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Towards Improved Event Generators

Explore the advancements in event generators for high-energy collisions, including parton showers, matching, and underlying event modeling. Delve into the complexities of quantum chromodynamics and non-perturbative effects in hadron decays. Understand the importance of resonance masses, hard jet tails, and event coherence. Discover the challenges and solutions in predicting hard additional jets and incorporating multiple soft emissions effectively.

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Towards Improved Event Generators

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  1. HEP Seminar, UO Eugene, April 2007 Towards Improved Event Generators Peter Skands Fermilab / Particle Physics Division / Theoretical Physics

  2. Overview • Introduction • The structure of high-energy collisions • Event Generators • Towards Improved Event Generators • Parton Showers • Matching • Minimum Bias and the ‘Underlying Event’ • String interactions and the top mass ? Event Generator Status

  3. QuantumChromoDynamics • Main Tool • Matrix Elements in perturbative Quantum Field Theory • Example: Reality is more complicated Event Generator Status

  4. The Event Generator Position Event Generator Status

  5. Monte Carlo Generators • Large-dimensional phase spaces • Monte Carlo integration Stratified sampling + stochastic error ~ N1/2 independent of dimension  ‘events’ • + Markov Chain formulation of fragmentation: Event Generator Status

  6. Classic Example: Number of tracks More Physics: Multiple interactions + impact-parameter dependence UA5 @ 540 GeV, single pp, charged multiplicity in minimum-bias events Simple physics models ~ Poisson Can ‘tune’ to get average right, but much too small fluctuations  inadequate physics model • Morale (will return to the models later): • It is not possible to ‘tune’ anything better than the underlying physics model allows • Failure of a physically motivated model usually points to more, interesting physics Event Generator Status

  7. Collider Energy Scales Hadron Decays Non-perturbative hadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton ratio, kaon/pion ratio, Bose-Einstein correlations ... Soft Jets + Jet Structure Multiple collinear/soft emissions (initial and final state brems radiation), Underlying Event (multiple perturbative 22 interactions + … ?), semi-hard separate brems jets Exclusive & Widths Resonance Masses … Hard Jet Tail High-pT wide-angle jets Inclusive s • + “UNPHYSICAL” SCALES: • QF , QR : Factorisation(s) & Renormalisation(s) Event Generator Status

  8. The Bottom Line HQET FO DGLAP • The S matrix is expressible as a series in gi, gin/tm, gin/xm, gin/mm, gin/fπm, … • To do precision physics: • Solve more of QCD • Combine approximations which work in different regions: matching • Control it • Good to have comprehensive understanding of uncertainties • Even better to have a way to systematically improve • Non-perturbative effects • don’t care whether we know how to calculate them BFKL χPT Event Generator Status

  9. QCD-based Event Generators Parton Showers & Matching

  10. Cross Sections and Kinematics • Starting point 2n hard scattering perturbative matrix element • Fold with parton distribution functions  pp cross section MC integration  22 ‘events’ defined at hard scale QF2: starting point for Markov Chain From here on, unitarity total sigma not changed Event Generator Status

  11. QuantumChromoDynamics • To connect this with ‘real’ final states, 2 fundamental problems: e+e- 3 jets to Landau Pole Problem 1: QCD becomes non-perturbative at scales below ~ 1 GeV Problem 2: bremsstrahlung corrections singular for soft and collinear configurations Event Generator Status

  12. Bremsstrahlung: Parton Showers • Starting observation: forward singularity of bremsstrahlung is universal •  Leading contributions to all radiation processes (QED & QCD can be worked out to all orders once and for all •  exponentiated (Altarelli-Parisi) integration kernels • Iterative (Markov chain) formulation = parton shower • Generates the leading “collinear” parts of QED and QCD corrections to any process, to infinite order in the coupling • The chain is ordered in an “evolution variable”: parton virtuality, jet-jet angle, transverse momentum, … •  a series of successive factorizations the lower end of which can be matched to a hadronization description at some fixed low hadronization scale ~ 1 GeV Schematic: Forward (collinear) factorization of QCD amplitudes  exponentiation dσn+1 = dσn dΠnn+1 Pnn+1  dσn+2 = dσn (dΠnn+1 Pnn+1)2 and so on …  exp[] Event Generator Status

