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

2. Peter SkandsEvent Generator Status 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!

3. Peter SkandsEvent 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: P YTHIA /H ERWIG, MLM, CKKW, MC@NLO, etc

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

5. Peter SkandsEvent Generator Status 5 ► 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 p T ►  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 Additional Sources of Particle Production

6. Peter SkandsEvent Generator Status 6 From Rick Field  tot =  EL  SD   DD   HC 1.8 TeV: 78mb = 18mb + 9mb + (4-7)mb + (47-44)mb The CDF “Min-Bias” trigger picks up most of the “hard core” cross-section plus a small amount of single & double diffraction. The “hard core” component contains both “hard” and “soft” collisions. Beam-Beam Counters 3.2 < |  | < 5.9 CDF “Min-Bias” trigger 1 charged particle in forward BBC AND 1 charged particle in backward BBC  tot =  EL  IN Proton - Antiproton Collisions at the Tevatron

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

8. Peter SkandsEvent Generator Status 8 ► Look at charged particle correlations in the azimuthal angle  relative to the leading calorimeter jet (JetClu R = 0.7, |  | < 2). ► Define |  | 120 o as “Away”. Each of the two “transverse” regions have area  = 2x60 o = 4  /6. The overall “transverse” region is the sum of the two transverse regions (  = 2x120 o = 4  /3). Charged Particle  Correlations p T > 0.5 GeV/c |  | < 1 “Transverse” region is very sensitive to the “underlying event”! Look at the charged particle density in the “transverse” region! The “Transverse” Regions as defined by the Leading Jet

9. Peter SkandsEvent Generator Status 9 ► Shows the  dependence of the charged particle density, dN chg /d  d , for charged particles in the range p T > 0.5 GeV/c and |  | < 1 relative to jet#1 (rotated to 270 o ) for “leading jet” events 30 < E T (jet#1) < 70 GeV. ► Also shows charged particle density, dN chg /d  d , for charged particles in the range p T > 0.5 GeV/c and |  | < 1 for “min-bias” collisions. Leading Jet Min-Bias 0.25 per unit  -  Log Scale! Charged Particle Density  Dependence

10. Peter SkandsEvent Generator Status 10 ► Look at the “transverse” region as defined by the leading jet (JetClu R = 0.7, |  | 150 o ) with almost equal transverse energies (E T (jet#2)/E T (jet#1) > 0.8) and with E T (jet#3) < 15 GeV. ► Shows the  dependence of the charged particle density, dN chg /d  d , for charged particles in the range p T > 0.5 GeV/c and |  | < 1 relative to jet#1 (rotated to 270 o ) for 30 < E T (jet#1) < 70 GeV for “Leading Jet” and “Back-to-Back” events. Refer to this as a “Leading Jet” event Refer to this as a “Back-to-Back” event Subset Charged Particle Density  Dependence

11. Peter SkandsEvent 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 N ch distributions. Peripheral collisions  little matter overlap  few interactions. Central collisions  many N ch Poissonian for each impact parameter  convolution with impact parameter profile  wider than Poissonian! Concrete evidence for ‘lumpiness’ in the proton! UA5 N ch 540 GeV T. Sjöstrand & M. van Zijl PRD36(1987)2019

12. Peter SkandsEvent Generator Status 12 ► Shows the average charged PTsum density, dPT sum /d  d , in the “transverse” region (p T > 0.5 GeV/c, |  | < 1) versus E T (jet#1) for “Leading Jet” and “Back-to-Back” events. ► Compares the (uncorrected) data with PYTHIA Tune A and HERWIG after CDFSIM. “Leading Jet” “Back-to-Back” “Transverse” PTsum Density PYTHIA Tune A vs HERWIG

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

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

15. Peter SkandsEvent Generator Status 15 ►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 p T as possible not to miss anything. LHC Forecasts 2 ~ 13-20

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

17. Peter SkandsEvent Generator Status 17 What’s the problem? How are the initiators and remnant partons correllated? in impact parameter? in flavour? in x (longitudinal momentum)? in k T (transverse momentum)? in colour (  string topologies!) What does the beam remnant look like? (How) are the showers correlated / intertwined?

18. Peter SkandsEvent Generator Status 18 Underlying Event and Colour ►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 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 M. Heinz (STAR), nucl-ex/0606020; nucl-ex/0607033 STAR pp @ 200GeV

19. Peter SkandsEvent Generator Status 19 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

20. Peter SkandsEvent Generator Status 20 The ‘New’ Model  Pythia 8 ►Sjöstrand and PS (2005): ‘Interleaved’ evolution of multiple interactions and parton showers Sjöstrand & PS : JHEP03(2004)053, EPJC39(2005)129 multiparton PDFs derived from sum rules Beam remnants Fermi motion / primordial k T Fixed order matrix elements p T -ordered parton shower (matched to ME for W/Z/H/G + jet) perturbative “intertwining”? NB: Tune A still default since more thoroughly tested. To use new models, see e.g. PYTUNE (Pythia6.408+)

21. Peter SkandsEvent Generator Status 21 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

22. Fixed Order Matrix Elements and Parton Shower Resummations

23. Peter SkandsEvent Generator Status 23 Fixed Order vs Parton Showers ME PS 1 PS 2 LHC - sps1a - m~600 GeV ►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 Plehn, Rainwater, PS: PLB645(2007)217 & hep-ph/0511306 ►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

24. Peter SkandsEvent Generator Status 24 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(g s n g w m ) …” – 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” ?

