1. HEP Seminar, UC Berkeley, April 2007 Towards Improved Event Generators Peter Skands Fermilab / Particle Physics Division / Theoretical Physics In collaboration with W. Giele (FNAL), D. Kosower (CEA/Saclay), T. Sjöstrand (CERN & Lund U), D. Wicke (DØ, Wuppertal)

2. Peter SkandsTowards Improved Event Generators 2Overview ►Parton Showers QCD & Event Generators Antenna Showers: the VINCIA code ►Matching LL shower + tree-level matching (through to α s 2 ) E.g. [X] (0), [X + jet] (0), [X + 2 jets] (0) + shower (~ CKKW, but different) LL shower + 1-loop matching (through to α s ) E.g. [X] (0,1), [X + jet] (0) + shower (~ MC@NLO, but different) A sketch of further developments ►The rest is strings The theory of hadron collisions: the underlying event, and colour Non-perturbative QCD effects and the top mass at the Tevatron

3. Peter SkandsTowards Improved Event Generators 3 ►Main Tool Approximate by truncation of perturbative series at fixed coupling order Example: Q uantum C hromo D ynamics Reality is more complicated

4. Peter SkandsTowards Improved Event Generators 4 Traditional Event Generators ►Basic aim: improve lowest order perturbation theory by including leading corrections  exclusive event samples 1.sequential resonance decays 2.bremsstrahlung 3.underlying event 4.hadronization 5.hadron (and τ ) decays E.g. PYTHIA 2006: first publication of PYTHIA manual JHEP 0605:026,2006 (FERMILAB-PUB-06-052-CD-T)

5. Peter SkandsTowards Improved Event Generators 5 T he B ottom L ine The S matrix is expressible as a series in g i, g i n /t m, g i n /x m, g i n /m m, g i n /f π m, … 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 FODGLAP BFKL HQET χPT

6. Peter SkandsTowards Improved Event Generators 6 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 p T1 >> p T2 >> p T3... (common misconception that showers are soft, but that need not be the case. They can err on either side of the right answer.) Unknown contributions from higher logarithmic orders 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 Unknown contributions from higher fixed orders

7. Peter SkandsTowards Improved Event Generators 7 Example: tops, gluinos, and squarks plus jets T. Plehn, D. Rainwater, PS -PLB645(2007)217 + hep-ph/0511306

8. Peter SkandsTowards Improved Event Generators 8 Double Counting ►Combine different multiplicites  inclusive sample? ►In practice – Combine 1.[X] ME + showering 2.[X + 1 jet] ME + showering 3.… ►  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 ►When going to X, X+j, X+2j, X+3j, etc, this problem gets worse  X inclusive X+1 inclusive X+2 inclusive ≠ X exclusive X+1 exclusive X+2 inclusive

9. Peter SkandsTowards Improved Event Generators 9Matching ►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) Evolution

10. Peter SkandsTowards Improved Event Generators 10MC@NLO Nason’s approach: Generate 1 st shower emission separately  easier matching Avoid negative weights + explicit study of ZZ production Frixione, Nason, Webber, JHEP 0206(2002)029 and 0308(2003)007 JHEP 0411(2004)040 JHEP 0608(2006)077 ►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

11. Peter SkandsTowards Improved Event Generators 11 VINCIA ►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 2 nd order in s ij ) 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?) Dipoles – a dual description of QCD 1 3 2 VIRTUAL NUMERICAL COLLIDER WITH INTERACTING ANTENNAE Giele, Kosower, PS : in progress

12. Peter SkandsTowards Improved Event Generators 12 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

13. Peter SkandsTowards Improved Event Generators 13 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

14. Peter SkandsTowards Improved Event Generators 14 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)

15. Peter SkandsTowards Improved Event Generators 15 Matching at NNLO: tree part ►Adding more tree-level MEs is straightforward ►Example: second emission term from NLO matched parton shower ►X+2 jet tree-level ME correction term and matching equation Matching equation looks identical to 2 slides ago If all indices had been shown: sub-leading colour structures not derivable by nested 2  3 branchings do not get subtracted

