Track reconstruction

Inferring a particle trajectory from recorded detector positions or a continuous trail. The inferred trajectory depends on spatial resolution, detector geometry and the assumed particle-motion model; it is not a direct picture of the particle itself.

A particle track is a reconstructed trajectory inferred from spatially separated detector measurements associated with a particle. Individual hits are observations; fitting a track combines them with a propagation model, measurement errors and possible scattering.

In a uniform magnetic field, a charged particle follows a helical trajectory in the ideal limit. Its transverse momentum is $p_{\perp }=|q|BR$, where $R$ is the projected curvature radius in SI units. Curvature therefore constrains momentum, while its direction constrains the charge sign. Neutral particles generally require indirect reconstruction through secondary charged particles or other interaction signatures rather than an ordinary continuous charged-particle track.

A particle track projected onto the plane perpendicular to a uniform magnetic field $B$ is a circular arc with radius $R=p_{\perp }/(|q|B)$. Here $p_{\perp }$ is the momentum component perpendicular to the magnetic field; it is the collider transverse momentum when the field follows the beam axis. For chord length $L$ and sagitta $s$, circle geometry givesFor a short arc with $s\ll L$, this yieldsThe measurement uncertainty follows by differentiating the inverse relation, treating $B$ and $L$ as known. A fixed spatial measurement uncertainty therefore makes fractional momentum uncertainty grow with momentum, whereas increasing the lever arm improves it quadratically in this idealization. Multiple Coulomb scattering, field uncertainties and alignment add other contributions; a helical particle track also requires its pitch to recover the full momentum.^[ref]