Event Shape Variables Research Articles

Three jet events and new strong couplings at LEP and NLC

We study the effects of new dimension-6 operators, resulting from a general SU(3) C ⊗ SU(2) L ⊗ U(1) Y invariant effective Lagrangian, on three jet production at LEP and at the Next Linear Collider. Contributions to the total event rate and to some event shape variables are analysed in order to establish bounds on these operators.

Local properties of local multiplicity distributions in hadronic Z decay

Preliminary results on local multiplicity fluctuations in hadronic Z decays are presented. The data were obtained using the L3 detector at LEP. It is investigated to what extent Monte-Carlo models, which are tuned to reproduce global event-shape variables and isingle-particle inclusive distributions, can describe the local fluctuations measured by means of bunching parameters.

QCD results from studies of hadronic events produced in e +e − annihilations at [formula omitted] GeV

We present results obtained from a study of the structure of hadronic events recorded by the L3 detector at a centre-of-mass energy of 183 GeV. The data sample corresponds to an integrated luminosity of 55.3 pb −1. The distributions of event shape variables and the energy dependence of their mean values are measured. From a comparison with resummed O ( α s 2) QCD calculations, we determine the strong coupling constant α s (183 GeV)=0.1086 ± 0.0026 (exp) ± 0.0054 (th) . The charged particle multiplicity distribution and momentum spectrum are studied and the energy dependence of the peak position of the ξ(=−ln x p ) distribution is compared with lower energy measurements and QCD expectations.

Two-loop enhancement factor for 1/Q corrections to event shapes in deep inelastic scattering

We compute the two-loop enhancement factors for our earlier one-loop calculations of leading (1/Q) power corrections to the mean values of some event shape variables in deep inelastic lepton scattering. The enhancement is found to be equal to the universal ``Milan factor'' for those shape variables considered, provided the one-loop calculation is performed in a particular way. As a result, the phenomenology of power corrections to DIS event shapes remains largely unaffected.

Recent QCD results above the Z 0 from OPAL

We present some of the OPAL QCD results at √s = 172 GeV , event shape variables, charged particle spectra and multiplicities. We determine the strong coupling strength to be α s(172 GeV) = 0.093±0.005( stat.)±0.006( sys.) , the mean charged multiplicity to be 〈η ch 〉(172 GeV) = 25.92±0.56( stat.)±0.81( sys.) and the position of the peak in the ξ p = ln( 1 x p ) distribution to be ξ 0(172 GeV) = 4.02±0.04( stat.)±0.02( sys.) . The results are compared with data taken at lower centre-of mass energies and analytic QCD and Monte Carlo predictions.

Next-to-leading order QCD corrections and massive quarks in e+e− → 3 jets

We present in detail a calculation of the next-to-leading order QCD corrections to the process e+e− → 3 jets with massive quarks. To isolate the soft and collinear divergencies of the four-parton matrix elements, we modify the phase space slicing method to account for masses. Our computation allows for the prediction of oriented three-jet events involving heavy quarks, both on and off the Z resonance, and of any event shape variable which is dominated by three-jet configurations. We show next-to-leading order results for the three-jet fraction, the differential two-jet rate, and for the thrust distribution at various c.m. energies.

Next-to-Leading Order Calculation of Four-Jet Shape Variables

We present the next-to-leading order calculation of two four-jet event shape variables, the D parameter and acoplanarity differential distributions. We find large, more than 100% radiative corrections. The theoretical prediction for the D parameter is compared to L3 data obtained at the Z peak and corrected to hadron level.

Study of hadronic events and measurements of αs between 30 and 91 GeV

We have studied the structure of hadronic events with a hard, %radiated isolated photon in the final state ($\mathrm{e^{+}e^{-}} \rightarrow$ Z $\rightarrow$ hadrons $+$ $\gamma$) in the 3.6 million hadronic data collected with the L3 detector at centre-of-mass energies around 91 GeV. The centre-of-mass energy of the hadronic system is in the range 30 GeV to 86 GeV. Event shape variables have been measured at these reduced centre-of-mass energies and have been compared with the predictions of different QCD Monte Carlo programs. The event shape variables and the energy dependence of their mean values are well reproduced by QCD models. We fit distributions of several global event shape variables to resummed $\cal{O} \alpha_{s}^{2})$ calculations to determine the strong coupling constant $\alpha_{s}$ over a wide range of energies. We find that the strong coupling constant $\alpha_{s}$ decreases with increasing energy, as expected from QCD.