16. Peter SkandsTowards Improved Event Generators 16 Matching at NNLO: tree part, with 2  4 ►Sketch only! But from matching point of view at least, no problem to include 2  4 ►Second emission term from NLO matched parton shower with 2  4 (For subleading colour structures, only |b| 2 term enters) ►Correction term and matching equation (Again, for subleading colour structures, only |b| 2 term is non-zero) ►So far showing just for fun (and illustration) Fine that matching seems to be ok with it, but … Need complete NLL shower formalism to resum 2  4 consistently If possible, would open the door to MC@NNLO

17. Peter SkandsTowards Improved Event Generators 17 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

18. Peter SkandsTowards Improved Event Generators 18 Under the Rug 2 ►We are now concentrating on completing the shower part for Higgs decays to gluons, so no detailed pheno studies yet The aim is to get a standalone paper on the shower out faster, accompanied by the shower plug-in for PYTHIA 8 We will then follow up with a writeup on the matching ►I will just show an example based on tree-level matching for H  gg

19. Peter SkandsTowards Improved Event Generators 19 Checks: Analytic vs Numerical vs Splines ►Calculational methods 1.Analytic integration over resolved region (as defined by evolution variable) – obtained by hand, used for speed and cross checks 2.Numeric: antenna function integrated directly (by nested adaptive gaussian quadrature)  can put in any function you like 3.In both cases, the generator constructs a set of natural cubic splines of the given Sudakov (divided into 3 regions linearly in Q R – coarse, fine, ultrafine) ►Test example Precision target: 10 -6 gg  ggg Sudakov factor (with nominal α s = unity) gg  ggg: Δ(s,Q 2 ) Analytic Splined p T -ordered Sudakov factor (= no-branching probability) Numeric / Analytic Spline (3x1000 points) / Analytic Ratios Spline off by a few per mille at scales corresponding to less than a per mille of all dipoles  global precision ok ~ 10 -6 VINCIA 0.010 (Pythia8 plug-in version)

20. Peter SkandsTowards Improved Event Generators 20 Why Splines? ►Example: m H = 120 GeV H  gg + shower Shower start: 120 GeV. Cutoff = 1 GeV ►Speed (2.33 GHz, g++ on cygwin) Tradeoff: small downpayment at initialization  huge interest later &v.v. (If you have analytic integrals, that’s great, but must be hand-made) Aim to eventually handle any function & region  numeric more general Initialization (PYTHIA 8 + VINCIA) 1 event Analytic, no splines2s(< 10 -3 s ?) Analytic + splines2s< 10 -3 s Numeric, no splines2s6s Numeric + splines50s< 10 -3 s Numerically integrate the antenna function (= branching probability) over the resolved 2D branching phase space for every single Sudakov trial evaluation Have to do it only once for each spline point during initialization

21. Peter SkandsTowards Improved Event Generators 21 VINCIA Example: H  gg  ggg VINCIA 0.008 Unmatched “soft” |A| 2 VINCIA 0.008 Unmatched “hard” |A| 2 VINCIA 0.008 Matched “soft” |A| 2 VINCIA 0.008 Matched “hard” |A| 2 y 12 y 23 y 12 ►First Branching ~ first order in perturbation theory ►Unmatched shower varied from “soft” to “hard” : soft shower has “radiation hole”. Filled in by matching. radiation hole in high-p T region Outlook: Immediate Future: Paper about gluon shower Include quarks  Z decays Matching Then: Initial State Radiation Hadron collider applications

22. Non-Perturbative Effects The Underlying Event and Colour String Interactions and the Top Mass at the Tevatron

23. Peter SkandsTowards Improved Event Generators 23 ► 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

24. Peter SkandsTowards Improved Event Generators 24 Classic Example: Number of tracks 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 More Physics: Multiple interactions + impact-parameter dependence Morale (will return to the models later) : 1)It is not possible to ‘tune’ anything better than the underlying physics model allows 2)Failure of a physically motivated model usually points to more physics

25. Peter SkandsTowards Improved Event Generators 25 Multiple Interactions  Balancing Minijets ►Look for additional balancing jet pairs “under” the hard interaction. ►Several studies performed, most recently by Rick Field at CDF  ‘lumpiness’ in the underlying event. (Run I) angle between 2 ‘best-balancing’ pairs CDF, PRD 56 (1997) 3811

26. Peter SkandsTowards Improved Event Generators 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 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! Colour correlations also essential Determine between which partons hadronizing strings form (each string  log(m string ) hadrons) Important ambiguity: what determines how strings form between the different interactions? UA5 N ch 540 GeV

