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Monte Carlo tools for the LHC

Monte Carlo tools for the LHC. Michelangelo Mangano TH Division, CERN Nov 6, 2002. Final states at the LHC. Goal of MC development for the LHC is to provide a description as accurate as possible of these events (and more), as well as of the features of new physics processes:

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Monte Carlo tools for the LHC

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  1. Monte Carlo tools for the LHC Michelangelo Mangano TH Division, CERN Nov 6, 2002

  2. Final states at the LHC Goal of MC development for the LHC is to provide a description as accurate as possible of these events (and more), as well as of the features of new physics processes: rates, distributions, fine details of the final states (overall multiplicities, heavy-quark content)

  3. Use and abuse of MC simulation • Use: • benchmarks for the design of detectors, trigger and analysis strategies • tests and measurements of SM • study of properties of new particles (masses, cross-sections, couplings) • Abuse: claims of discoveries! • top and SUSY discovery in UA1 • Rb at LEP • quark compositeness at CDF • Only the benchmarking against real data can turn MC simulation into powerful study tools

  4. Example: Hbb in qq Hqq • bbjj bg is ≈102 times the signal, but can be extracted from data (smooth behaviour under the signal peak) • bg from multiple collisions (jjb  jjb) ≈ signal, but peak under the signal! Much more sensitive to MC simulation uncertainties! MLM, Moretti, Piccinini, Pittau, Polosa

  5. F f(x,Qi) Factorization Theorem • transition from partonic final state to the hadronic observable (hadronization, fragm. function, jet definition, etc) • Sum over all histories with X in them • sum over all initial state histories leading, at the scale Q, to:

  6. The possible histories of initial and final state, and their relative probabilities, are in principle independent of the hard process (they only depend on the flavours of partons involved and on the scales Q) • Once an algorithm is developed to describe IS and FS evolution, it can be applied to partonic IS and FS arising from the calculation of an arbitrary hard process • Depending on the extent to which different possible FS and IS histories affect the value of the observable X, different realizations of the factorization theorem can be used

  7. `Cross-section evaluators’ • Only some component of the final state is singled out for the measurement, all the rest being ignored (i.e. integrated over). E.g. ppe+e- + X • No ‘events’ are ‘generated’, only cross-sections are evaluated: • Experimental selection criteria (e.g. jet definition or acceptance) are applied on parton-level quantities. Provided these are infrared/collinear finite, it therefore doesn’t matter what F(X) is, as we assume (fact. theorem) that: • Thanks to the inclusiveness of the result, it is `straightforward’ to include higher-order corrections, as well as to resum classes of dominant and subdominant logs

  8. State of the art • NLO available for: • jet and heavy quarks production • prompt photon production • gauge boson pairs • most new physics processes (e.g. SUSY) • NNLO available for: • W/Z/DY production • Higgs production

  9. Parton-level (akamatrix-element) MC’s • Parton level configurations (i.e. sets of quarks and gluons) are generated, with probability proportional to the respective perturbative M.E. • Transition function between a final-state parton and the observed object (jet, missing energy, lepton, etc) is unity • No need to expand f(x) or F(X) in terms of histories, since they all lead to the same observable • Experimentally, equivalent to assuming • `smart’ jet clustering (parton  jet) • linear detector response

  10. Codes available for: • W/Z/gamma + N jets (N6) • W/Z/gamma + Q Qbar + N jets (N4) • Q Qbar + N jets (N4) • Q Qbar Q’ Q’bar + N jets (N2) • Q Qbar H + N jets (N3) • nW + mZ + kH + N jets (n+m+k+N 8, N2) • N jets (N5)

  11. Shower Monte Carlo • After the generation of a given parton-level configuration (typically LO, 21 or 22) , each possible IS and FS parton-level history (`shower’) is generated, with probability defined by the shower algorithm (unitary evolution). • `Algorithm’: numerical, Markov-like evolution, implementing within a given appoximation scheme the QCD dynamics: • branching probabilities • infrared cutoff scheme • hadronization model • Herwig, Pythia, Isajet

