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Exclusive Fashion Trends for Spring 2008

CERN October 2007. Exclusive Fashion Trends for Spring 2008. Peter Skands CERN & Fermilab. Overview. Calculating collider observables Fixed order perturbation theory and beyond From inclusive to exclusive descriptions of the final state Uncertainties and ambiguities beyond fixed order

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Exclusive Fashion Trends for Spring 2008

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  1. CERN October 2007 Exclusive FashionTrends for Spring 2008 Peter Skands CERN & Fermilab

  2. Overview • Calculating collider observables • Fixed order perturbation theory and beyond • From inclusive to exclusive descriptions of the final state • Uncertainties and ambiguities beyond fixed order • The ingredients of a leading log parton shower • A brief history of matching • New creations: Fall 2007 • Designer showers, an example • Exploring showers with antennae • Some comments on matching at tree and 1-loop level • Trends for Spring 2008? Exclusive Fashion - Trends for Spring 2008 - 2

  3. Principal virtues Stochastic error O(N-1/2) independent of dimension Full (perturbative) quantum treatment at each order KLN theorem: finite answer at each (complete) order Inclusive Fashion “Experimental” distribution of observable O in production of X: Fixed Order (all orders) {p} : momenta k : legs ℓ : loops “Monte Carlo”: N. Metropolis, first Monte Carlo calcultion on ENIAC (1948), basic idea goes back to Enrico Fermi High-dimensional problem (phase space) d≥5  Monte Carlo integration Note 1: For k larger than a few, need to be quite clever in phase space sampling Note 2: For ℓ > 0, need to be careful in arranging for real-virtual cancellations Exclusive Fashion - Trends for Spring 2008 - 3

  4. Exclusive Fashion High-dimensional problem (phase space) d≥5  Monte Carlo integration + Formulation of fragmentation as a “Markov Chain”: A. A. Markov: Izvestiia Fiz.-Matem. Obsch. Kazan Univ., (2nd Ser.), 15(94):135 (1906) • Hadronization: • iteration of X  X’ + hadron, according to phenomenological models (based on known properties of QCD, on lattice, and on fits to data). • Parton Showers: • iterative application of perturbatively calculable splitting kernels for n  n+1 partons Exclusive Fashion - Trends for Spring 2008 - 4

  5. Traditional Generators • Generator philosophy: • Improve Born-level perturbation theory, by including the ‘most significant’ corrections  complete events • Parton Showers • Hadronisation • The Underlying Event • Soft/Collinear Logarithms • Power Corrections • Higher Twist roughly (+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) Asking for fully exclusive events is asking for quite a lot … Exclusive Fashion - Trends for Spring 2008 - 5

  6. Be wary of oracles • We are really only operating at the first few orders (fixed + logs + twists + powers) of a full quantum expansion PYTHIA Manual, Sjöstrand et al, JHEP 05(2006)026 Be even more wary if you are not told to be wary! Exclusive Fashion - Trends for Spring 2008 - 6

  7. Collider Energy Scales Hadron Decays Non-perturbative hadronisation, rearrangement de couleurs, restes de faisceau, fonctions de fragmentation non-perturbative, pion/proton, kaon/pion, ... Soft Jets and Jet Structure émissions molles/collineaires (brems), événement sous-jacent (interactions multiples perturbatives 22 + … ?), brems jets semi-durs Exclusive & Widths Resonance Masses… Hard Jet Tail haut-pT jets à grande angle Inclusive s • + Un-Physical Scales: • QF , QR : Factorization(s) & Renormalization(s) Exclusive Fashion - Trends for Spring 2008 - 7

  8. Beyond Fixed Order e+e- 3 jets Problem 1: bremsstrahlung corrections are singular for soft/collinear configurations  spoils fixed-order truncation Exclusive Fashion - Trends for Spring 2008 - 8

  9. Beyond Fixed Order Fixed Order (all orders) • Evolution Operator, S (as a function of “time” t=1/Q) • “Evolves” phase space point: X  … • Can include entire (interleaved) evolution, here focus on showers • Observable is evaluated on final configuration • S unitary (as long as you never throw away an event) •  normalization of total (inclusive)σ unchanged • Only shapes are affected (i.e., also σ after shape-dependent cuts) wX : |MX|2 S : Evolution operator {p} : momenta Pure Shower (all orders) Exclusive Fashion - Trends for Spring 2008 - 9

