Introduction to Particle Physics I particle detection

Introduction to Particle Physics I particle detection Risto Orava Spring 2016

Lecture II particle detection

outline Lecture I: Introduction, the Standard Model Lecture II: Particle detection Lecture III: Relativistic kinematics, Nonrelativistic Quantum Mechanics Lectures IV: Decay rates and cross sections Lecture V: The Dirac equation Lecture VI: Particle exchange Lecture VII: Electron-positron annihilation

outline continued... Lecture VIII: Electron-proton elastic scattering Lecture IX: Deeply inelastic scattering Lecture X: Symmetries and the quark model Lecture XI: Quantum Chromodynamics Lecture XII: The Weak Interaction Lecture XIII: Electroweak unification Lecture XIV: Tests of the Standard Model Lecture XV: The Higgs boson

interactions with matter 1. Charged particles ( only e - & p stable) ionization and excitation bremsstrahlung scattering in the Coulomb field of atoms inelastic scattering 2. Neutral particles (only ν stable) elastic&inelastic scattering 3. Electromagnetic radiation (γ) photoelectric effect Compton scattering pair production unstable particles decay after a distance of d = γvτ γ = 1/ (1-v 2 /c 2 ), τ = life time in rest frame

interactions with matter detection via transfer of energy by ionization or excitation of atomic electrons. most of the energy loss from ionization, in gases typical loss per ionization electron about 30 ev. the ionized electrons behave as de/e 2 - most electrons have small energies. some electrons have enough energy for extra ionization (δ-rays or knock-on electrons). In argon, an average of 30 primary ionizations/ cm, and a total of some 100 electrons/cm are ionized.

Bethe Bloch Formula the ionisation energy loss of a singly charged particle (v=βc) expressed by Hans Bethe and Felix Bloch in the 1930 s Bethe-Bloch Formula: de dx 4π!2 c 2 α 2 nz ln( 2β 2 γ 2 m e c 2 ) β 2 m e v 2 I e I e is the ionization potential averaged over all the atomic electrons (I e 10 Z ev) falls as 1/β 2 (β -5/3 ) to a minimum, then a broad minimum at βγ 4, and a slow relativistic rise with lnγ 2. The relativistic rise is cancelled at high γ by the density effect, i.e. polarization of the medium screens more distant atoms. here de/dx [MeVg -1 cm 2 ] depends only on β. Valid for heavy particles (m > m µ ), only. Electrons & positrons require special treatment (m proj = m tgt ) + Bremsstrahlung! Z/A does not differ much (H 2 a special case) Note: βγ = v / c 1 (v / c) 2 = p mc

de/dx Bethe Bloch Formula... most relativistic particles near the minimum 1.5 MeV/g/cm 2 ; Al has a density of 2.7 g/cm 3, a minimum ionizing particle passing through 1cm of Al loses about 4 MeV of energy the shallow rise above γ 3; the relativistic rise - due to the relativistic contraction of the EM fields. in liquids and solids, em field is effectively screened as δ(γ) Fermi plateau. de/dx depends on particle velocity, used to identify particles up to E 1 GeV. p GeV/c

nuclear interactions... long lived or stable charged particles, like π ±,K ±,p ±,n,k o, can be identified by their energy loss characteristics in matter: e absorbed by 35cm of Fe π ±,K ±,p ± absorbed by 1.7m of Fe µ ± not absorbed by 1.7m of Fe for the long life time or stable neutral particles γ absorbed by 35cm of Fe n,k o absorbed by 1.7m of Fe ν f s not absorbed by 1.7m of Fe

Delphi measurements p (GeV/c)

charged particle interactions rate of energy loss with distance (de/dx) depends on the momentum and particle type Bethe-Bloch formula for a given medium, and v c: de 2 2 / dx (1/ β )logγ γ = 1/ 1 β relativistic rise ~log γ

charged particle interactions - the rate of ionisation energy loss mainly depends on material density ρ - express the number density of atoms as n = ρ/(am u ) (A = atomic mass number, m u = 1.66 10-27 kg = unified atomic mass unit) - Bethe-Bloch formula now becomes. 1 de ρ dx 4π!2 c 2 α 2 m e v 2 m u Z 2 A ln(2β γ 2 m e c 2 ) β 2 I e - de/dx (usually expressed in units MeV g -1 cm 2 ) proportional to Z/A ( constant); a mip has βγ 3. - an example: a 10 GeV muon loses some 13 MeV cm -1 in Fe

