1. High Energy Theory Seminar, U of Toronto, May 2007 Hadron Collisions Inside and Out Peter Skands Fermilab / Particle Physics Division / Theoretical Physics

2. Peter SkandsEvent Generator Status 2Overview ►Introduction The structure of high-energy collisions Event Generators ►Combining higher-order matrix elements with parton showers The problem of double counting  matching The VINCIA code ►The Underlying Event Multiple Perturbative Interactions (multiple parton interactions) A study of string reconnections and the top mass at the Tevatron

3. Peter SkandsEvent Generator Status 3 Monte Carlo Generators Large-dimensional phase spaces  Monte Carlo integration Stratified sampling + stochastic error ~ N 1/2 independent of dimension  ‘events’ + Markov Chain formulation of fragmentation: 1.Parton showers: iterative application of universal and pertubatively calculable kernels for n  n+1 partons ( = resummation of soft/collinear Sudakov logarithms) 2. Hadronization: iteration of X  X’ + hadron, at present according to phenomenological models based on known properties of nonperturbative QCD, lattice studies, and fits to data.

4. Peter SkandsEvent Generator Status 4 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, interesting physics The Canadian Research Council phrases it more poetically: Sjöstrand & van Zijl PRD36(1987)2019

5. Peter SkandsEvent Generator Status 5 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 Resonance Masses … Hard Jet Tail High-p T wide-angle jets & Widths + “UNPHYSICAL” SCALES: Q F, Q R : Factorisation(s) & Renormalisation(s) s Inclusive Exclusive Hadron Decays Collider Energy Scales

6. Peter SkandsEvent Generator Status 6 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

7. Peter SkandsEvent Generator Status 7 to Landau Pole Q uantum C hromo D ynamics Problem 1: QCD becomes non-perturbative at scales below ~ 1 GeV Problem 2: bremsstrahlung corrections singular for soft and collinear configurations ►To connect Feynman diagrams with ‘real’ final states: e + e -  3 jets

8. Peter SkandsEvent Generator Status 8 ►Starting observation: forward singularity of bremsstrahlung is universal (synchrotron radiation)  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”: e.g. 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 Bremsstrahlung: Parton Showers dσ n+1 = dσ n dΠ n  n+1 P n  n+1  dσ n+2 = dσ n (dΠ n  n+1 P n  n+1 ) 2 and so on …  exp[] Schematic: Forward (collinear) factorization of QCD amplitudes  exponentiation

9. Peter SkandsEvent Generator Status 9 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.) 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

10. Peter SkandsEvent Generator Status 10 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

11. Peter SkandsEvent Generator Status 11Matching ►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

12. Peter SkandsEvent Generator Status 12 Improved Perturbative Monte Carlo ►Zero’th order approach to matching: Improve the parton showers themselves E.g. improved soft limit of ordering variable in HERWIG++ Completely new p T -ordered hybrid parton-dipole showers in PYTHIA 6.4 / PYTHIA 8 ►Step 1: A comprehensive look at the uncertainty Vary the evolution variable (~ factorization scheme) Vary the antenna function Vary the kinematics map (angle around axis perp to 2  3 plane in CM) Vary the renormalization scheme (argument of α s ) Vary the infrared cutoff contour (hadronization cutoff) ►Step 2: Systematically improve on it Understand how each variation could be cancelled when Matching to fixed order matrix elements Higher logarithms are included ►Step 3: Write a generator Make Step 1 explicit in a Markov Chain  Parton Shower MC algorithm ‘with error band’ Include Step 2  Matched Parton Shower algorithm, ‘with smaller error band’

13. Peter SkandsEvent Generator Status 13 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 INTERLEAVED ANTENNAE Giele, Kosower, PS : in progress

14. Peter SkandsEvent Generator Status 14 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, generating function for shower 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) (a few experiments with single & double logarithmic splines  not huge success. So far linear ones ok for desired speed & precision)

15. Peter SkandsEvent Generator Status 15 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

16. Peter SkandsEvent Generator Status 16 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

17. Peter SkandsEvent Generator Status 17 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 Any other subtraction function used in NLO is just a finite part away  use the polynomial terms Tree-level matching just corresponds to using zero (This time, too small |a|  correction negative)

18. Peter SkandsEvent Generator Status 18 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

19. Peter SkandsEvent Generator Status 19 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

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

21. Peter SkandsEvent Generator Status 21 ► 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

22. Peter SkandsEvent Generator Status 22 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 interactions (+ jet pedestal effect)  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? Sjöstrand & van Zijl PRD36(1987)2019

23. Peter SkandsEvent Generator Status 23 The ‘New’ Model ►Sjöstrand and PS (2005): ‘Interleaved’ evolution of event structure, all ordered in p T Sjöstrand & PS : NPB659(2003)243; JHEP03(2004)053; EPJC39(2005)129 multiparton PDFs derived from sum rules Beam remnants Baryon Junctions 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”? (incomplete) Pythia 6.4: available via PYTUNE (6.408+) Pythia 8: default

24. Peter SkandsEvent Generator Status 24 Underlying Event and Colour ►Not much was known about the colour correlations, so some “theoretically sensible” default values were 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 But needed ~ 100% correlation. So far not explained Virtually all ‘tunes’ now used by the Tevatron and LHC experiments employ these more ‘extreme’ correlations Tune A is now also the default in PYTHIA M. Heinz, nucl-ex/0606020; nucl-ex/0607033

25. Peter SkandsEvent Generator Status 25 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 Baryons Strangeness Neutral/Charged

26. Peter SkandsEvent Generator Status 26 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 D. B. Leinweber, hep-lat/0004025

27. Peter SkandsEvent Generator Status 27 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 D. Wicke (DØ) + PS, hep-ph/0703081 (Available via PYTUNE)

28. Peter SkandsEvent Generator Status 28 Preliminary Conclusions ►Delta(m top ) ~ 1 GeV from parton shower ►Delta(m top ) ~ 0.5 GeV from infrared effects Pole mass does have infrared sensitivity. Can we figure out some different observable which is more stable? Infrared physics ~ universal?  use complimentary samples to constrain it. Already used a few min-bias distributions, but more could be included Note: early days. May be under- or overestimated. Models are crude, mostly useful for reconnaissance D. Wicke (DØ) + PS, hep-ph/0703081

29. Peter SkandsEvent Generator Status 29Conclusion ►Still far from a complete description of hadron collisions We are really looking at just the first few terms in large expansions. Non-perturbative physics not well understood

30. Peter SkandsEvent Generator Status 30 Words of Warning ►Still far from a complete description of hadron collisions We are really looking at just the first few terms in large expansions. Non-perturbative physics not well understood J. D. Bjorken from a talk given at the 75th anniversary celebration of the Max-Planck Institute of Physics, Munich, Germany, December 10th, 1992. As quoted in: Beam Line, Winter 1992, Vol. 22, No. 4 […] The Monte Carlo simulation has become the major means of visualization of not only detector performance but also of physics phenomena. So far so good. But it often happens that the physics simulations provided by the Monte Carlo generators carry the authority of data itself. They look like data and feel like data, and if one is not careful they are accepted as if they were data. […] They do allow one to look at, indeed visualize, the problems in new ways. But I also fear a kind of “terminal illness”, perhaps traceable to the influence of television at an early age. There the way one learns is simply to passively stare into a screen and wait for the truth to be delivered. A number of physicists nowadays seem to do just this.