Search results for "Logarithm"
showing 10 items of 182 documents
Analytic result for a two-loop five-particle amplitude
2019
We compute the symbol of the full-color two-loop five-particle amplitude in $\mathcal{N}=4$ super Yang-Mills, including all non-planar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the non-planar terms, analyze its subleading power corrections, and present analytically the leading logarithmic terms.
Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
2018
Integration-by-parts identities between loop integrals arise from the vanishing integration of total derivatives in dimensional regularization. Generic choices of total derivatives in the Baikov or parametric representations lead to identities which involve dimension shifts. These dimension shifts can be avoided by imposing a certain constraint on the total derivatives. The solutions of this constraint turn out to be a specific type of syzygies which correspond to logarithmic vector fields along the Gram determinant formed of the independent external and loop momenta. We present an explicit generating set of solutions in Baikov representation, valid for any number of loops and external mome…
Loop quantum gravity and Planck-size black hole entropy
2007
The Loop Quantum Gravity (LQG) program is briefly reviewed and one of its main applications, namely the counting of black hole entropy within the framework is considered. In particular, recent results for Planck size black holes are reviewed. These results are consistent with an asymptotic linear relation (that fixes uniquely a free parameter of the theory) and a logarithmic correction with a coefficient equal to -1/2. The account is tailored as an introduction to the subject for non-experts.
Determination of the origin and magnitude of logarithmic finite-size effects on interfacial tension: Role of interfacial fluctuations and domain brea…
2014
The ensemble-switch method for computing wall excess free energies of condensed matter is extended to estimate the interface free energies between coexisting phases very accurately. By this method, system geometries with linear dimensions $L$ parallel and $L_z$ perpendicular to the interface with various boundary conditions in the canonical or grandcanonical ensemble can be studied. Using two- and three-dimensional Ising models, the nature of the occurring logarithmic finite size corrections is studied. It is found crucial to include interfacial fluctuations due to "domain breathing".
Balitsky-Kovchegov equation at next-to-leading order accuracy with a resummation of large logarithms
2016
We include resummation of large transverse logarithms into the next-to-leading order Balitsky-Kovchegov equation. The resummed NLO evolution equation is shown to be stable, the evolution speed being significantly reduced by higher order corrections. The contributions from $\alpha_s^2$ terms that are not enhanced by large logarithms are found to be numerically important close to phenomenologically relevant initial conditions.
Projection-invariant pattern recognition with a phase-only logarithmic-harmonic-derived filter.
2010
A phase-only filter based on logarithmic harmonics for projection-invariant pattern recognition is presented. This logarithmic-harmonic-derived filter is directly calculated in the Fourier plane. With respect to normal logarithmic-harmonic filters it provides a smaller variation of the correlation intensity with the projection factor of the target. Computer and optical experiments are presented.
Next-to-leading order Balitsky-Kovchegov equation with resummation
2016
We solve the Balitsky-Kovchegov evolution equation at next-to-leading order accuracy including a resummation of large single and double transverse momentum logarithms to all orders. We numerically determine an optimal value for the constant under the large transverse momentum logarithm that enables including a maximal amount of the full NLO result in the resummation. When this value is used the contribution from the $\alpha_s^2$ terms without large logarithms is found to be small at large saturation scales and at small dipoles. Close to initial conditions relevant for phenomenological applications these fixed order corrections are shown to be numerically important.
Molecular-dynamics studies of annihilation reactions
2004
The validity of the reaction-diffusion formulation of annihilation kinetics, with randomly distributed initial conditions, is investigated by molecular-dynamics simulations of dense hard-disk fluids. For the reaction A + B → C + C quantitative agreement is found. Yet, this proves not to be the case for the reaction A + A → C + C, where major discrepancies are observed. For this latter reaction, more sophisticated theories predict a logarithmic decay law of the form ln (t)/t. The microscopic simulations essentially confirm this prediction.
Factorization and resummation for jet broadening
2011
Jet broadening is an event-shape variable probing the transverse momenta of particles inside jets. It has been measured precisely in e+e- annihilations and is used to extract the strong coupling constant. The factorization of the associated cross section at small values of the broadening is afflicted by a collinear anomaly. Based on an analysis of this anomaly, we present the first all-order expressions for jet-broadening distributions, which are free of large perturbative logarithms in the two-jet limit. Our formulae reproduce known results at next-to-leading logarithmic order but also extend to higher orders.
Physical mechanism of the linear beam-size effect at colliders
1996
We present qualitative but precise description of the linear beam-size effect predicted for the processes in which unstable but long--living particles collide with each other. We derive physically pronounced equation for the events rate which proves that the linear beam-size effect corresponds to the scattering of one beam of particles on the decay products of the other. We compare this linear beam-size effect with the known logarithmic beam-size effect measured in the experiments on a single bremsstrahlung at VEPP-4 and HERA.