Search results for "Logarithm"
showing 10 items of 182 documents
Including resummation in the NLO BK equation
2017
We include a resummation of large transverse momentum logarithms in the next-to-leading order (NLO) Balitsky-Kovchegov equation. The resummed evolution equation is shown to be stable, the evolution speed being significantly reduced by NLO corrections. The contributions from NLO terms that are not enhanced by large logarithms are found to be numerically important close to phenomenologically relevant initial conditions. We numerically determine the value for the constant in the resummed logarithm that includes a maximal part of the full NLO terms in the resummation.
Top quark pair production at complete NLO accuracy with NNLO+NNLL′ corrections in QCD
2019
We describe predictions for top-quark pair differential distributions at hadron colliders, which combine state-of-the-art NNLO QCD calculations and NLO electroweak corrections together with double resummation at NNLL$'$ accuracy of threshold logarithms and small-mass logarithms. This is the first time that such a combination has appeared in the literature. Numerical results are presented for the invariant-mass distribution, the transverse-momentum distribution as well as rapidity distributions.
Factorization of the soft gluon divergence from the dipole picture deep inelastic scattering cross sections at next-to-leading order
2018
We use a factorization scheme analogous to one proposed for single inclusive forward hadron production to factorize the soft gluon divergence present in the deep inelastic scattering cross sections in the dipole picture at next-to-leading order (NLO). We show numerically that in this carefully constructed scheme it is possible to obtain meaningful results for the DIS cross sections at NLO, and so we are able to quantitatively study the recently derived NLO corrections to the DIS cross sections. We find that the NLO corrections can be significant and sensitive to the details of the factorization scheme used for the resummation of the large logarithms into the BK evolution equation. In the ca…
Energy dependence of event shapes and of $\alpha_s$ at LEP 2
1999
Infrared and collinear safe event shape distributions and their mean values are determined using the data taken at five different centre of mass energies above M-Z with the DELPHI detector at LEP. From the event shapes, the strong coupling alpha(s) is extracted in O(alpha(s)(2)), NLLA and a combined scheme using hadronisation corrections evaluated with fragmentation model generators as well as using an analytical power ansatz. Comparing these measurements to those obtained at M-Z, the energy dependence (running) of alpha(s) is accessible. The logarithmic energy slope of the inverse strong coupling is measured to be d alpha(s)(-1)/d log(E-cm) = 1.39 +/- 0.34 (stat) +/- 0.17(syst), in good ag…
Cluster size distributions in particle systems with asymmetric dynamics
2001
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with increasing system size for ordinary TASEP dynamics and as a logarithm divided by a double logarithm for generalized dynamics, where the hopping probability of a particle depends on the size of the cluster it belongs to. The connection with the asymptotic theory of extreme order statistics is discussed in detail. We also consider a related model of interface growth, where the deposited particles are allowed to relax to the local gravitational minimum.
Digital estimators of relaxation spectra
2007
Determination of the distribution of relaxation times (DRT) from a wide variety of the time- and the frequency-domain material functions, such as polarization current and charge, real and imaginary parts of complex dielectric permittivity and complex dielectric modulus, the appropriate mechanical and magnetic counterparts is generalized as a filtering problem on a logarithmic time or frequency scale. Algorithms of the appropriate digital DRT estimators are derived. A novel regularization strategy is proposed based on choosing sampling rate for the input data, which ensures acceptably low random error of the recovered spectra. Optimum frequency ranges and sampling rates are found for determi…
Effects of surface nonlinear interactions on the local critical behavior
1987
Effects of surface nonlinear interactions on the local critical behaviors are studied for an-component field in the semi-infinite space near the SB (surface-bulk) point by using renormalization group methods. The model Hamiltonian consists of a free (Gaussian) bulk part and a surface term containing aφ4 interaction. The interplay between the free bulk term and the nonlinear surface term gives rise to interesting behaviors of the local surface properties. Whereas the local susceptibility and correlation exponents retain their mean-field values, the surface crossover exponent ϕ is non-mean-field below three dimensions. To second order in e(e=3−d) we find:η‖ and\(\phi = \frac{1}{2} - \frac{{n …
Solving the Balitsky-Kovchegov equation at next to leading order accuracy
2016
We solve the Balitsky-Kovchegov small-x evolution equation in coordinate space. We find that the solution to the equation is unstable when using an initial condition relevant for phenomenological applications at leading order. The problematic behavior is shown to be due to a large double logarithmic contribution. The same problem is found when the evolution of the “conformal dipole” is solved, even though the double logarithmic term is then absent from the evolution equation.
Fluctuations, response and aging dynamics in a simple glass-forming liquid out of equilibrium
1999
By means of molecular dynamics computer simulations we investigate the out of equilibrium relaxation dynamics of a simple glass former, a binary Lennard-Jones system, after a quench to low temperatures. We study both one time quantities and two-times correlation functions. Two-times correlation functions show a strong time and waiting time $t_w$ dependence. For large $t_w$ and times corresponding to the early $\beta$-relaxation regime the correlators approach the Edwards-Anderson value by means of a power-law in time. at long times $\tau$ the correlation functions can be expressed as $C_{\rm AG}(h(t_w+\tau)/h(t_w))$ and compute the function $h(t)$. This function is found to show a $t$-depen…
Cosmological data analysis of f(R) gravity models
2009
A class of well-behaved modified gravity models with long enough matter domination epoch and a late-time accelerated expansion is confronted with SNIa, CMB, SDSS, BAO and H(z) galaxy ages data, as well as current measurements of the linear growth of structure. We show that the combination of geometrical probes and growth data exploited here allows to rule out f(R) gravity models, in particular, the logarithmic of curvature model. We also apply solar system tests to the models in agreement with the cosmological data. We find that the exponential of the inverse of the curvature model satisfies all the observational tests considered and we derive the allowed range of parameters. Current data s…