Detectors for Particle Physics

Transcript

1 Introduction Detectors for Particle Physics DESY Summer Student Lectures 2007 Carsten Niebuhr Cosmic Ray Background Radiation: T = 2.72 K, n! = 4x10 8 m -3 2 "#$%!&! &'%$()*+%,(' -.#/0123! 42'2$#1!5('+20%3 &'%2$#+%,('!(6!57#$82)! "#$%,+123!9,%7!:#%%2$ - -'2$8;!<(33=!>2%72!>1(+7!?($/*1# - :*1%,012!@+#%%2$,'8 Topics of the Lecture "#$%!&&! A32!(6!B$#+C!D2%2+%($3! 6($!:(/2'%*/!:2#3*$2E /2'%! 4#3!D2%2+%($3 - "$(0($%,('#1!57#/F2$ - D$,6%!57#/F2$ - B" ",.21!D2%2+%($3 Common Common lecture Lecture on Fr, by Robert Klanner Friday, Aug 11th, Sem 4 by Georg Steinbrück '(%!+(H2$2)! - B$,882$ - DJK "7(%()2%2+%($3 572$2'C(H!5(*'%2$3 B$#'3,%,('!I#),#%,(' 5#1($,/2%2$ %$(/#8'2%,+ - 7#)$(',+ Text books: K.Kleinknecht: Teubner, 1992 W.R. Leo: Springer 1994 G.F.Knoll: Wiley, 3rd edition Detektoren für Teilchenstrahlung C.Grupen: Teilchendetektoren BI Wissenschaftsverlag 1993 W.Blum, L.Rolandi: Springer, 1994 Review articles: T.Ferbel: Addison-Wesley 1987 Literatur Techniques for Nuclear and Particle Physics Experiments Radiation Detection and Measurement Particle Detection with Driftchambers Experimental Techniques in High Energy Physics Other sources: Particle Data Group: Review of Particle Physics Eur. Phys. J. C15, (2000) R.K.Bock, A.Vasilescu: The Particle Detector BriefBook Springer, 1998 and //physics.web.cern.ch/physics/particledetector/briefbook/ 3 4

2 What are the Objects? Fundamental Interactions and many more... -.#/012!!!!!!!!!!!!" 0 $ # + #!!!!!!!!!!!# 0 $ %%!!!!!!!! K 0 $ # + # <,62%,/2!M3N!!!!!!!!!!!OP EQR!!!!!!!!!!!!!!!OP EOS!!!!!!!!!!!!!!!!!!OP EOP +!!!M//N!!!!!!!!!!!!!!!T.OP EOT!!!!!!!!!!!!!T.OP EU!!!!!!!!!!!!!!!TP 5 6 Example for Resonance at HERA Pentaquark candidate: θ 0 c D p K π + π p minimal quark content: uuddc so far only seen by H1... is this a real signal?? or just a statistical fluctuation? or a detector effect? => very good understanding of detector response is required significance: signal/background resolution efficiency / acceptance 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$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!$+&3-0-&/;$:-,#10-&/ :#)(#10-&/$-/$.'%/#0-1$)-#(:$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!$ p 1'(&,-.#0,24$0&0'($#/#,%2$'63&,+0-&/$'/:$.#'35,#.#/0$$$$$$$$$$$$$$$$$$! = 0&0.'33$:#0#,.-/'0-&/$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!$.$?"#,#/@&>$,':-'0-&/$&,$0-.#$&)$)(-%"0$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$! # 0,'/3-0-&/$,':-'0-&/$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!$" 7 8

