123053533
Scale-scheme ambiguities in the Brodsky-Lepage-Mackenzie procedure
Abstract The recently proposed method of Brodsky, Lepage and Mackenzie for “eliminating scale ambiguities in perturbative QCD” yields different results in different renormalization schemes. We show that one cannot make a scheme-independent separation of fermion loop effects from other types of higher-order correction. The case of ϒ decay is discussed particularly.
119264999
Optimization of QCD perturbation theory: Results for Re+e− at fourth order
Abstract Physical quantities in QCD are independent of renormalization scheme (RS), but that exact invariance is spoiled by truncations of the perturbation series. “Optimization” corresponds to making the perturbative approximant, at any given order, locally invariant under small RS changes. A solution of the resulting optimization equations is presented. It allows an efficient algorithm for finding the optimized result. Example results for R e + e − = 3 ∑ q i 2 ( 1 + R ) to fourth order (NNNLO) are given that show nice convergence, even down to arbitrarily low energies. The Q = 0 “freezing” behavior, R = 0.3 ± 0.3 , found at third order is confirmed and made more precise; R = 0.2 ± 0.1 . Low-energy results in the MS ¯ scheme, by contrast, show the typical pathologies of a non-convergent asymptotic series.
119042764
Resolution of the lambda phi**4 puzzle and a 2-TeV Higgs boson
We argue that massless (lambda Phi^4)_4 is "trivial" without being entirely trivial. It has a non-trivial effective potential which leads to spontaneous symmetry breaking, but the particle excitations above the broken vacuum are non-interacting. The key to this picture is the realization that the constant background field (the mode with zero 4-momentum) renormalizes differently from the fluctuation field (the finite-momentum modes). This picture reconciles rigorous results and lattice calculations with one-loop and Gaussian-approximation analyses. Because of "triviality", these latter two methods should be effectively exact. Indeed, they yield the same renormalized effective potential and the same relation m_h^2 = 8 pi^2 v^2 between the particle mass and the physical vacuum expectation value. This relation predicts a Higgs mass m_h about 2 TeV in the standard model. The non-interacting nature of the scalar sector implies, by the equivalence theorem, that Higgs and gauge bosons interact only weakly, through their gauge and Yukawa couplings.
117188910
The renormalization‐scheme‐dependence problem and its solution
I explain, in ‘‘uncompromising’’ terms, the solution to the renormalization‐scheme‐dependence problem.
119880793
Optimized perturbation theory in the Gross-Neveu model
121312073
Gluon enhancements in charmed-meson decays
We address tests of nonspectator diagrams in charmed-meson decays. In particular, we explore the consequences of a model in which such diagrams are enhanced by the emission of a single gluon. For a lifetime ratio tau(D/sup +/)/tau(D/sup 0/)=5, we predict (i) tau(F/sup +/)/tau(D/sup +/) approx. = 0.6, (ii) an enhanced ..delta..S=0 rate for D/sup +/, (iii) a substantial multipion branching fraction for the F/sup +/, (iv) an F/sup +/ ..-->.. tau/sup +/..nu.. branching fraction of order 10 --20%, and (v) restrictive bounds on the D/sup 0/ ..-->.. K-bar/sup 0/..pi../sup 0/ mode.
14308528
Mass dispersions from giant dipole resonances using the Balian–Vénéroni variational approach
The Balian–Veneroni variational approach has been implemented using a three-dimensional time-dependent Hartree–Fock (TDHF) code with realistic Skyrme interactions and used to investigate the mass dispersions from giant dipole resonances in 32S and 132Sn decaying through particle emission. The fluctuations obtained are shown to be quantitatively larger than the standard TDHF results.
17333676
Isoscalar and Isovector Giant Monopole Resonances from a Continuum Hartree-Fock Method
We motivate and summarise some recent results in the application of formally exact boundary conditions in nuclear time-dependent Hartree-Fock calculations, mak- ing use of Laplace transformations to calculate the values of the wave functions at the boundaries. We have realised the method in the case of giant monopole resonances of spherically-symmetric nuclei, and present strength functions of 16 O and 40 Ca using a sim- plified version of the Skyrme force, showing that no artefacts from discretisation occur as contaminatnts
14447155
Charge radius isotope shift across the N=126 shell gap.
We revisit the problem of the kink in the charge radius shift of neutron-rich even isotopes near the N=126 shell closure. We show that the ability of a Skyrme force to reproduce the isotope shift is determined by the occupation of the neutron 1i(11/2) orbital beyond N=126 and the corresponding change it causes to deeply-bound protons orbitals with a principal quantum number of 1. Given the observed position of the single-particle energies, one must either ensure occupation is allowed through correlations, or not demand that the single-particle energies agree with experimental values at the mean-field level.
16386160
Extension of the continuum time-dependent Hartree-Fock method to proton states.
This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied to nuclear giant monopole resonances in the small amplitude regime. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region yields an artificial boundary, which is not present physically. The question of how to ensure the boundary does not interfere with the internal solution, while keeping the overall calculation time low is studied. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. An inverse Laplace transform required by the absorbing boundaries is calculated using a method of nonlinear least squares. The accuracy and efficiency of the scheme is tested and results presented to support the case that they are an effective way of handling the artificial boundary.
121929671
Nuclear matter and neutron star properties calculated with the skyrme interaction
The effective Skyrme interaction has been used extensively in mean-field models for several decades and many different parametrizations of the interaction have been proposed. All of these give similar agreement with the experimental observables of nuclear ground states as well as with the properties of infinite symmetric nuclear matter at the saturation density n0. However, when applied over a wider range of densities (up to ∼3n0) they predict widely varying behavior for the observables of both symmetric and asymmetric nuclear matter. A particularly relevant example of naturally occurring asymmetric nuclear matter is the material of which neutron stars are composed. At around nuclear matter density, this can be well represented as a mixture of neutrons, protons, electrons, and muons (n+p+e+μ matter) in β-equilibrium, and these densities turn out to be the key ones for determining the properties of neutron-star models with masses near to the widely used “canonical” value of 1.4M⊙. By constructing equations of state for neutron-star matter using the different Skyrme parametrizations, calculating corresponding neutron-star models and then comparing these with observational data, an additional constraint can be obtained for the values of the Skyrme parameters. Such a constraint is particularly relevant because the parametrizations are initially determined by fitting to the properties of doubly closed-shell nuclei and it is an open question how suitable they then are for nuclei with high values of isospin, such as those at the neutron drip-line and beyond. The neutron-star environment provides an invaluable testing ground for this. We have carried out an investigation of 87 different Skyrme parametrizations in order to examine how successful they are in predicting the expected properties of infinite nuclear matter and generating plausible neutron-star models. This is the first systematic study of the predictions of the various Skyrme parametrizations for the density dependence of the characteristic observables of nuclear matter; the density dependence of the symmetry energy for β-equilibrium matter turns out to be a crucial property for indicating which Skyrme parameter sets will apply equally well for finite nuclei and for neutron-star matter. Only 27 of the 87 parametrizations investigated pass the test of giving satisfactory neutron-star models and we present a list of these.