Event Shape Variables Research Articles

A combination by the LEP QCD Working Group of αs values derived from event shape variables at LEP

The LEP QCD Working Group has produced a combination of α s values derived from event-shape distributions. The distributions are measured at scales below the mass of the Z boson up to 206 GeV. Values of α s are all extracted using the consistent application of O ( α s 2 )+ NLLA predictions with the modified Log(R) matching scheme. A combined α s is obtained for each experiment and observable using at least two experiments in each case for energies above at ad above the mass of the Z boson. A consistent treatment and controlled breakdown is made of the sources of uncertainty on the input values. The combined best value for α s (M Z ) = 0.11 ± 0.003 ± 0.003. The dominant uncertainty is theoretical, due to the effects of missing higher order contributions.

Status of resummed predictions for QCD final state observables

We provide a brief review of the current status of resummed predictions for QCD final state observables such as event shapes and jet rates in a variety of different hard processes. Particular emphasis is given to more recent developments such as the study of non global observables, development of generalized resummation formulae and resummations for new types of event shape variables.

Studies of QCD at LEPII

A combination of measurements of α s in e+e– annihilation at LEP is presented. Distributions of various event-shape variables measured by ALEPH, DELPHI, L3 and OPAL at centre-of-mass energies from 41 GeV to 206 GeV are analysed in a common theoretical framework using $\cal{O}$ (α s 2)+NLLA predictions. The dominant theoretical uncertainties associated to missing higher orders are studied in detail.

Event shape and determination of α s at LEP

The 4 LEP experiments have reanalysed their data on event shape variables for e+e–→ hadrons to determine the strong coupling constant α s . A consistent treatment of these measurements and a better understanding of the theoretical uncertainties by the LEP QCD Working Group yields the result α s (M Z ) = 0.1202 ± 0.0003 (stat) ± 0.0009 (exp) ± 0.0009 (hadr) ± 0.0047 (theo). PACS: 12.38.Qk Experimental tests of QCD – 13.66.Bc Hadron production in e+e– interactions

Studies of QCD at ${\rm e}^ + {\rm e}^-$ centre-of-mass energies between 91 and 209 GeV

The hadronic final states observed with the ALEPH detector at LEP in e+e- annihilation are analysed using 730 pb-1 of data collected between 91 and 209 GeV in the framework of QCD. In particular event-shape variables and inclusive charged particle spectra are measured. The energy evolution of quantities derived from these measurements is compared to analytic QCD predictions. The mean charged particle multiplicity, the charged particle momentum spectrum and its peak position are compared to predictions of the modified-leading-logarithmic approximation. The strong coupling constant alpha_s is determined from a fit of the QCD prediction to distributions of six event-shape variables at eight centre-of-mass energies. A study of non-perturbative power law corrections is presented

Theoretical uncertainties on αsfrom event-shape variables in e+e−annihilations

The precision of measurements of the strong coupling constant using event-shape variables in e+e- annihilations is limited by theoretical systematic uncertainties. The uncertainties are related to missing higher orders in the perturbative predictions for the event-shape distributions. A new method is presented for the assessment of theoretical uncertainties in alpha_s. This method evaluates the systematic uncertainty of the parameter alpha_s from the uncertainty of the prediction for the distributions from which it is extracted. The perturbative uncertainties are calculated on a purely theoretical basis, without accessing measured distributions. The method is therefore especially suited for an unbiased combination of results from different observables or experiments. It is universal and can be applied to other processes like jet production in deep-inelastic ep scattering or in hadron collisions.

Next-to-leading order calculation of three-jet observables in hadron-hadron collisions

The production of three jets in hadron-hadron collisions is the first complex process which allows us to define a branch of variables in order to make more precise measurements of the strong coupling and the parton distribution function of the proton. This process is also suitable for studying the geometrical properties of the hadronic final state at hadron colliders. This requires a next-to-leading order prediction of the three-jet observables. In this paper we describe the theoretical formalism of such a calculation with sufficient detail. We use the dipole method to construct a Monte Carlo program for calculating three-jet observables at next-to-leading order accuracy. We present a theoretical prediction for inclusive and exclusive cross sections and for some relevant event shape variables such as the transverse thrust, transverse jet broadening, and ${E}_{t3}$ variable.

Determination of αs at LEP by L3 experiment

The results on strong coupling constant, α s in e +e − collision at LEP are reviewed, based on hadronic events collected at centre-of-mass energies between 30 GeV and 208 GeV by the L3 experiment. In particularly the recent results at √s ≥ 192 GeV are discussed. The distributions of several event shape variables are compared to resummed O( α s 2) QCD calculations. These measurements, combined with previous L3 measurements at lower energies, demonstrate the running of α s as expected in QCD and yield α s( m Z ) = 0.1227 ± 0.0012 ± 0.0058, where the first uncertainty is experimental and the second is theoretical.

Measurements of αs at centre-of-mass energies between 91 and 209 GeV

Consistent measurements of event-shape variables and as using the complete set of data taken with the ALEPH detector at LEP are presented. The strong coupling constant is determined from a fit of O( α s 2) + NLLA QCD calculations to distributions of six event-shape variables at eight centre-of-mass energies. A new method is proposed to estimate theoretical systematic uncertainties. The results are compared to the expected evolution of α s .

Measurements of αs from event shapes and the four-jet rate

New results from measurements of the strong coupling constant α s ( M Z ) at LEP are presented. In particular, a new LEP combination of results based on event-shape variables has become available, where a new method for the estimation of the theoretical uncertainty has been implemented. Furthermore, two other analyses are quoted, based on power corrections and the four-jet rate.

