Notes on alignment in NA64

This page describes tracking and alignment concepts and utils for NA64. First, a brief overview of the track reconstruction in NA64SW is given, followed by instructive description of alignment procedure. Details on the conventions are given at the end of the page.

NA64SW tracking in general

In NA64SW the setup geometry is described by placements document that is an ASCII file of certain columnar format with metadata (SDC).

Todo

Example of placements document content here.

This document defines positions and spatial orientation of detector entities – a kind of information typically used by tracking and Monte-Carlo code to define setup geometry.

Track reconstruction procedures use placements to derive track’s scores 1, based on information of raw hits (e.g. placements document + raw hits = scores). Scores bring information only relevant to tracking, like its type (1D, 2D, 3D), time, position and expected error estimation.

1

More common term would be a track point or measurement, but we prefer to call it a score to avoid confusion with 2D/3D spatial points and raw hits.

Track fitting procedure operates with a set of scores to reconstruct the track by fitting parameters of track’s physical model to the measured values provided by scores. Resulting fit is always a tradeoff because of internal detector imperfections, stochastic nature of the measurement and, what is most important for us, due to mistakes in placements. The latter is the subject of alignment procedure described further which purpose is to mitigate or even eliminate systematics introduced by survey uncertainties (typically .25-1mm).

Conventions

Below are some conventions settled for the placements and geometrical descriptions in the setup.

Coordinate frames

We operate in right-hand coordinate frame with Z axis directed towards the beam, X directed horizontally and Y vertically. For NA64 at H4/NA58 beamlines X is directed from Saleve to Jura.

(drawings here)

An emblmatic drawing showing global axes orientation, direction of rotation angles and “canonical” orientation of detectors by their kin.

In case of local, detector-based coordinate frames (DRS), the order of axes is X'Y'Z'. For each projection od the detector there is also a wire reference system (WRS) with axes UVW where U is always matching the first projection axis in DRS.

Work in WRS is important for hit-to-track score conversion and the alignment procedure and generally should not bother users much.

DRS is important for detector experts, to build efficiency maps and so on.

System of Units

NA64sw inherits its system of units from GenFit2 where following units are taken:

  • Length: cm

  • Induction: kGauss

  • Energy: GeV

Angles

In placements document for every detector entity (like GM01X, S1, ECAL0 etc) up to three angles can be defined as Tait-Bryan angles for extrinsic CW-rotation in order “ZYX”, corresponding to:

  1. Around Z – wire inclination wrt lab’s horizon (roll)

  2. Around Y – plane’s horizontal tilt defining difference between leftmost and rightmost wires

  3. Around X – plane’s vertical tilt defining difference between upper and lower wire with respect to the beam outlet. This angle is usually named “pitch” in Tait-Bryan convention, though we recommend to avoid this name since it can be misleadingly interpreted as effective stride of the wires, as it is seen by the beam).

Extrinsic “ZYX” rotation is known to be equivalent to “XY’Z’” intrinsic rotations.

So far in the alignment we only deal with the rotation around Z as the impact of the rest is relatively negligible and hard to correct.

Rationale comes from typical precision relations defined by technical reasons. First, tracking is mostly sensitive to roll (Z) angle and usually seen on the residuals distribution with the best absolute precision. Then comes Y rotation as for fixed-target experiment geometry planes are positioned perpendicular to undeflected beam direction that creates subtle distortions in tracking after beam is deflected in vertical magnetic field (in horizontal plane). Up/down differences are less probable and Y-deflection is used more rare, so rotation around X must be of least priority.