Power corrections to event shape distributions

We estimate the effects of non-perturbative physics on the differential distributions of infrared- and collinear-safe e + e − event shape variables, by extending the notion of an infrared-regular effective strong coupling, which accounts for the non-perturbative corrections to the mean values of several shape variables, to their distributions. This leads to 1/ Q power corrections over a range of values of the shape variables considered, where Q is the centre-of-mass energy. In the case of the thrust variable, the leading correction is simply a shift of the distribution, by an amount proportional to 1/ Q. We show that this gives an excellent description of the data throughout a wide range of T and Q.

QCD studies and determination of α s in e +e − collisions at [formula omitted] and 172 GeV

We present a study of the structure of hadronic events recorded by the L3 detector at LEP at the center of mass energies of 161 and 172 GeV. The data sample corresponds to an integrated luminosity of 21.25 pb −1 collected during the high energy runs of 1996. The distributions of event shape variables and the energy dependence of their mean values are well reproduced by QCD models. From a comparison of the data with resummed O ( α s 2 ) QCD calculations, we determine the strong coupling constant at the two energies. Combining this with our earlier measurements we find that the strong coupling constant decreases with increasing energy as expected in QCD.

Measurement of event shape variables in deep inelastic e p scattering

Deep inelastic e p scattering data, taken with the H1 detector at HERA, are used to study the event shape variables thrust, jet broadening and jet mass in the current hemisphere of the Breit frame over a large range of momentum transfers Q between 7 GeV and 100 GeV. The data are compared with results from e + e − experiments. Using second order QCD calculations and an approach to relate hadronisation effects to power corrections an analysis of the Q dependences of the means of the event shape parameters is presented, from which both the power corrections and the strong coupling constant are determined without any assumption on fragmentation models. The power corrections of all event shape variables investigated follow a 1/ Q behaviour and can be described by a common parameter α 0 .

αS determination and test of QCD models at various CM energies with L3

We present a study of hadronic events collected by the L3 detector at centre of mass energies around 91 and 133 GeV. Also using hadronic events with a hard radiated photon we obtain a sample at a reduced CM energy of the hadronic system. This will enable us to study event shape variables and determine the strong coupling constant α s in the range between 30 and 133 GeV. The results presented here are in good agreement with QCD models and the energy dependence of α S is consistent with expectations of QCD.

Measurement of event shape and inclusive distributions at $\sqrt{s} =$ 130 and 136 GeV

Inclusive charged particle and event shape distributions are measured using 321 hadronic events collected with the DELPHI experiment at LEP at effective centre of mass energies of 130 to 136 GeV. These distributions are presented and compared to data at lower energies, in particular to the precise Z data. Fragmentation models describe the observed changes of the distributions well. The energy dependence of the means of the event shape variables can also be described using second order QCD plus power terms. A method independent of fragmentation model corrections is used to determine s from the energy dependence of the mean thrust and heavy jet mass. It is measured to be: s(133 GeV) = 0:116 0:007exp +0:005 􀀀0:004theo from the high energy data.

Resummation of threshold corrections in QCD to power accuracy: The Drell-Yan cross section as a case study

Resummation of large infrared logarithms in perturbation theory can, in certain circumstances, enhance the sensitivity to small gluon momenta and introduce spurious nonperturbative contributions. In particular, different procedures -- equivalent in perturbation theory -- to organize this resummation can differ by $1/Q$ power corrections. The question arises whether one can formulate resummation procedures that are explicitly consistent with the infrared behaviour of finite-order Feynman diagrams. We explain how this problem can be treated and resolved in Drell-Yan (lepton pair) production and briefly discuss more complicated cases, such as top quark production and event shape variables in the $e^+e^-$ annihilation.

