Measurements of the strong coupling constant and the QCD colour factors using four-jet observables from hadronic Z decays

Data from annihilation into hadrons, taken with the ALEPH detector at the Z resonance, are analyzed. The four-jet rate is studied as a function of the resolution parameter and compared to next-to-leading order calculations combined with resummation of large logarithms. Angular correlations in four-jet events are measured and compared to next-to-leading order QCD predictions. With these observables two different measurements are performed. In a first analysis the strong coupling constant is measured from the four-jet rate yielding . In a second measurement the strong coupling constant and the QCD colour factors are determined simultaneously from a fit to the four-jet rate and the four-jet angular correlations, giving in good agreement with the expectation from QCD. Received: 14 May 2002 / Published online: 15 January 2003     

A simultaneous measurement of the QCD colour factors and the strong coupling

Using data from annihilation into hadrons, taken with the OPAL detector at LEP at the Z pole between 1991 and 1995, we performed a simultaneous measurement of the colour factors of the underlying gauge group of the strong interaction, and , and the strong coupling, . The measurement was carried out by fitting next-to-leading order perturbative predictions to measured angular correlations of 4-jet events together with multi-jet related variables. Our results, provide a test of perturbative QCD in which the only assumptions are non-abelian gauge symmetry and standard hadronization models. The measurements are in agreement with SU(3) expectations for and and the world average of . Received: 11 January 2001 / Published online: 29 June 2001     

On the model dependence of the determination of the strong coupling constant in second order QCD from e+e−-annihilation into hadrons

Hadronic events obtained with the CELLO detector at PETRA are compared with second order QCD predictions using different models for the fragmentation of quarks and gluons into hadrons. We find that the model dependence in the determination of the strong coupling constant persists when going from first to second order QCD calculations.     

Determination of the strong coupling constant using available experimental data

We determine the strong coupling constant α s up to 4-loop in perturbative QCD.Testing QCD requires the measurement of α s over ranges of energy scales.In this analysis,the value of α s is determined from the unpolarized structure functions data points by minimizing the χ 2 function between the theory result and experimental data.Using perturbative QCD calculations from threshold corrections,we obtain α s (M 2 Z ) = 0.1139±0.0020 at N 3 LO which is in good agreement with the very recently results from the inclusive jet cross section in pp collisions at√ s=1.96 TeV.     

Measurement of dijet azimuthal decorrelations at central rapidities in pp collisions at sqrt s =1.96 TeV

Correlations in the azimuthal angle between the two largest transverse momentum jets have been measured using the D0 detector in p (-)p collisions at a center-of-mass energy sqrt[s]=1.96 TeV. The analysis is based on an inclusive dijet event sample in the central rapidity region corresponding to an integrated luminosity of 150 pb(-1). Azimuthal correlations are stronger at larger transverse momenta. These are well described in perturbative QCD at next-to-leading order in the strong coupling constant, except at large azimuthal differences where contributions with low transverse momentum are significant.     

Determination of the strange quark mass from Cabibbo-suppressed tau decays with resummed perturbation theory in an effective scheme

We present an analysis of the -corrections to Cabibbo-suppressed -lepton decays employing contour improved resummation within an effective scheme which is an essential new feature as compared to previous analyses. The whole perturbative QCD dynamics of the -system is described by the -function of the effective coupling constant and by two -functions for the effective mass parameters of the strange quark in different spin channels. We analyze the stability of our results with regard to high-order terms in the perturbative expansion of the renormalization group functions. A numerical value for the strange quark mass in the scheme is extracted: $m_s(M_\tau)=130\pm 27_{\mathrm{{exp}}}\pm 9_{\mathrm{{th}}}{\mathrm{ MeV}}$. After running to the scale this translates into . Received: 1 October 2000 / Revised version: 22 February 2001 / Published online: 18 May 2001     

Strong coupling, charm-and bottom-quark masses from electron-positron annihilation

The cross section for electron-positron annihilation into hadrons allows for a precise determination of the strong coupling constant and the charm- and bottom-quark masses. Recent theoretical and experimental results are presented with emphasis on the energy region accessible by B-meson factories and below.     

Multi-jet event rates in deep inelastic scattering and determination of the strong coupling constant

Jet event rates in deep inelastic ep scattering at HERA are investigated applying the modified JADE jet algorithm. The data are corrected for detector and hadronization effects and then compared with perturbative QCD predictions using next-to-leading order calculations. The strong coupling constant is determined evaluating the jet event rates. Values of are extracted in four different bins of the negative squared momentum transfer in the range from 40 GeV to 4000 GeV. A combined fit of the renormalization group equation to these several values results in     

Critical Exponents from the Resummed Effective Potential of the ({\frac{g}{4}}\phi^{4}-J\phi)_{1+1} Scalar Field Theory

We establish a unified way for the calculation of the critical exponents, without the use of epsilon expansion, through the improvement of the perturbative effective potential of the 1+1 dimensional $({\frac{g}{4}}\phi^{4}-J\phi)$ scalar field theory. First, we obtain the perturbation series for the effective potential up to g ³. We improved the perturbative effective potential by establishing a parameter-free resummation algorithm, originally due to Kleinert, Thoms and Janke, which has the privilege of using the strong coupling as well as the large coupling behaviors rather than the conventional resummation techniques which use only the large order behavior. Accordingly, although the perturbation series available is up to g ³ order, we found a complete agreement between our resummed effective potential and the well known features from constructive field theory. We prove that the 1-PI correlation functions and the effective potential ought to have the same large order as well as strong coupling behaviors. We computed the critical exponents and our results show a good agreement with the exact Ising model values.     