  12. ME MC’s X-sect evaluators Shower MC’s Final state description Hard partons  jets. Describes geometry, correlations, etc Limited access to final state structure Full information available at the hadron level Higher order effects: loop corrections Hard to implement, require introduction of negative probabilities Straighforward to implement, when available Included as vertex corrections (Sudakov FF’s) Higher order effects: hard emissions Included, up to high orders (multijets) Straighforward to implement, when available Approximate, incomplete phase space at large angle Resummation of large logs ?? Possible, when available Unitary implementation (i.e. correct shapes, but not total rates) w=-∞ w=-∞ dw=-∞ dw=-∞ Complementarity of the 3 approaches

  13. q’ q q’ q Q2 = (q’- q)2 = - t q’ q 2’ guide to shower MC’s • Evaluate parton-level probability, from Feynman rules + phase space. E.g.: • As a result of acceleration, q’ will emit radiation • The probability that radiation will (or will not) be emitted is evaluated as a function of the acceleration of the colour charges:

  14. Generate  1  If 1 < P(Q , Q0)  no radiation, q’ goes directly on-shell at scale Q0≈GeV Else calculate Q1 / P(Q1,Q0)= 1 emission at scale Q1 Go back to 1) and reiterate, until shower stops in 2). At each step the probability of emission gets smaller and smaller Q1= relative momentum Sudakov prob. of no radiation between Q and Q0 1 2 1 P Q Q0 Q2 Q1

  15. 2 + 2 2 + Problems (1): Quantum coherence 

  16. 1 2 2  C1 2 C2 2 no emission outside C1 C2: • lack of hard, large-angle emission • poor description of multijet events incoherent emission inside C1 C2: • loss of accuracy for intrajet radiation Solution (a.k.a. angular ordering) (1 = + (2 Drawbacks:

  17.   p    N       p     N    Hadronization At the end of the perturbative evolution, the final state consists of quarks and gluons, forming, as a result of angular-ordering, low-mass clusters of colour-singlet pairs:

  18. Example: Wbb+jets

  19. Issues to be addressed for the evaluation of multiparton matrix elements • Complexity of multiparton amplitudes For example, for ggnj gluons: • Evaluation of probabilities for configurations with given colour flows

  20. Colour-flow decomposition The angular ordering prescription can be extended to cases with higher parton multiplicity. To enforce it, we need to be able to associate probabilities to colour-flow configurations. String theory taught us how to do it: m(p1,p2,…,pn) =

  21. 1. A multiparton amplitude can be obtained from: where and (x)is a classical field, solution of: 2. In the case of tree-level scattering, J(x) is a trivial source: and the solutions for (x) must be of the simple form: 3. E.g. for a 3 theory, we have: where 4. Minimization w.r.t. blgives: only the truncation of Z[J] multilinear in ai is required finite iterative solution of the above quadratic system!! 5. Since The ALPHA algorithm for the computation of multi-parton processes (Caravaglios, M.Moretti)

  22. Alpha, continue • No need to explicitly evaluate Feynman graphs • Technique extended to QCD: allows calculations of both dual and full amplitudes • Numerical complexity O(an) with a~2-3, instead of n! • Achieved calculation of processes with up to 10 final-state gluons -- over 5x109 Feynman diagrams (Maltoni et al) • Complete evaluation of multijet processes requires inclusion of quarks  extra complexity, due to all possible flavour combinations. Enumeration of independent amplitudes vs number of jets. Asymptotic estimates related to partition function of 0-dim field theories. (Kleiss&Draggiotis)

  23. q q g q g Problems (2): Q2 choice for evolution The choice is almost unambiguous for final states with 1 or 2 partons: q  Ex: Z, W Q2 = s Ex: Q2 pT2  – t  the factorization theorem is easily implemented, due to the existence of a single scale

  24. If pT1 << pT2 << … << pTn , or (pi+pj)2 varying significantly for different (i,j) • Ambiguous implementation of the factorization theorem • Potential problem of double counting: q q q g1 g2 q g2 g2 with pT1 << pT4 << pT2,pT3 g4 (from shower evolution) g1 (from shower evolution) q q gn versus g4 (from matrix element) g1 (from matrix element) g3 g3 The choice is more difficult in more complex cases