  13. Ordering Variables Event Generator Status

  14. Coherence Event Generator Status

  15. A Problem • The best of both worlds? We want: • A description which accurately predicts hard additional jets • + jet structure and the effects of multiple soft emissions • How to do it? • Compute emission rates by parton showering? • Misses relevant terms for hard jets, rates only correct for strongly ordered emissions pT1 >> pT2 >> pT3 ... • (common misconception that showers are soft, but that need not be the case. They can err on either side of the right answer.) • Compute emission rates with matrix elements? • Misses relevant terms for soft/collinear emissions, rates only correct for well-separated individual partons • Quickly becomes intractable beyond one loop and a handfull of legs Event Generator Status

  16. Double Counting X inclusive X exclusive ≠ X+1 inclusive X+1 exclusive X+2 inclusive X+2 inclusive • Combine different multiplicites  inclusive sample? • In practice – Combine • [X]ME+ showering • [X + 1 jet]ME+ showering • … •  Double Counting: • [X]ME + showering produces some X + jet configurations • The result is X + jet in the shower approximation • If we now add the complete[X + jet]MEas well • the total rate of X+jet is now approximate + exact ~ double !! • some configurations are generated twice. • and the total inclusive cross section is also not well defined • When going to X, X+j, X+2j, X+3j, etc, this problem gets worse  Event Generator Status

  17. Matching Evolution • Matching of up to one hard additional jet • PYTHIA-style (reweight shower: ME = w*PS) • HERWIG-style (add separate events from ME: weight = ME-PS) • MC@NLO-style (ME-PS subtraction similar to HERWIG, but NLO) • Matching of generic (multijet) topologies (at tree level) • ALPGEN-style (MLM) • SHERPA-style (CKKW) • ARIADNE-style (Lönnblad-CKKW) • PATRIOT-style (Mrenna & Richardson) • Brand new approaches (still in the oven) • Refinements of MC@NLO (Nason) • CKKW-style at NLO (Nagy, Soper) • SCET approach (based on SCET – Bauer, Schwarz) • VINCIA (based on QCD antennae – Giele, Kosower, PS) Event Generator Status

  18. VINCIA Dipole shower C++ code for gluon showers Standalone since ~ half a year Plug-in to PYTHIA 8 (C++ PYTHIA) since ~ last week Most results presented here use the plug-in version So far: 2 different shower evolution variables: pT-ordering (~ ARIADNE, PYTHIA 8) Virtuality-ordering (~ PYTHIA 6, SHERPA) For each: an infinite family of antenna functions shower functions = leading singularities plus arbitrary polynomials (up to 2nd order in sij) Shower cutoff contour: independent of evolution variable  IR factorization “universal”  less wriggle room for non-pert physics? Phase space mappings: 3 choices implemented ARIADNE angle, Emitter + Recoiler, or “DK1” (+ ultimately smooth interpolation?) VINCIA VIRTUAL NUMERICAL COLLIDER WITH INTERACTING ANTENNAE Giele, Kosower, PS : in progress 1 Dipoles – a dual description of QCD 2 3 Event Generator Status

  19. Expanding the Shower • Start from Sudakov factor = No-branching probability: (n or more  n and only n) • Decompose inclusive cross section • Simple example (sufficient for matching through NLO): NB: simplified notation! Differentials are over entire respective phase spaces Sums run over all possible branchings of all antennae Event Generator Status

  20. Matching at NLO: tree part • NLO real radiation term from parton shower • Add extra tree-level X + jet (at this point arbitrary) • Correction term is given by matching to fixed order: •  variations (or dead regions) in |a|2 canceled by matching at this order • (If |a| too hard, correction can become negative  constraint on |a|) • Subtraction can be automated from ordinary tree-level ME’s + no dependence on unphysical cut or preclustering scheme (cf. CKKW) -not a complete order: normalization changes (by integral of correction), but still LO NB: simplified notation! Differentials are over entire respective phase spaces Sums run over all possible branchings of all antennae Twiddles = finite (subtracted) ME corrections Untwiddled = divergent (unsubtracted) MEs Event Generator Status

  21. Matching at NLO: loop part • NLO virtual correction term from parton shower • Add extra finite correction (at this point arbitrary) • Have to be slightly more careful with matching condition (include unresolved real radiation) but otherwise same as before: • Probably more difficult to fully automate,but |a|2 not shower-specific • Currently using Gehrmann-Glover (global) antenna functions • Will include also Kosower’s (sector) antenna functions Tree-level matching just corresponds to using zero • (This time, too small |a|  correction negative) (for higher orders, see slides from LoopFest VI) Event Generator Status