primary and total Ionization - fast charged particles ionize the atoms of a medium. primary ionization total ionization - primary ionization often releases electrons which are energetic enough to ionize other atoms. - total number of created electron-ion pairs (ΔE=total energy loss, W i =effective average energy loss/pair): n total = ΔE W i = de dx Δx W i (3 4) n primary Note: The actual no. of primary electron-ion pairs is Poisson distributed: m n e Pm ( ) = m! n The detection efficiency is therefore limited to: εdet = 1 P(0) = 1 e n For thin layers, edet can then be significantly lower than this. For example, in Argon of d=1mm n primary =2.5 ε det =0.92.

Landau tails - real detectors have finite granularity- do not measure <de/dx>, but the energy ΔE deposited within a layer of finite thickness δx. ΔE results from a number of collisions, i, with energy transfer, E i, and a cross section of dσ/de. - for thin layers (and low density materials): a few collisions, some with high energy transfer energy loss distributions show large fluctuations towards high losses: Landau tails (For thick layers and high density materials: many collisions, Central Limit Theorem Gaussian distributions) relative probability below excitation threshold excitation ionization by a distant collision ionization by close collisions, δ-electrons energy transfer/photon exchange - how to relate F(ΔE,δx) to dσ/de? Williams (1929), Landau (1944), Allison & Cobb (1980) etc. - Monte Carlo: (1) divide the absorber into thin layers. probability for any energy transfer within a slice is low. (2) choose energy transfer randomly according to the distribution above, (3) sum over the slices.

particle detectors

bubble chambers... a historical event: one of the eight beam particles (K - at 4.2 GeV/c) entering the chamber, interacts with a proton: K - p Ω - K + K o followed by the decays K o π + π - Ω - ΛK - Λ pπ - K - π - π ο

Introduction to Particle Physics Lecture IX - BC picture 1 R. Orava Spring 2005

a gas ionization chamber

spark chambers cosmic muon plastic scintillator trigger counter Plate Gaps: 0.635cm Gas: 90% Ne + 10% He coincidence circuit plastic scintillator trigger counter HV pulser -10kV a cosmic muon triggers the scintillators at top & bottom the pulser charges alternate plates to a 10kV potential difference the cosmic muon strips electrons from the He & Ne atoms, leaves a ionization trail behind the trail serves as a path of least resistance for a spark to jump across the potential difference between the plates pattern of sparks in the 6 spark chambers traces the muon trajectory

gaseous tracking detectors proportional tube - measures a space-point ionisation process yields electron-ion pairs electrons attracted towards anode wire (r=a) Electric field E = V 0 / r log (b/a) (cathode, r=b) as r a, E large : avalanche multiplication occurs due to secondary ionisation by electrons signal amplitude proportional to anode voltage electron drift time * velocity = drift distance

gaseous tracking detectors multi-wire proportional chamber measures space-points on many tracks cathode planes and a large number of anode wires operates like a proportional tube electron drift time * velocity = drift distance

gaseous tracking detectors drift chamber - measures space point(s) on many tracks replace cathode planes with wires use additional field shaping wires longer drift distances possible can sample position of tracks at many depths

the MWPC Georges Charpak began work at CERN in 1959, after working on spark chambers, invented the wire chamber 1968, for which he was awarded the physics Nobel in 1992.

time projection chambers time projection chamber (TPC) measures space points in 3D large (2m long, 2m diameter) ionisation drift volume central cathode plane and anode wire planes at ends measure drift time (z-coordinate) and position of anode hits (xy coordinates) measure de/dx energy loss from signal amplitudes

the gas electron multiplier gem - - new generation gas amplified detectors

scintillation counter hodoscope 86 scintillator light guide photomultiplier incident charged particle focusing grid anode photo cathode pm base - the scintillator covered by a non-transparent material (black tape), connected to the PM by a light guide. - HT + output volts

