Dipole Showering

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Dipole Showering

• Scattering, Approximations Reordering
• Singular behavior of PQCD
• Sudakov factor Evolution Variables
• Numerical Dipole Branching
• Outlook

W. Giele D. Kosower, Fermilab, 10/30/04
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Scattering, Approximations Reordering

• Suppose we know partons ME
• And we know approximations with

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Scattering, Approximations Reordering

• Suppose we know
• with

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Scattering, Approximations Reordering

• Suppose we know
• with the subtracted matrix element

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Singular behavior of PQCD

• We take for the approximation function the
  soft/collinear (unresolved) approximation.
• As an immediate consequence
• The subtracted ME is subleading in logs
• The Shower resums the leading logs
• From NLO calculations we know this approximation
  function (subtraction/slicing/)

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Singular behavior of PQCD

• An explicit subtraction function for an ordered
  amplitude is
• The behavior of the ordered amplitude is

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Sudakov factor Evolution variable

• The event is evolved in cluster resolution
• The event Sudakov is defined as the
  probability of not resolving an additional
  cluster when reducing the resolution to
• At NLO the event Sudakov is a product of ordered
  dipole Sudakov factors
• By reducing the resolution a new cluster will be
  resolved in one of the dipoles

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Sudakov factor Evolution variable

• The dipole Sudakov is given by
• Pick according to Sudakov probability
• Pick according to
• Constructwith
• The resummed log is
• is only fixed at singular boundary

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Numerical Dipole Branching

• The subtraction function is
  implemented numerical. This gives control over
  hard radiation
• The Evolution function is
  implemented numerical.
• LO/NLO(/NNLO) matrix elements can be inserted
  without any modification. Also no so-called
  matching is needed
• Higher order corrections to the Sudakov factor is
  straightforward to implement.
• Massless partons at each stage of shower

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Outlook

• Construction of VIRCOL shower monte carlo
• gluons shower MC (based on LO)
• gluons shower MC (based on NLO)
• partons shower MC (LO/NLO(/NNLO))
• hadrons shower MC (LO/NLO(/NNLO))
• Hadron collider shower MCs
• Higher order Sudakov factor calculations(this
  will reduce a lot of implicit and explicit
  uncertainties e.g. renormalization scale, choice
  of subtraction function,)

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Outlook

• include "header.cc
• int main()
• int Nevent1000
• // Generate 1000 events
• Event P
• // Define the event class with no constraints on
  hard scattering parton content
• Shower Spartonic
• // Define the shower object using all default
  settings
• for (int i0iltNeventi)
• double wgtP.Generate()
• //Generate an event based on all available hard
  scattering matrix elements.
• Event finalSpartonic(P) // The results are
  stored in event structure final
• coutltlt"Event number "ltltiltltendl coutltlt"Number
  of particles "ltltfinal.Nparticles()ltltendl coutltlt
  "Event weight "ltltwgtltltendl coutltltParticle
  content"ltltendl final.print() coutltlt"---------
  --------------------------------------------------
  --"ltltendlltltendlltltendl  // Write shower event
  information