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Event Generators 2 Advanced Topics

This lecture covers advanced topics in event generators, including the underlying event in hadron collisions, matching techniques, and the complete picture of hadron collisions. It also explores additional sources of particle production and highlights the importance of understanding the underlying event for precise collider measurements.

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Event Generators 2 Advanced Topics

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  1. Aachen, November 2007 Evolution Event Generators 2Advanced Topics First day Hands-on-sessions Peter Skands CERN / Fermilab

  2. Master Plan • Lecture 1: Fundamental Topics • Fundamentals of Generators, Parton Showers, and Hadronization • Lecture 2: Advanced Topics • Hadron Collisions and the Underlying Event • Matching • Lecture 3: Practical Topics + Open Q & A • Overview of Event Generator Landscape • Overview of useful parameters in PYTHIA • Open Question-and-Answer Session • Beer Done! Event Generator Status

  3. Lecture 2: Advanced Topics • You are now experts on parton showers and all that • What more do you want to know? • The Hadron Collider Environment: the Underlying Event • Models • Tuning • Early constraints from LHC • Matching • What’s the problem? • When do you need matching? • What’s the difference: PYTHIA/HERWIG, MLM, CKKW, MC@NLO, etc Event Generator Status

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

  5. 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

  6. Proton - Antiproton Collisions at the Tevatron From Rick Field The CDF “Min-Bias” trigger picks up most of the “hard core” cross-section plus a small amount of single & double diffraction. stot = sEL + sIN stot = sEL + sSD+sDD+sHC 1.8 TeV: 78mb = 18mb + 9mb + (4-7)mb + (47-44)mb CDF “Min-Bias” trigger 1 charged particle in forward BBC AND 1 charged particle in backward BBC The “hard core” component contains both “hard” and “soft” collisions. Beam-Beam Counters 3.2 < |h| < 5.9 Event Generator Status

  7. QCD Monte-Carlo Models:High Transverse Momentum Jets “Hard Scattering” Component • Start with the perturbative 2-to-2 (or sometimes 2-to-3) parton-parton scattering and add initial and final-state gluon radiation (in the leading log approximation or modified leading log approximation). “Underlying Event” • The “underlying event” consists of the “beam-beam remnants” and from particles arising from soft or semi-soft multiple parton interactions (MPI). The “underlying event” is an unavoidable background to most collider observables and having good understand of it leads to more precise collider measurements! • Of course the outgoing colored partons fragment into hadron “jet” and inevitably “underlying event” observables receive contributions from initial and final-state radiation. Event Generator Status

  8. The “Transverse” Regionsas defined by the Leading Jet Charged Particle Df Correlations pT > 0.5 GeV/c |h| < 1 • Look at charged particle correlations in the azimuthal angle Df relative to the leading calorimeter jet (JetClu R = 0.7, |h| < 2). • Define |Df| < 60o as “Toward”, 60o < -Df < 120o and 60o < Df < 120o as “Transverse 1” and “Transverse 2”, and |Df| > 120o as “Away”. Each of the two “transverse” regions have area DhDf = 2x60o = 4p/6. The overall “transverse” region is the sum of the two transverse regions (DhDf = 2x120o = 4p/3). Look at the charged particle density in the “transverse” region! “Transverse” region is very sensitive to the “underlying event”! Event Generator Status

  9. Charged Particle Density Df Dependence Leading Jet • Shows the Df dependence of the charged particle density, dNchg/dhdf, for charged particles in the range pT > 0.5 GeV/c and |h| < 1 relative to jet#1 (rotated to 270o) for “leading jet” events 30 < ET(jet#1) < 70 GeV. Log Scale! Min-Bias 0.25 per unit h-f • Also shows charged particle density, dNchg/dhdf, for charged particles in the range pT > 0.5 GeV/c and |h| < 1 for “min-bias” collisions. Event Generator Status

