DataAnalysisTech11-ch10, Study notes of Advanced Data Analysis

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第第第 第第  (^) 第第第第第第第第  (^) 第第第第第第第第第第第第第第第  (^) 第第第第第第第第第第第第第第第第第第第第  (^) 第第第第第第第第第第第第第第第  (^) 第第第第第第第第第第第第 第第第 第第第第第第第第第第第第第第  (^) 第第第第第第第第第第第第  (^) 第第第第第第第第第第第第第第第第 第第第 第第第第第第第第  (^) 第第第第第第第第第第第第第第第第第第第第第  (^) 第第第第第第第第第第第第  (^) 第第第第第第第第第第第第第第第第 第第第 第第第第  (^) 第第第第第第第第第第第第第第第第第第第第  (^) 第第第第第第第第第第第第第  (^) 第第第第第第第第第第第第第第第第第第第 第第第 第第第第第第第第第第第第第第第第第  (^) 第第第第第第第第第第第  (^) 第第第第第第第第第第第第第第第第第 第第第 第第第第第第第第第  (^) 第第第第第第第第第第第第

BelleBelle 第第第第第第第第第第第第第第第第第第第第

 Extracted as

5 th^ order

polynomial

function or

linear

function

depending

on the time

regions

T

X

Drift distance X:

determined from track fitting

drift TDC_ Raw 0 T  T  t

第第第第第第第第第 第第第第第第第第第 (( X-TX-T ))

Time zero (Time zero ( tt (^00) **) for one layer (Step) for one layer (Step

1. 1)**  (^) Larger TDC value → earlier signal  (^) Drift time:  (^) One initial t 0 for each layer drift TDC_ Raw 0 T  T  t

Step 2:Step 2: tt 00 fine calibration for wirefine calibration for wire Δd Δd L Δd R left-right residuals 0 0 2 new old d^ R dL t t v     

v : drift velocity

several iterations

calibrated for each wire

Δ d L Δ d R Δ d L Δ d R

Time of Flight effectTime of Flight effect

correction :

: path length

velocity

flight

s

t

c

s

v c

Propagation delay effectPropagation delay effect

correction : : propagation length : stereo angle : propagation velocity, ~3.6ns/m cos prop prop prop D t v D v     g

 (^) Correction: y x Rz 2 y  az  bz  c

 (^) residual ↔ resolution depends on  (^) Primary ion (pair statistics)  (^) Diffusion (of the electron along the drift path)  (^) Distortion of the electric field around the field wire (non uniform)  (^) Electric noise  (^) Spatial resolution determination affects: error matrix (then, efficiency) for track fitting. It is very important for Monte Carlo simulation and data analysis

 Mechanical position

 Measuring the initial positions before

the commissioning of the detectors

 Using the control sample data for the

alignment

 Drift chamber case:

 (^) Using the collision data and/or cosmic ray data to achieve more precise wire position  (^) Measurement can be different for the case of with or without magnetic field  (^) Drift distance is affected by the Lorentz force.

Inner chamber (×2) Middle chamber ×6 (×2) Outer chamber (×2) In total 2+6x2+2= independent units 6 parameters for each units 3 displacements : Dx, Dy, Dz 3 rotations : Rx, Ry, Rz In total 96 alignment parameters Simpler version : Dx, Dy, Rz In total 48 alignment parameters y y Rz

Using outer chamber as reference

to align other chambers