Lecture 20. Calorimetry

Transcription

1 Ltur 0 Calorimtry

2 CLORIMTRY In nular and partil physis alorimtry rfrs to th dttion of partils through total absorption in a blok of mattr Th masurmnt pross is dstrutiv for almost all partil Th xption ar muons (and nutrinos) à idntify muons asily sin thy pntrat a substantial amount of mattr In th absorption, almost all partil s nrgy is vntually onvrtd to hat à origin of th nam alorimtr Calorimtrs ar ssntial to masur nutral partils CMS

3 Calorimtry nrgy masurmnt by total absorption with addd spatial ronstrution Calorimtr provids a dstrutiv masurmnt Dttor rspons ~ Calorimtry works both for ð hargd partils ( ± and hadrons) ð and nutral partils (n,γ) Basi mhanism: formation of ð ltromagnti ð or hadroni showrs Finally, th nrgy is onvrtd into ionization or xitation of th mattr (light)

4 Intration of hargd partils nrgy loss by Brmsstrahlung Radiation of ral photons in th Coulomb fild of th nuli of th absorbr d dx 4αN Z z 1 4πε0 m 183 ln 1 3 Z m Z, - Ngativ sign à nrgy loss /m à fft is important only for ± with momntum p > fw hundrd MV and for ultra-rlativisti muons with momntum p >1000 GV

5 For ltrons ln ln Z r Z N X X dx d Z r Z N dx d α α 0 / 0 X x X 0 - Radiation lngth, g/m distan ovr whih a high nrgy ltron loss all but a fration 1/ of its nrgy du to Brmsstrahlung

6 Intration of hargd partils (Lo) nrgy loss (radiativ + ionization) of ltrons and protons in oppr proton brmsstrahlung ltron proton ollision ross stion raiss slowly ~ log() ollision loss Critial nrgy, losss du to ionisation and Brmsstrahlung ar qual d dx ( ) ( ) Brms d dx ion solid + liq 610MV Z gas 710MV Z For muons l m m µ ( - ) in F(Z6).4 MV (µ) in F(Z6) 1 TV

7 Intration of photons In ordr to b dttd, a photon has to rat hargd partils and/or transfr nrgy to hargd partils Photo-ltri fft X X + ē γ + atom à atom Only possibl in th los nighborhood of a third ollision partnr à photo-fft rlass mainly ltrons from th K-shll. σ K photo γ 8 7 α Z σth ε σ Th πr 3 ε m Cross stion shows strong modulation if γ shll t high nrgis (ε >> 1) (Thomson) σ K photo 4π r 4 α Z 5 1 ε σ photo Z 5

8 Compton sattring γ + γ ' + ' θ γ γ γ 1 1+ ε osθ ( 1 ) γ Cross-stion on quasi-fr ltron: approximat Klin-Nishina formula at high nrgis σ lnε ε Cross stion on atoms γ /m σ atomi Z σ

9 Pair prodution - γ + nulus + + nulus + Z Only possibl in th Coulomb fild of a nulus (or an ltron) if γ m Cross-stion (high nrgy approximation) σ pair 4αr Z ln 1 9 indpndnt of nrgy! 3 Z N X λ pair 9 7 N X 0 1 λ 0 pair nrgy sharing btwn + and - boms slightly asymmtri at high nrgis.

10 Pair prodution Positron annihilation Z Z ppliation of positron annihilation in mdiin à PT Position mission Tomography Us 18 F labld radiotrar 18 F à 18 O à γ ( x 511 kv) γ s ar dttd by sintillators in oinidn. 18 F lis somwhr on this lin of rord! Nd many lins of rord + tomographi ronstrution.

11 I γ I µ µ 0 µ x photo Photon intrations + µ Compton + µ pair +... photo fft µ - attnuation offiint N µ [ ] m g i σi / Rayligh sattring (no nrgy loss!) pair prodution Compton sattring 1 MV (PDG)

12 ltromagnti showr Photons pair prodution is a dominant pross σ pair 7 9 4α r Z ln Z 1/ 3 9 X 0 radiation lngth in m or g/m Intnsity Whr th attnuation offiint N X 0 ltrons brmsstrahlung is a dominant pross d dx 4αN Z I(x) I 0 µx µ 7 9 ρ X 0 r ln 183 Z 1/ 3 X 0 0 x / X 0 ftr travrsing xx 0 th ltron has only 1/ 37% of its initial nrgy

13 ltromagnti showr Simpl showr modl: ltrnating brmsstrahlung and pair prodution t partils aftr t [X 0 ] ah with nrgy /t Stops if < Numbr of partils N / Maximum at t max ~ln(/ )

14 Longitudinal showr distribution ltron showr simulation t max ln + C γ 0 Som photons pntrating (almost) th ntir slab without intrating (pak at 0) Showr maximum at t max ln + C γ 0 C γ 0.5 for photons; 1 for ltrons

15 Longitudinal ontainmnt Longitudinal showr distribution inrass only logarithmially with th primary nrgy of th inidnt partil, i.. alorimtrs an b ompat. Containmnt lngth: à L(95%) t max Z [X 0 ] Numbr of partil in showr: Loation of showr maximum: N max tmax 0 / t max ln 0 / Longitudinal showr distribution: L ln 0 / Typial valus for X 0 : Pb m, Lr 14 m, sintillator 34 m 100 GV ltron is ontaind in 5 m of Pb

16 Dvlopmnt of th transvrs dimnsions of th showr Opning angl an b du to brmstrahlung and pair prodution θ m 1 γ multipl Coulomb sattring θ s x X 0 s 4π α (m ) 1.MV à Main ontribution from low nrgy ltrons

17 Largr dviations ar du to low nrgy photons produs in Compton s sattring, photo-ltri fft t. Prdominant part aftr showr max spially in high Z absorbrs Th showr gts widr at largr dpth Th width is usually xprssd in Molir radius R M R M s X 0 1.MV X 0 n infinit ylindr of radius 1 R M ontains 90% of th showr

18 3-D showr dvlopmnt Linar sal Logarithmi sal