27. Peter SkandsTowards Improved Event Generators 27 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 (will return to this …) M. Heinz (STAR), nucl-ex/0606020; nucl-ex/0607033 STAR pp @ 200GeV

28. Peter SkandsTowards Improved Event Generators 28 Correlation: vs N ch ►Both RHIC and Rick find the average hadron is harder in high-multiplicity events than in low-multiplicity ones ►If high multiplicity is interpreted as ~ large UE, this raises the question: ►Why do ‘active’ collisions produce harder hadrons? If I just stack independent collisions on top of each other, the prediciton would be ~ flat How do the hadrons from a central collision ‘know’ it was central? Do they talk to each other? What do they talk about? And how? Tevatron Run II Pythia 6.2 Min-bias (N ch ) Tune A old default Central Large UE Peripheral Small UE Non-perturbative component in string fragmentation (LEP value) Not only more (charged particles), but each one is harder Diffractive?

29. Peter SkandsTowards Improved Event Generators 29 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

30. Peter SkandsTowards Improved Event Generators 30 The ‘New’ Model ►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+)

31. Peter SkandsTowards Improved Event Generators 31 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 (N ch ) 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 (N ch ) distribution, but too little ►One place left to look Could there be some non-trivial physics at work in the final state itself?

32. Peter SkandsTowards Improved Event Generators 32 D. B. Leinweber, hep-lat/0004025 The (QCD) Landscape Anti-Triplet Triplet pbar beam remnant p beam remnant bbar from tbar decay b from t decay qbar from W q from W hadronization ? q from W Structure of a high- energy collision In reality, this all happens on top of each other (only possible exception: long-lived colour singlet)

33. Peter SkandsTowards Improved Event Generators 33 Existing models only for WW  a new toy model for all final states: colour annealing ►Searched for at LEP Major source of W mass uncertainty Most aggressive scenarios excluded But effect still largely uncertain P reconnect ~ 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 (N ch ) telling us? What (else) is RHIC, Tevatron telling us? Implications for Top mass? Implications for LHC? Normal WW Reconnected WW OPAL, Phys.Lett.B453(1999)153 & OPAL, hep-ex0508062 Sjöstrand, Khoze, Phys.Rev.Lett.72(1994)28 & Z. Phys.C62(1994)281 + more … Colour Reconnection (example) Soft Vacuum Fields? String interactions? Size of effect < 1 GeV? Color Reconnections Sandhoff + PS, in Les Houches ’05 SMH Proceedings, hep-ph/0604120

34. Peter SkandsTowards Improved Event Generators 34 Colour Annealing Sandhoff + PS, in Les Houches ’05 SMH Proceedings, hep-ph/0604120 ►Toy model of (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: P reconnect = 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

35. Peter SkandsTowards Improved Event Generators 35 A First Study ►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 N ch and (N ch ) No CR Field’s Tunes & new models ►Improved Description of Min-Bias ►Effect Still largely uncertain ►Worthwhile to look at top etc Tevatron Run II min-bias PYTHIA 6.408

36. Peter SkandsTowards Improved Event Generators 36 Event Generation Selection ►For each model 100k inclusive events were generated ►Jets are reconstructed using both Cone (ΔR = 0.5, p T > 15 GeV) k T (d cut = 150 GeV 2 ) ►Exactly 4 reconstructed Jets ►Technical simplifications: Generator semileptonic events. Unique assignment to MC truth by ΔR possible. ►Reconstruct mass on correct assignment only: m 2 = (p bjet + p qjet + p qbarjet ) 2 Top Mass Estimator D. Wicke (DØ) Used for paper

37. Peter SkandsTowards Improved Event Generators 37 Also considered +/- 30 GeV Also considered Gaussian + p1, and flat D. Wicke (DØ) Top Mass Estimator

38. Peter SkandsTowards Improved Event Generators 38 D. Wicke (DØ) Top Mass Estimator

39. Peter SkandsTowards Improved Event Generators 39 D. Wicke (DØ) Top Mass Estimator

40. Peter SkandsTowards Improved Event Generators 40 Preliminary Conclusions ►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? A few weeks ago: D. Wicke + PS, hep-ph/0703081