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// -*- C++ -*-
#ifndef RIVET_ParisiTensor_HH
#define RIVET_ParisiTensor_HH
#include "Rivet/Projection.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/Sphericity.hh"
#include "Rivet/Event.hh"
namespace Rivet {
/**
@brief Calculate the Parisi event shape tensor (or linear momentum tensor).
The Parisi event shape C and D variables are derived from the eigenvalues of
the linear momentum tensor
\f[
\theta^{\alpha \beta} =
\frac{\sum_i \frac{p_i^\alpha p_i^\beta}{|\mathbf{p}_i|}}
{\sum_i |\mathbf{p}_i|}
\f]
which is actually a linearized (and hence infra-red safe) version of the
{@link Sphericity} tensor.
Defining the three eigenvalues of \f$\theta\f$
\f$ \lambda_1 \ge \lambda_2 \ge \lambda_3 \f$, with \f$ \lambda_1 + \lambda_2 + \lambda_3 = 1 \f$,
the C and D parameters are defined as
\f[
C = 3(\lambda_1\lambda_2 + \lambda_1\lambda_3 + \lambda_2\lambda_3)
\f]
and
\f[
D = 27 \lambda_1\lambda_2\lambda_3
\f]
Internally, this Projection uses the Sphericity projection with the generalising
\f$r\f$ parameter set to 1.
*/
class ParisiTensor : public Projection {
public:
/// Constructor. The provided FinalState projection must live throughout the run.
ParisiTensor(const FinalState& fsp)
{
setName("ParisiTensor");
addProjection(fsp, "FS");
addProjection(Sphericity(fsp, 1.0), "Sphericity");
clear();
}
/// Clone on the heap.
virtual const Projection* clone() const {
return new ParisiTensor(*this);
}
protected:
/// Perform the projection on the Event.
void project(const Event& e);
/// Compare with other projections.
int compare(const Projection& p) const;
public:
/// Clear the projection.
void clear();
public:
/// @name Access the C and D params.
///@{
double C() const { return _C; }
double D() const { return _D; }
///@}
/// @name Access the eigenvalues of \f$\theta\f$.
///@{
double lambda1() const { return _lambda[0]; }
double lambda2() const { return _lambda[1]; }
double lambda3() const { return _lambda[2]; }
///@}
private:
/// The Parisi event shape variables.
double _C, _D;
/// Eigenvalues.
double _lambda[3];
};
}
#endif
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