3 Criteria for an ideal Detector Modern Collider Detectors C&30$-.+&,0'/04 "-%"$#))-1-#/12 "-%"$,#3&(50-&/ "-%"$'11#+0'/1#$!$0,2$0&$1&>#,$)5(($3&(-:$'/%(#$7D!8 under construction: LHC '(3&$>#,2$-.+&,0'/0$7+',0(2$1&/)(-10-/%$:#.'/:384 +',0-1(#$-:#/0-)-1'0-&/$1'+'6-(-02 )'30$,#3+&/3# "-%"$,'0#$1'+'6-(-02 3.'(($:#':$0-.# "#,.# (&/%#>-02$&)$:#0#10&,$1&.+&/#/03 "-%"$,#(-'6-(-02 %&&:$'11#33-6-(-02$7)&,$,#+'-,38 (&E$1&30 in operation: HERA/Tevatron!"# design phase: ILC 9 10 Example of Particle Physics Experiments A#3-:#3$0"#$(',%#$1&((-:#,$:#0#10&,3$0"#,#$',#$.'/2$&0"#,$#*+034$ Bates Linear Accelerator (MIT) BLAST, OOPS, SAMPLE Beijing IHEP ARGO-YBJ, BES, Tibet ASgamma Brookhaven BRAHMS, Crystal Ball (E913/914), E787, E821/muon g-2, E850, E852, E863/ EMU01, E864, E865, E869, E877, E881, E885, E890, E891, E895, E905, E906, E907, E909, E910, E913/914 (Crystal Ball), E917, E923, E926, E927, E949, E953, EIC, EMU01/E863, High Gain Harmonic Generation FEL, ICAE, IFEL, IMB, LEGS, MECO, Microundulator FEL, NuMass/E952, PHENIX, PHOBOS, pp2pp, Smith-Purcell, STAR, Zero Degree Calorimeter CERN ALEPH, ALICE, AMS, ANTARES, ASACUSA, ATHENA, Atlas (European), ATRAP, CDHS neutrino experiment/wa1, CERES/NA45, CHORUS, CMS, CosmoLEP, CPLEAR/PS195, Crystal Barrel/PS 197, Crystal Clear/RD18, DELPHI, EMU01, FELIX, HARP, ICANOE, ISOLDE, L3, LHC-B, MISTRAL, NTOF1, NTOF2, NTOF3, NA45.2/IONS/EL.PAR, NA47/SMC, NA48, NA48.1, NA48.2, NA49, NA50, NA51, NA52/ Newmass, NA56/SPY, NA57, NA58/COMPASS, NA59, NA60, NOMAD, OBELIX/PS201, OPAL, OPERA, PAMELA, PS185, PS205/HELIUMTRAP, PS210, PS212/DIRAC, PS214/HARP, RD8, RD11, RD12/TTC, RD13, RD27, RD39/SMSD, RD41/ MOOSE, RD42, RD44/Geant 4, RD45, RD46, RD48/ ROSE, RD49/RADTOL, TOSCA, TOTEM, WA85, WA92 (Beatrice), WA94, WA97, WA98, WA102 DESY H1, HERA-B, Hermes, TESLA, ZEUS Fermilab Antihydrogen/E862, APEX/E868, Auger Project, BooNE/E898, BTEV/C0, CDF/E830, CDMS/E981, CEX/E853, Charmonium/E835, CMS (US Server), COSMOS/E803, D0 (DZero)/E823, Donut/E872, E665, E771, E789, Fermi III Project, FOCUS/E831, HyperCP/E871, KTEV/E799/E832, MINOS/E875, NuMI, NUSEA/E866, NuTeV/E815, SDSS, SELEX/ E781, Zero Degrees/C0 Gran Sasso BOREXino, CRESST, CUORICINO, DAMA, EASTOP, GALLEX(finished), GENIUS, GNO, Heidelberg Dark Matter Search (HDMS), Heidelberg-Moscow Experiment, ICARUS, LUNA, LVD, MACRO, MONOLITH, NOE, OPERA, USA Search for Rare/Forbidden Decays!"#$%&'$()*&(*#%$#+%+)&,(*+)*-+./*012$%%$%*3(4)&).)*5-036*07&)8$%/+(9:;* 4$+%12*<,%*/$#),(=(.'>$%*?&,/+)&(@*#%,1$44;*!*$*" 4$(4&)&?&)A*@,+/;*BC =BD *E* ($$94*$"1$//$()*$($%@A*%$4,/.)&,(6*2&@2*$?$()*%+)$6*>.)*4'+//*)%+1F*'./)&#/&1&)A*#$%*$?$() 4)+%)*<.//*9+)+*)+F&(@*&(*GCCH Thin Superconducting Coil Muon Beam Drift Chamber? γ e + Stopping Target Liq. Xe Scintillation Detector Timing Counter 1m γ? Liq. Xe Scintillation Detector e + Drift Chamber 11 12

