Three-jet Rate Research Articles

High precision determination of \u03b1s from a global fit of jet rates

We present state-of-the-art extractions of the strong coupling based on N3LO+NNLL accurate predictions for the two-jet rate in the Durham clustering algorithm at e+e− collisions, as well as a simultaneous fit of the two- and three-jet rates taking into account correlations between the two observables. The fits are performed on a large range of data sets collected at the LEP and PETRA colliders, with energies spanning from 35 GeV to 207 GeV. Owing to the high accuracy of the predictions used, the perturbative uncertainty is considerably smaller than that due to hadronization. Our best determination at the Z mass is αs (MZ) = 0.11881 ± 0.00063(exp.) ± 0.00101(hadr.) ± 0.00045(ren.) ± 0.00034(res.), which is in agreement with the latest world average and has a comparable total uncertainty.

Higher Order Corrections in the CoLoRFulNNLO Framework

We discuss the CoLoRFulNNLO method for computing higher order radiative corrections to jet cross sections in perturbative QCD. We apply our method to the calculation of event shapes and jet rates in three-jet production in electron-positron annihilation. We validate our code by comparing our predictions to previous results in the literature and present the jet cone energy fraction distribution at NNLO accuracy. We also present preliminary NNLO results for the three-jet rate using the Durham jet clustering algorithm matched to resummed predictions at NLL accuracy, and a comparison to LEP data.

Measurement of strong coupling αs in e + e − annihilation using jet rate and event shape

The hadronic events from the AMY data at 60 GeV center-of-mass energy are studied. We measure the coupling constant α s first by using the three-jet rate method. From the event shape, we also extract the strong coupling constant, based on next-to-next leading order. Our results are consistent with the running of α s expected from quantum chromodynamics predictions at next-to-next leading order corrections.

Measurement of the strong coupling α S from the three-jet rate in e+e−-annihilation using JADE data

We present a measurement of the strong coupling α S using the three-jet rate measured with the Durham algorithm in \(\mathrm{e^{+}e^{-}}\)-annihilation using data of the JADE experiment at centre-of-mass energies between 14 and 44 GeV. Recent theoretical improvements provide predictions of the three-jet rate in \(\mathrm{e^{+}e^{-}}\)-annihilation at next-to-next-to-leading order. In this paper a measurement of the three-jet rate is used to determine the strong coupling α S from a comparison to next-to-next-to-leading order predictions matched with next-to-leading logarithmic approximations and yields a value for the strong coupling consistent with the world average.

Measurement of the strong coupling [formula omitted] in [formula omitted]-annihilation using the three-jet rate

We present a measurement of the strong coupling αS using data collected with the JADE detector at centre-of-mass energies between 14 and 44 GeV. The three-jet rate as a function of the transition parameter ycut is determined using the Durham jet algorithm and the distribution is compared to QCD predictions. Recent theoretical calculations predict the three-jet rate at next-to-next-to-leading order. For the first time a measurement of αS is presented using QCD predictions at next-to-next-to-leading order matched to predictions at next-to-leading logarithmic approximation, with subleading terms being included as well. We obtain αS(MZ0)=0.1199±0.0010(stat.)±0.0021(exp.)±0.0054(had.)±0.0007(theo.), being consistent with the world average value of αS.

The effect of top quark mass on three jet rate and measurement of strong coupling constant

We present the calculation of top quark mass corrections to three-jet rates in electron-positron annihilation at center of mass energies of 60 and 206 GeV. Furthermore, we also calculate the effects of quark-antiquark interactions on QCD model for three-jet rates. We extract the strong coupling constant, αs, through our results from the massive three-jet rate and the massless one. We observe that the effect of t quark on three jet rate does not contribute significantly to the calculations of strong coupling constant and we can ignore this effect in higher energies.

Erratum to: Jet algorithms in electron–positron annihilation: perturbative higher order predictions

This article gives results on several jet algorithms in electron-positron annihilation: Considered are the exclusive sequential recombination algorithms Durham, Geneva, Jade-E0 and Cambridge, which are typically used in electron-positron annihilation. In addition also inclusive jet algorithms are studied. Results are provided for the inclusive sequential recombination algorithms Durham, Aachen and anti-kt, as well as the infrared-safe cone algorithm SISCone. The results are obtained in perturbative QCD and are NNNLO for the two-jet rates, NNLO for the three-jet rates, NLO for the four-jet rates and LO for the five-jet rates.

