General Information. Muon Lifetime Update. Today s Agenda. The next steps. Reports due May 14

Transcription

1 General Information Muon Lifetime Update The next steps Organize your results Analyze, prepare plots, fit lifetime distribution Prepare report using the Latex templates from the web site Reports due May 14 Today s Agenda Interaction of Particles with Matter (Summary) Cherenkov and Transition Radiation Interaction of Photons with Matter

2 The concept of cross sections Cross sections or differential cross sections ddare used to express the probability of interactions between elementary particles. Example: colliding particle beams beam spot area A = N 1 /t = N /t What is the interaction rate R int.? R int t) = L has dimension area! Practical unit: 1 barn (b) = 10-4 cm Luminosity L [cm - s -1 ] target scattered beam solid angle element d N scat () N inc n A d = dd() N inc n A d incident beam.n A = area density of scattering centers in target

3 de/dx Review How do charged particles loose energy in matter? Discrete collisions with the atomic electrons of the absorber material. v,m 0, k - e de dx N : 0 electron d NE d de density Collisions with nuclei not important (m e <<m N ). If, k are big enough ionization (Bethe Bloch Equation) Instead of ionizing an atom, under certain conditions the photon can also escape from the medium. Cherenkov and Transition Radiation

4 Average Energy Loss <de/dx> de dx 4N A Z 1 1 mec max re mec z ln T A I de/dx in [MeV g -1 cm ] Bethe-Bloch formula only valid for heavy particles (mm ). de/dx depends only on independent of m! First approximation: medium simply characterized by Z/A (~ electron density) de 1 dx kinematical term Z/A = 1 Z/A~0.5 de dx 3-4 minimum ionizing particles, MIPs Fermi plateau ln relativistic rise

5 Minimum Ionizing Particles (MIPs) <de/dx> has broad minimum around = 0.96 or ~ 4 Relativistic particles with an energy loss corresponding to this minimum are called Minimum Ionizing Particles or MIPs. For a light absorber with Z/A ~ 0.5 -de/dx min ~ MeV/(g/cm ) Energy loss of minimum ionising particles de -1 de -1 Absorber MeVcm MeVg cm dx d( x) min Water Xenon (gaseous) Iron Lead min Hydrogen (gaseous)

6 Example

7 Bremsstrahlung Electrons and positrons lose energy via ionization just like other charged particles. Small changes to calculation (identical particles, m(target) = m(projectile)) BUT dominant energy loss mechanism for high energy electrons is electromagnetic radiation Circular acceleration: Synchrotron Radiation Motion through matter: Bremsstrahlung Semi-classical calculation yields: d e 5 dk c Z 4 1 Z mec Mv1 r e k ln Mv 1 k Cross section depends on Incident particle s mass (1/M ) Medium (Z )

8 Bremsstrahlung, QM Proportional to Z /A of the Material. Proportional to Z 14 of the incoming particle. Proportional to of the material. Proportional 1/M of the incoming particle. Proportional to the Energy of the Incoming particle E(x)=E o e (-x/x0) Radiation Length X 0 M A/ ( Z 14 Z ) X 0 : Distance where the Energy E 0 of the incoming particle decreases E = E 0 e -1 = 0.37E 0.

9 Radiation Length (L r ) The radiation length is a very important quantity describing energy loss of electrons traveling through material. We will also see L r when we discuss the mean free path for pair production (i.e. e + e - ) and multiple scattering. There are several expressions for L r in the literature, differing in their complexity. The simplest expression is: L 1 r 4r e N a ln(183z 1/ 3 )( Z / A) Leo and the PDG have more complicated expressions: L L 1 r 1 r 4r e N a [ln(183z 1/ 3 ) f ( Z )]( Z( Z 4re N a[ Z ( Lrad1 f ( Z )) ZLrad )] 1) / A) Leo, P41 PDG L rad1 is approximately the simplest expression and L rad uses 1194Z -/3 instead of 183Z -1/3, f(z) is an infinite sum. Both Leo and PDG give an expression that fits the data to a few %: 716.4A L r ( g cm ) Z( Z 1) ln(87 / Z ) The PDG lists the radiation length of lots of materials including: Air: 3040cm, 36.66g/cm teflon: 15.8cm, 34.8g/cm H O: 36.1cm, 36.1g/cm CsI: 1.85cm, 8.39g/cm Pb: 0.56cm, 6.37g/cm Be: 35.3cm, 65.g/cm Leo also has a table of radiation lengths on P4 but the PDG list is more up to date and larger.

10 Critical Energy For the muon, the second lightest particle after the electron, the critical energy is at 400GeV. The EM Bremsstrahlung is therefore only relevant for electrons at energies of past and present detectors. Critical Energy: If de/dx (Ionization) = de/dx (Bremsstrahlung) Muon in Copper: p 400 GeV Electron in Copper: p 5 MeV W. Riegler/CERN 10

11 Electromagnetic Interaction of Particles with Matter Z electrons, q= e 0 M, q=z 1 e 0 Interaction with the atomic electrons. The incoming particle looses energy and the atoms are excited or ionized. Interaction with the atomic nucleus. The particle is deflected (scattered) resulting in multiple scattering of the particle in the material. During these scattering events a Bremsstrahlung photons can be emitted. W. Riegler, Particle Detectors In case the particle s velocity is larger than the velocity of light in the medium, the resulting EM shockwave manifests itself as Cherenkov Radiation. When the particle crosses the boundary between two media, there is a probability of the order of 1% to produce an X ray photon, called Transition radiation.

