P308 – Particle Interactions

1. Dr David Cussans Mott Lecture Theatre Monday 11:10am Tuesday,Wednesday: 10am P308 – Particle Interactions

2. Aims of the course: • To study the interaction of high energy particles with matter. • To study the interaction of high energy particles with magnetic fields. • To study the techniques developed to use these interactions to measure the particle properties. • To look at how several different types of detector can be assembled into a “general purpose detector”

3. Aims of the course • (This course deals with particles as they are observed. We will try to be complementary to the material of the Quarks and Leptons course.)

4. Advised texts – Background on particles: • Everything you need to know about particles – and more – is in chapters 2 and 9 of Nuclear and Particle Physics, W.S.C.Williams, Oxford. If you want to know more, look at some general text on particles as advised for the Quarks and Leptons course, e.g. Particle Physics, Martin and Shaw, John Wiley

5. Advised texts - Particle interaction with matter: • Single Particle Detection and Measurement R. Gilmore, Taylor and Francis. • Detector for Particle Radiation K. Kleinknecht, Cambridge. • The Physics of Particle Detectors, D. Green, Cambridge.

6. Advised texts – astrophysicalapplications: • High Energy Astrophysics (Vol. 1) M. Longair, Cambridge • There are also some good subject reviews available online from the particle data group: • http://pdg.lbl.gov/2004/reviews/passagerpp.pdf • passage of particles through matter • http://pdg.lbl.gov/2004/reviews/pardetrpp.pdf • particle detectors • http://pdg.lbl.gov/2004/reviews/kinemarpp.pdf • relativistic kinematics Online Resources:

7. Outline and structure of the lectures: • Lectures 1–4: • Introduction and scope of the course • particle properties from the detector point of view • particle glossary • Kinematics • cross-sections and decay rates.

8. Outline and structure of the lectures: • Lectures 5–10: • Interactions of fast particles in a medium. • Ionisation by charged particles • Quantitative description of ionisation energy loss. • Other energy loss processes • Showering processes.

9. Outline and structure of the lectures: • Lectures 11–12 (Information from detectors): • Position and timing measurement. • Momentum, energy and velocity measurement. • Measurement errors • counting fluctuations.

10. Outline and structure of the lectures: • Lectures 13–18: • The general purpose detector. • Some specific detector technologies. • Technology choices for different applications.

11. Particle behaviour becoming more evident What is a Particle? Wave Particle Frequency Wavelength Energy Momentum e.g. EM radiation/photons: Radio/microwave Visible X-ray/g-ray Energy Wavelength

12. Relativity and QM • Relativity describes particle behaviour at • high speed ( close to speed of light) • I.e. high energy (compared with particle rest mass) • Quantum mechanics describes behaviour of waves (or fields) • Probability interpretation for individual particles • Often need both to analyse results of particle experiments

13. Relativity and QM • Alpha particle scattering from nuclei: • Rest mass of alpha = 3.7GeV • Typical energy ~ 10MeV • Can treat classically (fortunately for Rutherford!) a-emitter

14. Relativity and QM • Compton scattering of g from electron: • Rest mass of g = 0 eV • Rest mass of electron = 511 keV • Typical energy of g ~ 10MeV • Need to use both relativity and QM g -emitter g e

15. The “Fundamental Particles” • Quarks • u,c,t d,s,b • We do not see free quarks, the particles actually observed are the “traditional” particles such as protons, neutrons and pions. • Leptons • e, m, t, ne,nm, nt • Gauge bosons • g , W , Z, gluons ( only g is observed directly )

16. Types of Particle • Particles divided into • Fermions – spin ½ , 3/2 , 5/2 etc. • Bosons – spin 0, 1, 2 etc. • Hadrons – made up of quarks • Baryons and mesons • Antiparticles • … appear to be a necessary consequence of quantum field theory

17. Particle glossary • Most important particle properties from the detector point of view are: • Mass • Charge (electric, “strong”, “weak”) • Interactions ( EM, strong , weak ) • Lifetime

18. Stable particles • Can be used as beam particles or for “low-energy physics” • Decay prohibited by conservation laws • Photon ( g ) • Neutrinos ( n ) • Electron/positron • Proton/antiproton

19. At high energy, 90% of detected particles from an hadronic interaction are charged pions! Weakly decaying particles • Decay “parameter” • Gives mean decay distance for 1GeV energy • Neutron and muon • Light quark mesons: • Strange baryons or “Hyperons” • Heavy quark hadrons, t lepton n: 3×1011m m±: 6km p±,K±,K0L: 5-50m 1-10cm 50-200mm

20. Very short-lived particles • Detectable only by their decay products • Electromagnetic decays to photons or lepton pairs • Includes p0 giving high-energy photons • Strongly decaying “resonances” p0: ct/m= 180nm

21. Very massive fundamental particles • W±,Z0 • top quark • Higgs boson • Super-symmetric particles, … • Decay indiscriminately to lighter known (and possibly unknown) objects – leptons, quark “jets” (pions plus photons) etc.

22. Relativity "Henceforth spaceby itself, and time by itself, are doomed to fade away into mereshadows, and only a kind of union of the two will preserve anindependent reality." Hermann Minkowski,1908

23. Relativistic relations • Special relativity applies to inertial ( ie. Not accelerating ) frames. • Needed in most particle interaction physics.