87 photomultiplier tube (PMT) the dynones connected to a resistance chain in the external circuit, each one is at a succesively higher potential from cathode to anode.

detector characteristics Detector Type Resolution Time Dead Time Bubble Chamber 1ms 50ms Spark Chamber* a few ms a few ms Proportional Chamber 50ns 200ns Drift Chamber 2ns 100ns Scintillator 150ps 10ns Silicon Strip <15ns* unknown

measurements - observables

basic observables " momentum " time-of-flight " energy loss " particle identity " invariant mass

observables

data analysis

momentum " definition " Newtonian mechanics: " special relativity p = mv p = γmv γ = 1 1 ( v / c) 2 How is the momentum of a particle measured?

momentum " arrange a constant magnetic field B into the spectrometer volume " particles with electrical charges, velocity v, are deflected by the Lorentz force: F qv!! M = B " Since the Lorentz force acts in perpedicular to the direction of the B 2 field, it causes a centripetal force: mv " particle momentum is now obtained as: F C = R p = γmv = qbr

3-momentum curvature of a charged track: in magnetic field a charged particle moves along a helical track radius of the helix is given by: R psinθ qb for a unit charge use: =!! θ is the angle between v and B R = psinθ / 0.3B with p in GeV/c, B in Tesla and R in meters. also holds for relativistic particles

3-momentum

example: track chamber

track reconstruction

track fit A 200 MeV/c track in a storage ring detector in the rφ-plane from a Monte Carlo simulation. The curve shown is a circle fitted to the data points. The data points are two accurate hits measured in a silicon vertex detector, and hits measured in two drift chambers. Two hits with a reduced accuracy are measured between the two drift chambers in a special z- chamber. The χ 2 of the fit is, due to multiple scattering, rather large. The deviations of the hits from the circle are however not visible in this plot (see next page).

3-momentum... x y L s ρ Θ p T p ( GeV / c) = 0.3 Bρ( Tm) T = qbr L Θ Θ = sin Θ 2ρ 2 2 Δ p = p sin Θ 0.3LB T T 0.3LB p 2 2 Θ Θ 0.3 LB s = ρ(1 cos ) ρ 2 8 8 p T T x The sagitta s is determined by three measurements with error: σ ( x) = x 3 3 σ( x) σ( x)8p σ ( pt ) meas σ () s = = 2 = 2 2 p s s 0.3BL T For N equidistant measurements one obtains: σ( pt) meas σ( x) p 720 = p BL N T T 0.3 2 + 4 (for N 10) T 2 + x 2 1 3 Example: p = 1 GeV / c, L = 1 m, B = 1 T, σ ( x) = 200 µ m, N = 10 σ ( pt ) p T meas T 0.5% (s=3.75cm)

detection of electrons & photons at large energies, E > E critical, energy loss dominated by bremsstrahlung: photon emission in the electrostatic field created by the atomic nuclei

electron bremsstrahlung critical energy: E critical 800/Z MeV rate of the bremsstrahlung process proportional to 1/M 2 at low energies photons mainly interact through photoelectric effect (photon absorbed by an atomic electron ejected from the atom) at higher energies (E γ 1 MeV) the Compton scattering process: γe - -> γe - above E γ > 10 MeV, photon interactions leading to e + e - pairs dominate

radiation length em interactions of high energy electrons & photons characterized by the radiation length: X 0 = 1 4αnZ 2 r e 2 ln(287/z 1/2 r e = e 2 4πε 0 m e c 2 = 2.8 10 15 m classical radius of e - an average distance over which the electron energy is reduced by 1/e approximately 7/9 of the mean free path of the e + e - pair production process for example: X 0 (Fe) = 1.76 cm, X 0 (Pb) = 0.56 cm

electromagnetic showers secondary electrons/positrons produce bremsstrahlung which results in further pair production, leads to formation of an electromagnetic shower which grows until all the primary energy is consumed EM showers initiated by photons and electrons the shower particles approximately double after each X 0 of material: <E> E/2 x shower maximum at ln2, for Pb E critical 10 MeV, E = 100 GeV shower has a maximum at x max 13 X 0. x max = ln(e / E critical )

electromagnetic calorimeters em energy resolution typically: σ E E 3% 10% E / GeV

