Tracking in High Energy Physics

Tracking in High Energy Physics XIX Heidelberg Physics Graduate Days 2007 Carsten Niebuhr (DESY, Hamburg) Guillaume Leibenguth (IPP, ETH Zürich)

Motivation Verehrte An- und Abwesende! Wenn Ihr den Rundfunk höret, so denkt auch daran, wie die Menschen in den Besitz dieses wunderbaren Werkzeuges der Mitteilung gekommen sind. Der Urquell aller technischen Errungenschaften ist die göttliche Neugier und der Spieltrieb des bastelnden und grübelnden Forschers und nicht minder die konstruktive Phantasie des technischen Erfinders...... Sollen sich auch alle schämen, die gedankenlos sich der Wunder der Wissenschaft und Technik bedienen und nicht mehr davon geistig erfasst haben als die Kuh von der Botanik der Pflanzen, die sie mit Wohlbehagen frisst A. Einstein zur Eröffnung der 7. Großen Deutschen Funkausstellung 1930 http://www.staff.uni-marburg.de/~naeser/einstein.htm 2

Outline of Lecture Monday - introduction - interaction of charged particles with matter Wednesday - examples for gas detectors at the LHC energy loss by ionization multiple scattering Tuesday - momentum measurement in magnetic field Thursday & Friday - solid state detectors: Guillaume Leibenguth - principles of gas detectors gas amplification gas properties 3

Introduction Cosmic Ray Background Radiation: T = 2.72 K, nγ = 4x10 8 m -3 4

Literature Text books: K.Kleinknecht: Teubner, 1992 W.R. Leo: Springer 1994 G.F.Knoll: Wiley, 3rd edition Detektoren für Teilchenstrahlung Techniques for Nuclear and Particle Physics Experiments Radiation Detection and Measurement C.Grupen: Teilchendetektoren BI Wissenschaftsverlag 1993 W.Blum, L.Rolandi: Springer, 1994 Review articles: T.Ferbel: Addison-Wesley 1987 Particle Detection with Driftchambers Experimental Techniques in High Energy Physics Other sources: Particle Data Group: Review of Particle Physics Eur. Phys. J. C15, 1-878 (2000) R.K.Bock, A.Vasilescu: The Particle Detector BriefBook Springer, 1998 and //physics.web.cern.ch/physics/particledetector/briefbook/ 5 Please note: Most of the figures in this lecture are taken from these sources or from publicly available talks on the web, without making explicit reference to them in each case.

What are the Objects? and many more... 6

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Detection of Particles and Radiation!"#$%&'($&)$#*+#,-.#/0'($+',0-1(#$+"23-134$.#'35,#.#/0$&) - +',0-1(#$+,&+#,0-#3 -,#'10-&/$+,&6'6-(-0-#3$7!$1,&33$3#10-&/38!"-3$,#95-,#3$:#0#,.-/'0-&/$&)4 - +',0-1(#$02+#$7.'33;$1"',%#;$3+-/$#018 -.&.#/05.$<$#/#,%2$&)$+',0-1(# - #.-33-&/$'/%(#3 =(#.#/03$1&/0,-650-/%$0&$351"$.#'35,#.#/03$4 +&3-0-&/$3#/3-0->#$:#0#10&,3$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!$+&3-0-&/;$:-,#10-&/ :#)(#10-&/$-/$.'%/#0-1$)-#(:$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!$ p 1'(&,-.#0,24$0&0'($#/#,%2$'63&,+0-&/$'/:$.#'35,#.#/0$$$$$$$$$$$$$$$$$$! = 0&0.'33$:#0#,.-/'0-&/$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!$.$?"#,#/@&>$,':-'0-&/$&,$0-.#$&)$)(-%"0$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$! # 0,'/3-0-&/$,':-'0-&/$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!$" 8

Examples for Major Discoveries I!"#$%&%'&()*#+()#,-)&.'/%#,01*.'*!"2"#34-56/%*#+()#5-7()#8.*'(9%).%*##### 5-8%#6(**.:/%#:1#8%&%'&()#6)(;)%** $.*'(9%)1#(+#6(*.&)(<#:1#="><8%)*(<?@(:%/#6).A%#2BCDE# http://prola.aps.org/abstract/pr/v43/i6/p491_1 =/(F8#=0-5:%)?="G"H./*(< @(:%/# 6).A%#2B!IE Discovery photo Transparency taken from R. Klanner Uni HH >8.-:-&.'#%46-<*.(<#! *-&F)-&%8#9-6(F) =0-);%8#6-)&.'/%*#!.(<.*-&.(<#! '(<8%<*-&.(<#(+#8)(6/%&* 9 J.(<.*-&.(<#! %/%5%<&-)1#'0-);% J 'F)9-&F)%#.<#5-;"+.%/8! *.;<#(+## '0-);%#K#5%-*F)%#5(5%<&F5 J %<%);1#/(**#.<#D55#,:?K#'0-);%#-<8# 5(5%<&F5E#! 5-**#L#!M#4#5 %! %4'/F8%#6)(&(<#?!MMM#4#5 % E