  10. Perturbative Evolution “X + nothing” “X+something” wX : |MX|2 S : Evolution operator {p} : momenta Pure Shower (all orders) • Evolution Operator, S (as a function of “time” t=1/Q) • Defined in terms of Δ(t1,t2) – The integrated probability the system does not change state between t1 and t2(Sudakov) A: splitting function Analogous to nuclear decay: Exclusive Fashion - Trends for Spring 2008 - 10

  11. Constructing LL Showers • 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) • They are all “unphysical”, in the same sense as QFactorizaton, etc. • At strict LL, any choice is equally good • However, 20 years of parton showers have taught us: many NLL effects can be (approximately) absorbed by judicious choices • Effectively, precision is much better than strict LL, but still not formally NLL • E.g., story of “angular ordering”, using pT as scale in αs, …  Clever choices good for process-independent things, but what about the process-dependent bits? … + matching Exclusive Fashion - Trends for Spring 2008 - 11

  12. 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: Exclusive Fashion - Trends for Spring 2008 - 12

  13. 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 generalization of MC@NLO • VINCIA For more details  PhenClub.Thursday, 11 am, 1-1-025: 01 Nov : Sjöstrand, Richardson, PS: Modern Showers (Pythia8 (+ Vincia?), Herwig++) Exclusive Fashion - Trends for Spring 2008 - 13

  14. 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 Exclusive Fashion - Trends for Spring 2008 - 14

  15. 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 Exclusive Fashion - Trends for Spring 2008 - 15

  16. Example: Z decays • Dependence on evolution variable Giele, Kosower, PS : hep-ph/0707.3652 Exclusive Fashion - Trends for Spring 2008 - 16

  17. Example: Z decays • VINCIA and PYTHIA8 (using identical settings to the max extent possible) αs(pT), pThad = 0.5 GeV αs(mZ) = 0.137 Nf = 2 Note: the default Vincia antenna functions reproduce the Z3 parton matrix element; Pythia8 includes matching to Z3 Beyond the 3rd parton, Pythia’s radiation function is slightly larger, and its kinematics and hadronization cutoff contour are also slightly different Exclusive Fashion - Trends for Spring 2008 - 17

  18. 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 Exclusive Fashion - Trends for Spring 2008 - 18

  19. 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 Exclusive Fashion - Trends for Spring 2008 - 19

  20. 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 Exclusive Fashion - Trends for Spring 2008 - 20

  21. 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 Exclusive Fashion - Trends for Spring 2008 - 21

  22. Phase Space Population Positive correction Negative correction Exclusive Fashion - Trends for Spring 2008 - 22

  23. 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 Exclusive Fashion - Trends for Spring 2008 - 23

  24. 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 Exclusive Fashion - Trends for Spring 2008 - 24

  25. 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 Exclusive Fashion - Trends for Spring 2008 - 25

  26. What happened? • Brand new code, so bear in mind the green guy • Naïve conclusion: tree-level matching “better” than NLO? • No, first remember that the shapes we look at are not “NLO” • E.g., 1-T appears at O(α) below 1-T=2/3, and at O(α2) above • An “NLO” thrust calculation would have to include at least 1-loop corrections to Z3 • (The same is true for a lot of other distributions) • So: both calculations are LO/LL from the point of view of 1-T • What is the difference then? • Tree-level Z3 is the same (LO) • The O(α) corrections to Z3, however, are different • The first non-trivial corrections to the shape! • So there should be a large residual uncertainty  the 1-loop matching is “honest” • The real question: why did the tree-level matching not tell us? • I haven’t completely understood it yet … but speculate it’s to do with detailed balance • In tree-level matching, unitarity  Virtual = - Real  cancellations. Broken at 1 loop • + everything was normalized to unity, but tree-level  different norms Exclusive Fashion - Trends for Spring 2008 - 26

  27. 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 Exclusive Fashion - Trends for Spring 2008 - 27

  28. Summary: Trends for 2008 • Designer showers • Does matching get easier? • Can matching be extended deeper into the perturbative series ? • A practical demonstration combining 1-loop and multi-leg matching ? • A practical demonstration of 1-loop matching beyond first order ? • Unexplored territory beyond first few orders, leading NC, (N)LL • Generators in 2008: theorists are learning C++ • Enter PYTHIA-8 (SHERPA & HERWIG++ already there) • What more is needed for high precision at LHC ? • Need improvements beyond showers: e.g., higher twist / UE / … ? • Is hadronization systematically improvable? • + even the most super-duper Monte Carlo is useless without constraints on its remaining uncertainties! (“validation”) Exclusive Fashion - Trends for Spring 2008 - 28

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