25. Peter SkandsEvent Generator Status 25 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

26. Peter SkandsEvent Generator Status 26 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 p T1 >> p T2 >> p T3... 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

27. Peter SkandsEvent Generator Status 27 A (Stupid) Solution ►Combine different starting multiplicites  inclusive sample? ►In practice – Combine 1.[X] ME + showering 2.[X + 1 jet] ME + showering 3.… ►Doesn’t work [X] + shower is inclusive [X+1] + shower is also inclusive X inclusive X+1 inclusive X+2 inclusive ≠ X exclusive X+1 exclusive X+2 inclusive Run generator for X (+ shower) Run generator for X+1 (+ shower) Run generator for … (+ shower) Combine everything into one sample What you get What you want Overlapping “bins”One sample

28. Peter SkandsEvent Generator Status 28 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] ME as 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 

29. Peter SkandsEvent Generator Status 29Matching ►Traditional Approach: take the showers you have, expand them to 1 st order, and fix them up Sjöstrand (1987): Introduce re-weighting factor on first emission  1 st order tree-level matrix element (ME) (+ further showering) Seymour (1995): + where shower is “dead”, add separate events from 1 st order tree-level ME, re-weighted by “Sudakov-like factor” (+ further showering) Frixione & Webber (2002): Subtract 1 st order expansion from 1 st 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, slicing phase 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:

30. Peter SkandsEvent Generator Status 30 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

31. Peter SkandsEvent Generator Status 31 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”

32. Peter SkandsEvent Generator Status 32 S. Catani, F. Krauss, R. Kuhn, B.R. Webber, JHEP 0111 (2001) 063 CKKW and L-CKKW ►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 p T > p Tcut Modify it by “rejections” according to the parton shower  “unitarise” Use parton showers for p T < p Tcut 1.[W] ME |pT>pTcut * W veto (p Tcut ) + showering pT<pTcut 2.[W + j] ME|pT>pTcut * W veto (p Tcut ) + showering pT<pTcut 3.… W veto are there to kill the “double counting” = The probability that no emission happened above p Tcut 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 p Tcut L. L¨onnblad, JHEP05 (2002) 046 Rejection Factors W veto < 1

33. Peter SkandsEvent Generator Status 33 Matched Mix of W+0,1,2,3,4 jets S. Mrenna, P. Richardson, JHEP0405 (2004) 040 ►Matching can also be done with AlpGen/MadGraph/… + Pythia/Herwig

34. Peter SkandsEvent Generator Status 34ALPGEN ►“MLM” matching (Mangano) Simpler but similar in spirit to CKKW ►First generate events the “stupid” way: 1.[W] ME + showering 2.[W + jet] ME + showering 3.… ►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  n jets 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

35. Peter SkandsEvent Generator Status 35MC@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

36. Peter SkandsEvent Generator Status 36 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 ? MC@NLO MLMCKKW New Methods – Why? Much recent work

37. Really Advanced Topics … (werbung) …

38. Peter SkandsEvent Generator Status 38 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 ( dΦ n+1 /dΦ n ) The renormalization scheme (argument of α s ) 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

39. Peter SkandsEvent Generator Status 39 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 VINCIA ►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 α s (evolution scale, p T, mother antenna mass, 2-loop, …) Phase space mappings: 2 different choices implemented Antenna-like (ARIADNE angle) or Parton-shower-like: Emitter + longitudinal Recoiler Dipoles (=Antennae, not CS) – a dual description of QCD a b r VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE Giele, Kosower, PS : hep-ph/0707.3652

40. Peter SkandsEvent Generator Status 40 Dipole-Antenna Showers ►Dipole branching and phase space Giele, Kosower, PS : hep-ph/0707.3652

41. Peter SkandsEvent Generator Status 41 Dipole-Antenna Functions ►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 y ar = s ar / s i s i = invariant mass of i’th dipole-antenna Giele, Kosower, PS : hep-ph/0707.3652 Gehrmann-De Ridder, Gehrmann, Glover, JHEP 09 (2005) 056 Singular parts fixed, finite terms arbitrary

42. Peter SkandsEvent Generator Status 42 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 α s (M Z )=0.137, μ R =1/4m dipole, p Thad = 0.5 GeV

43. Peter SkandsEvent Generator Status 43Matching Fixed Order (all orders) Matched shower (including simultaneous tree- and 1-loop matching for any number of legs) Tree-level “real” matching term for X+k Loop-level “virtual+unresolved” matching term for X+k Pure Shower (all orders) Giele, Kosower, PS : hep-ph/0707.3652

44. Peter SkandsEvent Generator Status 44 Tree-level matching to X+1 1.Expand parton shower to 1 st order (real radiation term) 2.Matrix Element (Tree-level X+1 ; above t had )  Matching Term:  variations in finite terms (or dead regions) in A i canceled (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

45. Peter SkandsEvent Generator Status 45 SoftStandardHard Matched SoftStandardMatched Hard Phase Space Population Positive correctionNegative correction

46. Peter SkandsEvent Generator Status 46 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 α s (M Z )=0.137, μ R =1/4m dipole, p Thad = 0.5 GeV

47. Peter SkandsEvent Generator Status 47 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 A i (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

48. Peter SkandsEvent Generator Status 48 Note about “NLO” matching ►Shower off virtual matching term  uncanceled O(α 2 ) contribution to 3-jet observables (only canceled by 1-loop 3-parton matching) ►While normalization is improved, shapes are not (shape still LO) Using α s (M Z )=0.137, μ R =1/4m dipole, p Thad = 0.5 GeV Tree-Level Matching“NLO” Matching

49. Peter SkandsEvent Generator Status 49 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

50. The Generator Outlook

51. Peter SkandsEvent Generator Status 51 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)