Examples for Major Discoveries II!"#$%&'()*%+*!" #,-*./0*12345! 67,(89%:'; :'9%<#-(,-':* http://prola.aps.org/abstract/prl/v12/i8/p204_1.7==;'*>?,9='( 1!@A;,#'( B /%=';* C("D'*EFGH5*I :%9"<,-':*'JC'("9'<-,;* C,(-"$;'*C?)#"$#*7<-";*-?'*'"K?-"'#L!"#$%&'()*! B =)**,*#"<K;'*'&'<-*LLL Transparency taken from R. Klanner Uni HH 0"M7":*N7#-*=';%O*&,C%7(*C('##7('*I,+-'(*C,##,K'*%+*C,(-"$;'*1P'&'<-Q5*+,#-* 1E9#5*'JC,<#"%<*! 'J$'':*&,C%7(*C('##@ 10 7<,9="K%7#R 6SBET3SBUT 9SEGVG!EWX'Y

Examples for Major Discoveries III!"#$%&'()*%+*",-'(.'/"0-'*&'$-%(* 1%#%,#*2 3 45 6 4*789*0,/*78:*0-*;<=>* ",*0,-"?@*@*",-'(0$-"%,# A9BCD*>%1'E*@("F' ;G=H11"04*IG&G/GJ''(K ;<=>*IQ;*0$$'E'? (0-%(! $%EE"/'( pp L*/'&'E%@.',-*%+*E0(M'*&%EH.'*M0#'%H#** /'-'$-%(*N"-O*P8!;*('0/?%H-! via missing p T Transparency taken from R. Klanner Uni HH e Z 0! e + e - e -%*#-%('*#H++"$"',-*0,-"?@*N"-O*#.0EE* @O0#'*#@0$'! #-%$O0#-"$*1'0.*$%%E",M* e 11

Detector Requirements for Different Accelerators $%&'()%*%+,-.#/012-(3-4#! /05)5*%,%)-#67#%8%+,#-6')3%#9533%:%)5,6);4 Accelerator date physics HERA (DESY) 1992-2007 structure proton, strong+electroweak i.a. beyond standard model LHC (CERN) 2007 -???? high energy reach Higgs, top, BSM, SUSY strong+electroweak i.a. Transparency taken from R. Klanner Uni HH ILC (Linear Collider) 2015 (?) -???? precision reach Higgs, top, BSM, SUSY unification of forces max. E[GeV] particles 27.5 e + /e -! 920 p 7000 p! 7000 p 500 e +! 500 e - "e!"#!!# length 2 x 6.3 km "$# 2 x 27 km "$# < (2 x 15 km) currents 110 ma! 55 ma 540 ma! 540 ma 10 ma! 10 ma bunch crossing 96 ns 25 ns ~ 300 ns luminosity 5x10 31 cm -2 s -1 10 34 cm -2 s -1 2-5x10 34 cm -2 s -1 event rate ~ 10 khz 1 GHz ~ 1 khz radiation dose < 5x10 12 n(equ.)/cm 2 10 15 n(equ.)/cm 2 10 12 n/cm 2 (excl.forward) %p@100gev/c 20 % 1.6 % 0.5 % %p&$'@100gev/c 10 % 1.6 % 0.5 % %E(e)@100GeV 1 2 % 0.6 % 1 2 % %E(had)@100GeV 4 6 % 5 10 % 3 % %position@vertex 20 $m 20 $m 5 $m trigger reduction 10 3 3x10 6 < 100 1.April 1 2005 Chapter 12 1: R.Klanner 8

Criteria for an ideal Detector A#1'53#$-/$%#/#,'($0"#,#$1'/$6#$>#,2$1&.+(#*$#>#/0$0&+&(&%-#3$&/#$&)0#/$'-.3$'0,#1&/30,510-&/$&)$)5(($#>#/0$@-/#.'0-13$76'1@%,&5/:$,#B#10-&/8 C&30$-.+&,0'/04 "-%"$#))-1-#/12 "-%"$,#3&(50-&/ "-%"$'11#+0'/1#$!$0,2$0&$1&>#,$)5(($3&(-:$'/%(#$7D!8 '(3&$>#,2$-.+&,0'/0$7+',0(2$1&/)(-10-/%$:#.'/:384 +',0-1(#$-:#/0-)-1'0-&/$1'+'6-(-02 )'30$,#3+&/3# "-%"$,'0#$1'+'6-(-02 3.'(($:#':$0-.# "#,.#0-1-02 (&/%#>-02$&)$:#0#10&,$1&.+&/#/03 "-%"$,#(-'6-(-02 %&&:$'11#33-6-(-02$7)&,$,#+'-,38 (&E$1&30 13

Important Parameters characterizing Detectors!"#$%&'%() *%)%()+&,"-./(."(011+)"2%"(03/2&0)%*"/4",$%'%()35 64%3%447" 8*%)%()+&9"! 8&%0*+6)9"! 8(03/2&0)/+19! 8010354/49! 033.0:%")+"2%"61*%&4)++*";" <%1%&/("*%)%()+&= &0*/0)/+1>"""""/1)%&0()/+1 4/?103"""""""""(+33%()""%3@4/?103 %3@4/?103 *0)0" $0&)/(3% %1%&?5"*%$+4/) 3/?.)>(.0&?%"""""(.0&?%"'+&A0)/+1""""""$&+(%44/1?""""&%(+&*/1? (03/2&0)/+1""""""010354/4 Transparency taken from R. Klanner Uni HH B''/(/%1(5= 5 0((%$)01(%= 8&%(+&*%*"%:%1)49>8%A/))%*"25"4+6&(%9="C?%+A%)&5"D"%''/(/%1(5E 5 %''/(/%1(5>4%14/)/:/)5="8&%(+&*%*"%:%1)4>$0&)/(3%4"$044/1?"*%)%()+&9 5 $%0F"%''/(/%1(5="8&%(+&*%*"%:%1)4"/1"0((@-/1*+->$0&)/(3%4"$044/1?"*%)%()+&E G%4$+14%"8&%4+36)/+19= 84$%()&6A"'&+A"A+1+H9"" %1%&?%)/("&0*/0)/+19 &%4$+14%")+"IIJ"F%K!4 H <%H*%)%()+& H +&?01/("4(/1)/330)+& 11.April 2005 Chapter 3: R.Klanner 1 14

