Pythia Mini-Tutorial 2 Advanced Topics

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					Carleton U, May 2007

            Pythia Mini-Tutorial 2
             Advanced Topics
                                     Peter Skands

             Fermilab / Particle Physics Division / Theoretical Physics

             Sjöstrand, PS : NPB659(2003)243, JHEP03(2004)053, EPJC39(2005)129
  ► Matching
          • When needed?
          • MLM, CKKW, MC@NLO, and all that

  ► The Underlying Event
          • Models
               •   The „Old‟ PYTHIA model (e.g. Tune A): impact parameter dependence
               •   The „Intermediate‟ PYTHIA model: fancy beam remnants
               •   The „New‟ PYTHIA model: interleaved evolution
               •   Not an expert on HERWIG/JIMMY, but I can still tell you as much as I know
               •   What is still not there?
          • Tuning
          • Early constraints from LHC

  ► The Event Generator Outlook
          • The move to C++

Peter Skands                                 Event Generator Status                            2
Fixed Order Matrix Elements and Parton Shower Resummations
                                 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 (PS)?
               • Misses relevant terms for hard jets, rates only correct for strongly
                 ordered emissions pT1 >> pT2 >> pT3 ...
               • (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 (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

Peter Skands                             Event Generator Status                               4
                          Double Counting
  ► Combine different multiplicites  inclusive sample?

  ► In practice – Combine
                                                            X inclusive             X exclusive
          1. [X]ME + showering
          2. [X + 1 jet]ME + showering
                                                            X+1 inclusive
                                                            X+2 inclusive   ≠       X+1 exclusive
                                                                                    X+2 inclusive
          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

Peter Skands                                  Event Generator Status                                5
                                                                                  ME: Matrix Element
                                          Matching                                PS: Parton Shower

      ► Matching of up to one hard additional jet, for specific processes
               • PYTHIA-style (reweight shower: MEX+jet = w*PS)
               • HERWIG-style (add separate X+jet events: w = MEX+jet-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 (Frixione, Nason, Oleari)
               •   CKKW-style at NLO + “Quantum Monte Carlo” (Nagy, Soper)            Evolution
               •   SCET approach (based on SCET – Bauer, Tackmann; Alwall, Mrenna, Schwarz)
               •   VINCIA (based on QCD antennae – Giele, Kosower, PS)

Peter Skands                                     Event Generator Status                                6
                                   MC@NLO      Frixione, Nason, Webber, JHEP 0206(2002)029 and 0308(2003)007

                                                                                     JHEP 0411(2004)040
                                                                                    Generate 1st shower
                                                                                    emission separately 
                                                                                    easier matching
                                                                                     JHEP 0608(2006)077
                                                                                    Avoid negative weights
  ► MC@NLO in comparison                                                            + explicit study of ZZ
          •    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

Peter Skands                               Event Generator Status                                            7
                   SHERPA and ARIADNE                                                                L. L¨onnblad,
                                                                                                     JHEP05 (2002) 046
                                                      S. Catani, F. Krauss, R. Kuhn, B.R. Webber, JHEP 0111 (2001) 063

               ► The CKKW algorithm
                   •    Slices phase space – two regions:
                        •   uses matrix elements to describe the distribution of particles with a
                            phase-space separation pT > pTcut
                        •   uses parton showers to describe particles with a smaller separation
                   1.   [W]ME |pT>pTcut * Wveto(pTcut) + showeringpT<pTcut
                   2.   [W + j]ME|pT>pTcut * Wveto(pTcut) + showeringpT<pTcut
                   3.   …

               •   Where Wveto < 1 is there to get rid of the double counting
               •   Wveto is : the probability that no parton shower emission happened
                   above pTcut (this is called the Sudakov factor, the no-emission probability)
                   •    SHERPA uses an approximate analytical formula
                   •    Lönnblad‟s ARIADNE-style is to run a „trial‟ or „pseudo‟ shower, vetoing those
                        events which branch above pTcut

               ►   This gets rid of double counting since those events that would have
                   caused it are precisely those which do branch above pTcut

Peter Skands                                    Event Generator Status                                             8
      Matched Mix of W+0,1,2,3,4 jets
  ► Matching can also be done with PYTHIA, HERWIG, but so far not
    automated                             S. Mrenna, P. Richardson, JHEP0405 (2004) 040

Peter Skands                         Event Generator Status                               9
  ► “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  njets
          •    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

Peter Skands                               Event Generator Status                      10
     New Approaches – Why Bother?
                           •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
                           very 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 

Peter Skands
                      more, see
                For Generator Status theory seminar tomorrow
                Event                                                    11
The Underlying Event
  Towards a complete picture of hadron collisions
      Additional Sources of Particle Production
               ► 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 pT
               ►  multiple perturbative parton-parton collisions should occur

                                   e.g. 44, 3 3, 32
               ► 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?

