PHY492: Nuclear & Particle Physics. Lecture 23. HW Particle Detectors

Transcription

1 PHY49: Nuclear & Particle Phyic Lecture 3 HW Particle Detector

2 Homework 13.1 x min = mω λ 1 x min = mω λ ; x 3 = mω min λ V ( x min + x, y) = 1 mω x min + x ( ) + y + λ 4 3 ; 4 xmin = m ω 4 λ x min + x ( ) + y = 1 mω x min + x min x + x + y + λ 4 3 x min + 4x min x + 6x min x + 4x min x 3 + x ( x min + x min x + x ) y + y 4 1 = 1 m ω 4 mω mω 1 λ λ x mω x m ω 4 mω + mω 3 4 λ λ x + mω x + = 1 m ω 4 + mω x + Q.E.D. 4 λ April 9, 007 Carl Bromberg - Prof. of Phyic

3 Homework 14.1 a) Top lifetime b) No time to interact δ Eδt ; τ Γ = MeV MeV = t i = 1 fm/c = τ = c) Top quark decay t W + b = 1.3 t i E W + E b = m t ; E W = m Energy Con.: t m t E b + E b E a = x a Momentum Con.: E b = m t + m b m W E W m W = p = E b m b ; E W = E b m b + m W ( m t ) = 69 GeV; p b = E 1 ( b m b ) d) Parton-parton colliion ; p a = x a c ; ŝ = ( E a + E b ) p a c + p b c = x a x b E b = x b ( ) = x a + x b ; p = x b b c x + x a b ( ) 4 + x a x b = 69 GeV/c April 9, 007 Carl Bromberg - Prof. of Phyic 3 ( ) 4 + x a x b top ma = TeV TeV =( TeV) = 4 TeV LHC =(14 TeV) = 00 TeV (.350) = x a x b ( 4); x a x b = 0.03; x a x b =.03 = 0.18 x a x b = 0.05

4 Homework April 9, 007 Carl Bromberg - Prof. of Phyic 4

5 d = coθ inθ C C d inθ C coθ C K 0 = ( d, ) Quark content d = d coθ C inθ C = d inθ C + coθ C Weak interaction act on mixed tate Homework 14.5 Quark mixing matrix nd order weak decay (u/c) d, Z = d, d Z coθ C inθ C, Z coθ C inθ C + d, Z co θ C +, d Z in θ C Z couple only to the ame weak flavor quark d, Z and, d Z are both ZERO d, d Z =, Z 0 But 4 quark mixing matrix give thi cancellation Not een: 1t order weak decay flavor changing neutral current d Z 0 K 0 µ µ + d, Z = d, d Z coθ C inθ C, Z coθ C inθ C = 0 April 9, 007 Carl Bromberg - Prof. of Phyic 5

6 14.7 a) 4-vector dot product (lab frame) Q = ( k k ),ν ; P = 0,m p c Q P = m p c ν (invariant) Homework b) parton aborb Q but remain male infinite momentum frame DIS ( xp + Q ) = 0 = x P + xp Q + Q x = Q P Q = Q m p νc for Q >> x P = x m p c 4 c) from 14.6 e) two point on plot W = m p + m p c ν c 4 Q c 4 i) ν = E E = 9 GeV; Q = 4E E in θ / m p ν = 17 GeV / c ; Q = 10 GeV ( ) ( ) ii) ν = E E = 6 GeV; Q = 4E E in θ / m p ν = 11.3 GeV / c ; Q = 10.7 GeV Q c GeV c d) haded region i) ii) 5 10 m p ν / c 15 W = m p 0 (GeV / c 4 ) x = 1 W = 5m p W = 3m p x = 0.5 x = 0.1 April 9, 007 Carl Bromberg - Prof. of Phyic 6