Response Function of Detector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ln 2! % 2$ 355!! * ). /012 3412?4),@(4+,$%1 & "! % $ % / ( 1), -( 1),! 1 2 - " /K.#"0 L./4),@(4+,$%./$%&+4%+&.0"#"%0.$%.#$&,+,$%K.+,6".'MK#KNKL- ",3./'C-.L.%$%2),%"4(.("&#$%&" 4%4)$9$*&.3$(.#$&,+,$%2K.+,6"2K."+/2 6"4&*("6"%+&, 2 1 + 3(4 2 )&%& 2%5#6 + + 1 15 2,0#)( 1 ((.-. /0+ (,(+-. '(%)*+('(,&) Transparency taken from R. Klanner Uni HH

Example Time Response, -$./0%1"#$+ 1"#$%2$13$$*%(/&1"4.$%(/''/5$%6$7$*18%/*-%'"5*/.%9)&#/1")*, -$/-%1"#$+ #"*"#:#%1"#$%-"'1/*4$%1;/1%$7$*1'%4/*%2$%&$4)&-$-%'$(/&/1$.0% 6-$($*-'%)*%(&)($&1"$'%)9%-$1$41)&%/*-%$.$41&)*"4'%6<"*1$5&/1"*5=%)&%<-$/-=8%/*-% )*%&$').:1")*%4&"1$&"/8, (".$%:(%$99$41'+ )7$&./(("*5%$7$*1'%4/:'$%/%-$5&/-/1")*%)9%($&9)&#/*4$%, 1"#$%&$').:1")*+ /44:&/40%3"1;%3;"4;%<$7$*1,1"#$=%4/*%2$%#$/':&$- Transparency taken from R. Klanner Uni HH >?/#(.$%9)&%4):*1"*5%.)''$'%-:$%1)%-$/-%1"#$+ *@%1&:$%"*1$&/41")*%&/1$ #@%&$4)&-$-%4):*1%&/1$!"@%'0'1$#%-$/-%1"#$! " % 1 $!#! #!! "'%9&/41")*%1"#$%-$1$41)&%<-$/-=%! &/1$%/1%3;"4;%1&:$%$7$*1'%.)'1+%*!#!! A%*,# 69)&%(:.'$-%'):&4$%B *)%$99$41%"9%! C%DE9&$F:$*408 16

Modern Collider Detectors under construction: LHC!"# design phase: ILC in operation: HERA/Tevatron 17

Search for Rare/Forbidden Decays!"#$%&'$()*&(*#%$#+%+)&,(*+)*-+./*012$%%$%*3(4)&).)*5-036*07&)8$%/+(9:;* 4$+%12*<,%*/$#),(=(.'>$%*?&,/+)&(@*#%,1$44;*µ!*$*" 4$(4&)&?&)A*@,+/;*BC =BD *E* ($$94*$"1$//$()*$($%@A*%$4,/.)&,(6*2&@2*$?$()*%+)$6*>.)*4'+//*)%+1F*'./)&#/&1&)A*#$%*$?$() 4)+%)*<.//*9+)+*)+F&(@*&(*GCCH Liq. Xe Scintillation Detector Liq. Xe Scintillation Detector Thin Superconducting Coil Muon Beam? γ Stopping Target γ? e + Timing Counter e + Drift Chamber Drift Chamber 1m 18

ALICE @ LHC I$+?A*3,(*-2A4&14;*)2&4*4&'./+)&,(*42,74*BJBC*,<*+//*BCCCC=GCCCC*$"#$1)$9*)%+1F4*&(*+* )A#&1+/*$?$()K*L2$*4$#+%+)&,(*,<*+//*)2$4$*)%+1F4*#.)4*?$%A*2&@2*9$'+(94*,(*)2$*#,4&)&,(* %$4,/.)&,(*+(9*9,.>/$*2&)*4$#$%+)&,(*,<*)2$*9$?&1$K 19

Real Event in STAR at RHIC 2000 tracks per event 20

Satellite based Detectors >-?'"??)(6,&+=0&+)?"/)@=.=(')ABBC D>@8;)D1##19E13)"2(&/F1'"/3)?"/),-.,)&%&/.3)$,"'"%()-%)',&)/1%.&)ABG&H) '")IJBB)D&H @('/")$1/'-60&)$,3(-6(,-('"/3)"?)('1/)?"/#1'-"% 166&0&/1'-"%)#&6,1%-(#)"?)@DKL( ("=/6&()"?).1##1)/13)2=/('( %1'=/&)"?)+1/7)#1''&/!"#$"%&%'()*%&&+),-.,&(')/&0-12-0-'3)45 $/&6-(-"%)'/167&/)*8-9('/-$(5 610"/-#&'&/)*!(:*;055 +1'1)16<=-(-'-"%)(3('&# 1%'-6"-%6-+&%6&)+&'&6'"/ 21