electromagnetic calorimeter -OPAL individual lead glass blocks - OPAL EM Calorimeter

nuclear Iinteractions hadrons entering material create a cascades by nuclear interactions much more diverse and larger compared to the EM showers characteristics: Material X o λ l/x o Air 300m 740m 2.5 Al 8.9cm 39.4cm 4.4 Fe 1.78cm 17.0cm 9.5 Pb 0.56cm 17.9cm 30.4 λ is the nuclear absorption length, I = I o exp(-λ/λ ο )

hadron showers a calorimeter measures energies and positions of particles through total absorption the energy resolution of a calorimeter is paramterized as σ = E a E b c E where: a = stochastic term b = constant (containment) c = electronic noise σ E E 50% E / GeV

combined calorimetry

collider experiments

top-antitop production

Cherenkov counters Cherenkov light caused by local polarization of the material due to the passing charged particle a particle moving faster than light in the medium, v >> c/n, where n=refractive index of the material, an electromagnetic shock wave is produced. during the time between a travel from O to P, the succesive centers of polarized material along the path radiate em waves which, add up coherently to produce a wave front - moves in an angle θ with respect to the particle direction c / n cos θ = 1 nβ O θ βc light is emitted on the surface of a cone with the particle moving along the axis of the cone light intensity 1% of typical scintillation light P

Mirror Cherenkov.. Detector. Cherenkov media e-! e+! γ γ e" γ e" e"

detection charged particle tracks energy muon tracks scintillating fiber The Interaction silicon tracking calorimeters (dense) Point B EM hadronic absorber material electron photon wire chambers jet neutrino -- or any non-interacting particle -- missing transverse momentum p x = p y = 0, p z 0, measurements often in the x-y plane muon

layout of a typical collider experiment

layout of a typical collider experiment

cms experiment at the LHC

CERN accelerator complex

luminosity fixed target

colliding beams

luminosity - colliding beams

luminosity two equal beams 1 and 2

luminosity - examples

luminosity - challenges

particle physics measurement system - physics analysis pipe-line IP5 Detectors: subdetector systems FEE: front-end electronics DAQ: data acquisition system DRS: data reduction system PAS: physics analysis system Physics DCS SUPPLY ON-LINE DOMAIN RAW DATA OFF-LINE DOMAIN OUTPUT

trigger interaction rates are typically too high to store every event for analysis - 40MHz at the LHC! collision rate has to be suppressed a fast trigger fast electronics and buffer memories used to pick up the interesting events store the full data of triggered events only

data acquisition use computer driven fast electronic readout only readout triggered events analogue drift times and signal pulse heights are converted into digital form digitised data stored on computer disk/tape

event reconstruction computer analyse digitised data offline use detector calibration constants to convert digitised signals from each detector element into distances, times and/or energies apply detector alignment information reconstruct space points perform pattern recognition to find tracks perform track fit to find track momentum compute EM and hadronic shower energies calculate de/dx, TOF, Cherenkov angles, etc

event reconstruction and display

Monte Carlo simulation Monte Carlo technique - based on random number generation for sampling known distributions rely on detailed and accurate simulation of detector response to correct for detector imperfections (inefficiencies, geometric acceptance) requires a validated model for the basic physics processes (production, decays, interactions) requires a validated description of the detector geometries and material distributions use simulation to determine the resolution function for unfolding the corrected data points

data analysis techniques identify particles (e,µ,τ,γ,π,k,p, ) identify jets of hadrons search for decay vertices of shortlived hadrons (charm and beauty quark decays) combine 4-momenta of particles to search for other decays e.g. π o γγ, H o bb apply kinematic cuts to reduce background i.e. reject events with improbable values extract physics parameters (e.g. H mass) using various fitting methods (e.g. least squares, maximumlikelihood, etc) multivariate techniques!

