Hadronisation Corrections Research Articles

(N)NLO+NLL’ accurate predictions for plain and groomed 1-jettiness in neutral current DIS

The possibility to reanalyse data taken by the HERA experiments offers the chance to study modern QCD jet and event-shape observables in deep-inelastic scattering. To address this, we compute resummed and matched predictions for the 1-jettiness distribution in neutral current DIS with and without grooming the hadronic final state using the soft-drop technique. Our theoretical predictions also account for non-perturbative corrections from hadronisation through parton-to-hadron level transfer matrices extracted from dedicated Monte Carlo simulations with Sherpa. To estimate parameter uncertainties in particular for the beam-fragmentation modelling we derive a family of replica tunes to data from the HERA experiments. While NNLO QCD normalisation corrections to the NLO+NLL’ prediction are numerically small, hadronisation corrections turn out to be quite sizeable. However, soft-drop grooming significantly reduces the impact of non-perturbative contributions. We supplement our study with hadron-level predictions from Sherpa based on the matching of NLO QCD matrix elements with the parton shower. Good agreement between the predictions from the two calculational methods is observed.

Interplay between perturbative and non-perturbative effects with the ARES method

We present a new semi-numerical method to compute leading hadronisation corrections to two-jet event shapes in e+e− annihilation. The formalism we present utilises the dispersive approach, where the magnitude of power corrections is controlled by suitable moments of an effective strong coupling, but it can be adapted to other methods. We focus on observables where the interplay between perturbative and non-perturbative effects is crucial in determining the power corrections. A naive treatment of power corrections for some of these observables gives rise to an unphysical behaviour in the corresponding distributions for moderate observable values, thus considerably limiting the available range to fit the non-perturbative moments. We present a universal treatment to handle such observables, based on a suitable subtraction procedure, and compare our results to the analytic result in the case of total broadening. Finally, for the first time we present predictions for the thrust major, which cannot be handled with analytic methods.

Lund and Cambridge multiplicities for precision physics

We revisit the calculation of the average jet multiplicity in high-energy collisions. First, we introduce a new definition of (sub)jet multiplicity based on Lund declusterings obtained using the Cambridge jet algorithm. We develop a new systematic resummation approach. This allows us to compute both the Lund and the Cambridge average multiplicities to next-to-next-to-double (NNDL) logarithmic accuracy in electron-positron annihilation, an order higher in accuracy than previous works in the literature. We match our resummed calculation to the exact NLO ( mathcal{O} ( {alpha}_s^2 )) result, showing predictions for the Lund multiplicity at LEP energies with theoretical uncertainties up to 50% smaller than the previous state-of-the-art. Adding hadronisation corrections obtained by Monte Carlo simulations, we also show a good agreement with existing Cambridge multiplicity data. Finally, to highlight the flexibility of our method, we extend the Lund multiplicity calculation to hadronic collisions where we reach next-to-double logarithmic accuracy for colour singlet production.

C-parameter hadronisation in the symmetric 3-jet limit and impact on alpha _s fits

Hadronisation corrections are crucial in extractions of the strong coupling constant (alpha _s) from event-shape distributions at lepton colliders. Although their dynamics cannot be understood rigorously using perturbative methods, their dominant effect on physical observables can be estimated in singular configurations sensitive to the emission of soft radiation. The differential distributions of some event-shape variables, notably the C parameter, feature two such singular points. We analytically compute the leading non-perturbative correction in the symmetric three-jet limit for the C parameter, and find that it differs by more than a factor of two from the known result in the two-jet limit. We estimate the impact of this result on strong coupling extractions, considering a range of functions to interpolate the hadronisation correction in the region between the 2 and 3-jet limits. Fitting data from ALEPH and JADE, we find that most interpolation choices increase the extracted alpha _{s}, with effects of up to 4% relative to standard fits. This brings a new perspective on the long-standing discrepancy between certain event-shape alpha _s fits and the world average.