Applications in Medicine :#1.-%.)#-6/".1$)+&'&6'"/M N,"'"%)/1'&()!)OB P )## 9A )( 9O K:QR8 K"%9-%F1(-F&)Q"/"%1/3)@%.-"./1$,3) =(-%.))(3%6,/"'/"%)/1+-1'-"% 22

Interplay between Physics and Technology @0#"(')100)&??&6'()=(&+)-%)$1/'-60&) +&'&6'"/()1/&)21(&+)"%)',&)&0&6'/"#1.9 %&'-6)-%'&/16'-"%)"%03S)G"(')#"+&/%) +&'&6'"/()6"%F&/')',&)12("/2&+)&%&/.3) -%'")1%)&0&6'/-610)(-.%10S ;,&)+&'&6'-"%)(&%(-'-F-'3)1%+)+&'&6'"/) $&/?"/#1%6&)+&$&%+()"% ('1'-('-610)$/"6&((&()-%)',&)+&'&6'"/?0=6'=1'-"%()-%)',&)&0&6'/"%-6( ;")#1T-#-U&)+&'&6'-"%)(&%(-'-F-'3)1%+)) /&("0='-"%)"%&)#=(')6"%(-+&/)1%+)"$'-#-U& (-.%10)?"/#1'-"%)-%)',&)+&'&6'"/ 6"=$0-%.)"?)',&)+&'&6'"/)'")',&)/&1+"=') &0&6'/"%-6( %"-(&).&%&/1'&+)-%)',&)&0&6'/"%-6( V%+&/('1%+-%.)"?)&S.S)1)#"+&/%)'/167-%.) +&'&6'"/)-%),-.,9&%&/.3)$,3(-6()"/)1) #&+-610)-#1.-%.)(3('&#)',=()/&<=-/&() 7%"W0&+.&)"? ("0-+)('1'&)$,3(-6( (&#-6"%+=6'"/)+&F-6&)$,3(-6( (&#-6"%+=6'"/)?12/-61'-"%)'&6,%"0".3 0"W9%"-(&)&0&6'/"%-6()'&6,%-<=&( 1%10".)1%+)+-.-'10)#-6/"&0&6'/"%-6(,-.,9($&&+)+1'1)'/1%(#-((-"% 6"#$='&/921(&+)+1'1)16<=-(-'-"%) (3('&#( 23

Interaction of Radiation with Matter!,1/.&+)N1/'-60&( K&='/10)N1/'-60&(,&1F3)6,1/.&+)$1/'-60&( %&='/"%( &0&6'/"%(.1##1)/1+-1'-"% %&='/-%"(!"=0"#29:%'&/16'-"%)W-', &0&6'/"%()"?)#&+-=#!)&0&6'/-610)(-.%10)-%)+&'&6'"/) G1-%03)X(-%.=01/Y)-%'&/16'-"%(Z /&(=0'-%.)-%)&%&/.3)'/1%(?&/)'" 6,1/.&+)$1/'-60&( 24

Cross Section of a typical Collider Detector Particle type: neutrinos (missing energy) muons µ absorber (mostly Fe) flux return yoke μ heavy medium (Fe, Cu, U) + active material hadrons: p, π, K... [quarks, gluons jets] electrons, photons charged particles beam pipe vacuum Track detectors for charged particles gas detectors solid state detectors Calorimeter for energy meas. (neutral & charged) electromagnetic high Z (Pb) + magnet coil hadronic active medium (solenoid, field beam axis) 25

Example 1: HERA ep Event with 3 Jets e e transverse view: p Jet 1 Jet 2 Jet 3 hadronic calorimeter electromagn. calorimeter track detector 27.5 GeV e? 920 GeV p almost hermetic detector side view detection of nearly all produced particles exploit energy- and momentum conservation 26

Example 2: Muon Detection Because muons do not interact strongly and because of their large mass (compared to electrons) they don t shower so easily and thus can penetrate calorimeter and iron yoke µ µ e e µ µ 27

Example 3: Neutrinos ν Missing transverse energy and transverse momentum: i p trans = 43GeV carried away by neutrino? 28

Example 4: Secondary Vertices Some mesons containing heavy quarks (charm or beauty) only decay via the weak interaction. example: D K + π π Resulting lifetimes are relatively long: τ O(10-12 s) or cτ 100-500 µm With the help of high precision track detectors one can distinguish if particles originate from secondary or primary vertex: vertex detectors [in most cases based on silicon] 29

Interaction of Charged Particles K7+(+&)(+&'3/&?("$2"?)<&+AA+2'#&37"27&27)()2'+("L+&'7+&?)##)%+&/A&27)(%+-&?)('"2<+#& '7(/0%7&.)''+(1 - +$+(%,&</## - 27)$%+&/A&-"(+2'"/$ 4/'7&+AA+2'#&(+#0<'&A(/.&'7+&A/<</3"$%&+<+2'(/.)%$+'"2&?(/2+##+#1 - &"$+<)#'"2&2/<<"#"/$#&3"'7&#7+<<&+<+2'(/$#&/A&.+-"0. - &+<)#'"2&#2)''+("$%&/AA&$02<+" (+<+*)$'&"#&'7+&#')'"#'"2)<&#0.&/A&.)$,&#027&"$'+()2'"/$#= M$&)--"'"/$&'7+(+&)(+&'7+&A/<</3"$%&?(/2+##+#1 - &4(+.##'()7<0$% - &+."##"/$&/A&N7+(+$9/*&()-")'"/$ - &$02<+)(&(+)2'"/$# - &+."##"/$&/A&'()$#"'"/$&()-")'"/$ 37"27&7/3+*+(&"$&%+$+()<&/220(&.027&<+##&A(+80+$'&'7)$&)'/."2&2/<<"#"/$#=& O/(&27)(%+-&?)('"2<+#&/$+&.0#'&-"#'"$%0"#7&<"%7'&?)('"2<+#&:"=+=&+ P Q&+ R ; )$-&7+)*,&?)('"2<+#&:"=+=&)<<&'7+&(+#'1&µ, $,?&, ' Q&<"%7'&$02<+"Q&===; 30

