1

Some notes on the Track and Vertex Reconstruction

29 L29.pdfP627 YK3/30/2012

• Track reconstruction is needed for determination of the momentum of particle moving in magnetic field

• For reconstruction of primary and secondary vertices• For errors estimation on these quantities

Following O. Steinkamp lecture

Tracking models:

no magnetic field, no material straight line homogeneous field, no material helix inhomogeneous field + material

(energy loss, multiple scattering) iterative numericalextrapolation of track segments over short distances

Conceptual main steps:

1. Pattern recognition (track finding): hits track candidate2. Track fit: parameters + covariance matrix3. Check track quality (e.g. 2 of fit, remove “ghost” tracks) 4. at each point along the trajectory describe track by

5-component state vector and its 5 x 5 covariance matrix.

5. vertex reconstruction

, , , ,dx dy q

x ydz dz p

æ ö÷ç ÷ç ÷÷çè ø

2

A hard track finding problem. 100 tracks in a cylindrical tracking detector with13 layers. The tracks and the position measurements (hits) are shown in theprojection transverse to the magnetic field. In this projection the track model isa circle. Bottom: Only the hits are shown. (from Are Strandlie and Rudolf Frühwirth,

Track and Vertex Reconstruction: From Classical to Adaptive Methods)

3

Good algorithms are important (Kalman filter)

4A hard vertex finding problem. Top: The primary vertex with  10 tracks, and a secondary vertex with four tracks at a  distance of 1 cm from the primary vertex (MC). Bottom:  All tracks extrapolated into the beam tube. BT=beam tube, L1=Layer 1, etc.

Distinguishing vertices is an essential tool in the collider physics.

5

0 12

012 14

0

e.g. meson lifetime is =1.5 10 ;1.5 10 3 10 / 457

If particle is moving with velocity andwith -factor, then the distance between primary and secondary vertices:

B sct s m s m

L c

tm m

bg

g b t

-

-⋅

= ⋅ ´ ⋅ »

= ⋅ ⋅

6

Energy measurement by total absorption.Calorimetry

Literature:

PDG chapter 28 “Particle Detectors” Book: Claus Grupen “Particle Detectors” , Cambridge Uni. Press 1996, Ed. 1999, ISBN 0 521 55216 8 Book: Richard Wigmans “Calorimetry”, Oxford 2000,ISBN 0 19 850296 6Book: “Experimental Techniques in High-Energy Nuclear and Particle Physics”, edited by T. Ferbel, World Scientific, second edition 1991, ISBN 981-02-0868-5

Many different detectors can be built where measured signal is proportional to primary energy E

Counting secondary particles

Primary particle with energy E

Electron-ionpairs

Light

Cherenkovradiation

Phonons

Interaction with matter

H

e

a

tMatter

7

0 50 100 150 200 250 300 350 400

Wavelength (nm)

0.1

1

10

100

Ele

ctro

ns p

er in

cide

nt p

hoto

n

IRD Si diode AXUV100G

NIST Calibration

IRD Calibration

Generic sensitivity

Si-diode of InternationalRadiation Detectors (IRD) for detection of UV photons in wavelengthrange 5-400 nm

Example: Detection of UV photons

http://www.ird-inc.com/

8

Good resolution is a goal

Comment:resolutionsmearing is in principlerecoverableby unfolding procedure

0 2p g

2h g

9

Semiconductor detectors = calorimeters usually used for photons and

low-energy heavy-ionizing particles

Energy required to produce electron-hole pair in Si (Ge) is 3.6 (2.8) eV.Compare e.g. with NaI(Tl): 25 eV/photon x light collection efficiency xdetector non-uniformity x QE of photon detection 300 – 1000 eV/p.e.

e.g. P, As are electron donors;Li is electron donor

e.g. trivalent B, In introduce holes

Ionizing particles produce electron-hole carriers+ excite lattice vibrations (phonons)

Lecture on Wednesday next week April 4 by Prof. Bill Bugg on semiconductor detectors

10

typical d ~ 300 m; E ~ 1000 V/cm; charge carrier mobility ~ 1000 cm2/Vs and charge collection time:

nssE

dt 30103 8

typical d ~ 170 mfor HV ~ 100 V

d(i) up to 5 mm can be produced

Cooled Ge(Li) detectors.

Large size detectors:pure Ge crystals

(e.g. Majorana expt.)

e.g. m

11

Absorption range in 5 mm Si for different particles

Modern pixel detector ~ 20 x 20 m2,CCD ~ 105 pixels for 1 x 1 cm2

12

Heat measurement. Bolometer

( )

( )19

9

E.g. at normal conditions, absorbed dose of 1 gray (100 rad)

1J kg 1 eV 1.6 10 J in water

[it corresponds e.g. to full absorption of ~ 10 particles

with energy 6.25 MeV in

E T temperature

a

-

D D

= = ´

4p

1 g of matter] results in a temperature

rise of 2.39 10 C. (C 75.29 J/K/mol)

-´ =

pC

QT

The heat capacity of dielectric materials and crystals at low temperaturesis proportional to T3. Detection of single particle in small mass detectors coupled to thermistor is possible when T<1K.

Background, due to statistical fluctuation of temperature (due to the randomvariation in the flow of phonons across the thermal coupling between the absorber and the surrounding media). RMS of these fluctuations is T5.

Ultimate theoretical energy resolution (set by thermodynamics considerations)can be down to few eV or less. Typical detector is a crystalline or semiconductor material with volume ~ 1 mm3 hold in the thermostat by low thermal-heat suspension. E.g. resolution measured with cryogen Si detector has FWHM of 7.3 eV ~ 20 times better than this obtained with Si(Li) detector for X-rays.

Response time is determined by the speed of phonon (sound) propagationand typically is in the range of 100 s.

Cryogenic technique:

77K – liquid N2

4K – boiling liquid He<4K – 3He/4He mixture (dilution refrigerators)