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Event shapes in e+e- annihilation and deep inelastic scattering

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Mrinal Dasgupta, Gavin P. Salam

High Energy Physics - Phenomenology · Submitted 19 Dec 2003 · 196 references

Pith's verdict: A careful, honest reference review whose central synthesis is sound, though the α_0 universality claim is presented with more confidence than the quoted systematics support.

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arXiv IDhep-ph/0312283 (version 2)
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CitationGavin P. Salam, Mrinal Dasgupta. "Event shapes in e+e- annihilation and deep inelastic scattering." arXiv:hep-ph/0312283 (2003). https://pith.science/paper/W3EUD5U2
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The paper

The paper claims

Event shapes in electron-positron annihilation and deep inelastic scattering are described by resummed perturbative QCD plus a single universal $1/Q$ power correction, making them a controlled laboratory for the strong coupling and the QCD色

The reading

The review asks whether the shapes of hadronic final states — thrust, jet masses, jet broadenings, the $C$-parameter and their relatives — can be turned into quantitative tests of QCD rather than qualitative pictures of jets. Its answer is that they can, provided three ingredients are combined: next-to-leading-order fixed-order matrix elements, all-orders resummation of the soft and collinear logarithms that dominate the two-jet region, and a non-perturbative correction that falls as a single inverse power of the hard scale. The striking part of the claim is that this power correction is universal: one parameter, the infrared-average coupling $a_0$, with a value near $0.45$ to $0.50$, is claimed to describe many different observables in both $e^+e^-$ annihilation and deep inelastic scattering. If that holds, event shapes stop being a nuisance for precision QCD and become one of its sharpest tools, delivering the strong coupling, the colour factors $C_A$ and $C_F$, and constraints on the $\beta$ function from the same data set.

What carries the argument

The load-bearing object is the shift ansatz for the integrated distribution, $D_{NP,V}(v) = D_{PT,V}(v - C_V P)$, together with the universal form $P = (4 C_F/pi^2) M (mu_I/Q) [a_0(mu_I) - a_s(mu_R) - ...]$ that subtracts the perturbative contribution from scales below the infrared matching scale $mu_I$ and replaces it with a single non-perturbative number. The Milan factor $M$ accounts for the fact that the naive coefficient $C_V$ is computed from a decaying virtual gluon without the observable's non-inclusiveness; once corrected, the coefficients become universal across observables. The machinery only works because the perturbative side is under control: next-to-leading-logarithmic resummation in the exponentiated form, matched to next-to-leading-order matrix elements so that the matched distribution vanishes as $v$ goes to zero. For the broadenings the shift becomes $v$-dependent, $D_1(v) ~ ln(1/v)$, which is what produces the $1/sqrt(a_s)$ enhancement of their power correction and explains why they behave differently from thrust.

Extended reading notes

Core claim

The paper's central claim is that the Dokshitzer-Webber picture works: for observables that vanish in the two-jet limit, the mean value is $1/Q$-corrected according to $a_0$, and the full distribution is obtained from the perturbatively resummed and matched distribution by a shift of size $C_V P$, with $P$ built from $a_0$ and the calculable coefficient $C_V$. The review collects simultaneous fits of the strong coupling and $a_0$ to mean values and to distributions across many observables and finds consistency at the level of the quoted uncertainties, with $a_0$ clustering in the range $0.45$ to $0.50$ and $e^+e^-$ values of the coupling in agreement with the world average. It also records where the picture is strained: the heavy-jet mass and wide-jet broadening resist a common description, the deep inelastic scattering fits prefer somewhat larger couplings, and the default jet-mass scheme carries known hadron-mass contributions that break universality. The review treats these as open problems rather than refutations, and it sets out the extensions — shape functions, dressed-gluon exponentiation, three-jet observables — that are meant to address them.

Load-bearing premise

The load-bearing premise is that a single non-perturbative parameter $a_0$ is genuinely universal across different event shapes and across two different processes, which the review itself calls the true test of the approach while noting that the uncertainties in the comparison are probably underestimated.

