accounts for part of the transverse photon exchange correction in the calculation of the energy levels in helium Rydberg states. The remaining leading corrections are identified and each is expressed in an effective potential form. The relevance to the Casimir correction potential in various limits is also discussed.

Core/valence partition and relativistic effects in effective potentials for transition metals

AbstractTwo different versions, relativistic and nonrelativistic, of the “shape‐consistent” effective potential (EP) formalism are analyzed in ab initio calculations for transition metals. The influence of alternative core/valence partitions on the reliability of the procedure is discussed. The accuracy of EP results for transition metals is shown to depend on adequate choices of the valence subspace and proper inclusion of relativistic effects.

Core polarization corrections on the relativistic core effective potentials formalism

The ab initio shape-consistent Relativistic Effective Potential (REP) formalism, recently improved, implicitly incorporates relativistic corrections. However, since the frozen core approximation is assumed, intershell correlation can not be taken into account. This is a serious drawback in REP treatments on alkali systems, where the core polarization is especially pronounced. An easy way to correct the REP method by adding to the core operators a phenomenological core polarization potential is proposed. With no adjustable parameters, the corrected REPs account for a major contribution to the full core/valence correlation at virtually no computational cost.

Refinement of the solution structure of the DNA dodecamer 5'd(CGCGPATTCGCG)2 containing a stable purine-thymine base pair: combined use of nuclear magnetic resonance and restrained molecular dynamics.

The solution structure of the self-complementary dodecamer 5'd(CGCGPATTCGCG)2, containing a purine-thymine base pair within the hexameric canonical recognition site GAATTC for the restriction endonuclease EcoRI, is investigated by nuclear magnetic resonance spectroscopy and restrained molecular dynamics. Nonexchangeable and exchangeable protons are assigned in a sequential manner. A set of 228 approximate interproton distance restraints are derived from two-dimensional nuclear Overhauser enhancement spectra recorded at short mixing times. These distances are used as the basis for refinement using restrained molecular dynamics in which the interproton distance restraints are incorporated into the total energy function of the system in the form of effective potentials. Eight calculations are carried out, four starting from classical A-DNA and four from classical B-DNA. In all cases convergence to very similar B-type structures is achieved with an average atomic root mean square (rms) difference between the eight converged structures of 0.7 +/- 0.2 A, compared to a value of 6.5 A for that between the two starting structures. It is shown that the introduction of the purine-thymine mismatch does not result in any significant distortion of the structure. The variations in the helical parameters display a clear sequence dependence. The variation in helix twist and propeller twist follows Calladine's rules and can be attributed to the relief of interstrand purine-purine clash at adjacent base pairs. Overall the structure is straight. Closer examination, however, reveals that the central 5 base pair steps describe a smooth bend directed toward the major groove with a radius of curvature of approximately 38 A, which is compensated by two smaller kinks in the direction of the minor groove at base pair steps 3 and 9. These features can be explained in terms of the observed variation in roll and slide.

Refinement of the solution structure of the ribonucleotide 5'r(GCAUGC)2: combined use of nuclear magnetic resonance and restrained molecular dynamics

The solution structure of the self-complementary hexamer 5'r(GCAUGC)2 is investigated by means of nuclear magnetic resonance spectroscopy and restrained molecular dynamics. The proton resonances are assigned in a sequential manner, and a set of 110 approximate interproton distance restraints are derived from the two-dimensional nuclear Overhauser enhancement spectra. These distances are used as the basis of a structure refinement by restrained molecular dynamics in which the experimental restraints are incorporated into the total energy function of the system in the form of effective potentials. Eight restrained molecular dynamics simulations are carried out, four starting from a structure with regular A-type geometry and four from one with regular B-type geometry. The atomic root mean square (rms) difference between the initial structures is 3.2 A. In the case of all eight simulations, convergence is achieved both globally and locally to a set of very similar A-type structures with an average atomic rms difference between them of 0.8 +/- 0.2 A. Further, the atomic rms differences between the restrained dynamics structures obtained by starting out from the same initial structures but with different random number seeds for the assignment of the initial velocities are the same as those between the restrained dynamics structures starting out from the two different initial structures. These results suggest that the restrained dynamics structures represent good approximations of the solution structure. The converged structures exhibit clear sequence-dependent variation in some of the helical parameters, in particular helix twist, roll, slide, and propellor twist.(ABSTRACT TRUNCATED AT 250 WORDS)