Near-to-planar three-jet events at NNLL accuracy

We extend the ARES method for next-to-next-to-leading-logarithmic (NNLL) QCD resummations to three-jet event shapes in e+e− collisions in the near-to-planar limit. In particular, we define a NNLL radiator for three hard emitters, and discuss new features of NNLL corrections arising specifically in this case. As an example, we present predictions for the D-parameter, matched to exact next-to-leading order (NLO). After inclusion of hadronisation corrections in the dispersive approach, we compare our predictions with LEP1 data.

Fitting the strong coupling constant with soft-drop thrust

Soft drop has been shown to reduce hadronisation effects at e+e− colliders for the thrust event shape. In this context, we perform fits of the strong coupling constant for the soft-drop thrust distribution at NLO+NLL accuracy to pseudo data generated by the Sherpa event generator. In particular, we focus on the impact of hadronisation corrections, which we estimate both with an analytical model and a Monte-Carlo based one, on the fitted value of αs(mZ). We find that grooming can reduce the size of the shift in the fitted value of αs due to hadronisation. In addition, we also explore the possibility of extending the fitting range down to significantly lower values of (one minus) thrust. Here, soft drop is shown to play a crucial role, allowing us to maintain good fit qualities and stable values of the fitted strong coupling. The results of these studies show that soft-drop thrust is a promising candidate for fitting αs at e+e− colliders with reduced impact of hadronisation effects.

Soft-drop thrust

Soft drop, a technique originally developed in the context of jet physics in proton-proton collisions in order to reduce the contamination from non-perturbative effects, is applied to event shapes in electron-positron annihilation. In particular, we study the thrust distribution at the Z pole and show that the region where non-perturbative corrections due to the hadronisation process are small is considerably extended if soft drop is applied. Therefore, we argue that the use of soft drop to reduce hadronisation effects is potentially of great benefit in the context of strong coupling determination using event shapes, which would be otherwise characterised by a strong correlation between αs and non-perturbative parameters. However, reduced sensitivity to hadronisation corrections is only one of the aspects that need to be considered. In this context, we show that perturbative calculability, especially away from the soft and collinear region of the event-shape spectrum, has a nontrivial interplay with the soft-drop observable of choice. To this purpose, besides thrust, we investigate the behaviour of the hemisphere mass as well as the jet mass. We find that the latter shows the most promising behaviour in the intermediate region of the spectrum, especially if small jet radii are considered.

Inclusive jet spectrum for small-radius jets

Following on our earlier work on leading-logarithmic (LLR) resummations for the properties of jets with a small radius, R, we here examine the phenomenological considerations for the inclusive jet spectrum. We discuss how to match the NLO predictions with small-R resummation. As part of the study we propose a new, physically-inspired prescription for fixed-order predictions and their uncertainties. We investigate the R-dependent part of the next-to-next-to-leading order (NNLO) corrections, which is found to be substantial, and comment on the implications for scale choices in inclusive jet calculations. We also examine hadronisation corrections, identifying potential limitations of earlier analytical work with regards to their $p_t$-dependence. Finally we assemble these different elements in order to compare matched (N)NLO+LLR predictions to data from ALICE and ATLAS, finding improved consistency for the R-dependence of the results relative to NLO predictions.

Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e−annihilations

We present a determination of the strong coupling constant from a fit of QCD predictions for six event-shape variables, calculated at next-to-next-to-leading order (NNLO) and matched to resummation in the next-to-leading-logarithmic approximation (NLLA). These event shapes have been measured in e+e- annihilations at LEP, where the data we use have been collected by the ALEPH detector at centre-of-mass energies between 91 and 206 GeV. Compared to purely fixed order NNLO fits, we observe that the central fit values are hardly affected, but the systematic uncertainty is larger because the NLLA part re-introduces relatively large uncertainties from scale variations. By combining the results for six event-shape variables and eight centre-of-mass energies, we find alpha_s(MZ)= 0.1224 +/- 0.0009 (stat) +/- 0.0009 (exp) +/- 0.0012 (had) +/- 0.0035 (theo), which improves previously published measurements at NLO+NLLA. We also carry out a detailed investigation of hadronisation corrections, using a large set of Monte Carlo generator predictions.

