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Transverse-Momentum-Ordered Showers and Interleaved Multiple Interactions

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T. Sjöstrand, P. Skands

High Energy Physics - Phenomenology · Submitted 26 Aug 2004 · 37 references

Pith's verdict: The pT-ordered showers are the durable contribution; the interleaving headline rests on an uncalibrated multi-parton density ansatz that the paper itself concedes is unconstrained.

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arXiv IDhep-ph/0408302 (version 1)
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CitationP. Skands, T. Sj\"ostrand. "Transverse-Momentum-Ordered Showers and Interleaved Multiple Interactions." arXiv:hep-ph/0408302 (2004). https://pith.science/paper/65EF65CO
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The paper

The paper claims

The paper proposes that multiple parton collisions and initial-state radiation in a hadron collision be generated as a single interleaved sequence in one falling transverse-momentum variable, so that the amount of underlying-event activity,

The reading

In a high-energy proton–proton collision, several parton–parton scatterings can happen at once, and each incoming parton can also radiate gluons before it collides. Normally these two sources of activity are generated one after the other, in a fixed order, so the generator decides how much radiation happens and then how many extra collisions fit, or vice versa. This paper argues that the two should instead be generated together: at each step the generator asks whether the next thing to happen at the current transverse momentum is a new parton–parton scattering or a further branching of one of the already-extracted incoming partons, and whichever comes at the highest transverse momentum wins. The claim is that this turns the size of the underlying event into a phase-space competition rather than an artefact of the order in which the two mechanisms are run. To make that possible the authors first had to rewrite the initial- and final-state showers so that they are ordered in transverse momentum rather than in virtuality or mass, and that rewriting is presented as a contribution in its own right.

What carries the argument

The load-bearing device is the transverse-momentum evolution variable, defined as $p^2_{⊥evol} = z(1-z)Q^2$ for final-state branchings and $p^2_{⊥evol} = (1-z)Q^2$ for initial-state ones, where $Q^2$ is the virtuality and $z$ the energy-sharing fraction in the radiator-plus-recoiler rest frame. This choice is what lets a shower branching and a parton–parton scattering be compared on the same scale and placed in one ordered sequence. Around it sit two supporting pieces: a dipole-style kinematics in which each branching parton has a recoiler whose energy and momentum are shuffled to keep the dipole invariant, and the correlated multi-parton density ansatz that decides how much phase space each competing step is allowed. The authors note the deliberate split between using lightcone relations to define the evolution variable and energy fractions to build the kinematics, and argue the former is the more meaningful hardness measure than the transverse momentum of the daughters alone.

Extended reading notes

Core claim

The central claim is that multiple parton interactions and initial-state radiation can be merged into one common sequence of decreasing transverse momentum, governed by a single combined no-activity factor obtained by exponentiating the sum of the two rates, $dP/dp_⊥ = (dP_{MI}/dp_⊥ + Σ dP_{ISR}/dp_⊥) exp(-∫ (dP_{MI}/dp'_⊥ + Σ dP_{ISR}/dp'_⊥) dp'_⊥)$. The competition is made physical through correlated parton densities: each interaction or branching removes momentum from the beam remnant, so the densities used for all later steps are squeezed into the remaining $x$ range, valence distributions are scaled down by the number of surviving valence quarks, and sea quarks are accompanied by partner antiquarks drawn from a gluon-splitting ansatz. The authors support the scheme with three rough tunes of the new framework compared against the older Tune A on Tevatron minimum-bias, jet, and $Z^0$ $p_⊥$ observables, finding comparable charged-multiplicity distributions and a somewhat improved low-$p_⊥$ $Z^0$ spectrum, though the observed rise of average $p_⊥$ with charged multiplicity is not reproduced. They also give a first estimate of the rate at which two shower chains would turn out to share a common ancestor, finding roughly one such joining per fifteen minimum-bias events, and conclude that omitting them is not a major shortcoming.

Load-bearing premise

The amount of phase space each competing step receives is set entirely by an unmeasured ansatz for how partons are distributed inside the proton once some have already been pulled out, built from squeezing the single-parton densities into the leftover momentum range, rescaling valence quarks by how many survive, and restoring the momentum sum rule with a multiplicative fudge on the sea and gluon normalizations.