Dispersive approach to power-behaved contributions in QCD hard processes

We consider power-behaved contributions to hard processes in QCD arising from non-perturbative effects at low scales which can be described by introducing the notion of an infrared-finite effective coupling. Our method is based on a dispersive treatment which embodies running coupling effects in all orders. The resulting power behaviour is consistent with expectations based on the operator product expansion, but our approach is more widely applicable. The dispersively generated power contributions to different observables are given by (log-)moment integrals of a universal low-scale effective coupling, with process-dependent powers and coefficients. We analyze a wide variety of quark-dominated processes and observables, and show how the power contributions are specified in lowest order by the behaviour of one-loop Feynman diagrams containing a gluon of small virtual mass. We discuss both collinear-safe observables (such as the e + e − total cross section and τ hadronic width, DIS sum rules, e + e − event shape variables and the Drell-Yan K-factor) and collinear divergent quantities (such as DIS structure functions, e + e − fragmentation functions and the Drell-Yan cross section).

Measurement of the partial decay width $R_b^0 = \Gamma_{b\bar{b}}/\Gamma_{had}$ of the $Z$ with the DELPHI detector at LEP

The partial decay width of the Z to b\overline{ b} quark pairs has been measured by the DELPHI detector at LEP. B-hadrons, containing b-quarks, were tagged by several methods using tracks with large impact parameters to the primary vertex complemented sometimes by event shape variables or using leptons with high transverse momentum relative to the hadron. In order to reduce the systematic uncertainties, in all methods the b-tagging efficiency has been extracted directly from the data. Combining all methods, the value: ΓbbˉΓhad=0.2216 ± 0.0016(stat.)±0.0021(syst.) was found, where the c\overline{c} production fraction was fixed to its Standard Model value.

Large logarithm behaviour ofe + e − jet cross sections and event shape distributions inO(α s 2 )

We have calculated the leading and next-to-leading logarithm coefficients of $O(\alpha_s^2)$ $e^+e^-$ annihilation jet cross sections, thrust distribution and energy-energy correlation in the two-jet limit when the jet resolution and the event shape variables vanish. We have compared our results with expectations based on leading logarithm approximations used to resum the pertubative cross sections where this is possible. There is good agreement for the leading and next-to-leading coefficients of jet cross sections in the Durham scheme. Also for the thrust distribution and energy-energy correlation we find results which are consistent with the leading logarithm predictions.

Power corrections and renormalons in Drell-Yan production

The resummed Drell-Yan cross section in the double-logarithmic approximation suffers from infrared renormalons. Their presence was interpreted as an indication for non-perturbative corrections of order Λ QCD/( Q(1 − z)). We find that, once soft gluon emission is accurately taken into account, the leading renormalon divergence is cancelled by higher-order perturbative contributions in the exponent of the resummed cross section. From this evidence, “higher twist” corrections to the hard cross section in Drell-Yan production should intervene only at order Λ 2 QCD/( Q 2(1 − z) 2) in the entire perturbative domain Q(1 − z) > Λ QCD. We compare this result with hadronic event shape variables, comment on the potential universality of non-perturbative corrections to resummed cross sections, and on possible implications for phenomenology.

On the universality of the leading, [formula omitted] power corrections in QCD

We discuss 1 Q corrections to hard processes in QCD where Q is a large mass parameter like the total energy in e + e − annihilation. The main problem we address ourselves to is whether these corrections to different processes (concentrating for definiteness on the certain event shape variables and the Drell-Yan cross section) can be related to each other in a reliable way so that the phenomenology of the 1 Q corrections can be developed. We derive first the relation valid to lowest order using both the renormalon and finite-gauge-boson mass techniques to check its independence on the infrared cut-off procedure. We then argue that the 1 Q corrections are due to soft gluons which factorize into a universal factor such that the lowest order relations are preserved in higher orders.

Test of the flavour independence of αs

Using about 950000 hadronic events collected during 1991 and 1992 with the ALEPH detector, the ratios r b = α s b α s udsc and r uds = α s uds α s cb have been measured in order to test the flavour independence of the strong coupling constant α s . The analysis is based on event-shape variables using the full hadronic sample, two b-quark samples enriched by lepton tagging and lifetime tagging, and a light-quark sample enriched by lifetime antitagging. The combined results are r b = 1.002±0.023 and r uds = 0.971 ± 0.023.