Energy Loss of Charged Particles in Matter Several important physicists have contributed to the theoretical understanding of energy loss of charged particles in matter - N. Bohr classical derivation of de dx - Bethe & Bloch quantum mechanical treatment of de dx - L. Landau distribution function - E. Fermi density correction - and several other physicists 31

Energy Loss of Heavy Charged Particles The exact derivation is quite involved. * Here only the classical derivation, which was first performed by Bohr is given: Energy loss mainly occurs through inelastic collisions with the shell electrons of the medium. Assuming (1) M >> m e and (2) that the electrons before the collision are at rest => classically the change of momentum is given by: p = + F Coulomb dt <H= 8 ( @ % & C Since for symmetry reasons the longitudinal component averages to 0, only the transverse component is relevant: F = F Coulomb b r = F Coulomb b x2 + b 2 with impact parameter b. Integration yields: p(b) = + F dx v = + ze 2 b dx (x 2 + b 2 ) 3/2 v = 2ze2 vb and therefore E(b) = p2 2m e = 2z2 e 4 m e v 2 b 2 with velocity v and charge z of the moving particle 32 * J. D. Jackson, Klassische Elektrodynamik, (Walter de Gruyter, Berlin, 1993) Kapitel 13.

Bohr s Classical Formula The energy transfer to shell electrons in the ring b to b+db in a layer of thickness dx is given by (with N e = density of electrons) :,C,@ de(b) = E(b) N e dv = 4πz2 e 4 m e v 2 N e db b dx Integration over valid range of impact parameters b min to b max yields: de dx = 4πz2 e 4 m e v 2 N e ln b max b min The valid limits of integration follow from the maximum momentum transfer p = 2m e v (-> b min ) and the minimum energy transfer E min = I, which must at least correspond to the excitation energy I (-> b max ): b min = ze2 m e v 2 ; b max = ze2 v 2 m e I This yields for the classical case of inelastic collisions: de dx = 4πz2 e 4 m e v 2 Z A N A 1 2 ln 2m ev 2 I 33

Bethe-Bloch Formula The correct quantum mechanical result is: de dx = 4πN Arem 2 e c 2 z 2 Z A 1 [ 1 β 2 2 ln 2m ec 2 β 2 γ 2 T max I 2 β 2 δ 2 C Z ] [ MeV ] (g/cm 2 ) where T max = 2m e c 2 β 2 γ 2 1 + 2γm e /M + (m e /M) 2 Meaning of additional terms: is the maximum kinetic energy, which can be transfered to the electron in a single collision, N A is the Avagadro number, r e the classical electron radius and I the excitation energy in [ev]. δ density term due to polarization: important at high energies (leading to saturation of the relativistic raise) C/Z shell correction only relevant at low energies (when v velocity of electrons in the orbit > capture processes are important) Range of validity of the Bethe-Bloch formula: For higher energies radiative processes dominant. 10 MeV/c p 50 GeV/c 34 $ I ( 16 Z 0.9 ev für Z>1

Relativistic Raise: Calculations and Measurements de dx = 4πN Arem 2 e c 2 z 2 Z A 1 [ 1 β 2 2 ln 2m ec 2 β 2 γ 2 T max I 2 β 2 δ 2 C Z ] [ MeV ] (g/cm 2 ) CQR#', - Methan [5%] "+$O/3# $$\$W [&51"#5/+-(N/+B) 8M3&)&QI6(&5N)"&+(Q9&,#''? 35 ]'0(("(237 Classical explanation: I+@023(#+$,#5$)50+(%#5(0'#+$ transverse component of electric ]&1N&+#+)#$,#($#'#B)5"(23#+$ field of moving particle growths R#',#($,#($6#@#-)#+$^#"'23#+($1")$ with factor γ,#1$r0b)&5$$$$ saturation of de/dx, once the F*))"-/+-$%&+$,C;,AD$@#++$,"#(#$ extension of field comparable to I/(,#3+/+-$%#5-'#"23605$1")$,#+$ distance between atoms I6()*+,#+$E@"(23#+$I)&1#+J

Fermi s Density Correction This parameter takes into account, that the shell electrons of the atoms of the medium shield the transversely extended field of the relativistic particle. This leads to a reduction of the effective reach-through and therefore of the energy loss. Physically the effect is related to the fact that the electromagnetic wave gets damped in the transverse direction by the dispersion in the medium (also related to Cherenkov effect). density effect Fermi plateau especially relevant in dense absorbers, e.g. iron or lead ( v c - cos ) C = 1 can be practically neglected for gases at 1 atm approximation for energetic particles δ 2 = ln (βγ) + ln hω p I with plasma frequency and electron density 1 2 hω p = 4πN e r 3 e m e c 2 /α N e & Dielektrizitätskonstante 36