Peter Skands                                  Event Generator Status                                 13
        Classic Example: Number of tracks
      UA5 @ 540 GeV, single pp, charged multiplicity in minimum-bias events

                Simple physics                                    More Physics:
               models ~ Poisson                                        Multiple
                Can ‘tune’ to get                                   interactions +
                average right, but                                impact-parameter
                 much too small                                      dependence
                                              Morale (will return to the models later):
                 inadequate
                physics model        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
Peter Skands                             Event Generator Status                           14
        Multiple Interactions  Balancing Minijets

  ► Look for additional balancing
    jet pairs “under” the hard                          angle between 2 „best-balancing‟ pairs


  ► Several studies performed,
    most recently by Rick Field at
    CDF  „lumpiness‟ in the
    underlying event.

   (Run I)

                                                                              CDF, PRD 56 (1997) 3811

Peter Skands                        Event Generator Status                                              15
                                    Basic Physics
  ► Sjöstrand and van Zijl (1987):
          •    First serious model for the underlying
          •    Based on resummation of perturbative
               QCD 22 scatterings at successively
               smaller scales  multiple parton-
               parton interactions
          •    Dependence on impact parameter
               crucial to explain Nch distributions.
                 •   Peripheral collisions  little matter overlap             UA5
                     few interactions. Central collisions  many
                 •   Nch Poissonian for each impact parameter                   Nch
                     convolution with impact parameter profile 
                     wider than Poissonian!
                                                                               540 GeV
          •    Colour correlations also essential
                 •   Determine between which partons
                     hadronizing strings form (each string 
                     log(mstring) hadrons)
                 •   Important ambiguity: what determines how
                     strings form between the different

Peter Skands                                          Event Generator Status             16
       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.
                                                                     M. Heinz (STAR), nucl-ex/0606020; nucl-ex/0607033
          •    (The same is seen at RHIC:)
          •    For „Tune A‟ etc, Rick noted
               that <pT> increased when he
               increased the colour correlation                                                  STAR
               parameters                                                                     pp @ 200GeV
          •    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 tomorrow…)
Peter Skands                                Event Generator Status                                                       17
               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

Peter Skands                                  Event Generator Status                                  18
                       The „New‟ Model
                                               NB: Tune A still default since more thoroughly tested.
  ► Sjöstrand and PS (2005):                   To use new models, see e.g. PYTUNE (Pythia6.408+)

          • „Interleaved‟ evolution of multiple interactions and parton showers

 Fixed order
 matrix elements

 parton shower
 (matched to ME
 for W/Z/H/G + jet)

 PDFs derived
 from sum rules


 Beam remnants
 Fermi motion /
 primordial kT

                        Sjöstrand & PS : JHEP03(2004)053, EPJC39(2005)129

Peter Skands                             Event Generator Status                                         19
                                     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 Nch and <pT>(Nch)
                 Tevatron Run II min-bias                   Field’s       ► Improved Description
                                                            Tunes &         of Min-Bias
                                                          new models
                                                                          ► Effect Still largely
                                                                  No CR   ► Worthwhile to look at
                                                                            top etc
                   PYTHIA 6.408                      PYTHIA 6.408

Peter Skands                                 Event Generator Status                                   20
          (Beam Remnants and Multiple Interactions)

Peter Skands               Event Generator Status     21
The Generator Outlook
      The C++ Monte Carlos
                             C++ Players
               ► HERWIG++: complete reimplementation
                   •   Improved parton shower and decay algorithms
                   •   Eventually to include CKKW-style matching (?)
                   •   B.R. Webber; S. Gieseke, D. Grellscheid, A. Ribon, P. Richardson, M.
                       Seymour, P. Stephens, . . .

               ► SHERPA: complete implementation, has CKKW
                   •   ME generator + wrappers to / adaptations of PYTHIA, HERWIG parton
                       showers, underlying event, hadronization
                   •   F. Krauss; T. Fischer, T. Gleisberg, S. Hoeche, T. Laubrich, A.
                       Schaelicke, S. Schumann, C. Semmling, J. Winter

               ► PYTHIA8: selective reimplementation
                   •   Improved parton shower and underlying event, limited number of hard
                   •   Many obsolete features not carried over  simpler, less parameters
                   •   T. Sjöstrand, S. Mrenna, P. Skands
               ► (+ various more specialized packages)

Peter Skands                            Event Generator Status                              23
                   PYTHIA 8

               Basic generator already there
               Includes a few processes (+ full Pythia6 library), new pT-
               ordered showers, new UE, Les Houches interfaces, and

               You are invited to try it out
               Click /future/ on the Pythia homepage, download pythia8080.tgz,
               follow instructions in readme (./configure, ./make, and have fun)
               Still not advised for production runs
               If you have suggestions, now is the time!

               Spring 2007: QED showers, LHAPDF, interleaved FSR, beam
               remnants, colour reconnections  useful
               Fall-Winter 2007: resonance decays, GUI, official release?

Peter Skands                Event Generator Status                                 24
                   The Generator Outlook
  ► Generators in state of continuous development:

  ► Better & more user-friendly general-purpose matrix element

  ► 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)

Peter Skands                                   Event Generator Status     25