7 Particle are detected by making them ionize atom! Detecting charged particle The electric field of a moving charged particle can ionize the atom of the material in which it move. Ionization electron are mall and low ma, and can be collected by an electric field. Poitive ion are big and heavy, and luggih. A charged particle accelerated by a magnetic or electric field radiate photon that can ionize atom and releae electron Detecting neutral particle How to detect particle Interact the neutral particle with matter and in the proce releae ionization electron. Sometime you mut completely detroy the neutral particle, but it energy ha been ued to create ionization. Mut tudy Ionization to undertand detector April 9, 007 Carl Bromberg - Prof. of Phyic 7

8 Ionization Ionization potential minimum energy to ionize (outer e hell) Hydrogen 13.5 ev Helium 5 ev Lithium 5 ev Neon ev Average ionization potential, include inner hell reaction dependent for charged particle (e.g., electron) ~16Z 0.9 (ev) for Z>1 Low Z Nobel Gae (He, Ne, Ar, a little higher) April 9, 007 Carl Bromberg - Prof. of Phyic 8

9 Photon induced ionization Photon (<0 ev) induced ionization Only valence electron (a few) Non-penetrating Gae & urface high temperature thermionic emiion high electric field ultraviolet light photoelectric effect ozone photo-cathode (C) ilicon photodiode X-ray (<1 MeV) induced All electron (Z) Penetrating Gae & olid interior Ueful converion λ wavelength, ν frequency hc = π c E = hν = hc λ ( ) = π ( 00 MeV fm) ( ) = ev nm Photon energie ( ) 100 ev nm = λ April 9, 007 Carl Bromberg - Prof. of Phyic 9

10 Particle Phyic Booklet Particle Data Group - Product Order booklet Detector Lecture for Student/Teacher April 9, 007 Carl Bromberg - Prof. of Phyic 10

11 S(T ) = dt dx = n ion I Charged particle induced ionization Moving particle, ma M, ionize atom in medium T : kinetic energy of moving particle n ion : number of electron-ion pair unit path length I : average energy electron-ion pair n ion i particle velocity and charge dependent (Bethe and Bloch) Stopping power S(T ) = 4πQ e nz ln m e c γ β m e β c I β γ = E Mc ; β = pc E ; γβ = p Mc S(T ) 1 β c = 1 v S minimize, γβ 3 S lnγ β = v/c = < 0.8 heavy ionization when β ~ 0.95 minimum ionization ultra relativitic rie of ionization April 9, 007 Carl Bromberg - Prof. of Phyic 11

12 Ionization in gae (relevant to all particle) Ionization v momentum Normalized Ionization v γβ for variou particle mae Argon Ga γβ = April 9, 007 pc Mc Carl Bromberg - Prof. of Phyic 1

13 Saturation of ionization in olid Relativitic rie of ionization i due to electric field concentration perpendicular to direction of motion Atom along the line of motion ee a tronger field a v -> c. Effect i larget in large Z gae, e.g., Xe Solid polarize and hield far electron from field effect aturate at only a few % above the minimum April 9, 007 Carl Bromberg - Prof. of Phyic 13

14 S(T ) = dt dx nz = ρa 0 Unit for energy lo Minimum ionization in thin olid Z A Z : atomic number of medium n : number of atom/unit volume n = ρa 0 A ; A : atomic number of medium Z/A ~ 0.4 at large A, energy lo proportional to denity S~ρ, Divided by the denity -> value nearly independent of material. (de/dx) min tabularized for variou material in MeV/(g/cm ) Polytyrene cintillator: 1.95 ρ cintillator = 1.03 g/cm 3 dt dx min = 1.95 MeV g/cm ρ Scintillator =.0 MeV/cm Iron (teel) : 1.45 ρ iron = 7.87 g/cm 3 dt dx min = 1.45 MeV g/cm ρ iron = 11.4 MeV/cm Relativitic muon loe ~ MeV/cm in platic, ~11.4 MeV/cm in Iron April 9, 007 Carl Bromberg - Prof. of Phyic 14