12 Cherenkov Radiation A charged particle travels through a medium at a speed larger than the local speed of light

13 Cherenkov light Named after the Russian scientist P. Cherenkov who was the first to study the effect in depth (he won the Nobel Prize for it in 1958) From Relativity, nothing can go faster than the speed of light c (in vacuum) However, due to the refractive index n of a material, a particle can go faster than the local speed of light in the medium c p = c/n This is analogous to the bow wave of a boat travelling over water or the sonic boom of an aeroplane travelling faster than the speed of sound Roger Forty Particle ID (Lecture I) 13

14 Propagating waves A stationary boat bobbing up and down on a lake, producing waves Roger Forty Particle ID (Lecture I) 14

15 Propagating waves Now the boat starts to move, but slower than the waves No coherent wavefront is formed Roger Forty Particle ID (Lecture I) 15

16 Propagating waves Next the boat moves faster than the waves A coherent wavefront is formed Roger Forty Particle ID (Lecture I) 16

17 Propagating waves Finally the boat moves even faster The angle of the coherent wavefront changes cos = v wave v boat Roger Forty Particle ID (Lecture I) 17

18 Speed calculation Using this construction, we can determine (roughly) the boat speed: 70º, v wave = knots on water v boat = v wave /cos 6 knots Cherenkov light is produced when charged particle (v boat = c) goes faster than the speed of light (v wave = c/n) cos C = 1 / n Produced in three dimensions, so the wavefront forms a cone of light around the particle direction Measuring the opening angle of cone particle velocity can be determined º For Ne gas (n = ) Roger Forty Particle ID (Lecture I) 18

19 Nov Cherenkov Radiation () Wave front comes out at certain angle cos c 1 n Threshold: > 1/n

20 Threshold Momentum for Cherenkov Radiation Example: Threshold momentum for Cherenkov light: 1 1 n 1 t t n 1 n 1 n 1 t t 1 1 n 1 ( n 1)( n 1) t Example: Thresholds for different particles in He 1 For gases it is useful to set = n-1 t t ( ) The momentum (p t ) at which we get Cherenkov radiation is: p t m t t m ( ) For a gas + so the threshold momentum can be approximated by: m pt mt t For helium =3.3x10-5 so we find the following thresholds: electrons 63 MeV/c kaons 61 GeV/c pions 17 GeV/c protons 115GeV/c t Medium =n-1 t helium 3.3x CO 4.3x H O glass

21 Nov Cherenkov Radiation (3) How many Cherenkov photons are detected? We can calculate the number of photons/dx by integrating over the wavelengths that can be detected by our phototube ( 1, ): dn dx sin 1 d sin 1 [ 1 1 ] For a highly relativistic particle going through a gas the above reduces to: dn dx 780( n 1) photons/cm GAS Photons are preferentially emitted at small s (blue) For He we find: -3 photons/meter (not a lot!) For CO we find: ~33 photons/meter For H O we find: ~34000 photons/meter

22 Nov 004 Different Cherenkov Detectors Threshold Detectors Yes/No on whether the speed is β>1/n Differential Detectors β max > β > β min Ring-Imaging Detectors Measure β

23 Nov Threshold Counter Particle travel through radiator Cherenkov radiation

24 Types of Cerenkov Counters Differential Cerenkov Counter: Makes use of the angle of Cerenkov radiation and only samples light at certain angles. For fixed momentum cos is a function of mass: cos 1 n 1 n( p / E) m np p Differential cerenkov counters typically on work over a fixed momentum range (good for beam monitors, e.g. measure or K content of beam). Problems with differential Cerenkov counters: Optics are usually complicated. Have problems in magnetic fields since phototubes must be shielded from B-fields above a few tenths of a gauss. Not all light will make it to phototube

25 Nov Ring Imaging Detectors (1)

26 Ring Imaging Cerenkov Counters (RICH) RICH counters use the cone of the Cerenkov light. The ½ angle () of the cone is given by: 1 cos n 1 cos 1 m p np r L The radius of the cone is: r=ltan, with L the distance to the where the ring is imaged. For a particle with p=1gev/c, L=1 m, and LiF as the medium (n=1.39) we find: deg r(m) K Great /K/p separation! P Thus by measuring p and r we can identify what type of particle we have. Problems with RICH: optics very complicated (projections are not usually circles) readout system very complicated (e.g. wire chamber readout, channels) elaborate gas system photon yield usually small (10-0), only a few points on circle