4 ALICE at LHC I$+?A*3,(*-2A4&14;*)2&4*4&'./+)&,(*42,74*BJBC*,<*+//*BCCCC=GCCCC*$"#$1)$9*)%+1F4*&(*+* %$4,/.)&,(*+(9*9,.>/$*2&)*4$#$%+)&,(*,<*)2$*9$?&1$K ALICE at LHC LHC Real Event in STAR at RHIC I$+?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$K c ars t en. ni e buh r@ desy.de 14 c ars t en. ni e buh r@ desy.de 14! 2000 tracks per event Pa r t i cl e D e t ec t o r s 1 Pa r t i cl e D e t ec t o r s 1 13 Super Kamiokande (Japan) (Japan) Super-Kamiokande 14 Satellite Satellite based based Detectors Detectors 0$+%12*<,%**#%,),(=9$1+A*+(9*<,%*($.)%&(,*,41&//+)&,(4 MCCCC*),(4*,<*7+)$% Super-Kamiokande (Japan) BGCCC*#2,),*).>$4* 0$+%12*<,%**#%,),(=9$1+A*+(9*<,%*($.)%&(,*,41&//+)&,(4 D>@8;)D1##19E13)"2(&/F1'"/3)?"/),-.,)&%&/.3)$,"'"%()-%)',&)/1%.&)ABG&H) '")IJBB)D&H >-?'"??)(6,&+=0&+)?"/)@=.=(')ABBC MCCCC*),(4*,<*7+)$% 166&0&/1'-"%)#&6,1%-(#)"?)@DKL( ("=/6&()"?).1##1)/13)2=/('( N$+1)&,(4*; %1'=/&)"?)+1/7)#1''&/ # N! N!"#$"%&%'()*%&&+),-.,&(')/& '3)45 $/&6-(-"%)'/167&/)*8-9('/-$(5 610"/-#&'&/)*!(:*;055 *******O2$%$(F,? N$+1)&,(4*; # e N! en # N! N +1'1)16<=-(-'-"%)(3('&# *****42,7$% *******O2$%$(F,? c ars t en. ni e buh r@ desy. de c ars t en. ni e buh r@ desy. de # e N! en *****42,7$% 1%'-6"-%6-+&%6&)+&'&6'"/ Pa r t i c le D e t e ct or s 1 Pa r t i c le D e t e ct or s 1 c ar s te n. n iebu hr@d e sy.de Par ticle Det ect or s 1

5 Applications in Medicine Interplay between Physics and Technology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nteraction of Radiation with Matter!,1/.&+)N1/'-60&( K&='/10)N1/'-60&(,&1F3)6,1/.&+)$1/'-60&( %&='/"%( Particle type: Cross Section of a typical Collider Detector neutrinos (missing energy) muons absorber (mostly Fe) flux return yoke heavy medium (Fe, Cu, U) + active material hadrons: p,!, K... [quarks, gluons " jets] &0&6'/"%(.1##1)/1+-1'-"% electrons, photons %&='/-%"( charged particles Track detectors for charged particles beam pipe vacuum!"=0"#29:%'&/16'-"%)w-', &0&6'/"%()"?)#&+-=#!)&0&6'/-610)(-.%10)-%)+&'&6'"/) 19 G1-%03)X(-%.=01/Y)-%'&/16'-"%(Z /&(=0'-%.)-%)&%&/.3)'/1%(?&/)'" 6,1/.&+)$1/'-60&( gas detectors solid state detectors Calorimeter for energy meas. (neutral & charged) electromagnetic hadronic magnet coil (solenoid, field beam axis) 20 high Z material (Pb)