Jet algorithms in electron–positron annihilation: perturbative higher order predictions

This article gives results on several jet algorithms in electron–positron annihilation: Considered are the exclusive sequential recombination algorithms Durham, Geneva, Jade-E0 and Cambridge, which are typically used in electron–positron annihilation. In addition also inclusive jet algorithms are studied. Results are provided for the inclusive sequential recombination algorithms Durham, Aachen and anti-k t , as well as the infrared-safe cone algorithm SISCone. The results are obtained in perturbative QCD and are N3LO for the two-jet rates, NNLO for the three-jet rates, NLO for the four-jet rates and LO for the five-jet rates.

Electroweak corrections to hadronic event shapes and jet production in [formula omitted] annihilation

We present a complete calculation of the electroweak O ( α 3 α s ) corrections to three-jet production and related event-shape observables at electron–positron colliders. The Z-boson resonance is described within the complex-mass scheme, rendering the calculation valid both in the resonance and off-shell regions. Higher-order initial-state radiation is included in the leading-logarithmic approximation. We properly account for the corrections to the total hadronic cross section and for the experimental photon isolation criteria. To this end we implement contributions of the quark-to-photon fragmentation function both in the slicing and subtraction formalism. The effects of the electroweak corrections on various event-shape distributions and on the three-jet rate are studied. They are typically at the few-percent level, and remnants of the radiative return are found even after inclusion of appropriate cuts.

Precise Determination of the Strong Coupling Constant at NNLO in QCD from the Three-Jet Rate in Electron–Positron Annihilation at LEP

We present the first determination of the strong coupling constant from the three-jet rate in e{+}e{-} annihilation at LEP, based on a next-to-next-to-leading-order (NNLO) perturbative QCD prediction. More precisely, we extract alpha{s}(M{Z}) by fitting perturbative QCD predictions at O(alpha{s}{3}) to data from the ALEPH experiment at LEP. Over a large range of the jet-resolution parameter y{cut}, this observable is characterized by small nonperturbative corrections and an excellent stability under renormalization scale variation. We find alpha{s}(M{Z})=0.1175+/-0.0020(expt)+/-0.0015(theor), which is more accurate than the values of alpha{s}(M{Z}) from e{+}e{-} event-shape data currently used in the world average.

Electroweak corrections to three-jet production in [formula omitted] annihilation

We compute the electroweak O(α3αs) corrections to three-jet production and related event-shape observables at electron–positron colliders. We properly account for the experimental photon isolation criteria and for the corrections to the total hadronic cross section. Corrections to the three-jet rate and to normalised event-shape distributions turn out to be at the few-percent level.

Determination of the b quark mass at the MZ scale with the DELPHI detector at LEP

An experimental study of the normalized three-jet rate of b quark events with respect to light quarks events (light = l equivalent to u, d, s) has been performed using the CAMBRIDGE and DURHAM jet algorithms. The data used were collected by the DELPHI experiment at LEP on the Z peak from 1994 to 2000. The results are found to agree with theoretical predictions treating mass corrections at next-to-leading order. Measurements of the b quark mass have also been performed for both the b pole mass: M-b and the b running mass: m(b)(M-Z). Data are found to be better described when using the running mass. The measurement yields: m(b)(M-Z) = 2.85 +/- 0.18(stat) +/- 0.13(exp) +/- 0.19(had) +/- 0.12(theo) GeV/c(2). for the CAMBRIDGE algorithm. This result is the most precise measurement of the b mass derived from a high energy process. When compared to other b mass determinations by experiments at lower energy scales, this value agrees with the prediction of quantum chromodynamics for the energy evolution of the running mass. The mass measurement is equivalent to a test of the flavour independence of the strong coupling constant with an accuracy of 7 parts per thousand.

Improvement measurements of the b quark mass at LEP

An improved determination of the b-quark mass at the M z scale, m b(M z) , has been obtained by the Delphi and Opal experiments at LEP. The normalized three-jet rate of b-quarks with respect to light quarks, R 3 bl , has been measured with different jet clustering algorithms and compared with the massive NLO calculations to extract m b(M z) . For Delphi, the increase in statistics and a better understanding of the flavour tagging, hadronization process and the gluon splitting rates leads to a precision of 380 MeV. The effect of the b-quark mass on the four-jet rate has also been studied by Delphi.