  22. Under the Rug • The simplified notation allowed to skip over a few issues we want to understand slightly better, many of them related • Start and re-start scales for the shower away from the collinear limit • Evolution variable: global vs local definitions • How the arbitrariness in the choice of phase space mapping is canceled by matching • How the arbitrariness in the choice of evolution variable is canceled by matching • Constructing an exactly invertible shower (sector antenna functions) • Matching in the presence of a running renormalization scale • Dependence on the infrared factorization (hadronization cutoff) • Degree of automation and integration with existing packages • To what extent negative weights (oversubtraction) may be an issue • None of these are showstoppers as far as we can tell Event Generator Status

  23. VINCIA Example: H  gg  ggg • First Branching ~ first order in perturbation theory • Unmatched shower varied from “soft” to “hard” : soft shower has “radiation hole”. Filled in by matching. • Outlook: • Immediate Future: • Paper about gluon shower • Include quarks  Z decays • Matching • Then: • Initial State Radiation • Hadron collider applications y23 y23 VINCIA 0.008 Unmatched “soft” |A|2 VINCIA 0.008 Matched “soft” |A|2 radiation hole in high-pT region y23 y23 VINCIA 0.008 Unmatched “hard” |A|2 VINCIA 0.008 Matched “hard” |A|2 y12 y12 Event Generator Status

  24. The Underlying Event Towards a complete picture of hadron collisions

  25. Additional Sources of Particle Production • Domain of fixed order and parton shower calculations: hard partonic scattering, and bremsstrahlung associated with it. • But hadrons are not elementary • + QCD diverges at low pT •  multiple perturbative parton-parton collisions should occur • Normally omitted in explicit perturbative expansions • + Remnants from the incoming beams • + additional (non-perturbative / collective) phenomena? • Bose-Einstein Correlations • Non-perturbative gluon exchanges / colour reconnections ? • String-string interactions / collective multi-string effects ? • Interactions with “background” vacuum / with remnants / with active medium? e.g. 44, 3 3, 32 Event Generator Status

  26. Basic Physics • Sjöstrand and van Zijl (1987): • First serious model for the underlying event • Based on resummation of perturbative QCD 22 scatterings at successively smaller scales multiple parton-parton interactions • Dependence on impact parameter crucial to explain Nch distributions. • Peripheral collisions  little matter overlap  few interactions • Central collisions  many interactions (+ jet pedestal effect) •  wider than Poissonian! • Colour correlations also essential • Determine between which partons hadronizing strings form (each string  log(mstring) hadrons) • Important ambiguity: what determines how strings form between the different interactions? Event Generator Status

  27. In PYTHIA (up to 6.2), some “theoretically sensible” default values for the colour correlation parameters had been chosen Rick Field (CDF) noted that the default model produced too soft charged-particle spectra. The same is seen at RHIC: For ‘Tune A’ etc, Rick noted that <pT> increased when he increased the colour correlation parameters Virtually all ‘tunes’ now used by the Tevatron and LHC experiments employ these more ‘extreme’ correlations Tune A, and hence its more extreme colour correlations are now the default in PYTHIA (will return to this …) Underlying Event and Colour M. Heinz, nucl-ex/0606020; nucl-ex/0607033 Event Generator Status

  28. The ‘Intermediate’ Model • Sjöstrand and PS (2003): • Further developments on the multiple-interactions idea • First serious attempt at constructing multi-parton densitities • If sea quark kicked out, “companion” antiquark introduced in remnant (distribution derived from gluon PDF and gluon splitting kernel) • If valence quark kicked out, remaining valence content reduced • Introduction of “string junctions” to represent beam baryon number • Detailed hadronization model for junction fragmentation  can address baryon number flow separately from valence quarks Sjöstrand & PS : Nucl.Phys.B659(2003)243, JHEP03(2004)053 Event Generator Status

  29. The ‘New’ Model NB: Tune A still default since more thoroughly tested. To use new models, see e.g. PYTUNE (Pythia6.408+) • Sjöstrand and PS (2005): • ‘Interleaved’ evolution of multiple interactions and parton showers Fixed order matrix elements pT-ordered parton shower (matched to ME for W/Z/H/G + jet) multiparton PDFs derived from sum rules perturbative “intertwining”? Beam remnants Fermi motion / primordial kT Sjöstrand & PS : JHEP03(2004)053, EPJC39(2005)129 Event Generator Status