Editorial extensions

If this is right

  • Event-shape data yield a determination of the strong coupling that agrees with other methods while simultaneously returning the same non-perturbative parameter across observables, so the two cannot be tuned against each other freely.
  • Because the dependence on $C_A$ and $C_F$ is explicit in both the perturbative and the power-correction terms, a single fit can constrain the colour factors independently, and the review reports this as the tightest independent determination of $C_A$ and $C_F$ among the methods compared.
  • The same shift picture extends from mean values to full distributions, so the $Q$-dependence of a distribution, not just its average, becomes a test of the non-perturbative model.
  • Three-jet observables such as the $D$-parameter and the thrust minor introduce sensitivity to gluon fragmentation, giving a qualitatively new test that flux-tube-type models cannot mimic as easily.
  • Shape functions replace the delta-function shift with a smeared convolution, extending the description deeper into the two-jet region where the shift breaks down, at the price of losing predictivity between observables.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If a common $a_0$ truly holds, then the residual scatter between observables in the fits is a direct measure of the neglected higher-order perturbative terms rather than of hadronisation, which would give an independent handle on theoretical uncertainty in event-shape fits.
  • The review's own observation that renormalisation-group-improved perturbation theory removes most of the apparent need for a power correction in mean values suggests that part of what is being fitted as $a_0$ may be a reorganised perturbative series; a future next-to-next-to-leading-order calculation could shrink the fitted $a_0$ without any change in the data.
  • The reported tension in the wide-jet broadening and heavy-jet mass, both of which select one hemisphere, points at a concrete calculational target: the power correction in the three-jet region for these observables, which does not yet exist.
  • Because the deep inelastic scattering fits prefer larger couplings and are dominated by lower $Q$, a reanalysis restricted to high $Q$ with heavy-quark and photon-Z interference effects included would be a clean discriminator between a genuine process dependence of $a_0$ and a low-scale artefact.
Original abstract

This article reviews the status of event-shape studies in e+e- annihilation and DIS. It includes discussions of perturbative calculations, of various approaches to modelling hadronisation and of comparisons to data.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,225 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.23 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

This article reviews the status of event-shape studies in e+e- annihilation and DIS. It includes discussions of perturbative calculations, of various approaches to modelling hadronisation and of comparisons to data.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This article reviews the status of event-shape studies in e+e- annihilation and DIS. contribution 0.74 0.15 0.08 asserted 0.80
s1 It includes discussions of perturbative calculations, of various approaches to modelling hadronisation and of comparisons to data. contribution 0.84 0.16 0.05 asserted 0.98