  10. Charged Particle Density Df Dependence Refer to this as a “Leading Jet” event • Look at the “transverse” region as defined by the leading jet (JetClu R = 0.7, |h| < 2) or by the leading two jets (JetClu R = 0.7, |h| < 2). “Back-to-Back” events are selected to have at least two jets with Jet#1 and Jet#2 nearly “back-to-back” (Df12 > 150o) with almost equal transverse energies (ET(jet#2)/ET(jet#1) > 0.8) and with ET(jet#3) < 15 GeV. Subset Refer to this as a “Back-to-Back” event • Shows the Df dependence of the charged particle density, dNchg/dhdf, for charged particles in the range pT > 0.5 GeV/c and |h| < 1 relative to jet#1 (rotated to 270o) for 30 < ET(jet#1) < 70 GeV for “Leading Jet” and “Back-to-Back” events. Event Generator Status

  11. Basic Physics Sjöstrand and van Zijl (1987): • First serious model for the underlying event • Based on multiple 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 • Nch Poissonian for each impact parameter  convolution with impact parameter profile  wider than Poissonian! • Concrete evidence for ‘lumpiness’ in the proton! UA5 Nch 540 GeV Event Generator Status T. Sjöstrand & M. van Zijl PRD36(1987)2019

  12. “Transverse” PTsum Density PYTHIA Tune A vs HERWIG “Leading Jet” “Back-to-Back” • Shows the average charged PTsum density, dPTsum/dhdf, in the “transverse” region (pT > 0.5 GeV/c, |h| < 1) versus ET(jet#1) for “Leading Jet” and “Back-to-Back” events. • Compares the (uncorrected) data with PYTHIA Tune A and HERWIG after CDFSIM. Event Generator Status

  13. The “Underlying Event” inHigh PT Jet Production (LHC) • Charged particle density in the “Transverse” region versus PT(jet#1) at 1.96 TeV for PY Tune AW and HERWIG (without MPI). Charged particle density versus PT(jet#1) The “Underlying Event” “Underlying event” much more active at the LHC! • Charged particle density in the “Transverse” region versus PT(jet#1) at 14 TeV for PY Tune AW and HERWIG (without MPI). Event Generator Status

  14. LHC Forecasts 1 • Theory “predictions” for tracker occupancy (idealized 4π tracker): • This was theory – how related to what is more realistically measured? • Restrict to |η| < 2.5, pT > 0.5 GeV <Nch> ~ 80-120 A bunch of models and tunes Event Generator Status

  15. LHC Forecasts 2 • Theory “predictions” for tracker occupancy: • Even 500 000 events will tell us a lot about which models could be right • But not all. Interesting to go to as low pT as possible not to miss anything. <Nch> ~ 13-20 Event Generator Status

  16. Under the Hood (theory) • How is this multiplicity built up? Number of “colour sparks” per pp collision <Nint> ~ 4 - 11 PS: you don’t have to believe this, but you should know that this is what you get if you run Pythia Event Generator Status

  17. 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 Underlying Event and Colour M. Heinz (STAR), nucl-ex/0606020; nucl-ex/0607033 STAR pp @ 200GeV Event Generator Status

  18. The ‘Intermediate’ Model • Meanwhile in Lund: 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

  19. The ‘New’ Model  Pythia 8 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

  20. The Underlying Event • Latest Developments • Parton Showers also for the Multiple Interactions: Pythia 6.4, Pythia 8, Sherpa • Re-interactions of partons  Pythia 8 • Non-QCD multiple interactions • Double Drell-Yan  Pythia 8 (e.g., W+W+ production = background) • New interest in non-perturbative phenomena: • Reconnections / interactions of strings  precision top mass, Pythia 6 • Summary • Even in the perturbative region, there is much left to understand. Early experimental studies at LHC will be extremely influential • The non-perturbative region is even more interesting, but also always more difficult … meaning that the experiments will be even more important to show us the way Event Generator Status

  21. Fixed Order Matrix Elements and Parton Shower Resummations

  22. Fixed Order vs Parton Showers ME PS 1 PS 2 • We saw yesterday that: • Parton Showers include all orders, but only the singular terms • Matrix Elements include all terms, but only up to the given order • Conventional Wisdom • When “close” to singularities (soft jets), use parton showers • When “far away” from singularities (hard jets), use matrix elements • In the past, these approaches were often pursued independently LHC - sps1a - m~600 GeV Plehn, Rainwater, PS: PLB645(2007)217 & hep-ph/0511306 Event Generator Status

