Rivet
1.8.0
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Calculate the sphericity event shape. More...
#include <Sphericity.hh>
Public Member Functions | |
void | clear () |
Reset the projection. | |
Constructors etc. | |
Sphericity (const FinalState &fsp, double rparam=2.0) | |
Constructor. | |
virtual const Projection * | clone () const |
Clone on the heap. | |
Access the event shapes by name | |
double | sphericity () const |
double | transSphericity () const |
Transverse Sphericity. | |
double | planarity () const |
Planarity. | |
double | aplanarity () const |
Aplanarity. | |
Access the sphericity basis vectors | |
Sphericity axis | |
const Vector3 & | sphericityAxis () const |
const Vector3 & | sphericityMajorAxis () const |
Sphericity major axis. | |
const Vector3 & | sphericityMinorAxis () const |
Sphericity minor axis. | |
const Vector3 & | axis1 () const |
AxesDefinition axis accessors. | |
const Vector3 & | axis2 () const |
The 2nd most significant ("major") axis. | |
const Vector3 & | axis3 () const |
The least significant ("minor") axis. | |
Access the momentum tensor eigenvalues | |
double | lambda1 () const |
double | lambda2 () const |
double | lambda3 () const |
Direct methods | |
Ways to do the calculation directly, 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) |
Manually calculate the sphericity, without engaging the caching system. | |
Protected Member Functions | |
void | project (const Event &e) |
Perform the projection on the Event. | |
int | compare (const Projection &p) const |
Compare with other projections. |
Calculate the sphericity event shape.
The sphericity tensor (or quadratic momentum tensor) is defined as
, 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 , with
, the sphericity is
The aplanarity is and the planarity is
. 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 to the definition:
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
values without fear of a clash.