Material Dependence 10 8.',-(/)0$11)&1)2)34'5#&$')$3)6789):9)2';)#<,) ;,'1&#/)!)=))>,'5,)41,)&'1#,2;)? de/dx (MeV g 1 cm 2 ) 6 5 4 3 2 1 0.1 1.0 10 100 1000 10 000 βγ = p/mc 0.1 0.1 H 2 liquid He gas Fe Sn Pb 1.0 10 100 1000 Muon momentum (GeV/ c) 1.0 10 100 1000 Pion momentum (GeV/ c) Al C de 1 de ))) X = x #!) ")))------ = -- # ------ ))))@A,B)( C)D 5E F G=) dx! dx ");.7;H),11,'#&200/)2)34'5#&$')$3)678) de/dx min (MeV g 1 cm 2 ) 2.5 2.0 1.5 1.0!"#$%%&'()*$+,-! H 2 gas: 4.10 H 2 liquid: 3.97 Solids Gases 2.35 0.64 log 10 (Z) 0.1 1.0 10 100 1000 10 000 Proton momentum (GeV/ c) 0$(2-&#<E&5)-&1,)E$-,)%-$'$4'5,;) 3$-)(21,1)I>,J 0.5 H He Li Be B CNO Ne Fe Sn 1 2 5 10 20 50 100 Z 33 Particle Detectors 1 37

Energy Loss of Electrons :')2;;&#&$')#$),',-(/)0$11)K/)&$'&12#&$')<&(<),',-(/)%2-#&50,1)201$)0$$1,),',-(/);4,)#$) &'#,-25#&$')+&#<)#<,)L$40$EK)3&,0;)$3)#<,)'450,&?))M-,E11#-2<04'( N4,)#$)#<,&-)1E200)E211)#<&1),33,5#)&1),1%,5&200/)%-$E&','#)3$-),0,5#-$'1)I%$1&#-$'1J? $ Z 2 # E m 2 de dx &#)&1)41,340)#$)&'#-$;45,)-2;&2#&$')0,'(#<) X 0 x,',-(/)2##,'42#&$'?) E = E 0 exp ----- % ' & ( X 0.O2E%0,?)L4 Example: Cu 716g cm 2%%-$O=?)) X 2 A 0 = ------------------------------------------------------ Z( Z + 1) ln( 287 Z) 5-&#&520),',-(/)?) ))))))))))))) E c de ------------------- Brems dx de ------------------------- collision dx 610MeV 2%%-$O&E2#,0/?) E c = -------------------- ) Z + 1.24 =. 5 E c )0'. αlne 34 Particle Detectors 1 38

Energy Loss of Muons. β 5/ 3 relativistic rise MIP = minimum-ionising particles 39

de/dx Applications for different Detector Types R21 &$'&12#&$')))))))))))))))))))))))))))))))))))))))")))%-$%$-#&$'20)$-);-&3#)5<2EK,- S&T4&; 0$520)<,2#&'())))))))))))))))))))))))))))))))))"!))K4KK0,)5<2EK,- &$'&12#&$')))))))))))))))))))))))))))))))))))))))")))520$-&E,#,-)IS&T4&;)8-($')$-)U-/%#$'J "$0&;,O5&#2#&$')$3),0,5#-$'1 +)5$'Q,-1&$')&'#$)0&(<#)))))))))))))))))")))15&'#&002#$-1 5-,2#&$')$3),0,5#-$'C<$0,)%2&-1)))))")))1$0&;)1#2#,);,#,5#$-1 36 Particle Detectors 1 40

de/dx in a TPC Measurements in PEP4/9-TPC (Ar-CH 4 = 80:20 @ 8.5atm) If de/dx is plotted versus momentum of particle the curves are shifted horizontally for different masses Application: if also the momentum of the particle is known the measurement of the specific ionisation can be used for particle identification In this example each dot represents 185 single measurements in a drift chamber 41

Ionization along the Track!"#$%&'(&)&'&*%+,(-$%./0/1$-,#,. 2/34',(5,-(-$%./1#.$" 5&1(%+&-4,.(6$#+(772 %&-,.&(.,&0/3# "!-Elektron! Teilchen in CF 4 "!-Elektron "! 8*(&'',*(9$'0,.*($1#(0$,(:3*&+-,(0,.(8/*$1&#$/*(5,5,*(;*0,(0,.(<,$%+6,$#,(&3=5.3*0(0,.( The increase of ionization at the end of the range due to the 1/β 2 -dependence of the energy loss is visible in all examples. 42

z-dependence of Ionization B(E(FG(HI,J B(!(KL(HM+J <,'&#$)$1#$1%+,(8/*,*($*(D,.*,-3'1$/* Relativistic ions in nuclear emulsion 43

Bragg-Peak and Medical Application 8/*$1&#$/*1"./=$'()/*( NF 7(8/*,*($*(O&11,. Applications in therapy: R9.&55(V,&AR better targeted treatment of tumors with reduced radiation damage of tissue in front due to concentration of energy loss at the end of the range (in contrast to X-ray treatment) 44

Example: Proton Therapy at PSI S".,&0(/3#(9.&55(V,&A1(HS!9VJ(-$#( 3*#,.1%+$,0'$%+,*(?41/.4,.*(%( &**@+,.*0(A/*1#&*#,(2/1$1),.#,$'3*5($-( 9,.,$%+(0,1(M3-/.1 45

