Jet Resolution Parameter Research Articles

Jet production cross-section and jet properties in proton-proton collisions at [formula omitted] with the ATLAS detector

Jet cross sections have been measured in proton-proton collisions at a centre-of-mass energy of 7 TeV using the ATLAS detector. The measurement uses an integrated luminosity of 17 nb −1 recorded at the Large Hadron Collider. The anti- k t algorithm is used to identify jets with a jet resolution parameter R = 0.6 . The dominant uncertainty comes from the jet energy scale, which is determined to within 7% for central jets above 60 GeV transverse momentum. Inclusive single-jet differential cross sections are presented as functions of jet transverse momentum and rapidity. The results are compared to expectations based on next-to-leading-order QCD, which agree with the data, providing a validation of the theory in a new kinematic regime.

Measurement of inclusive jet and dijet cross sections in proton-proton collisions at 7 TeV centre-of-mass energy with the ATLAS detector

Jet cross sections have been measured for the first time in proton-proton collisions at a centre-of-mass energy of 7 TeV using the ATLAS detector. The measurement uses an integrated luminosity of 17 nb-1 recorded at the Large Hadron Collider. The anti-kt algorithm is used to identify jets, with two jet resolution parameters, R = 0.4 and 0.6. The dominant uncertainty comes from the jet energy scale, which is determined to within 7% for central jets above 60 GeV transverse momentum. Inclusive single-jet differential cross sections are presented as functions of jet transverse momentum and rapidity. Dijet cross sections are presented as functions of dijet mass and the angular variable $\chi$. The results are compared to expectations based on next-to-leading-order QCD, which agree with the data, providing a validation of the theory in a new kinematic regime.

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.

Jet Rates in Electron-Positron Annihilation atO(αs3)in QCD

We compute production rates for two, three, four, and five jets in electron-positron annihilation at the third order in the QCD coupling constant. At this order, three-jet production is described to next-to-next-to-leading order in perturbation theory while the two-jet rate is obtained at next-to-next-to-next-to-leading order. Our results yield an improved perturbative description of the dependence of jet multiplicity on the jet resolution parameter y{cut}, particularly at small values of y{cut}.

QCD explanation of oscillating hadron and jet multiplicity moments

Ratios of multiplicity moments, H_q (cumulant over factorial moments K_q/F_q), have been observed to show an oscillatory behaviour with respect to order, q. Recent studies of e^+e^- annihilations at LEP have shown, moreover, that the amplitude and oscillation length vary strongly with the jet resolution parameter y_{cut}. We study the predictions of the perturbative QCD parton cascade assuming low non-perturbative cut-off (Q_0\sim \Lambda_{QCD}\sim few 100 MeV) and derive the expectations as a function of the cms energy and jet resolution from threshold to very high energies. We consider numerical solutions of the evolution equations of gluodynamics in Double Logarithmic and Modified Leading Logarithmic Approximations (DLA,MLLA), as well as results from a parton MC with readjusted parameters. The main characteristics are obtained in MLLA, while a more numerically accurate description is obtained by the MC model. A unified description of correlations between hadrons and correlations between jets emerges, in particular for the transition region of small y_{cut}.

Mb(mZ)from jet production at theZpeak in the Cambridge algorithm

We consider the production of heavy quark jets at the $Z$-pole at the next-to-leading order (NLO) using the {\it Cambridge jet-algorithm}. We study the effects of the quark mass in two- and three-jet observables and the uncertainty due to unknown higher order corrections as well as due to fragmentation. We found that the three-jet observable has remarkably small NLO corrections, which are stable with respect to the change of the renormalization scale, when expressed in terms of the {\it running quark mass} at the $m_Z$-scale. The size of the hadronization uncertainty for this observable remains reasonably small and is very stable with respect to changes in the jet resolution parameter $y_c$.

The jet multiplicity as a function of thrust

We calculate the average multiplicity of jets in e +e − annihilation as a function of both the jet resolution parameter, y cut, and the thrust T. Our result resums to all orders the leading and next-to-leading logarithms in y cut and 1− T, and is exact up to second order in α S. This allows a comparison between the number of jets found using jet algorithms and the ability to distinguish different jet topologies via thrust.