Editorial extensions

If this is right

  • Underlying-event activity becomes a prediction of phase-space competition rather than a tuned consequence of the order in which radiation and extra scatterings are generated.
  • The new transverse-momentum-ordered showers can be stopped and restarted at any intermediate scale without changing the result, which is the property that makes interleaving with multiple interactions, and later with matrix-element matching, technically possible.
  • A common ordered sequence of scatterings and branchings gives a natural interface for merging with higher-order matrix elements, since a single hardness scale is available at every stage.
  • The first estimate of joined interactions, about one per fifteen minimum-bias events and about one per seven events with a hard scattering above 100 GeV, indicates that a full implementation of shower chains sharing a common ancestor can be deferred.
  • The authors report that the new final-state shower, tuned to LEP data by an external collaborator, reaches a total chi-squared about two thirds of the older mass-ordered algorithm, with agreement at roughly the percent level for most $Z^0$-peak observables.

Reading between the lines

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

  • If the interleaving is right, then measurements that separate radiation from extra scatterings, such as charged multiplicity in a rapidity region far from any jet as a function of the leading-jet transverse momentum, should distinguish this scheme from generators that run the two mechanisms sequentially.
  • The paper's own sanity check, switching off initial-state radiation and finding that the multiple-interaction multiplicity distribution then broadens as expected, suggests a clean experimental handle: the multiplicity of additional interactions at fixed hardest scale is the observable most sensitive to whether the competition is real.
  • The failure to reproduce the rise of average transverse momentum with charged multiplicity, which the authors attribute to colour connections between scattering chains, points to a place where the perturbative interleaving alone cannot be the whole story; a generator that gets the interleaving right but the colour flow wrong would still miss this distribution.
  • Because the relative rates of the two competing steps depend directly on the squeezed and rescaled parton densities, an independent determination of multi-parton densities, for instance from double-parton scattering cross sections, would test the mechanism at its weakest joint rather than at its most visible output.
Original abstract

We propose a sophisticated framework for high-energy hadronic collisions, wherein different QCD physics processes are interleaved in a common sequence of falling transverse-momentum values. Thereby phase-space competition is introduced between multiple parton-parton interactions and initial-state radiation. As a first step we develop new transverse-momentum-ordered showers for initial- and final-state radiation, which should be of use also beyond the scope of the current article. These showers are then applied in the context of multiple interactions, and a few tests of the new model are presented. The article concludes with an outlook on further aspects, such as the possibility of a shower branching giving partons participating in two different interactions.

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, 4,245 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.33 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We propose a sophisticated framework for high-energy hadronic collisions, wherein different QCD physics processes are interleaved in a common sequence of falling transverse-momentum values. Thereby phase-space competition is introduced between multiple parton-parton interactions and initial-state radiation. As a first step we develop new transverse-momentum-ordered showers for initial- and final-state radiation, which should be of use also beyond the scope of the current article. These showers are then applied in the context of multiple interactions, and a few tests of the new model are presented. The article concludes with an outlook on further aspects, such as the possibility of a shower branching giving partons participating in two different interactions.

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 We propose a sophisticated framework for high-energy hadronic collisions, wherein different QCD physics processes are interleaved in a common sequence of falling transverse-momentum values. contribution 0.94 0.79 0.17 asserted 0.97
s1 Thereby phase-space competition is introduced between multiple parton-parton interactions and initial-state radiation. method 0.41 0.66 0.10 asserted 1.00
s2 As a first step we develop new transverse-momentum-ordered showers for initial- and final-state radiation, which should be of use also beyond the scope of the current article. contribution 0.54 0.91 0.07 hedged possibility 0.69
s3 These showers are then applied in the context of multiple interactions, and a few tests of the new model are presented. contribution 0.57 0.89 0.12 asserted 0.99
s4 The article concludes with an outlook on further aspects, such as the possibility of a shower branching giving partons participating in two different interactions. future work 1.00 0.27 0.16 hedged possibility 0.84

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from simulation or computation 0.70.

