Search results for "Dimension"
showing 10 items of 2766 documents
Mass singularities in light quark correlators: the strange quark case
1995
The correlators of light-quark currents contain mass-singularities of the form log(m^2/Q^2). It has been known for quite some time that these mass- logarithms can be absorbed into the vacuum expectation values of other operators of appropriate dimension, provided that schemes without normal- ordering are used. We discuss in detail this procedure for the case of the mass logarithms m^4 log(m^2/Q^2), including also the mixing with the other dimension-4 operators to two-loop order. As an application we present an improved QCD sum rule determination of the strange-quark mass. We obtain m_s(1 GeV)=171 \pm 15 MeV.
Taming the higher power corrections in semileptonic B decays
2016
We study the effect of dimension 7 and 8 operators on inclusive semileptonic B decays and the extraction of |Vcb|. Using moments of semileptonic B decay spectra and information based on the Lowest-Lying State saturation Approximation (LLSA) we perform a global fit of the nonperturbative parameters of the heavy quark expansion including for the first time the O(1/mb^{4,5}) contributions. Higher power corrections appear to have a very small effect on the extraction of |Vcb|, independently of the weight we attribute to the LLSA.
Effective kink-kink interaction in a one-dimensional model mediated by phonon exchange
1994
The general 1D double-well model with anharmonic interaction is considered in the displacive limit. Expansion of the Hamiltonian around a multikink state results in a phonon-kink Hamiltonian. It is shown that at rather low temperatures and short wave lengths the phonon-kink interaction can be treated in Born approximation, leading to a decomposition of the multikink-phonon Hamiltionian. Elimination of the phonons results in an effective potential for the kink-kink interaction, which corresponds to the one-dimensional analog of the RKKY interaction. This long-range interaction is inherent only for models with anharmonic on-site potentials and not in case of a double-parabola model.
Exchange-correlation potential with a proper long-range behavior for harmonically confined electron droplets
2010
The exchange-correlation potentials stemming from the local-density approximation and several generalized-gradient approximations are known to have incorrect asymptotic decay. This failure is independent of the dimensionality but so far the problem has been corrected---within the mentioned approximations---only in three dimensions. Here we provide a cured exchange-correlation potential for two-dimensional harmonically confined systems that cover a wide range of applications in quantum Hall and semiconductor physics, especially in quantum-dot modeling. The given potential is a generalized-gradient approximation and we demonstrate that it agrees very well with the analytic result of a two-ele…
Dimensional Regularization. Ultraviolet and Infrared Divergences
2015
The cornerstone of Quantum Field Theory is renormalization. We shall speak more about in the next chapters. Before, it is necessary to discuss the method. The best and most simple is, of course, dimensional regularization (doesn’t break the symmetries, doesn’t violate the Ward Identities, preserves Lorentz invariance, etc.). When explained consistently, it becomes very simple and clear. Here, we shortly discuss ultraviolet (UV) and infrared (IR) divergences with a few examples. However, in Chap. 8, we shall extensively treat one-loop two and three-point functions and analyse many more examples of IR and UV divergences.
Axial behaviour of Cantor ring diffractals
2003
Cantor ring diffractals describe rotationally symmetric pupils constructed from a one-dimensional polyadic Cantor set. The influence on the axial irradiance of several fractal descriptors of such pupils, including fractal dimension, number of gaps and lacunarity, are investigated. It is shown that, contrary to their transversal response, the axial behaviour of these pupils does not resemble the fractal structure of the aperture. The sensitivity of such pupils to the spherical aberration is also analysed.
On the Multifractal Character of the Lorenz Attractor
1992
A detailed analysis of the Lorenz attractor in connection with generalized dimensions is presented in this work. Different methods have been employed to estimate these dimensions. Two of them are of standard type. A new method, based on the minimal spanning tree of the point distribution, is extensively tested in this work. It turns out that the Lorenz attractor is very appropriate for being analyzed through this technique, which produces a very clean estimate of the extrema scaling indices α min and α max . The different methods give qualitatively the same result: The Lorenz attractor has a multifractal character
Fractals and multifractals in the description of the cosmic structure
1990
Abstract The concepts of fractals and multifractals are applied to describe the large scale galaxy distribution. It is shown how the Universe fits the fractal geometry on small scales (several Mpc), but that there exists some cut-off where the scale invariance is broken. Even in the scaling region the cosmic structure is not a simple fractal, and the task is to introduce more complex and complete clustering descriptors. At this stage, the concept of multifractals appears to be more efficient to describe the texture of the Universe.
Measurement of theB0→π−l+νForm-Factor Shape and Branching Fraction, and Determination of|Vub|with a Loose Neutrino Reconstruction Technique
2007
We report the results of a study of the exclusive charmless semileptonic decay, B-0 ->pi(-)center dot(+)nu, undertaken with approximately 227x10(6) BB pairs collected at the Upsilon(4S) resonance with the BABAR detector. The analysis uses events in which the signal B decays are reconstructed with an innovative loose neutrino reconstruction technique. We obtain partial branching fractions in 12 bins of q(2), the momentum transfer squared, from which we extract the f(+)(q(2)) form-factor shape and the total branching fraction B(B-0 ->pi(-)l(+)nu)=(1.46 +/- 0.07(stat)+/- 0.08(syst))x10(-4). Based on a recent unquenched lattice QCD calculation of the form factor in the range q(2)> 16 GeV2, we f…
Dimensionality Dependence of the Metal-Insulator Transition in the Anderson Model of Localization
1996
The metal-insulator transition is investigated by means of the transfer-matrix method to describe the critical behavior close to the lower critical dimension 2. We study several bifractal systems with fractal dimensions between 2 and 3. Together with 3D and 4D results, these data give a coherent description of the dimensionality dependence of the critical disorder and the critical exponent in terms of the spectral dimension of the samples. We also show that the upper critical dimension is probably infinite, certainly larger than 4.