Differential (2+1) jet event rates and determination of $\alpha_s$ in deep inelastic scattering at HERA

Events with a (2+1) jet topology in deep–inelastic scattering at HERA are studied in the kinematic range 200 $<$ Q $^2<$ 10 000 GeV $^2$ . The rate of (2+1) jet events has been determined with the modified JADE jet algorithm as a function of the jet resolution parameter and is compared with the predictions of Monte Carlo models. In addition, the event rate is corrected for both hadronization and detector effects and is compared with next–to–leading order QCD calculations. A value of the strong coupling constant of $\alpha_s(M_Z^2)=0.118 \pm 0.002\,(stat.)\,^{+0.007}_{-0.008}\, (syst.)\,^{+0.007}_{-0.006}\,(theory)$ is extracted. The systematic error includes uncertainties in the calorimeter energy calibration, in the description of the data by current Monte Carlo models, and in the knowledge of the parton densities. The theoretical error is dominated by the renormalization scale ambiguity.

A complete [formula omitted] (αα s)calculation of the photon + 1 jet rate in e+e− annihilation

We present a complete calculation of the photon + 1 jet rate in e + e − annihilation up to O (αα s). Although formally of next-to-leading order in perturbation theory, this calculation contains several ingredients appropriate to a next-to-next-to-leading order calculation of jet observables. In particular, we describe a generalization of the commonly used phase space slicing method to isolate the singularities present when more than one particle is unresolved. Within this approach, we analytically evaluate the singularities associated with the following double unresolved regions: triple collinear, soft/collinear and double single collinear configurations as well as those from the collinear limit of virtual graphs. By comparing the results of our calculation with the existing data on the photon + 1 jet rate from the ALEPH Collaboration at CERN, we make a next-to-leading order determination of the process-independent non-perturbative quark-to-photon fragmentation function D q→ γ ( z, μ F ) at O (αα s). As a first application of this measurement allied with our improved perturbative calculation, we determine the dependence of the isolated photon + 1 jet cross section in a democratic clustering approach on the jet resolution parameter y cut at next-to-leading order. The next-to-leading order corrections to this observable are moderate but improve the agreement between theoretical prediction and experimental data.

Remarks on the resolvability of high-energy particle jets

The optimal conditions for separating multi-jet events from background events in particle physics are examined. It is shown that the maximal information about such events is not always obtained with the standard application of jet-resolution parameters. A modified criterion is proposed and a new extrapolation method is introduced.

CompleteO(αs3)results fore+e−→(γ,Z)→four jets

We present the next-to-leading-order $[O({\ensuremath{\alpha}}_{s}^{3})$] perturbative QCD predictions for ${e}^{+}{e}^{\ensuremath{-}}$ annihilation into four jets. A previous calculation omitted the $O({\ensuremath{\alpha}}_{s}^{3})$ terms suppressed by one or more powers of ${1/N}_{c}^{2}$, where ${N}_{c}$ is the number of colors, and the ``light-by-glue scattering'' contributions. We find that all such terms are uniformly small, constituting less than 10% of the correction. For the Durham clustering algorithm, the leading and next-to-leading logarithms in the limit of the small jet resolution parameter ${y}_{\mathrm{cut}}$ can be resummed. We match the resummed results to our fixed-order calculation in order to improve the small ${y}_{\mathrm{cut}}$ prediction.

Electron-Positron Annihilation into Four Jets at Next-to-Leading Order inαs

We calculate the rate for ${e}^{+}{e}^{\ensuremath{-}}$ annihilation into four jets at next-to-leading order in perturbative QCD, but omitting terms that are suppressed by one or more powers of ${1/N}_{c}^{2}$, where ${N}_{c}$ is the number of colors. The $O({\ensuremath{\alpha}}_{s}^{3})$ corrections depend strongly on the jet resolution parameter ${y}_{\mathrm{cut}}$ and on the clustering and recombination schemes, and they substantially improve the agreement between theory and data.

Observable jets from the BFKL chain.

We derive a modified form of the BFKL equation which enables the structure of the gluon emissions to be studied in small $x$ deep inelastic scattering. The equation incorporates the resummation of the virtual and unresolved real gluon emissions. We solve the equation to calculate the number of small $x$ deep-inelastic events containing 0,1,2 ...resolved gluon jets, that is jets with transverse momenta $q_{T} > \mu$. We study the jet decomposition for different choices of the jet resolution parameter $\mu$.