What was examined, and what was not

sources read
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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. Schematic figure illustrating one incoming hadron
Figure 2. Schematic figure with our standard terminology for
Figure 3. (a) Schematic figure of the clustering of two partic
Figure 4. Parton p⊥ spectra when 2-parton events of a fixed p⊥ = 50 GeV, for an 1800 GeV pp collider, are modified by a single ISR branching with p⊥evol = 50 GeV, using CTEQ5L parton distributions and the standard DGLAP splitting kernels. Owing to p⊥evol 6= p⊥, the parton emitted at the ISR branching has a tail to p⊥ values well below 50 GeV. However, this spectrum is comparable with the lower-p⊥ of the two hard-scattering partons, after the recoil from the ISR has been taken into account, so there is a certain symmetry if it all is viewed as a 2 → 3 process. interaction in full before moving…
Figure 5. Charged multiplicity distributions, for 1.96 TeV
Figure 6. Average p⊥ as a function of charged multiplicity, hp⊥i(nch), for 1.96 TeV pp minimum-bias events. Note that the origo of the plot is not at (0,0). 26
Figure 7. a) Number of multiple interactions (in addition to the hardest one) and b) the average number of additional interactions as a function of the p⊥ of the hardest interaction, both for 1.96 TeV pp minimum-bias events. 4.2 Event activity We now take a closer look at the relative proportions of the MI, ISR, and FSR make-up of minimum-bias events, for the models in
Figure 8. z distributions for the first ISR branching, z1, in 1.96 TeV pp minimum-bias events. number of fairly soft emissions than the smoothly regularized models, Low and High FSR. Also note that the smaller number of branchings in these models partly is compensated by the larger h1 − zi for the branchings that do occur. The large number of FSR branchings,
Figure 9. a) Number of ISR branchings and b) the average number of ISR branchings as a function of the p⊥ of the hardest interaction, both for 1.96 TeV pp minimum-bias events. 10 -3 10 -2 10 -1 1 0 10 20 30 nFSR P(nFSR ) Tevatron Run II: number of FSR branchings Tune A Rap Sharp ISR Low FSR High FSR 0 10 20 30 40 0 5 10 15 20 p⊥1 <nFSR>(p⊥1 ) Tevatron Run II: <nFSR>(p⊥1 ) Tune A Rap Sharp ISR Low FSR High FSR a) b) b)
Figure 10. Number of FSR branchings and b) the average number of FSR branchings as a function of the p⊥ of the hardest interaction, both for 1.96 TeV pp minimum-bias events. 29
Figure 11. Total p⊥ sum for hadrons in 1.96 TeV pp minimum-bias events. multiplicity of the tunes. However, these difference do not have a large impact on most other observables. Thus e.g. the minijet rates and charged hadron p⊥ distributions in Figs. 13 and 14 are hardly distinguishable between Tune A and the new models. The minijet E⊥ spectrum, defined by a simple cone algorithm with a cone radius of R = q (∆η) 2 + (∆φ) 2 = 0.7 and an E⊥min = 5 GeV, which was slightly softer in the Rap model than in Tune A, has become slightly harder. On the other hand, the charged hadron p⊥ spectrum, which…
Figure 12. Charged multiplicity as a function of pseudorapi
Figure 13. Minijet rates, for 1.96 TeV pp minimum-bias events. 31
Figure 14. Charged hadron p⊥ spectra in 1.96 TeV pp minimum-bias events. The normal￾ization corresponds the total average charged multiplicity. less jet activity than any of the other ones, clearly indicating the impact of the reduced FSR in these events. The other rates come surprisingly close, given that both the ISR and the FSR algorithms are quite different between the old and the new scenarios. At high jet multiplicities the new ones are somewhat above the older ones. Next we study the properties of the jets produced. Since the two hardest jets both arise already as a consequence of the…
Figure 15. Charged multiplicity distribution for 1.96 TeV p
Figure 16. Given that the models have been tuned to each other ex
Figure 17. Jet multiplicity distribution for 1.96 TeV p
Figure 18. E⊥ spectra for the hardest and third hardest jet in 1.96 TeV pp events with p⊥hard > 100 GeV. 34
Figure 19. The a) hardest and b) third hardest jet E⊥ profile for 1.96 TeV pp events with p⊥hard > 100 GeV. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 5 10 15 20 25 30 35 40 45 50 Probability nch,jet Tune A Rap Sharp ISR Low FSR High FSR 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 d(nch/nch,jet)/d(r/R) r/R Tune A Rap Sharp ISR Low FSR High FSR a) b)
Figure 20. The a) charged multiplicity distribution and b) charged particle profile of the hardest jet in 1.96 TeV pp events with p⊥hard > 100 GeV. 35
Figure 21. The p⊥ spectrum at a) low and b) all p⊥ for dilepton pairs in the 66–116 GeV mass range, γ ∗/Z 0 simulation compared with CDF corrected data at 1.8 TeV [35]. 37
Figure 22. Illustration of the three terms in the two-parton
Figure 23. Kinematics of the b + d and c + e colliding systems (a) before and (b) after the a → b + c branching is reconstructed. from the p⊥max = p⊥i−1 scale given by the previous step. If such a trial joining occurs at a larger p⊥ scale than any of the other trial possibilities, then it is allowed to occur. Also the regularization procedure at small p⊥ values is the same as for MI and ISR. The parton densities we will use are defined in the same spirit as previously discussed, e.g. fb(xb, p2 ⊥) and fc(xc, p2 ⊥) are squeezed into ranges x ∈ [0, X], where X is reduced from unity by the…
Figure 24. Probability distributions of MI, ISR, FSR, and JI
Figure 25. p⊥evol distributions showing the scale at which multiple interactions (MI), ISR branchings, FSR branchings, and joined interactions (JI) occur, in 1.96 TeV pp min-bias events. a) Minimum-bias events, with the p⊥ scale of the hardest interaction shown for reference (solid line). b) events with p⊥hard > 100 GeV. Note that the p⊥ axis goes out to 20 GeV in a) and to 50 GeV in b). 42
Figure 26. P p⊥ distributions for MI, ISR, FSR and JI, in 1.96 TeV pp a) minimum-bias events and b) events with p⊥hard > 100 GeV. Note that the MI distribution does not include the hardest scattering. 6 Conclusions It would seem natural to consider the evolution of a high-energy event in the normal time order. In such a framework, the incoming hadrons are evolved from a simple partonic con￾figuration at a low Q0 scale, up through a number of short-lived fluctuations at different virtuality scales. At the moment of collision, the two sets of partons may undergo several independent…