24. Four-vectors • Extension of “normal” 3-vector e.g. • Position: x = ( ct , x ) • Velocity:  = ( c ,  ) • Momentum: p = m • = ( mc , m ) = ( E/c , p ) • Have time-like component(scalar) and space-like component(vector)

25. “Length” of a 4-vector • Length of a 3-vector doesn’t change under rotations in (three-) space: x2 + y2 + z2 = x’2 + y’2 + z’2 = constant • Lorentz 4-vectors are such that their “length” (magnitude) does not change under Lorentz transformation: xx= x`x` = x02 – (x12+x22+x32) = constant

26. Four-vector terminology • Contravariant vectors eg. x = ( ct , x ) • Covariant vectors eg. x= ( ct , -x ) • Contravariant and covariant differ in their behaviour under Lorentz transform (basically use them in Contra+covariant pairs) • ( Don’t worry about the terminology – included only for completeness.)

27. Four-vector Operations: • “dot-product” for 4-vectors: • E.g. “length” of a 4-vector is the vector “dotted” with itself: • NB. The components of a 4-vector change under transformation, but its magnitude does not. minus sign comes from minus in space component of pm

28. The Lorentz Transformation • Lorentz transformation:

29. Energy, momentum and mass • N.B. Will use “natural units” ,set and use units of eV for energy from now on.

30. Useful Reference Frames • CM frame is Centre-of-Mass or Centre-of-Momentum • “Rest frame” for a system of particles • I.e. pi=0 ( where p is the usual 3-vector) • LAB frame – may be: • Rest frame of some initial particle, or • CM frame,or • Neither

31. Invariant Quantities –Invariant Mass • Lorentz invariantquantities exist for individual particles and systems. • Invariant mass of a system:

32. Invariant Mass • Invariant mass is equivalent to the CM frame energy for a particle system • If (pi)=0 then • NB within a frame pi =constant • (conservation of momentum)

33. Four-momentum Transfer • 4-momentum transfer is change in (E,p) between initial and final states • q= p` - p • Its magnitude, q², is an invariant p` p k k`

34. Total CM Energy in Fixed Target • “Fixed target” experiment with a beam of particles, energy Eb, mass mb incident on a target of stationary particles, mass mt mb,Eb M,Ef mt

35. Threshold Energy for Particle Production: • If we want a fixed target experiment to have a CM energy, , higher than M then the beam energy Eb :

36. Mass of Short-lived Particle • From invariant mass of its decay products, e.g. 2-body: • How to measure ma? mb,Eb bc ma mc,Ec

37. Two-body Decay • Initial invariant mass s= ma2 • Final invariant mass = • If Eb, Ec >> mc , mcthen Eb, Ec~ pb, pc • So,

38. q² for a Scattering Reaction p`,E`  m,p,E • For E,E` >> m • In elastic scattering, can use energy conservation to get energy lost by incident particle ... mt

39. Energy Loss in Elastic Scattering p`,E`  m,p,E mt • Energy transfer to target: • Maximum energy transfer in scatter: • Quoted without proof…

40. Time Dilation and Decay Distance • Often measure particle lifetime by distance between creation and decay. • If mean life of particle is  in its rest frame, in the lab frame the mean life is • During this time it travels a distance c • Since p=m, … mean decay distance in lab * Decay length proportional to momentum

41. Interaction Rates and Cross-sections • Experiments measure rates of reactions – these depend on both • “kinematics” e.g. energy available to final state particles, and • “dynamics”, e.g. strength of interaction, propagator factors etc.

42. Cross section,  • Cross section incorporates: • Strength of underlying interaction (vertices) • Propagators for virtual exchange factors • Phase space factors (available energy) • Does not depend on rate of incoming particles. • Called the “cross-section” because it has units of area. • Normally quoted in units of barns ( 10-28m2 ) … or multiples eg. Nanobarns (nb), picobarns (pb)

43. Cross-Section – “physical” interpretation. • Can be thought of as an effective area centred on the target – if the incident particle passes through this area an interaction occurs. • Physical picture only realistic for short range interactions. (target behaves like a featureless extended ball) • For long range interactions, like EM, integrated cross-section is infinite. • Cross-section invariant under boost along incoming particle direction.

44. Cross-section and Interaction rate. • For fixed target, with a target larger than the beam • W=r  L  • W = interaction rate • r = rate of incoming particles •  = number of target particles per unit volume • L = thickness of target •  = cross-section for interaction r L

45. Cross-section and Interaction rate. • For fixed target, in terms of particle flux, J • W=J n  • W = interaction rate • J = Flux: particles per unit area per unit time. • n = total number of particles in target. •  = cross-section for interaction

46. Colliding Beam Interaction Rate • In a colliding beam accelerator particles in each beam stored in bunches. • Bunches pass through each other at interaction point, with a frequency f • Have an effective overlap area, A • Can express in terms of beam currents I=nf • Factors n1n2f/A normally called the Luminosity, L

47. Differential Cross-section, d • We have just defined the total cross-section,, related to the probability that an interaction of any kind occurred. • Often interested in the probability of an interaction with a given outcome ( e.g. particle scatters through a given angle )

48. Cross-section - Solid Angle • Consider a particle scattering through  ,  • What is probability of scatter between (, +d) and (  , +d) ? • Element of solid angle d = d(cos). d • Differential cross section: • For, e.g. fixed target:

49. Differential Total Cross-section • To get from differential to total cross-section: • With unpolarized beams – no dependence on  - integrate to get d()/d • If measuring some other variable ( e.g. final state energy, E) other differential cross-sections, e.g:

50. Decay Width,  • The lifetime of particles can tell us about the strength of the interaction in decay process (and about channels available) • Decay rate, W=1/ (in rest frame) •  - lifetime in rest frame • For short lived particles – reconstruct the mass, m, of the particle from decay products. • Uncertainty principle: • t ~  , so