This work revisits recent results on maximal multiplicity induced-dominancy for spectral values in reduced-order time-delay Systems and extends it to the general class of second-order retarded differential equa- tions. A parametric multiplicity-induced-dominancy property is characterized, allowing to a delayed stabilizing design with reduced complexity. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates’ delays and gains result from the manifold defining the maximal multiplicity of a real spectral value, then, the dominancy is shown using the argument principle. Sensitivity of the control design with respect to the pa- rameters uncertainties/variation is discussed. Various reduced order examples illustrate the applicative perspectives of the approach.
Abstract:We discuss correlations between two particles in jets at high energy colliders and exactly solve the MLLA evolution equations in the small x limit. We thus extend the Fong-Webber analysis to the region away from the hump of the single inclusive energy spectrum. We give our results for LEP, Tevatron and LHC energies, and compare with existing experimental data.
Keywords: Perturbative Quantum Chromodynamics, Particle Correlations in jets, High Energy Colliders
The hadronic k ⊥ -spectrum inside one jet is determined including corrections of relative magnitude O ( √ αs) with respect to the Modified Leading Logarithmic Approximation (MLLA), at and beyond the limiting spectrum (assuming an infrared cut-off Q0 = Λ QCD and Q0 = Λ QCD ). The agreement between our results and preliminary measurements by the CDF collaboration is impressive, much better than at MLLA, pointing out very small overall non-perturbative contributions.PACS numbers: 12.38. Cy, 13.87.Fh Jet production -a collimated bunch of hadrons -in e + e − , e − p and hadronic collisions is an ideal playground for parton evolution in perturbative QCD (pQCD). One of the major successes of pQCD is the hump-backed shape of inclusive spectra, predicted in [1] within MLLA, and later discovered experimentally (see e.g. [2]). Refining the comparison of pQCD calculations with data taken at LEP, Tevatron and LHC will ultimately allow for a crucial test of the Local Parton Hadron Duality (LPHD) hypothesis [3] and for a better understanding of color neutralization processes. In this Letter, a class of next-tonext-to-leading logarithmic (NMLLA) corrections to the single inclusive k ⊥ -distribution of hadrons inside one jet is determined. Unlike other NMLLA corrections, these terms better account for recoil effects and were shown to drastically affect multiplicities and particle correlations in jets [4]. We start by writing the MLLA evolution equations for the fragmentation function D h B x z, zEΘ 0 , Q 0 of a parton B (energy zE and transverse momentum k ⊥ = zEΘ 0 ) into a gluon (identified as a hadron h with energy xE according to LPHD) inside a jet of energy E. As a consequence of angular ordering in parton cascading, partonic distributions inside a quark and gluon jet, Q, G(z) = x z D h Q,G x z, zEΘ 0 , Q 0 , obey the system of two coupled equations [5] (the subscript y denotes ∂/∂y)
The moments of the single inclusive momentum distribution of hadrons in QCD jets, are studied in the next-to-modified-leading-log approximation (NMLLA) including next-to-leading-order (NLO) corrections to the α s strong coupling. The evolution equations are solved using a distorted Gaussian parametrisation, which successfully reproduces the spectrum of charged hadrons of jets measured in e + e − collisions. The energy dependencies of the maximum peak, multiplicity, width, kurtosis and skewness of the jet hadron distribution are computed analytically. Comparisons of all the existing jet data measured in e + e − collisions in the range √ s ≈ 2-200 GeV to the NMLLA+NLO * predictions allow one to extract a value of the QCD parameter Λ QCD , and associated two-loop coupling constant at the Z resonance α s (m 2 Z ) = 0.1195 ± 0.0022, in excellent numerical agreement with the current world average obtained using other methods.
The hadronic k ? -spectrum inside a high-energy jet is determined including corrections of relative magnitude Oð ffiffiffiffiffi ffi s p Þ with respect to the Modified Leading Logarithmic Approximation (MLLA) in the limiting spectrum approximation (assuming an infrared cutoff Q 0 ¼ Ã QCD ) and beyond (Q 0 Þ Ã QCD ). The results in the limiting spectrum approximation are found to be, after normalization, in impressive agreement with preliminary measurements by the CDF Collaboration, unlike what occurs at MLLA, pointing out small overall nonperturbative contributions. Within the same framework, 2-particle correlations inside a jet are also predicted at next-to-MLLA and compared to previous MLLA calculations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.