Variational perturbation theory for Fokker-Planck equation with nonlinear drift

We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a set of first-order linear ordinary differential equations. Resumming the series in the spirit of variational perturbation theory we are able to determine the probability density for all values of the coupling constant. Comparison with numerical results shows exponential convergence with increasing order.     

One-loop Effective Potential in Higher-dimensional Yang-Mills Theory

We study the effective action in Euclidean Yang-Mills theory with a compact simple gauge group in one-loop approximation assuming a covariantly constant gauge field strength as a background. For groups of higher rank and spacetimes of higher dimensions such field configurations have many independent color components taking values in Cartan subalgebra and many “magnetic fields” in each color component. In our previous investigation it was shown that such background is stable in dimensions higher than four provided the amplitudes of “magnetic fields” do not differ much from each other. In the present paper we exactly calculate the relevant zeta-functions in the case of equal amplitudes of “magnetic fields”. For two “magnetic fields” with equal amplitudes the behavior of the effective action is studied in detail. It is shown that in dimensions d = 4,5,6,7 (8), the perturbative vacuum is metastable, i.e., it is stable in perturbation theory but the effective action is not bounded from below, whereas in dimensions d = 9,10,11 (8) the perturbative vacuum is absolutely stable. In dimensions d = 8 (8) the perturbative vacuum is stable for small values of the coupling constant but becomes unstable for large coupling constant leading to the formation of a non-perturbative stable vacuum with nonvanishing “magnetic fields”. The critical value of the coupling constant and the amplitudes of the vacuum “magnetic fields” are evaluated exactly. PACS numbers: 11.10Kk, 11.15Tk, 11.15.-q, 12.38Aw, 12.38Lg     

Inclusive production of charged hadrons and {\rm K}^0_{\rm S} mesons in photon–photon collisions

The production of charged hadrons and mesons in the collisions of quasi-real photons has been measured using the OPAL detector at LEP. The data were taken at centre-of-mass energies of 161 and 172 GeV. The differential cross-sections as a function of the transverse momentum and the pseudorapidity of the charged hadrons and mesons have been compared to the leading order Monte Carlo simulations of PHOJET and PYTHIA and to perturbative next-to-leading order (NLO) QCD calculations. The distributions have been measured in the range GeV of the hadronic invariant mass W. By comparing the transverse momentum distribution of charged hadrons measured in interactions with -proton and meson-proton data we find evidence for hard photon interactions in addition to the purely hadronic photon interactions. Received: 4 June 1998 / Published online: 6 November 1998     

Test of the anti-de Sitter-space/conformal-field-theory correspondence using high-spin operators

In two remarkable recent papers the planar perturbative expansion was proposed for the universal function of the coupling appearing in the dimensions of high-spin operators of the N=4 super Yang-Mills theory. We study numerically the integral equation derived by Beisert, Eden, and Staudacher, which resumes the perturbative series. In a confirmation of the anti-de Sitter-space/conformal-field-theory (AdS/CFT) correspondence, we find a smooth function whose two leading terms at strong coupling match the results obtained for the semiclassical folded string spinning in AdS5. We also make a numerical prediction for the third term in the strong coupling series.     

Measurement of the strong coupling αS from the four-jet rate in e+e- annihilation using JADE data

Data from e⁺e^- annihilation into hadrons collected by the JADE experiment at centre-of-mass energies between 14 GeV and 44 GeV are used to study the four-jet event production rate as a function of the Durham jet algorithm’s resolution parameter y_cut. The four-jet rate is compared to QCD next-to-leading order calculations including resummation of large logarithms in the next-to-leading logarithmic approximation. The strong coupling measured from the four-jet rate is in agreement with the world average.     

Strong QCD corrections to p-wave quarkonium decays

We have calculated one-loop QCD corrections to the annihilation widths of P-wave quarkonium states into hadrons and into two photons. Comparison with accurate experimental data may lead to a clear test of perturbative QCD if α_S turns out to be small enough for reasonable convergence.     

Investigation of power corrections to event shape variables measured in deep-inelastic scattering

Deep-inelastic ep scattering data, taken with the H1 detector at HERA, are used to study the event shape variables thrust, jet broadening, jet mass, C parameter and two kinds of differential two-jet rate. The data cover a large range of the four-momentum transfer Q, which is considered to be the relevant energy scale, between 7 GeV and 100 GeV. The Q dependences of the mean values are compared with second order calculations of perturbative QCD applying power law corrections proportional to to account for hadronization effects. The concept of power corrections is investigated by fitting simultaneously a non-perturbative parameter and the strong coupling constant . Received: 22 December 1999 / Published online: 25 February 2000     

Electromagnetic mass shifts in non-Lagrangian field theory

The electromagnetic interactions of hadrons are considered in a model in which both the hadrons and the photons are spinless. The perturbation theory of this model is developed in a way which takes the strong interactions rigorously into account. An expression for the second-order electromagnetic mass shifts of the hadrons is derived. The customary formula expressing these mass shifts as integrals over the Compton scattering amplitude is shown to be inaccurate. The correct expression differs from the old one by a changed integration contour. In favourable cases the two expressions coincide if the integrations over the four components of the photon momentum are carried out in a certain order. This order of integration must in general not be changed.     

Heavy quark correlations ine + e − annihilations

In heavy quark jets the quark mass acts as a regulator of collinear singularities, making the quark momentum an infra-red safe variable in perturbative QCD. This allows a direct comparison of measured heavy hadron momentum spectra with perturbative calculations. We exploit the factorisation of heavy quark fragmentation to derive QCD predictions for momentum correlations between heavy hadrons produced ine ⁺ e ^? annihilations. We study the practical feasibility and model sensitivity of our approach using Monte Carlo simulations. Higher order perturbative corrections and contributions from non-perturbative effects are found to be at the level of 10%.