  23. More About Fixed Order • What “Order” are we talking about, and of what? • Naively, it’s the order of the coupling at which we truncate the perturbative expansion. • However, only in Germany will you often hear “This is the distribution of zo und zo, calculated up to O(gsn gwm) …” – more often, you will hear words like “LO” and “NLO” ... • Is it a number of emissions? • “Tree-level” • Is it a number of emssions plus loops? • “Complete Orders” • And what is meant by an “LO” or “NLO” event generator? • Are all distributions calculated with an “NLO” generator now “NLO” ? Event Generator Status

  24. 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  an “inclusive” sample on which we could evaluate any observable, whether it is sensitive or not to extra hard jets, or to soft radiation Event Generator Status

  25. A Problem • How to do it? • Compute emission rates by parton showering (PS)? • Misses relevant terms for hard jets, rates only correct for strongly ordered emissions pT1 >> pT2 >> pT3 ... • Unknown contributions from higher logarithmic orders, subleading colors, … • Compute emission rates with matrix elements (ME)? • 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 • Unknown contributions from higher fixed orders Event Generator Status

  26. A (Stupid) Solution X inclusive X exclusive ≠ X+1 inclusive X+1 exclusive X+2 inclusive X+2 inclusive • Combine different starting multiplicites •  inclusive sample? • In practice – Combine • [X]ME+ showering • [X + 1 jet]ME+ showering • … • Doesn’t work • [X] + shower is inclusive • [X+1] + shower is also inclusive Run generator for X (+ shower) Run generator for X+1 (+ shower) Run generator for … (+ shower) Combine everything into one sample What you want What you get Overlapping “bins” One sample Event Generator Status

  27. Double Counting •  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 • Is it the “LO” cross section? • Is it the “LO” cross section plus the integral over [X + jet] ? • What about “complete orders” and KLN ? • When going to X, X+j, X+2j, X+3j, etc, this problem gets worse  Event Generator Status

  28. Matching • Traditional Approach: take the showers you have, expand them to 1st order, and fix them up • Sjöstrand (1987): Introducere-weightingfactor on first emission  1st order tree-level matrix element (ME) (+ further showering) • Seymour (1995): + where shower is “dead”, add separate events from 1st order tree-level ME, re-weighted by “Sudakov-like factor” (+ further showering) • Frixione & Webber (2002):Subtract1st order expansion from 1st order tree and 1-loop ME  add remainder ME correction events (+ further showering) • Multi-leg Approaches (Tree level only): • Catani, Krauss, Kuhn, Webber (2001): Substantial generalization of Seymour’s approach, to multiple emissions, slicingphase space into “hard”  M.E. ; “soft”  P.S. • Mangano (?): pragmatic approach to slicing: after showering, match jets to partons, reject events that look “double counted” A brief history of conceptual breakthroughs in widespread use today: Event Generator Status

  29. New Creations: Fall 2007 • Showers designed specifically for matching • Nagy, Soper (2006):Catani-Seymour showers • Dinsdale, Ternick, Weinzierl (Sep 2007) & Schumann, Krauss (Sep 2007): implementations • Giele, Kosower, PS (Jul 2007): Antenna showers • (incl. implementation) • Other new showers: partially designed for matching • Sjöstrand (Oct 2007): New interleaved evolution of FSR/ISR/UE • Official release of Pythia8 last week • Webber et al (HERWIG++): Improved angular ordered showers • Nagy, Soper (Jun 2007):Quantum showers •  subleading color, polarization (implementation in 2008?) • New matching proposals • Nason (2004): Positive-weight variant of MC@NLO • Frixione, Nason, Oleari (Sep 2007): Implementation: POWHEG • Giele, Kosower, PS (Jul 2007):Antenna subtraction • VINCIA Event Generator Status

  30. Matching – When? • Matching is not necessary if • You are only interested in an observable which only contains well separated scales (e.g., top pair + 1 jet at 25 GeV) • The matching in HERWIG/PYTHIA times K-factor is sufficient if • Your reaction is one of the “matched” ones (see respective manual) and your observable at most contains 1 “hard jet” • MC@NLO matching is relevant if • Your reaction is one of the “matched” ones (see manual) and your observable ne at most contains 1 “hard jet”, and the total normalization is important • Multi-leg matching (CKKW/MLM, …) is relevant if • Your observable contains 2 or more “hard jets” Event Generator Status