The effective potential and the coupling constant at high temperature

The calculation of the effective potential at non-zero temperature is considered. A method of including relevant multi-loop diagrams in the effective potential formalism avoids problems that appear in some earlier treatments. This method is then used to calculate the temperature dependence of the effective coupling constant V (4) in a scalar λø (4) theory. The implementation of the renormalization group at high temperature is described, and is used ti show that V (4) ≈λ/ [1 - (3/16π 2)λ ln ( T / μ)].

Stereochemistry of binding of the tetrapeptide acetyl-Pro-Ala-Pro-Tyr-NH 2 to porcine pancreatic elastase : Combined use of two-dimensional transferred nuclear overhauser enhancement measurements, restrained molecular dynamics, X-ray crystallography and molecular modelling

A nuclear magnetic resonance study of the conformation of the tetrapeptide acetyl-Pro-Ala-Pro-Tyr-NH 2 bound to porcine pancreatic elastase is presented. From two-dimensional transferred nuclear Overhauser enhancement measurements, a set of 23 approximate distance restraints between pairs of bound ligand protons, indicative of an extended type structure, is derived. The structure of the bound tetrapeptide is then refined from two different starting structures (an extended β-strand and a polyproline helix) by restrained molecular dynamics, in which the interproton distances are incorporated into the total energy of the system in the form of effective potentials. Convergence to essentially the same average restrained dynamics structures is achieved. The refined structures are then modelled into the active site of elastase by interactive molecular graphics. The determination of the anchor point of the bound tetrapeptide on the enzyme was aided by a simultaneous crystallographic study which, despite the fact that only electron density for a Pro-X dipeptide fragment was visible, enabled both the approximate position and orientation of binding to be determined. It is found that the tetrapeptide is bound in the S′ binding site in the reverse orientation found in other serine protease-inhibitor complexes and is stabilized both by hydrogen-bonding and by van der Waals' interactions.

Structure refinement of oligonucleotides by molecular dynamics with nuclear overhauser effect interproton distance restraints: Application to 5′ d(C-G-T-A-C-G) 2

The solution structure of the self-complementary DNA hexamer 5′ d(C-G-T-A-C-G) 2 is refined by restrained molecular dynamics in which 192 interproton distances, determined from pre-steady-state nuclear Overhauser enhancement measurements, are incorporated into the total energy of the system in the form of effective potentials. First the method is tested by applying an idealized set of distance restraints taken from classical B-DNA to a simulation starting off from A-DNA and vice versa. It is shown that in both cases the expected transition between A- and B-DNA occurs. Second, a set of restrained molecular dynamics calculations is carried out starting from both A- and B-DNA with the experimental interproton distances for 5′ d(C-G-T-A-C-G) 2 as restraints. Convergence to the same B-type structure is achieved with the interproton distances equal to the measured values within experimental error. The root-mean-square atomic difference between the two average restrained dynamics structures (<1 Å) is approximately the same as the root-mean-square fluctuations of the atoms.

Finite-field SCF calculations of the dipole polarisabilities of heavy atoms using relativistic effective potentials

The static dipole polarisabilities of Xe, Lu, Hg+, Hg, Tl and At have been determined from finite-field SCF calculations within a valence-electron relativistic effective potential formalism. The effect of the self-consistent inclusion of spin-orbit coupling on the calculated polarisabilities have been investigated by comparing j-averaged (L, Lambda ) results with j-dependent (J, Omega ) calculations. The atoms selected provide a range of closed-shell, particle and hole states for comparative study. The results suggest that self-consistent inclusion of spin-orbit coupling is far more important for the particle states than for the hole states. In the case of Xe, results are presented from calculations using relativistic effective potentials based on both Hamiltonian-consistent and shape-consistent pseudo-orbitals. The shape-consistent approach is found to produce polarisabilities in better agreement with previously determined all-electron Hartree-Fock values. In addition, for Hg the shape-consistent approach yields a polarisability in excellent agreement with all-electron numerical Dirac-Fock calculations.