Spherocity.hh

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// -*- C++ -*-
#ifndef RIVET_Spherocity_HH
#define RIVET_Spherocity_HH

#include "Rivet/Projection.hh"
#include "Rivet/Projections/AxesDefinition.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Event.hh"

namespace Rivet {


  /// @brief Get the transverse spherocity scalars for hadron-colliders.
  ///
  /// @author Holger Schulz
  ///
  /// The scalar (minimum) transverse spherocity is defined as
  /// \f[
  /// S = \frac{\pi^2}{4} \mathrm{min}_{\vec{n}_\perp} \left( \frac{\sum_i \left|\vec{p}_{\perp,i} \times \vec{n}_\perp \right|}{\sum_i |\vec{p}_{\perp,i}|} \right)^2
  /// \f],
  /// with the direction of the unit vector \f$ \vec{n_\perp} \f$ which minimises \f$ T \f$
  /// being identified as the spherocity axis. The unit vector which maximises the spherocity
  /// scalar in the plane perpendicular to \f$ \vec{n} \f$ is the "spherocity major"
  /// direction, and the vector perpendicular to both the spherocity and spherocity major directions
  /// is the spherocity minor. Both the major and minor directions have associated spherocity
  /// scalars.
  ///
  /// Care must be taken in the case of Drell-Yan processes - there we should use the
  /// newly proposed observable \f$ a_T \f$.
  class Spherocity : public AxesDefinition {
  public:

    // Default Constructor
    Spherocity() {}

    /// Constructor.
    Spherocity(const FinalState& fsp)
      : _calculatedSpherocity(false)
    {
      setName("Spherocity");
      addProjection(fsp, "FS");
    }

    /// Clone on the heap.
    virtual const Projection* clone() const {
      return new Spherocity(*this);
    }


  protected:

    /// Perform the projection on the Event
    void project(const Event& e) {
      const vector<Particle> ps
        = applyProjection<FinalState>(e, "FS").particles();
      calc(ps);
    }


    /// Compare projections
    int compare(const Projection& p) const {
      return mkNamedPCmp(p, "FS");
    }


  public:

    /// @name Spherocity scalar accessors
    //@{
    /// The spherocity scalar, \f$ S \f$, (minimum spherocity).
    double spherocity() const { return _spherocities[0]; }
    //@}


    /// @name Spherocity axis accessors
    //@{
    /// The spherocity axis.
    const Vector3& spherocityAxis() const { return _spherocityAxes[0]; }
    /// The spherocity major axis (axis of max spherocity perpendicular to spherocity axis).
    const Vector3& spherocityMajorAxis() const { return _spherocityAxes[1]; }
    /// The spherocity minor axis (axis perpendicular to spherocity and spherocity major).
    const Vector3& spherocityMinorAxis() const { return _spherocityAxes[2]; }
    //@}


    /// @name AxesDefinition axis accessors.
    //@{
    const Vector3& axis1() const { return spherocityAxis(); }
    const Vector3& axis2() const { return spherocityMajorAxis(); }
    const Vector3& axis3() const { return spherocityMinorAxis(); }
    ///@}


  public:

    /// @name Direct methods
    /// Ways to do the calculation directly, without engaging the caching system
    //@{

    /// Manually calculate the spherocity, without engaging the caching system
    void calc(const FinalState& fs);

    /// Manually calculate the spherocity, without engaging the caching system
    void calc(const vector<Particle>& fsparticles);

    /// Manually calculate the spherocity, without engaging the caching system
    void calc(const vector<FourMomentum>& fsmomenta);

    /// Manually calculate the spherocity, without engaging the caching system
    void calc(const vector<Vector3>& threeMomenta);

    //@}


  private:

    /// The spherocity scalars.
    vector<double> _spherocities;

    /// The spherocity axes.
    vector<Vector3> _spherocityAxes;

    /// Caching flag to avoid costly recalculations.
    bool _calculatedSpherocity;


  private:

    /// Explicitly calculate the spherocity values.
    void _calcSpherocity(const vector<Vector3>& fsmomenta);

  };

}

#endif