/usr/include/Rivet/Projections/Sphericity.hh is in librivet-dev 1.8.3-1.1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 | // -*- C++ -*-
#ifndef RIVET_Sphericity_HH
#define RIVET_Sphericity_HH
#include "Rivet/Projection.hh"
#include "Rivet/Projections/AxesDefinition.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Event.hh"
namespace Rivet {
/**
@brief Calculate the sphericity event shape.
The sphericity tensor (or quadratic momentum tensor) is defined as
\f[
S^{\alpha \beta} = \frac{\sum_i p_i^\alpha p_i^\beta}{\sum_i |\mathbf{p}_i|^2}
\f],
where the Greek indices are spatial components and the Latin indices are used
for sums over particles. From this, the sphericity, aplanarity and planarity can be
calculated by combinations of eigenvalues.
Defining the three eigenvalues
\f$ \lambda_1 \ge \lambda_2 \ge \lambda_3 \f$, with \f$ \lambda_1 + \lambda_2 + \lambda_3 = 1 \f$,
the sphericity is
\f[
S = \frac{3}{2} (\lambda_2 + \lambda_3)
\f]
The aplanarity is \f$ A = \frac{3}{2}\lambda_3 \f$ and the planarity
is \f$ P = \frac{2}{3}(S-2A) = \lambda_2 - \lambda_3 \f$. The eigenvectors define a
set of spatial axes comparable with the thrust axes, but more sensitive to
high momentum particles due to the quadratic sensitivity of the tensor to
the particle momenta.
Since the sphericity is quadratic in the particle momenta, it is not an
infrared safe observable in perturbative QCD. This can be fixed by adding
a regularizing power of \f$r\f$ to the definition:
\f[
S^{\alpha \beta} =
\frac{\sum_i |\mathbf{p}_i|^{r-2} p_i^\alpha p_i^\beta}
{\sum_i |\mathbf{p}_i|^r}
\f]
\f$r\f$ is available as a constructor argument on this class and will be
taken into account by the Cmp<Projection> operation, so a single analysis
can use several sphericity projections with different \f$r\f$ values without
fear of a clash.
*/
class Sphericity : public AxesDefinition {
public:
/// @name Constructors etc.
//@{
/// Constructor
Sphericity(double rparam=2.0): _regparam(rparam){}
Sphericity(const FinalState& fsp, double rparam=2.0);
/// Clone on the heap.
virtual const Projection* clone() const {
return new Sphericity(*this);
}
//@}
protected:
/// Perform the projection on the Event
void project(const Event& e);
/// Compare with other projections
int compare(const Projection& p) const;
public:
/// Reset the projection
void clear();
/// @name Access the event shapes by name
/// @{
/// Sphericity
double sphericity() const { return 3.0 / 2.0 * (lambda2() + lambda3()); }
/// Transverse Sphericity
double transSphericity() const { return 2.0 * lambda2() / ( lambda1() + lambda2() ); }
/// Planarity
double planarity() const { return 2 * (sphericity() - 2 * aplanarity()) / 3.0; }
/// Aplanarity
double aplanarity() const { return 3 / 2.0 * lambda3(); }
/// @}
/// @name Access the sphericity basis vectors
/// @{
/// Sphericity axis
const Vector3& sphericityAxis() const { return _sphAxes[0]; }
/// Sphericity major axis
const Vector3& sphericityMajorAxis() const { return _sphAxes[1]; }
/// Sphericity minor axis
const Vector3& sphericityMinorAxis() const { return _sphAxes[2]; }
/// @}
///@{ AxesDefinition axis accessors.
const Vector3& axis1() const { return sphericityAxis(); }
const Vector3& axis2() const { return sphericityMajorAxis(); }
const Vector3& axis3() const { return sphericityMinorAxis(); }
///@}
/// @name Access the momentum tensor eigenvalues
/// @{
double lambda1() const { return _lambdas[0]; }
double lambda2() const { return _lambdas[1]; }
double lambda3() const { return _lambdas[2]; }
/// @}
/// @name Direct methods
/// Ways to do the calculation directly, without engaging the caching system
//@{
/// Manually calculate the sphericity, without engaging the caching system
void calc(const FinalState& fs);
/// Manually calculate the sphericity, without engaging the caching system
void calc(const vector<Particle>& fsparticles);
/// Manually calculate the sphericity, without engaging the caching system
void calc(const vector<FourMomentum>& fsmomenta);
/// Manually calculate the sphericity, without engaging the caching system
void calc(const vector<Vector3>& fsmomenta);
//@}
private:
/// Eigenvalues.
vector<double> _lambdas;
/// Sphericity axes.
vector<Vector3> _sphAxes;
/// Regularizing parameter, used to force infra-red safety.
const double _regparam;
private:
/// Actually do the calculation
void _calcSphericity(const vector<Vector3>& fsmomenta);
};
}
#endif
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