Figures reproduced from arXiv:hep-ph/0408302 by the authors.

References
How later papers used it

138 later papers cite it

Evidence: substantial. 104 of the citing papers share no author with it, and 34 of those carry a confident label from Pith's citation classifier.

Pith read 23 of the 224 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 6 of 37 papers with this label · 1 by the same authors

By the same authors

How the literature uses it

122 arXiv papers cite this in 202 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 129 sentences without a confident label

Builds on it 2 papers
  • This is similar to what was done previously in VINCIA for final-state radiation (FSR) [ref] , but is here extended to initial state radiation (ISR) and adapted to PYTHIA's parton-shower framework [ref] .

    Automated Parton-Shower Variations in Pythia 8 · Introduction · 1.00

  • For the current studies, the Pythia $$-ordered parton showers [ref] are extended to the secluded sector, and the approach used to take into account massive radiating particles [ref] must, for the $U̸(1)$ scenario, be extended to the case where also the radiated gauge boson is massive.

    Discerning Secluded Sector gauge structures · Valley parton showers · 0.97

Uses its method or tool 31 papers
Compares with it 3 papers
Cites it as support 1 paper
  • This is suggested both by an exploratory study of “intertwined” multiple interactions [ref] (that is, letting several partons from the same shower chain undergo perturbative interactions, thus letting the perturbative shower evolution generate their colour correlations) which numerically found only very small effects, and by a more heuristic argument; that the multiple interactions are likely to be taking place slightly displaced from each other in space-time.

    General-purpose event generators for LHC physics · Introduction · 0.97

Cites it as background 33 papers
  • There is also the flavour excitation ($Q g →Q g$) that occurs for the hard scatter and in the timelike QCD parton shower quarkonia can be produced by gluon splitting ($g →QQ̅$) [ref] .

    J/$\psi$ and $\Upsilon$(1S) production in jets at LHC energies · Color reconnection and quarkonia production in PYTHIA 8 · 0.83

  • Whereas traditional parton showers, such as those implemented in the standalone version of PYTHIA [ref] , are based on an iterated sequence of $1→2$ splittings, supplemented to include 4-momentum conservation, running couplings, and (approximately) the effects of QCD coherence, VINCIA is based on the QCD antenna formalism [ref] , which in the MC shower context was originally pioneered by the ARIADNE program [ref] .

    The VINCIA Antenna Shower for Hadron Colliders · VINCIA's Antenna Showers · 0.84

  • In the new (interleaved) MPI model in PYTHIA 6 [ref] , showers and MPI were carried out in parallel, with physical colour flows.

    String Formation Beyond Leading Colour · Existing MPI Models and Colour Space · 0.85

Discussion

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