  31. CKKW and L-CKKW S. Catani, F. Krauss, R. Kuhn, B.R. Webber, JHEP 0111 (2001) 063 L. L¨onnblad, JHEP05 (2002) 046 • The CKKW algorithm • Divide phase space into two regions: • Use matrix elements to describe the initial distribution of all particles having a separation larger than some minimum pT > pTcut • Modify it by “rejections” according to the parton shower  “unitarise” • Use parton showers for pT < pTcut • [W]ME |pT>pTcut* Wveto(pTcut)+ showeringpT<pTcut • [W + j]ME|pT>pTcut* Wveto(pTcut)+ showeringpT<pTcut • … • Wveto are there to kill the “double counting” • = The probability that no emission happened above pTcut • This probability is also called the Sudakov factor, or the no-emission probabilit, Δ • SHERPA uses an analytical approximation • Lönnblad’s ARIADNE uses ‘trial’ or ‘pseudo’ showers • The “double counting” disappears since the events which would have caused it are exactly those which have emissions above pTcut Rejection Factors Wveto < 1 Event Generator Status

  32. Matched Mix of W+0,1,2,3,4 jets • Matching can also be done with AlpGen/MadGraph/… +Pythia/Herwig S. Mrenna, P. Richardson, JHEP0405 (2004) 040 Event Generator Status

  33. ALPGEN • “MLM” matching (Mangano) • Simpler but similar in spirit to CKKW • First generate events the “stupid” way: • [W]ME+ showering • [W + jet]ME+ showering • … • a set of fully showered events, with double counting. To get rid of the excess, accept/reject each event based on: • (cone-)cluster showered event  njets • match partons from the ME to the clustered jets • If all partons are matched, keep event. Else discard it. • Roughly equivalent to the pseudoshower approach above • Virtue: can be done without knowledge of the internal workings of the generator. Only the fully showered final events are needed Event Generator Status

  34. MC@NLO Frixione, Nason, Webber, JHEP 0206(2002)029 and 0308(2003)007 • MC@NLO in comparison • Superior precision for total cross section • Equivalent to tree-level matching for event shapes (differences higher order) • Inferior to multi-jet matching for multijet topologies • So far has been using HERWIG parton shower  complicated subtractions HERWIG++: O. Latunde-Dada, hep-ph/0708.4390 Event Generator Status

  35. New Methods – Why? CKKW MLM MC@NLO • MC@NLO: • Used to think it was impossible!  • But complicated  much work needed for each process  • “Only” gets first jet right (rest is PS)  • Hardwired to HERWIG • CKKW & MLM: • Best approach when multiple hard jets important. • Relatively straightforward (but still time-consuming) • Retains LO normalization  • Dependence on matching scale  • All constructed to use existing showers (HW or PY)  hard to trace analytically • Not easy to control theoretical uncertainty on exponentiated part  • How to add X+1 @ 1 loop ? Much recent work Event Generator Status

  36. Really Advanced Topics … (werbung) …

  37. Towards Improved Generators • The final answer will depend on: • The choice of evolution variable • The splitting functions (finite terms not fixed) • The phase space map ( dΦn+1/dΦn ) • The renormalization scheme (argument of αs) • The infrared cutoff contour (hadronization cutoff) • Step 1, Quantify uncertainty: vary all of these (within reasonable limits) • Step 2, Systematically improve: Understand the importance of each and how it is canceled by • Matching to fixed order matrix elements • Higher logarithms, subleading color, etc, are included • Step 3, Write a generator: Make the above explicit (while still tractable) in a Markov Chain context  matched parton shower MC algorithm Event Generator Status

  38. Based on Dipole-Antennae Shower off color-connected pairs of partons Plug-in to PYTHIA 8.1 (C++) So far: Final-state QCD cascades (massless quarks) 2 different shower evolution variables: pT-ordering (~ ARIADNE, PYTHIA 8) Mass-ordering (~ PYTHIA 6, SHERPA) For each: an infinite family of antenna functions Laurent series in branching invariants with arbitrary finite terms Shower cutoff contour: independent of evolution variable IR factorization “universal” Several different choices for αs (evolution scale, pT, mother antenna mass, 2-loop, …) Phase space mappings: 2 different choices implemented Antenna-like (ARIADNE angle) or Parton-shower-like: Emitter + longitudinal Recoiler VINCIA VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE Gustafson, PLB175(1986)453; Lönnblad (ARIADNE), CPC71(1992)15. Azimov, Dokshitzer, Khoze, Troyan, PLB165B(1985)147 Kosower PRD57(1998)5410; Campbell,Cullen,Glover EPJC9(1999)245 Dipoles (=Antennae, not CS) – a dual description of QCD a Giele, Kosower, PS : hep-ph/0707.3652 r b Event Generator Status