A measurement of the b-quark mass from hadronic Z decays

Hadronic Z decay data taken with the ALEPH detector at LEP1 are used to measure the three-jet rate as well as moments of various event-shape variables. The ratios of the observables obtained from b-tagged events and from an inclusive sample are determined. The mass of the b quark is extracted from a fit to the measured ratios using a next-to-leading order prediction including mass effects. Taking the first moment of the $y_3$ distribution, which is the observable with the smallest hadronization corrections and systematic uncertainties, the result is \[m_b(M_{\mathrm Z}) = \left[3.27 \pm 0.22 (\mathrm{stat}) \pm 0.22 (\mathrm{exp}) \pm 0.38 (\mathrm{had}) \pm 0.16 (\mathrm{theo})\right] \;\gevcc\quad. \] The measured ratio is alternatively employed to test the flavour independence of the strong coupling constant for b and light quarks.

Double unresolved approximations to multiparton scattering amplitudes

We present approximations to tree-level multiparton scattering amplitudes which are appropriate when two partons are unresolved. These approximations are required for the analytic isolation of infrared singularities of n + 2 parton scattering processes contributing to the next-to-next-to-leading order corrections to n jet cross sections. In each case the colour ordered matrix elements factorise and yield a function containing the singular factors multiplying the n-parton amplitudes. When the unresolved particles are colour unconnected, the approximations are simple products of the familiar eikonal and Altarelli-Parisi splitting functions used to describe single unresolved emission. However, when the unresolved particles are colour connected the factorisation is more complicated and we introduce new and general functions to describe the triple collinear and soft/collinear limits in addition to the known double soft gluon limits of Berends and Giele. As expected the triple collinear splitting functions obey an N = 1 SUSY identify. To illustrate the use of these double unresolved approximations, we have examined the singular limits of the tree-level matrix elements for e + e − → 5 partons when only three partons are resolved. When integrated over the unresolved regions of phase space, these expressions will be of use in evaluating the O(α s 3) corrections to the three-jet rate in electron-positron annihilation.

Next-to-leading order QCD corrections to three-jet rates with massive quarks

The reaction e + e − annihilation into three jets was recently computed for massive quarks at next-to-leading order in perturbative QCD. We discuss some results of our calculation for b jets produced at the Z jets produced at the Z resonance.

Rapidity gaps and other final state properties in the colour dipole model for deep inelastic scattering

In the light of recent results from the experiments at HERA, the treatment of DIS in the Colour Dipole Model is reviewed and improved. A procedure where the first emission in the dipole cascade is matched onto the exact\(\mathcal{O}(\alpha _{\text{S}} )\) matrix element is introduced, giving a more correct dependence of the three-jet rate onQ 2. Also a new treatment of the proton remnant is introduced assuming a pomeron-like part of the proton structure function, resulting in an, at least qualitatively, good description of the rapidity gap events found by the HERA experiments.

The three-jet rate in e+e− annihilation

Progress has been made on the calculation of R 3, the three-jet rate in e + e − annihilation, in the k ⊥ (Durham) scheme. Using the coherent branching formalism [A.H. Mueller, Phys. Lett. B 104 (1981) 161; B.I. Ermolaev and V.S. Fadin, JETP Lett. 33 (1981) 285; Yu.L. Dokshitzer, V.S. Fadin and V.A. Khoze, Z. Phys. C 15 (1982) 325; C 18 (1983) 37; A. Bassetto, M. Ciafaloni and G. Marchesini, Phys. Rep. 100 (1983) 202; Yu.L. Dokshitzer and S. Troyan, Leningrad Report LNPI-922 (1984); Yu.L. Dokshitzer, V.A. Khoze and S. Troyan, in: Perturbative QCD, ed. A.H. Mueller (World Scientific, Singapore, 1989)], an explicit expression for R 3 is calculated. In this, leading and next-to-leading large logarithms (LL and NLL) are resummed to all orders in QCD perturbation theory. In addition to exponentials an error function is involved.

New jet cluster algorithms: next-to-leading order QCD and hadronization corrections

New algorithms have been proposed as alternatives to the standard JADE-type algorithms for quantifying jet production in e+e− annihilation. We study in detail the “Durham” algorithm, based on clustering according to relative transverse momentum, and introduce a new “Geneva” variation which is expected to exhibit similar theoretical properties of exponentiation at small jet resolution. In particular, we calculate the next-to-leading order perturbative corrections to the three-jet rate for the new algorithms, and we study non-perturbative corrections using the JETSET parton-shower Monte Carlo. In each case we compare to the results obtained with the usual JADE-type algorithms. We conclude that the new algorithms exhibit somewhat smaller perturbative corrections compared to the standard algorithms, and that the non-perturbative corrections are of comparable size. Thus the new algorithms appear to be at least as well suited to precision measurements of the strong coupling.