  30. Hooking it Up • But the old ambiguity remained. • How are the interaction initiators (and thereby their final states) correlated in colour? • Fundamentally a non-perturbative question, so hard to give definite answers • Simple-minded guess • There are many partons in the proton. Only a few interact  to first approximation their colour correlations should just be random • But random connections produced the usual flat <pT>(Nch) behaviour • Clearly, the new model and showers did not change the fact that some non-trivial colour correlations appear to be necessary • We also tried deliberately optimizing the correlations between the initiators to give the most highly correlated final states • This did lead to a small rise in the <pT>(Nch) distribution, but too little • One place left to look • Could there be some non-trivial physics at work in the final state itself? Event Generator Status

  31. hadronization bbar from tbar decay pbar beam remnant p beam remnant qbar from W q from W q from W b from t decay ? Triplet Anti-Triplet The (QCD) Landscape Structure of a high-energy collision In reality, this all happens on top of each other (only possible exception: long-lived colour singlet) D. B. Leinweber, hep-lat/0004025 Event Generator Status

  32. Color Reconnections W W Normal W W Reconnected Colour Reconnection (example) Soft Vacuum Fields? String interactions? Size of effect < 1 GeV? Sjöstrand, Khoze, Phys.Rev.Lett.72(1994)28 & Z. Phys.C62(1994)281 + more … OPAL, Phys.Lett.B453(1999)153 & OPAL, hep-ex0508062 • Searched for at LEP • Major source of W mass uncertainty • Most aggressive scenarios excluded • But effect still largely uncertain Preconnect ~ 10% • Prompted by CDF data and Rick Field’s studies to reconsider. What do we know? • Non-trivial initial QCD vacuum • A lot more colour flowing around, not least in the UE • String-string interactions? String coalescence? • Collective hadronization effects? • More prominent in hadron-hadron collisions? • What is <pT>(Nch) telling us? • What (else) is RHIC, Tevatron telling us? • Implications for Top mass? Implications for LHC? Existing models only for WW  a new toy model for all final states: colour annealing Sandhoff + PS, in Les Houches ’05 SMH Proceedings, hep-ph/0604120 Event Generator Status

  33. Colour Annealing • Toy modelof (non-perturbative) color reconnections, applicable to any final state • at hadronisation time, each string piece has a probability to interact with the vacuum / other strings: Preconnect = 1 – (1-χ)n • χ = strength parameter: fundamental reconnection probability (free parameter) • n = # of multiple interactions in current event ( ~ counts # of possible interactions) • For the interacting string pieces: • New string topology determined by annealing-like minimization of ‘Lambda measure’ • Similar to area law for fundamental strings: Lambda ~ potential energy ~ string length ~ log(m) ~ N •  good enough for order-of-magnitude Sandhoff + PS, in Les Houches ’05 SMH Proceedings, hep-ph/0604120 Event Generator Status

  34. A First Study A few weeks ago: D. Wicke + PS, hep-ph/0703081 • Using Tevatron min-bias as constraint • Those were the distributions that started it all • High-multiplicity tail should be somewhat similar to top  less extrapolation required • Why not use LEP? Again, since the extrapolation might not be valid. • No UE in ee, no beam remnants, less strings, no ‘bags’ in initial state. • The comparison would still be interesting and should be included in a future study • As a baseline, all models were tuned to describe Nch and <pT>(Nch) Tevatron Run II min-bias • Improved Description of Min-Bias • Effect Still largely uncertain • Worthwhile to look at top etc Field’s Tunes & new models No CR PYTHIA 6.408 PYTHIA 6.408 Event Generator Status

  35. Delta(mtop) ~ 1 GeV from parton shower To some extent already accounted for by HERWIG – PYTHIA, should still be investigated Match to hard matrix elements for top + jets + further constrain shower parameters Delta(mtop) ~ 0.5 GeV from infrared effects Early days. May be under- or overestimated. Models are crude, mostly useful for reconnaissance and order-of-magnitude Pole mass does have infrared sensitivity. Can we figure out some different observable which is more stable? It may be difficult to derive one from first principles, given the complicated environment, but proposals could still be tested on models Infrared physics ~ universal?  use complimentary samples to constrain it. Already used a few min-bias distributions, but more could be included As a last resort, take top production itself and do simultaneous fit? Preliminary Conclusions A few weeks ago: D. Wicke + PS, hep-ph/0703081 Event Generator Status

  36. The Generator Outlook • Generators in state of continuous development: • Better & more user-friendly general-purpose matrix element calculators+integrators • Improved parton showers and improved matching to matrix elements • Improved models for underlying events / minimum bias • With perturbative parts better under control  less wriggle room for non-perturbative physics  better constraints?  better models? • (Moving to C++)  always better, but never enough But what are the alternatives, when event structures are complicated and analytical methods inadequate? Event Generator Status

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