6 Example 1: HERA ep Event with 3 Jets Example 2: Muon Detection e p e Jet 1 Jet 2 Jet 3 hadronic calorimeter electromagn. calorimeter track detector transverse view: 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 e e 27.5 GeV e? 920 GeV p almost hermetic detector! detection of nearly all produced particles side view exploit energy- and momentum conservation Example 3: Neutrinos Missing transverse energy and transverse momentum: carried away by neutrino?!! p trans = 43GeV i Example 4: Secondary Vertices Some mesons containing heavy quarks (charm or beauty) only decay via the weak interaction. example: D! K + " " Resulting lifetimes are relatively long: #! O(10-12 s) or c#! m 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] 23 24

7 Interaction of Charged Particles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de &&&&&&&&&&&&&&&&&& $N dx A r 2 e m e c 2 z 2Z Ā -- 1 = ) ( 2 ) "$2"-+$'&?)('"2<+ - ( = v c&*+</2"',&/a&?)('"2<+ - z &27)(%+&/A&?)('"2<+.+-"0. - Z, A&&/A&.+-"0. Bethe-Bloch Formula - & I, 16 ) Z 0.9 &)*+()%+&"/$"#)'"/$&?/'+$'")<&"$&I+TJ - + &-+#2("4+#&-+$#"',&+AA+2'&-0+&'/&?/<)("#)'"/$& &&&&/A&.+-"0.&:&&#)'0()'"/$&/A&(+<)'"*"#'"2&("#+; /'7+(&2/$#')$'# - & N A &V*/%)-(/W#&$0.4+( - & r e = 2.8 fm &2<)##"2)<&+<+2'(/$&()-"0# - & m e &+<+2'(/$&.)##& 2m e c 2 ( 2 * 2 ln ( I X(/?+('"+#1 &&&&I!+TU2.J& -+?+$-+$2+&/$<,&/$&?)('"2<+&*+</2"',& $/'&/$&?)('"2<+&.)## )'&#.)<<&+$+(%"+# - -(/?#&<"9+& - 1 ( 2 )'&(+<)'"*"#'"2&+$+(%"+#&"=+=&(*» 1 - </%)("'7."2&("#+&& - ln ( ln(βγ) * = ln= E ln p m )'&(+#' S&A"+<- )??(/>".)'+&()$%+&/A&*)<"-"',1& 10MeV/c. p. 50GeV/c *&Y&C 32 Particle Detectors Material Dependence Energy Loss of Electrons de/dx (MeV g 1 cm 2 ) βγ = p/mc Muon momentum (GeV/ c) 0.1 H 2 liquid He gas Al Fe Sn Pb Pion momentum (GeV/ c) Proton momentum (GeV/ c) 0$(2-&#<E&5)-&1,)E$-,)%-$'$4'5,;) 3$-)(21,1)I>,J C.',-(/)0$11)&1)2)34'5#&$')$3)6789):9)2';)#<,) ;,'1&#/)!)=))>,'5,)41,)&'1#,2;)? de 1 de ))) X = x #!) "))) = -- # ))))@A,B)( C)D 5E F G=) dx! dx ");.7;H),11,'#&200/)2)34'5#&$')$3)678) de/dx min (MeV g 1 cm 2 )!"#$%%&'()*$+,-! 33 Particle Detectors H 2 gas: 4.10 H 2 liquid: 3.97 Solids Gases log 10 (Z) H He Li Be B CNO Ne Fe Sn Z :')2;;&#&$')#$),',-(/)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? de dx $ Z 2 # E m 2 &#)&1)41,340)#$)&'#-$;45,)-2;&2#&$')0,'(#<) X 0 x,',-(/)2##,'42#&$'?) E = E 0 exp % ' X 0 & ( 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 O2E%0,?)L4 Example: Cu. 5 E c )0'.!lnE 34 Particle Detectors