  39. Dipole-Antenna Showers • Dipole branching and phase space Giele, Kosower, PS : hep-ph/0707.3652 Event Generator Status

  40. Dipole-Antenna Functions Giele, Kosower, PS : hep-ph/0707.3652 • Starting point: “GGG” antenna functions, e.g., • Generalize to arbitrary Laurent series:  Can make shower systematically “softer” or “harder” • Will see later how this variation is explicitly canceled by matching •  quantification of uncertainty •  quantification of improvement by matching Gehrmann-De Ridder, Gehrmann, Glover, JHEP 09 (2005) 056 yar = sar / si si = invariant mass of i’th dipole-antenna Singular parts fixed, finite terms arbitrary Event Generator Status

  41. Quantifying Matching • The unknown finite terms are a major source of uncertainty • DGLAP has some, GGG have others, ARIADNE has yet others, etc… • They are arbitrary (and in general process-dependent) Using αs(MZ)=0.137, μR=1/4mdipole, pThad = 0.5 GeV Event Generator Status

  42. Matching Fixed Order (all orders) Pure Shower (all orders) Matched shower (including simultaneous tree- and 1-loop matching for any number of legs) Loop-level “virtual+unresolved” matching term for X+k Tree-level “real” matching term for X+k Giele, Kosower, PS : hep-ph/0707.3652 Event Generator Status

  43. Tree-level matching to X+1 • Expand parton shower to 1st order (real radiation term) • Matrix Element (Tree-level X+1 ; above thad)  Matching Term: •  variations in finite terms (or dead regions) in Aicanceled (at this order) • (If A too hard, correction can become negative  negative weights) Inverse phase space map ~ clustering Giele, Kosower, PS : hep-ph/0707.3652 Event Generator Status

  44. Phase Space Population Positive correction Negative correction Event Generator Status

  45. Quantifying Matching • The unknown finite terms are a major source of uncertainty • DGLAP has some, GGG have others, ARIADNE has yet others, etc… • They are arbitrary (and in general process-dependent) Using αs(MZ)=0.137, μR=1/4mdipole, pThad = 0.5 GeV Event Generator Status

  46. 1-loop matching to X • NLO “virtual term” from parton shower (= expanded Sudakov: exp=1 - … ) • Matrix Elements (unresolved real plus genuine virtual) • Matching condition same as before (almost): • You can choose anything for Ai (different subtraction schemes) as long as you use the same one for the shower Tree-level matching just corresponds to using zero • (This time, too small A  correction negative) Giele, Kosower, PS : hep-ph/0707.3652 Event Generator Status

  47. Note about “NLO” matching • Shower off virtual matching term  uncanceled O(α2) contribution to 3-jet observables (only canceled by 1-loop 3-parton matching) • While normalization is improved, shapes are not (shape still LO) Tree-Level Matching “NLO” Matching Using αs(MZ)=0.137, μR=1/4mdipole, pThad = 0.5 GeV Event Generator Status

  48. What to do next? • Go further with tree-level matching • Demonstrate it beyond first order (include H,Z  4 partons) • Automated tree-level matching (w. Rikkert Frederix (MadGraph) + …?) • Go further with one-loop matching • Demonstrate it beyond first order (include 1-loop H,Z  3 partons) • Should start to see cancellation of ordering variable and renormalization scale • Should start to see stabilization of shapes as well as normalizations • Extend the formalism to the initial state • Extend to massive particles • Massive antenna functions, phase space, and evolution Event Generator Status

  49. The Generator Outlook

  50. 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 • Upgrades of hadronization and decays • Moving to C++ • Data needed to constrain models & rule out crazy ideas • New methods  could QCD become a precision science? • Important for virtually all other measurements + can shed light on fundamental & interesting aspects of QCD (e.g. string interactions) Event Generator Status

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