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Comparison of the fixed-order (LO, NLO) and resummed (NLL) predictions for the thrust distribution in e+e− at Q = MZ . The resummed distribution has been matched (ln R scheme, see below) so as to include the full LO and NLO contributions. The inset differs from the main plot only in the scales. To illustrate the impact of resummations we show in figure 1 the LO, NLO and resummed results for the thrust distribution. Not only is the divergence in the LO distribution clearly visible, but one also observes a marked difference in the qualitative behaviour of the LO and NLO results, both…
Figure 2. Left: data for the mean value of the e+e− thrust, compared to LO, NLO and NLO+O (Λ/Q); right: data for the Durham jet resolution y23 compared to the NLO prediction (figure taken from [108]). 4. Mean values, hadronisation corrections and comparisons to experiment Much of the interest in event shapes stems from the wealth of data that is available, covering a large range of centre of mass energies (e +e −) or photon virtualities (DIS). The e +e − data comes from the pre-LEP experiments [79], the four LEP experiments [80–85] [86–89] [90–98] [99–103] and SLD [104]. In addition, because
Figure 3. Left: αs, α0 fit to e +e − data on mean values of event shapes, with the jet masses converted to the p-scheme (the arrow indicates the change in going from default to p-scheme) [28]. Right: fits to DIS mean event-shape data by H1 [115, 116] and ZEUS [117] (curves taken from figures in [116, 117]). Contours indicate 1-σ uncertainties (statistical and experimental systematic, except for the ZEUS results which are just statistical). Taking into account the uncertainties, which are not necessarily correlated from one observable to another, fig. 3 indicates remarkable success for the reno
Figure 4. The mean value of the thrust distribution in e +e − annihilation as a function of Q with αMS s (MZ) = 0.110. The upper (dashed) line corresponds to the principal value result which then is fitted to the data adding a 1/Q term. Figure taken from Ref. [160]. obtained for α MS s (MZ) and λ are respectively 0.110±0.006 and 0.62±0.11. We note that λ ≃ 0.6 in this approach corresponds to a smaller power correction than is required in the DW model. This is probably a consequence of the inclusion of pieces of higher perturbative orders via a principal value prescription, although it lea
Figure 5. Results for αs(Mz) from comparisons to e+e− event-shape data using the RGI approach. The band shows the mean value of αs and uncertainty, as obtained from the observables below the dashed line. Figure taken from Ref. [89]. Thus the first term in the perturbative expansion of R is simply αs/π. The ρi are renormalisation scheme independent quantities. In particular the quantity ρ1 = β1/(2β0) is simply the ratio of the first two coefficients of the QCD β function while ρ2 additionally depends on the first three (up to NNLO) perturbative coefficients in the expansion of hfi. Current…
Figure 6. Event shape distributions at MZ compared to a variety of event generators [10–12]. The shaded band in the lower plot indicates the experimental statistical and systematic errors added in quadrature. Figure taken from [163]. generators such as Herwig [10], Jetset/Pythia [11] and Ariadne [12]
Figure 7. SLD data for the total and wide-jet broadenings, transformed to ‘parton’ level using a multiplicative bin-by-bin factor (CH, with uncertainties, as discussed in the text) obtained from the ratio of Jetset parton to hadron-level distributions. It is compared to NLO and NLL+NLO predictions. Also shown is the detector to hadron-level correction factor CD. Figure taken from [104]. of the perturbative studies made possible by this approach. The majority of them use NLL+NLO perturbative calculations to fit for the strong coupling (as discussed below some, e.g. [88], just use NLO results,…
Figure 8. Values for αs obtained by fitting NLL+NLO event-shape distributions to L3 data at a range of centre of mass energies (figure taken from [98]). Only experimental uncertainties are shown. the evidence for the running of the coupling in the region above Q = MZ. Work in this direction is currently in progress [168]. So far only preliminary results are available [169], and as well as improving the picture of the high-energy running of the coupling, they suggest a slightly smaller value of αs than that quoted above, more in accord with world averages [170, 171]. Secondly, in the overall…
Figure 9. Theoretical uncertainties for the thrust. The shaded area represents the overall theoretical uncertainty on the distribution, determined as the maximum/minimum of all the dashed, dotted, etc. curves; the solid curves indicate the variation of αs allowed such that the prediction stays within the uncertainty band. have examined various options for estimating higher orders so as to improve the agreement. Their main approach involves a simultaneous fit of the coupling and the renormalisation scale, i.e. the renormalisation scale dependence is taken as a way of parameterising possible…
Figure 10. Left: Illustration of the BT -dependent non-perturbative shift in the jet broadening distribution for e +e − annihilation. The dashed curve is the perturbative prediction (NLL+NLO), while the solid curve includes a non￾perturbative (B-dependent) shift. Figure taken from [135]. Right: NLL+NLO distribution with a 1/Q shift for τtE = 1 − TtE in DIS at a range of Q values (round dots indicate points used in fits) [33]. The Q values range from 15 GeV (bottom) to 81 GeV (top). 0.4 0.5 0.6 0.7 0.8 0.9 0.08 0.1 0.12 average 1-T MH , MH 2 BT BW C α0 αS (MZ ) Distributions a) 0.25 0.3 0.35…
Figure 11. Left: 1-σ contours for simultaneous fits of αs and α0 to e +e − event￾shape distributions. The error contours account for statistic, systematical and theoretical uncertainties. The shaded band indicates the result for αs when using Monte Carlo hadronisation models. Figure taken from [184]. Right: 1-σ contours from fits to H1 DIS event shape distributions [115] with statistical and systematic errors added in quadrature. Figure taken from [33]. e +e − and DIS. This statement holds holds also for the EEC, fitted in [89], not shown in fig. 11. There is also good agreement with the resul
Figure 12. Determination of colour factors from resummed distributions with 1/Q (shift) power corrections and a variety of other methods. Figure taken from [188]. The ellipses show correlated measurements from studies of the angular distributions of 4-jet events [189, 190] and event shapes [187], while the lines are obtained from studies of the gluon fragmentation function [191] and from multiplicities in gluon jets [192]. 5.2.2. Shape functions. We have already mentioned that the approximation of a simple shift is valid only in the region Λ/Q ≪ v ≪ 1. To better understand the origin of the…
Figure 13. Left: the thrust distribution using the NLL+NLO perturbative dis￾tribution with the shape function eq. (36). Shown for Q = 14, 22, 35, 44, 55, 91, 133 and 161 GeV. Figure taken from [193]. Right: the thrust distribution at the per￾turbative (DGE) level, with a non-perturbative shift, and with a shape function. Figure taken from [29]. This is a clear success for the shape-function approach as compared to the simple shift discussed above. However the drawback of shape-functions is that a priori one loses all predictivity (save for the first moment) when going from one observable

Figures reproduced from arXiv:hep-ph/0312283 by the authors.

References
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