  25. p4 p1 is of s relative to the LO process unless: p3 p2 p2 p4 p1 which gives a contribution to 3-jet of order p3 p3 p1 p2 Double counting is sub-leading provided R and are not too large Leading vs subleading double countingExample: corrections to 3-parton final states

  26. Example -- W+3 jet events

  27. Bottom line: • Implementation of quantum coherence in shower MC’s is possible, in the limit of large-Nc and for soft and collinear emission. • Large-angle, hard emission cannot be described accurately • Possible cure requires starting the shower with “seed” multi-parton configurations, evaluated using exact (possibly tree-level only) matrix elements. • Potential problems, however, due to double counting for extra jet emission

  28. x1=2E1/MZ ≤ x x2≤2 x2=1 gq1 1 I1 I2 x2 x1=1 gq2 x2=2E2/MZ 1 0 x1 Progress towards solutions (I) matrix element corrections • Algorithm: (M.Seymour) • generate events in I2 with (finite!) probability: Ex: Z03 jets and distributions given by I1: ph.space covered by angular-ordered emission • Use (qqg) matrix element to correct MC weights in I1 • Drawback: • requires analytic representation of the phase-space domain generated by the angular-ordering prescription I2: ph.space NOT covered by angular-ordered emission

  29. From the sample of 3-hard-parton events (splitting rejected if y45<ycut ) 1 4 From the sample of 4-hard-parton events 3 1 5 3 y34 > ycut 4 2 2 : Sudakov correction Progress towards solutions (II) vetoed showers(Catani, Krauss, Kuhn, Webber) • Generate samples of different jet multiplicities according to exact tree-level ME’s, with Njet defined using a kperp algorithm • Reweight the matrix elements by vertex Sudakov form factors, assuming jet clustering sequence defines the colour flow • Remove double counting by vetoing shower histories (i.e. yijsequences already generated by the matrix elements) • Fully successfull for e+e-collisions, being extended to hadronic collisions

  30. Parton Level generators at NLO • KLN  negative-wgt events • Formalism for extension to NNLO • Implementation of NNLO • Implementaiton of resummation corrections to X-sections • Formalism for inclusion of NLO • Applications to WW and QQ • Formalism for extraction of colour flows • Common standards for event coding • Implementaiton of resummation corrections to X-sections • NLO accuracy in shower evolution • Inclusion of power corrections • Implementation of double-counting removal in hadronic collisions available in progress M(ontecarlo) o(f) E(verything) Matrix Element MC’s Cross-Section Evaluators Shower MC’s • Better treatment of radiation off heavy quarks • Full treatment of spin correlations in production and decay • Better description of underlying event • Better decay tables • …………..

  31. Urgent items, nobody working on them to my knowledge: • Parton-level NNLO MC for W and Z: • matrix elements available, simplest and most useful system where to test NNLO formalism • should allow O(1%) accuracy in determination of cross-section  best possible luminometer at the LHC: • NLL description of `jet shapes’, and inclusion of power corrections (see LEP) • formalism established and tested with great success at LEP, where it provides an essential tool for the high-accuracy determination of s • essential to extend the formalism to hadronic collisions, to exploit the lever arm in Q in the measurement of s

  32. Power corrections • Classes of non-perturbative effects linked to the dominant power-like (1/Q) corrections can be parametrised in terms of a single quantity, formally given by: Their effect is expected to be very large even at the Tevatron, and in general for LHC events with jets in the few-hundred GeV energy range. • In the case of 1st moments of shape variables, for example: F=FPT + Fnon-PT Fnon-PT=cF P, with and P=P0 [0()-0( S)]  /S • The impact of these effects at LEP is very large, and their understanding is essential for any quantitative QCD study

  33. Final remarks • A lot of progress has taken place in the recent years, but • 30 yrs after QCD, still a lot of work to be done to achieve a satisfactory description of all high-Q2 processes accessible at LHC • most of the key conceptual difficulties have been recently, or are being, solved, and their implementation into concrete MC schemes should be achievable in the next 5 years • forthcoming data from Tevatron will help improving our tools, but the final test will need real LHC data • there is plenty of room for creative and rewarding work for young phenomenologists! • Workshop on MCs for the LHC, July 7 - Aug 2 2003, at CERN

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