Definition

The coordinate system used for defining the parametrization of tracks is Cartesian and right-handed with its origin located at the interaction point. The z axis is given by the detector z axis and the y axis lies along the vertical direction, pointing upwards.

Whenever a charged particle is affected by a constant magnetic field it moves on a helicoidal trajectory, where here and in the following both energy loss and multiple scattering are neglected. It is assumed that this magnetic field is homogeneous and parallel to the z axis. In this case the trajectory of a charged particle is a segment of a circle in the xy projection and the z displacement is a linear function of the length s of the arc that is described in the xy plane. This results in a straight line in the sz plane.

The parametrisation of the movement of a charged particle is defined by a reference point, Pr = (Prx, Pry, Prz ), and five so-called "track parameters" (Ω,Φ0,d0, z0 and tan λ). In general the reference point can be any point in space but usually it is set to the origin of the coordinate system. The five track parameters refer to a specific point P0 = (P0x ; P0y ; P0z ) along the helix, here P0 is defined as the point of closest approach (p.c.a.) to the reference point in the xy plane.

  • Projection of a track helix segment in the xy plane:
    LCIOTrackDefinitionXY.png

  • Projection of a track helix in the sz plane:
    LCIOTrackDefinitionZS.png

Simulation and Reconstruction

Results for SuperBelle and SuperBelle Upgrade

-- AndreasMoll - 20 Mar 2009

Topic attachments
I Attachment History Action Size Date Who Comment
PNGpng LCIOTrackDefinitionXY.png r1 manage 17.6 K 2009-03-20 - 10:15 AndreasMoll Projection of a track helix segment in the xy plane
PNGpng LCIOTrackDefinitionZS.png r1 manage 12.3 K 2009-03-20 - 10:16 AndreasMoll Projection of a track helix in the sz plane
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Topic revision: r1 - 2009-03-20 - AndreasMoll
 
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