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Dipole Showering

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. Scattering, Approximations & Reordering. Suppose we know partons ME:

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Dipole Showering

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  1. 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

  2. Scattering, Approximations & Reordering Suppose we know partons ME: And we know approximations: with

  3. Scattering, Approximations & Reordering Suppose we know with

  4. Scattering, Approximations & Reordering Suppose we know with the subtracted matrix element

  5. 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/…)

  6. Singular behavior of PQCD • An explicit subtraction function for an ordered amplitude is: • The behavior of the ordered amplitude is

  7. 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

  8. 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

  9. 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

  10. 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 MC’s • Higher order Sudakov factor calculations(this will reduce a lot of implicit and explicit uncertainties: e.g. renormalization scale, choice of subtraction function,…)

  11. Outlook #include "header.cc“ int main() { int Nevent=1000; // 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 i=0;i<Nevent;i++); { double wgt=P.Generate(); //Generate an event based on all available hard scattering matrix elements. Event final=Spartonic(P); // The results are stored in event structure final cout<<"Event number: "<<i<<endl; cout<<"Number of particles: "<<final.Nparticles()<<endl; cout<<"Event weight: "<<wgt<<endl; cout<<Particle content:"<<endl; final.print(); cout<<"-------------------------------------------------------------"<<endl<<endl<<endl;  // Write shower event information } };

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