Average number of jets in deep inelastic scattering

Using the recently formulated k ⊥-clustering algorithm for lepton-hadron collisions, we compute the average number of hadronic jets produced in deep inelastic scattering, as a function of the momentum transfer Q 2, the Bjorken variable x and the jet resolution parameter ƒ cut . For samll values of ƒ cut we are able to resum leading and next-to-leading logarithms of ƒ cut to all orders in QCD perturbation theory. The result is simply related to the average jet multiplicity in e + e − annihilation, with a structure-function-dependent correction. For larger values of ƒ cut we match the resummed predictions to first-order numerical results.

Multi-jet rates in deep inelastic scattering and in e+e− annihilation

Predictions for multi-jet rates in deep inelastic scattering (DIS), in the current fragmentation region, and in e+e− annihilation are derived using the so-called «k1-clustering» algorithm. The dependence of these ratesvs. Q2 andycut (the jet resolution parameter) is studied in detail and presented as an interesting test of perturbative QCD approaches for HERA and LEP (I and II) experiments.

Jet cross sections and multiplicities in the modified leading-logarithmic approximation

Perturbative QCD is applied to multiple jet production in e +e − annihilation. We propose modified evolution equations for deriving the all-order perturbative expressions for jet cross sections, defined in the framework of the recently introduced ‘ k ⊥’ clustering logarithm. The mean number of jets as a function of the jet resolution parameter y cut is studied to relate the effective MLLA scale parameter Λ to Λ MS . Analytical predictions are compared with the results of ARIADNE and JETSET Monte Carlo simulations.

First measurements of jet production rates in deep-inelastic lepton-proton scattering.

The first measurements of forward multijet rates in deep-inelastic lepton scattering are presented. Data were taken with a 490-GeV muon beam incident on a hydrogen target. The jets were defined using the GADE algorithm. The measured rates are presented as a function of the jet resolution parameter {ital y}{sub cut}, and as a function of the virtual-photon--proton center-of-momentum energy {ital W}, in the range 13{le}{ital W}{le}33 GeV. Comparisons are made to the predictions of the Lund Monte Carlo programs and good agreement is obtained when QCD corrections are included in the model.

Average number of jets in e +e − annihilation

Using the recently introduced “ k ⊥” jet clustering algorithm, we are able to compute the average number of hadronic jets produced in e +e − annihilation, as a function of both the centre-of-mass energy and the jet resolution parameter y cut. For large values of y cut, we give complete numerical results to order α S 2, using the results of Bethke et al. on multi-jet fractions to this order. For small values, we give the results of resumming leading and next-to-leading logarithms of y cut to all orders in QCD perturbation theory. Our predictions should be useful both for determining α S and for studying the transition from the perturbative to the hadronization regime at very small y cut.

New clustering algorithm for multijet cross sections in e +e − annihilation

Cross sections for e +e − → n- jets, as functions of the jet resolution parameter y cut, are computed according to a new clustering algorithm. The jet multiplicity n is defined in such a way that jets i and j with energies E i and E j at relative angle angle θ ij are resolved if y ij = 2(1− cosθ ij) min (E i 2, E j 2) s>y cut , where s is the centre-of-mass energy squared. Using this algorithm, large higher-order corrections at small values of y cut can easily be evaluated. Our calculations include resummation of leading and next-to-leading logarithms of y cut to all orders in QCD perturbation theory. This enables us to predict the jet cross sections at small y cut for arbitrary n. Simple analytical results for n⩽5 are presented.

A measurement of the electroweak couplings of up and down type quarks using final state photons in hadronic Z0 decays

The production rate of final state photons in hadronic Z 0 decays is measured as a function of y cut = M ij 2 / E cm 2 the jet resolution parameter and minimum mass of the photon-jet system. Good agreement with the theoretical expectation from an O( αα s ) matrix element calculation is observed. Comparing the measurement and the prediction for y cut = 0.06, where the experimental systematic and statistical errors and the theoretical uncertainties are small, and combining this measurement with our result for the hadronic width of the Z 0 , we derived partial widths of up and down type quarks to be Γ u = 333 ± 55 ± 72 MeV and Γ d = 358 ± 37 ± 48 MeV in agreement with the standard model expectations. We compare our yield with the QCD shower models including photon radiation. At low γ cut JETSET underestimates the photon yield, and ARIADNE describes the production rate well.