Using coulomb gauge for next-to-leading order numerical calculations

Calculations of observables in quantum chromodynamics can be performed using a method in which all of the integrations, including integrations over virtual loop momenta, are performed numerically. We use this method to perform next-to-leading order calculations for event shape variables in electron-positron annihilation in Coulomb gauge. The use of a physical gauge provides the potential to go beyond a purely order α s 2 calculation by including, for instance, renormation or parton showering effects.

Measurement of event shapes in deep inelastic scattering at HERA

Inclusive event-shape variables have been measured in the current region of the Breit frame for neutral current deep inelastic ep scattering using an integrated luminosity of 45.0 pb^-1 collected with the ZEUS detector at HERA. The variables studied included thrust, jet broadening and invariant jet mass. The kinematic range covered was 10 < Q^2 < 20,480 GeV^2 and 6.10^-4 < x < 0.6, where Q^2 is the virtuality of the exchanged boson and x is the Bjorken variable. The Q dependence of the shape variables has been used in conjunction with NLO perturbative calculations and the Dokshitzer-Webber non-perturbative corrections (`power corrections') to investigate the validity of this approach.

Next-to-leading order numerical calculations in the Coulomb gauge

Calculations of observables in quantum chromodynamics can be performed using a method in which all of the integrations, including integrations over virtual loop momenta, are performed numerically. We use the flexibility inherent in this method in order to perform next-to-leading order calculations for event shape variables in electron-positron annihilation in Coulomb gauge. The use of Coulomb gauge provides the potential to go beyond a purely order alpha_s^2 calculation by including, for instance, renormalon or parton showering effects. We expect that the approximations needed to include such effects at all orders in alpha_s will be simplest in a gauge in which unphysically polarized gluons do not propagate over long distances.

Resummed event-shape variables in DIS

We complete our study of resummed event-shape distributions in DIS by presenting results for the class of observables that includes the current jet mass, the C-parameter and the thrust with respect to the current-hemisphere thrust axis. We then compare our results to data for all observables for which data exist, fitting for alpha_s and testing the universality of non-perturbative 1/Q effects. A number of technical issues arise, including the extension of the concept of non-globalness to the case of discontinuous globalness; singularities and non-convergence of distributions other than in the Born limit; methods to speed up fixed-order Monte Carlo programs by up to an order of magnitude, relevant when dealing with many x and Q points; and the estimation of uncertainties on the predictions.

Determination of αs from hadronic event shapes in e +e − annihilation at [formula omitted] GeV

Results are presented from a study of the structure of high energy hadronic events recorded by the L3 detector at s ⩾192 GeV. The distributions of several event shape variables are compared to resummed O(α s 2) QCD calculations. We determine the strong coupling constant at three average centre-of-mass energies: 194.4, 200.2 and 206.2 GeV. These measurements, combined with previous L3 measurements at lower energies, demonstrate the running of α s as expected in QCD and yield α s( m Z)=0.1227±0.0012±0.0058, where the first uncertainty is experimental and the second is theoretical.

Dressed gluon exponentiation

Perturbative and non-perturbative aspects of differential cross-sections close to a kinematic threshold are studied applying “dressed gluon exponentiation” (DGE). The factorization property of soft and collinear gluon radiation is demonstrated using the light-cone axial gauge: it is shown that the singular part of the squared matrix element for the emission of an off-shell gluon off a nearly on-shell quark is universal. We derive a generalized splitting function that describes the emission probability and show how Sudakov logs emerge from the phase-space boundary where the gluon transverse momentum vanishes. Both soft and collinear logs associated with a single dressed gluon are computed through a single integral over the running-coupling to any logarithmic accuracy. The result then serves as the kernel for exponentiation. The divergence of the perturbative series in the exponent indicates specific non-perturbative corrections. We identify two classes of observables according to whether the radiation is from an initial-state quark, as in the Drell–Yan process, or a final-state quark, forming a jet with a constrained invariant mass, as in fragmentation functions, event-shape variables and deep inelastic structure functions.

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

Using data from e + e − annihilation into hadrons, taken with the OPAL detector at LEP at the Z 0 pole between 1991 and 1995, we performed a simultaneous measurement of the strong coupling α s and the colour factors of the underlying gauge group of the strong interaction, C F and C A . The measurement was carried out by fitting next-to-leading order perturbative predictions to measured angular correlations of 4-jet events together with either a multi-jet rate or an event-shape variable. Our combined results provide a test of perturbative QCD with the assumptions only of non-abelian gauge symmetry and standard hadronization models. Our results are in agreement with SU(3) expectations for C F and C A and the world average of α s ( M Z 0 ).

Topology of the hadronic final state in diffractive DIS

An extensive study of the hadronic final state in diffractive deep inelastic scattering (DIS) at HERA is presented. The hadronic final state was investigated by the ZEUS and H1 collaborations in terms of global event shape variables, inclusive particle distributions and dijet and three-jet production, and compared to various Monte Carlo models. Most aspects of the final state topology are described by a model assuming a resolved Pomeron dominated by gluons.

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

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

QCD studies in e +e − annihilation from 30 GeV to 189 GeV

We present results obtained from a study of the structure of hadronic events recorded by the L3 detector at various centre-of-mass energies. The distributions of event shape variables and the energy dependence of their mean values are measured from 30 GeV to 189 GeV and compared with various QCD models. The energy dependence of the moments of event shape variables is used to test a power law ansatz for the non-perturbative component. We obtain a universal value of the non-perturbative parameter α 0 = 0.537 ± 0.073. From a comparison with resummed O ( α s 2) QCD calculations, we determine the strong coupling constant at each of the selected energies. The measurements demonstrate the running of α s as expected in QCD with a value of α s( m Z) = 0.1215 ± 0.0012 (exp) ± 0.0061 (th).