On the universality of hadronisation corrections to QCD jets

We improve previously derived analytical estimates of hadronisation corrections to QCD jets at hadron colliders, firmly establishing at the two-loop level the link to the well-known power corrections to LEP event-shape variables. The results of this paper apply to jets defined in the kt and anti-kt algorithms but the general framework presented here holds also for other algorithms for which calculations are in progress.

Non-perturbative QCD effects in jets at hadron colliders

We discuss non-perturbative QCD contributions to jet observables, computing their dependence on the jet radius R, and on the colour and transverse momentum of the parton initiating the jet. We show, using analytic QCD models of power corrections as well as Monte Carlo simulations, that hadronisation corrections grow at small values of R, behaving as 1/R, while underlying event contributions grow with the jet area as R2. We highlight the connection between hadronisation corrections to jets and those for event shapes in e+e− and DIS; we note the limited dependence of our results on the choice of jet algorithm; finally, we propose several measurements in the context of which to test or implement our predictions. The results presented here reinforce the motivation for the use of a range of R values, as well as a plurality of infrared-safe jet algorithms, in precision jet studies at hadron colliders.

The measurement of $\alpha_s$ from event shapes with the DELPHI detector at the highest LEP energies

Hadronic event shape distributions are determined from data in e+e- collisions between 183 and 207 GeV. From these the strong coupling alpha_s is extracted in O(alpha_s^2), NLLA and matched O(alpha_s^2)+NLLA theory. Hadronisation corrections evaluated with fragmentation model generators as well as an analytical power ansatz are applied. Comparing these measurements to those obtained at and around M_Z allows a combined measurement of alpha_s from all DELPHI data and a test of the energy dependence of the strong coupling.

Measurement of the QCD β-function using renormalisation group invariant perturbation theory

It is shown that RGI (for Renormalisation Group Improved or Invariant) perturbation theory describes the energy dependence of 7 event shape distribution means. Consistent values of the strong coupling are obtained, 〈 α s ( M Z )〉 = 0.121 ± 0.002 RMS , without need for Power or hadronisation corrections. The scatter of the results is much smaller than for standard Monte Carlo or Power correction methods. In particular no artificial theory error is required. The non-pert. parameters of MS Power correction models can be predicted using RGI theory.

Energy dependence of event shapes and of αs at LEP 2

Infrared and collinear safe event shape distributions and their mean values are determined using the data taken at five different centre of mass energies above M Z with the DELPHI detector at LEP. From the event shapes, the strong coupling α s is extracted in O ( α s 2), NLLA and a combined scheme using hadronisation corrections evaluated with fragmentation model generators as well as using an analytical power ansatz. Comparing these measurements to those obtained at M Z, the energy dependence (running) of α s is accessible. The logarithmic energy slope of the inverse strong coupling is measured to be d α −1 s d log(E cm ) =1.39±0.34( stat)±0.17( syst) , in good agreement with the QCD expectation of 1.27.

The photon + 1 jet event rate with the cone algorithm in hadronic events at LEP

Abstract Using the recently measured photon fragmentation function, we make predictions for ‘isolated’ photon +1 jet events using a cone type algorithm at LEP energies. For small cone half-angles, perturbation theory breaks down due to the presence of large logarithms. Furthermore, large hadronisation corrections are present. We suggest a definition of an ‘isolated’ photon which avoids these problems at small cone sizes and can be extrapolated to the reliably calculated large cone region.

A study of the recombination scheme dependence of jet production rates and of ? s ( $$M_{Z^0 } $$ ) in hadronicZ 0 decays

Jet production rates in hadronicZ 0 decays are studied using four different recombination schemes to define resolvable jets. The strong coupling constant α s (\(M_{Z^0 } \)) is determined in fits of the correspondingO(α 2 s ) QCD calculations to the differential 2-jet distributionsD 2(y). Hadronisation corrections and renormalisation scale uncertainties are found to be different for each recombination scheme. Within their overall systematic uncertainties, the four schemes yield consistent values of α s (\(M_{Z^0 } \)), leading to a final result of $$\alpha _s (M_{Z^0 } ) = 0.118 \pm 0.008.$$ .The error includes the experimental uncertainties (±0.003), uncertainties of hadronisation corrections and of the degree of parton virtualities to which the data are corrected, as well as the uncertainty of choosing the renormalisation scale.