Landau Distribution The Bethe-Bloch formula only gives the average energy loss. The total energy loss is the sum of many individual processes:!"#$%#&'#(%)*+'$,#-&#")./0$0"1&$/.-$2#/$3"&&)#-#/$ thick 4/#-0"#5#-).6&$7/8$!#-$0#673&#$4/#-0"#5#-).6&$#-0"1&$ layers ((de/dx) δx T max ): many 6"+'$7.6$2#-$9.33#$5*/$5"#)#/$4"/:#);-*:#66#/< collisions with small E i in good 2"+=#$9+'"+'&#/$> " de! dx##x» T max?@$5"#)#$9&ab#$3"&$ approximation Gaussian distributed =)#"/#3$!4 " $"$$C7.665#-&#")./0 for thin layers (e.g. gases) two effects DE-$2E//#$9+'"+'&#/$>:8%8$C76#?$$6;"#)#/$F#2*+'$ are important: :G#"$4DD#=&#$#"/#$G"+'&"0#$H*))#< - - rare 6#)&#/#/#$9&AB#$3"&$0-*B#3$ collisons with large E ( > ionization!!!!!!4$$$>i$$j*/"6"#-./06;*&#/&"7)? potential) δ-electrons or knock-on!!!!!"!#$4)#=&-*/#/$*2#-$k/*+=(*/ $$$$4)#=&-*/#/$G#-2#/$D-#"0#6#&:&@$2"#$ electrons are liberated, which have $$$$E1#-$0#/E0#/2$4/#-0"#$5#-DE0#/@$.3$ sufficient energy to ionize themselves $$$$"'-#-6#"&6$:.$"*/"6"#-#/$ - energy loss due to Bremsstrahlung - 4/#-0"#5#-).6&$2.-+'$%-#366&-7')./0 asymmetric Landau distribution "!76L33#&-"6+'#$M7/27.(,#-&#")./0< 1 1 -- "% + e $$$$$$$ P "!E# ----------e 2 % # P ( E) = 1 e 1!E!E 2 = (λ+e λ ) with λ mit = E E mp % = --------------------------- mp 2π ξ 2$ & ξ material constant $$$$$$ $"6&$#"/#$N7&#-"7)=*/6&7/&# & 46 -#)8$R7'-6+'#"/)"+'=#"& N*2"D":"#-&#$O/6P&:#$#/&G"+=#)& 5*/< Alternative approaches by:,75")*5$ Vavilov %)./+=(M#"6#07/0 Blunck-Leisegang 9L3*/ Symon 3"&&)#-#- 4/#-0"#5#-).6&$S24T2UI G7'-6+'#"/)"+'6&#- 4/#-0"#5#-).6& O))"6*/@$Q*11$ Allison, Cobb :8%$3";V6$"/$O-0*/<$!4 38;8 W$X8Y$=#,T+3 S!4I$$W$Y8Z[$=#,T+3 4/#-0"#$,#-).6&$!4

Example for measured Energy Loss 3 GeV electrons in a thin-gap multi wire proportional chamber(alpeph) 3 GeV pions in c1.5 cm gas mixture of Argon and 7% CH 4 O))"6*/dQ*11 47

Restricted Energy Loss A given detector usually only measures the deposited energy and not the energy the particle has lost in total. Significant differences for example occur in gas detectors, when part of the energy, which is transfered to the knock-on electron is lost for the measurement, since the knock-on electrons leaves the detector. it is useful to introduce the so called restricted energy loss: only take into account the part of the energy loss processes with energy transfer T < T cut de dx = Kz 2 Z T<Tcut A 1 β 2 [ 1 2 ln 2m ec 2 β 2 γ 2 T cut I 2 β2 2 ( 1 + T ) cut T max δ 2] Note, that for T cut > T max the standard Bethe-Bloch formula is recovered 48

Energy Spectrum of δ-electrons The distribution of secondary electrons with kinetic energy d 2 N dt dx = 1 2 Kz2 Z A 1 F (T ) β 2 T 2 T, I T T max is given by: F(T) is spin dependent [ F (T ) = (1 β 2 T/T max ) for spin 0]. Integration from T cut to T max yields just the difference between normal and restricted Bethe-Bloch formula. 10 0 10-2 10-4 100 kev Elektronen in H 2 O 100 GeV Muonen in Eisen 10-6 10-8 10-10 Anregung durch entfernte Stöße E max 49

Coulomb Scattering F"'?#*,()#11'4$0;$=#)'N d! ------- d" z 2 Z 2 r2 m c e e ------------------ --------- 4 $ & #p % ' 2 = -------------------- 1 sin 4 (! 2 G1(%#)A&)/$.&);#* FCD#)";#'(#**$8"-%("4#$=&',#W1#'?N$$/"#$7"#*A0-%,()#11'4$,(#**($&A($#"'#$#)',(#$ Important experimental consequence: multiple scattering often represents a serious limitation for the achievable resolution of direction or momentum measurement 50

Multiple Scattering z,β Scattering of charged particles off the atoms in the medium causes a change of direction: the statistical sum of many such small angle scatterings results in a gaussian angular distribution with a width given by: 13.6MeV $ ( 0 = ----------------------z #pc x ----- 1 + 0.038 X 0 x ln ----- $ & % ' X 0 log scale! D)&_"?"#)(#$<()#18"'+#*5#)(#"*1'4$",($# example: p = 1 GeV/c, d = 300µm Si, X 0 =9.4cm θ 0 0.8 mrad. For 10cm distance this corresponds to 80µm, which is significantly larger than typical resolution of Si-strip detector θ the less likely scattering off the atomic nuclei causes large scattering angles resulting in a deviation from a gaussian distribution at large angles 51

