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

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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

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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.)

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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

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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.

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

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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.

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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.

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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.

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

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

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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

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

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

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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,,, e,, Gauge bosons –, W, Z, gluons ( only is observed directly )

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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

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

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Stable particles Can be used as beam particles or forlow-energy physics Decay prohibited by conservation laws –Photon ( ) –Neutrinos ( ) –Electron/positron Proton/antiproton

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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, lepton n: 3×10 11 m : 6km 1-10cm m At high energy, 90% of detected particles from an hadronic interaction are charged pions!,K,K 0 L : 5-50m

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Very short-lived particles Detectable only by their decay products Electromagnetic decays to photons or lepton pairs –Includes 0 giving high-energy photons Strongly decaying resonances c m= 180nm

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Very massive fundamental particles –W ±,Z 0 –top quark –Higgs boson –Super-symmetric particles, … Decay indiscriminately to lighter known (and possibly unknown) objects – leptons, quark jets (pions plus photons) etc.

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Relativity "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." Hermann Minkowski,1908

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

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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)

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Length of a 4-vector Length of a 3-vector doesnt change under rotations in (three-) space: x 2 + y 2 + z 2 = 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` = x 0 2 – (x 1 2 +x 2 2 +x 3 2 ) = constant

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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) ( Dont worry about the terminology – included only for completeness.)

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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 p

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The Lorentz Transformation Lorentz transformation:

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

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

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Invariant Quantities – Invariant Mass Lorentz invariant quantities exist for individual particles and systems. Invariant mass of a system:

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

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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

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Total CM Energy in Fixed Target Fixed target experiment with a beam of particles, energy E b, mass m b incident on a target of stationary particles, mass m t m b,E b mtmt M,E f

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

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Mass of Short-lived Particle From invariant mass of its decay products, e.g. 2-body: –How to measure m a ? m c,E c mama m b,E b bc

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Two-body Decay Initial invariant mass s = m a 2 Final invariant mass = If E b, E c >> m c, m c then E b, E c ~ p b, p c So,

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

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Energy Loss in Elastic Scattering Energy transfer to target: Maximum energy transfer in scatter: Quoted without proof… p`,E` m,p,E mtmt

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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

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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.

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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 ( m 2 ) … or multiples eg. Nanobarns (nb), picobarns (pb)

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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.

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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 L r

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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

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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 n 1 n 2 f/A normally called the Luminosity, L

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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 )

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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:

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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:

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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

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Decay Width Define the decay width,, to be the uncertainty in the mass, m For particle with several different modes of decay, can define partial widths, i –Total width is the sum of all partial widths

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Decay Width Example Invariant mass of W = 80GeV Width=2.2GeV Mean life 3.25 x s c ~ m (I.e. less than size of proton )

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End of Kinematics

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