27 Super Kamiokande

28 SuperK SuperK is a water RICH. It uses phototubes to measure the Cerenkov ring. Phototubes give time and pulse height information 481 MeV muon neutrino produces 394 MeV muon which later decays at rest into 5 MeV electron. The ring fit to the muon is outlined. Electron ring is seen in yellow-green in lower right corner. This is perspective projection with 110 degrees opening angle, looking from a corner of the Super-K detector (not from the event vertex). Color corresponds to time PMT was hit by Cerenkov photon from the ring. Color scale is time from 830 to 1816 ns with 15.9 ns step. In the charge weighted time histogram to the right two peaks are clearly seen, one from the muon, and second one from the delayed electron from the muon decay. Size of PMT corresponds to amount of light seen by the PMT. From: For water n=1.33 For =1 particle cos=1/1.33, =41 o SuperK has: 50 ktons of H O Inner PMTS: 1748 (top and bottom) and 7650 (barrel) outer PMTs: 30 (top), 308 (bottom) and 175(barrel) From SuperK site

29 The BaBar DIRC Detector of Internally Reflected Cerenkov light Here the challenge is to separate s and K s in the range: 1.7<p< 4. GeV DIRC uses quartz bars (490x1.7x3.5cm 3 ) as radiator (n=1.473) and light guide The cerenkov light is internally reflected to the end of a bar bar must be very flat <5Å DIRC is a 3D device, measures x, y, and time of Cerenkov photons Detect the photons with an array of phototubes Typical photon has: =400 nm 00 bounces 5m path in quartz bar ns propagation time laser light propagating in a quartz bar 880.P0 Winter 006 Richard Kass 9

30 The BaBar DIRC Detector of Internally Recflected Cherenkov Light (DIRC) 1.5 T Solenoid Electromagnetic Calorimeter (EMC) Drift Chamber (DCH) Instrumented Flux Return (IFR) Silicon Vertex Tracker (SVT) phototube array 880.P0 Winter 006 Richard Kass 30

31 Performance of the BaBar DIRC Timing information very useful to eliminate photons not associated with a track Note: the pattern of phototubes with signals is very complicated. The detection surface is toroidal and therefore the cerenkov rings are disjoint and distorted. ±300 nsec window background hits ±8 nsec window 1- background hits Use a maximum likelihood analysis to separate /K/p: L=L( c, t, n ) DIRC works very well! 880.P0 Winter 006 Richard Kass 31

32 Transition Radiation Z electrons, q= e 0 M, q=z 1 e 0 When the particle crosses the boundary between two media, there is a probability of the order of 1% to produced and X ray photon, called Transition radiation. 4/18/01 3

33 Transition Radiation Produced by relativistic charged particles when they cross the interface of two media of different dielectric constants (Note that n ~ sqrt()) Qualitative Explanation: Since the electric field of the particle is different in the two media, the particle has to shake off the difference when it crosses the boundary. The total energy loss depends on the Lorentz factor = E/mc Mostly forward directed Intensity roughly proportional to the energy E Typically X-ray photons with energies between 5 15 kev The number of photons produced is very small. About 0.8 photons per transition for a particle with = 000 (highly relativistic) Stack foils to increase number of transitions

34 Interactions of Photons with Matter There are three main contributions to photon interactions: Photoelectric effect (E < hundreds of kev) Compton scattering (Medium energies ~ MeV) Pair production (dominates at energies > few MeV) A beam of s with initial intensity N 0 passing through a medium is attenuated in number (but not energy) according to: dn=-ndx or N(x)=N 0 e -x With = linear attenuation coefficient which depends on the total interaction cross section ( total = coh + incoh + +).

35 Intensity: I I 0 e Interaction of photons x photo Compton : mass attenuation coefficient N A cm g i i / A pair... photo effect 1 MeV pair production Rayleigh scattering (no energy loss!) Compton scattering

36 Interaction of Photons Thomson and Rayleigh Scattering No energy transfer (just change in photon direction) Low energies Rayleigh scattering off the atom as a whole (coherent effect) Photo Effect Low energy (~ binding energy of electrons in atoms) Higher cross section for high Z material (~ Z 4-5 ) Compton Scattering Medium energies Klein Nishina formula d r d e Compton edge (maximum recoil energy) T max h 1 Pair Production E > 1.0 MeV cos 1 cos 1 1 cos h with 1 cos m e c

37 Photon Conversions Otherwise known as pair production. Threshold: m e c (nucleus) 4m e c (atomic electron) Total cross section increases rapidly with photon energy, approximately proportional to Z. Comparing pair production with bremsstrahlung: pair 7 9 brem Or for the mean free path:

38 Electromagnetic Showers a beam of electrons impinging on solid matter will have a linear absorption coefficient of 1/X0 this process repeats, giving rise to an e.m. shower: the process continues until the resulting photons and electrons fall below threshold so how do we get some sort of signal out? ultimately we need ionization Will discuss more when we talk about calorimetry

39 Basic EM Interactions e + / e - Ionization de/dx ~ 1/, z de/dx E Bremsstrahlung de/dx ~ 1/m, z 4 de/dx E Photoelectric effect E Compton effect E Pair production E