Properties of some Materials (PDG) Material Z A Z/A Nuclear a collision length λ T {g/cm 2 } Nuclear a de/dx b min { } interaction MeV length λ I {g/cm 2 g/cm 2 } Radiation length c X 0 {g/cm 2 } {cm} Density {g/cm 3 } ({g/l} for gas) Liquid Refractive boiling index n point at ((n 1) 10 6 1 atm(k) for gas) H 2 gas 1 1.00794 0.99212 43.3 50.8 (4.103) 61.28 d (731000) (0.0838)[0.0899] [139.2] H 2 liquid 1 1.00794 0.99212 43.3 50.8 4.034 61.28 d 866 0.0708 20.39 1.112 D 2 1 2.0140 0.49652 45.7 54.7 (2.052) 122.4 724 0.169[0.179] 23.65 1.128 [138] He 2 4.002602 0.49968 49.9 65.1 (1.937) 94.32 756 0.1249[0.1786] 4.224 1.024 [34.9] Li 3 6.941 0.43221 54.6 73.4 1.639 82.76 155 0.534 Be 4 9.012182 0.44384 55.8 75.2 1.594 65.19 35.28 1.848 C 6 12.011 0.49954 60.2 86.3 1.745 42.70 18.8 2.265 e N 2 7 14.00674 0.49976 61.4 87.8 (1.825) 37.99 47.1 0.8073[1.250] 77.36 1.205 [298] O 2 8 15.9994 0.50002 63.2 91.0 (1.801) 34.24 30.0 1.141[1.428] 90.18 1.22 [296] F 2 9 18.9984032 0.47372 65.5 95.3 (1.675) 32.93 21.85 1.507[1.696] 85.24 [195] Ne 10 20.1797 0.49555 66.1 96.6 (1.724) 28.94 24.0 1.204[0.9005] 27.09 1.092 [67.1] Al 13 26.981539 0.48181 70.6 106.4 1.615 24.01 8.9 2.70 Si 14 28.0855 0.49848 70.6 106.0 1.664 21.82 9.36 2.33 3.95 Ar 18 39.948 0.45059 76.4 117.2 (1.519) 19.55 14.0 1.396[1.782] 87.28 1.233 [283] Ti 22 47.867 0.45948 79.9 124.9 1.476 16.17 3.56 4.54 Fe 26 55.845 0.46556 82.8 131.9 1.451 13.84 1.76 7.87 Cu 29 63.546 0.45636 85.6 134.9 1.403 12.86 1.43 8.96 Ge 32 72.61 0.44071 88.3 140.5 1.371 12.25 2.30 5.323 Sn 50 118.710 0.42120 100.2 163 1.264 8.82 1.21 7.31 Xe 54 131.29 0.41130 102.8 169 (1.255) 8.48 2.87 2.953[5.858] 165.1 [701] W 74 183.84 0.40250 110.3 185 1.145 6.76 0.35 19.3 Pt 78 195.08 0.39984 113.3 189.7 1.129 6.54 0.305 21.45 Pb 82 207.2 0.39575 116.2 194 1.123 6.37 0.56 11.35 U 92 238.0289 0.38651 117.0 199 1.082 6.00 0.32 18.95 Air, (20 C, 1 atm.), [STP] 0.49919 62.0 90.0 (1.815) 36.66 [30420] (1.205)[1.2931] 78.8 (273) [293] H 2 O 0.55509 60.1 83.6 1.991 36.08 36.1 1.00 373.15 1.33 CO 2 gas 0.49989 62.4 89.7 (1.819) 36.2 [18310] [1.977] [410] 52

Summary Part I *0,*.0-(.)#,"#$("".0.3-#*40-(5+.)#0.Y1(0.)#2439#$("".0.3-#-9*.)#,"#$.-.5-,0) 0,1B6#5+4))("(54-(,3 - -045<&*,)(-(,3#$.-.5-,0)#I3,3#$.)-015-(/.P#(#D40-#!! +III gas detectors - 54+,0(2.-.0)#I$.)-015-(/.P#(#D40-#!!! [not covered in this lecture] >4)(54++9#4++#$.-.5-,0)#>4).$#,3#.+.5-0,24B3.-(5#(3-.045-(,3 $.-.5-,0)#4+),#2,0.#43$#2,0.#1).$#",0#,-6.0#4**+(54-(,3)#I.OBO#2.$(54+#4**+OP.3.0B9#+,))#,"#5640B.$#*40-(5+.);#Z.-6.8Z+,56#$.)50(>.)#+,))#$1.#-,#(,3()4-(,3 z 2 # 2 ( lne - #(#W.02(*+4-.41-2(3(212#4-# ;#?8M#F.S#*.0#B52 8M # - 6,=./.0#+(B6-#*40-(5+.)#I.+.5-0,3)T#21,3)P#4-#6(B6#.3.0B(.)#+,).#.3.0B9#*0.$,2(343-+9#>9# >0.2))-046+13B;# #) * 3 21+-(*+.#)54--.0(3B de dx, Z 2 + E m 2 - B41))(43#5,0.#,"#$()-0(>1-(,3#=(-6#43B1+40#)*0.4$;### 1 " 0 - -- p - $./(4-(,3#"0,2#B41))(,3#$()-0(>1-(13#4-#+40B.#43B+.)#$1.#-,#[1-6.0",0$#)54--.0(3B#I315+.(P x ----- X 0 53