natural units The Planck constant The speed of light The natural units :! = c = 1 c h 34! = = 1.0546 10 2 π = 2.998 10 8 m s Js 1 1 [ c] = [ length] [ time] = [ L][ T ] [ L] = [ T ] 2 1 [!] = [ energy] [ time] = [ M ][ L] [ T ] [ M ] = [ L] 1 1 1 [ M ] = [ L] = [ T ] and [ E] = [ M ]

unit for energy ev PeV ev TeV ev GeV ev MeV ev kev J ev 15 12 9 6 3 19 10 10 10 10 10 10 1.602 1 = = = = = = PeV VHE E TeV LHC E GeV Tevatron E GeV LEP E MeV m MeV m kev m p p p e n p e 1 cosmic rays) ( 7 ) ( 980 ) ( 104.5 ) ( 939 938 511 = = = = = = =

energy scales - examples 230 µev: the thermal energy k B T of the cosmic microwaves 25 mev: the thermal energy k B T at room temperature; one air molecule has an average kinetic energy 38 mev 1.6 ev to 3.4 ev: the photon energy of visible light 13.6 ev: the energy required to ionize atomic hydrogen; molecular bond energies are on the order of 1 ev to 10 ev per bond 1 MeV: megaev (1.602 10 13 J): about twice the rest energy of an electron 17.6 MeV: the average energy released in the fusion of deuterium and tritium to form He-4; this is 0.41 PJ per kilogram of product produced 200 MeV: the average energy released in nuclear fission of one U-235 atom 210 MeV: the average energy released in fission of one Pu-239 atom

energy scales examples... 1 TeV: a tera electronvolts, or 1.602 10 7 J, about the kinetic energy of a flying mosquito [9] 14 TeV: the designed proton collision energy at the Large Hadron Collider (which has operated at half of this energy since 30 March 2010) 1 PeV: one petaelectronvolt, the amount of energy measured in each of two different cosmic neutrino candidates detected by the IceCube neutrino telescope in Antarctica [8] 300 EeV: exaev (3 10 20 ev = ~50 J): [7] the so-called Oh-My-God (herranjestas!) particle (the most energetic cosmic ray particle ever observed) ~0.624 ZeV: zettaev (6.24 10 20 ev): energy consumed by a single 100-watt light bulb in one second (100 W = 100 J/ s 6.24 10 20 ev/s) 2435 YeV: yottaev = 2.435 x 10 27 ev 4.341 10 9 kg = nature s maximum allowed mass for point-masses 5.25 10 8 YeV = 5.25 10 32 ev: total energy released from a 20 kt nuclear fission device 125.3±0.6 GeV: the energy emitted by the decay of the Higgs Boson, as measured by two separate detectors at the LHC to a certainty of 5 sigma [10]

unit conversions MeV m fm s m c s GeV s GeV 200 1 10 1 1 10 2.998 and resonance, a is the width of where, 1 particle life time 10 6.58 1 1 10 6.58 15 8 25 1 1 25 = = Γ Γ = = τ!

unit conversions Cross sections have dimensions 2 [ σ ] = [ L] = [ M ] 2 = 1 ( ev ) 2 of area : As the unit, we choose 1 ( GeV ) 2 = 389379nb = 389379 10 9 b with 1b :1barn = 10 24 cm 2 the typical scale of nuclear absorption

the unit of electrical charge α = 2 e 4πε! c 0 SI = 7.2972 10 3 1 137 = 2 e! c CGS = 2 e 4π! c Heaviside Lorenz Therefore, in Heaviside - Lorentz units, the electron charge is fixed to be e = 4πα Heaviside Lorentz

elementary interactions Gravitation, Electromagnetic, Weak and Strong Interactions

how to measure? - the scattering experiment detector beam energy determines R min - resolution particle in R min particle out Θ measure the energies and polar angles (θ) of the scattered particles

the scattering experiment - determine the laws of interactions probability hard ball scattering probability charged particle scattering 1 sin 4 (θ / 2) Θ 0 0 180 0 0 0 180 0 Θ E pot E pot 1/R R R

the scattering experiment - what more to learn? from over-all scattering probability ècoupling constant from energy of the scattered particle è momentum of the target particle energy of the beam particle determines the distance of approach: R min è resolution of the experiment - need high energies for finding the systematics at small distances usually many particles produced è gain more details on the scattering process/type of interaction

electron-proton scattering - DESY ep collider - HERA

electron-proton scattering - ep collider DESY

electron-proton scattering - ep collider DESY

NEXT: Lecture III;Special relativity, kinematics, non-reativistic Quantum Mechanics