8 Energy Loss of Muons de/dx Applications for different Detector Types R21. "! 5/ 3 &$'&12#&$')))))))))))))))))))))))))))))))))))))))")))%-$%$-#&$'20)$-);-&3#)5<2EK,- relativistic rise 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 MIP = minimum-ionising particles 36 Particle Detectors de/dx in a TPC Properties of some Materials (PDG) Measurements in PEP4/9-TPC (Ar-CH 4 = 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 Material Z A Z/A Nuclear a Nuclear a de/dx b min { } collision interaction MeV Radiation length c X0 length λ T length λ I g/cm 2 {g/cm 2 } {cm} {g/cm 2 } {g/cm 2 } Density {g/cm 3 } ({g/l} for gas) Liquid Refractive boiling index n point at ((n 1) atm(k) for gas) H2 gas (4.103) d (731000) (0.0838)[0.0899] [139.2] H2 liquid d D (2.052) [0.179] [138] He (1.937) [0.1786] [34.9] Li Be C e N (1.825) [1.250] [298] O (1.801) [1.428] [296] F (1.675) [1.696] [195] Ne (1.724) [0.9005] [67.1] Al Si Ar (1.519) [1.782] [283] Ti Fe Cu Ge Sn Xe (1.255) [5.858] [701] W Pt Pb U Air, (20 C, 1 atm.), [STP] (1.815) [30420] (1.205)[1.2931] 78.8 (273) [293] H2O CO2 gas (1.819) 36.2 [18310] [1.977] [410] 31 32

9 Multiple Scattering Summary Part I z,! 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: *0,*.0-(.)#,"#$("".0.3-#*40-(5+.)#0.Y1(0.)#2439#$("".0.3-#-9*.)#,"#$.-.5-,0) 0,1B6#5+4))("(54-(, <&*,)(-(,3#$.-.5-,0)#I3,3#$.)-015-(/.P#(#D40-#!! - 54+,0(2.-.0)#I$.)-015-(/.P#(#D40-#!!! >4)(54++9#4++#$.-.5-,0)#>4).$#,3#.+.5-0,24B3.-(5#( (,3 $.-.5-,0)#4+),#2,0.#43$#2,0.#1).$#",0#,-6.0#4**+(54-(,3)#I.OBO#2.$(54+#4**+OP log scale! 13.6MeV $ ( 0 = z #pc x X 0 x ln $ & X 0 % ' D)&_"?"#)(#$<()#18"'+#*5#)(#"*1'4$",($# example: p = 1 GeV/c, d = 300m Si, X 0 =9.4cm! " 0! 0.8 mrad. For 10cm distance this corresponds to 80m, which is significantly larger than typical resolution of Si-strip detector.3.0b9#+,))#,"#5640b.$#*40-(5+.);#z.-6.8z+,56#$.)50(>.)#+,))#$1.#-,#(,3()4-(,3 - z 2 # 2 ( lne #(#W.02(* (3(212#4-# #) * 3 ;#?8M#F.S#*.0#B52 8M # - 6,=./.0#+(B6-#*40-(5+.)#I.+.5-0,3)T#21,3)P#4-#6(B6#.3.0B(.)#+,).#.3.0B9#*0.$,2(343-+9#>9# >0.2)) B;# de dx, Z 2 + E m (*+.#)54--.0(3B " the less likely scattering off the atomic nuclei causes large scattering angles resulting in a deviation from a gaussian distribution at large angles 1 - B41))(43#5,0.#,"#$()-0(>1-(,3#=(-6#43B1+40#)*0.4$;### " 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 Part II!"#$%&$'()*+$,#-#*-%("$&%($.%/#0-1/$.#)"1(#/#0-$ 2)"$,#-#*-%(" - 3(%4%(-5%0)6$78)/9#( -,(5&-$78)/9#( - '37 -.:27;$<37;$2=. :%65>$:-)-#$,#-#*-%(" - :-(54$,#-#*-%(" - 35?#6$,#-#*-%(" Common <@$A6)00#( lecture on Fr, by B(5>)C;$:#/$D Georg Steinbrück 35