17/01/17 F. Ould-Saada

Transcription

1 Chapter 3

2 3.1 Why Do We Need Accelerators? The Center-of-Mass (c.m.) System The Laboratory System Fixed Target Accelerator and Collider 3.2 Linear and Circular Accelerators Linear Accelerators Circular Accelerators 3.3 Colliders and Luminosity Example: the CERN Accelerator Complex 3.4 Conversion of Energy into Mass Use of Fixed Target Accelerators Baryonic Number Conservation 3.5 Particle Production in a Secondary Beam Time-of-Flight Spectrometer 3.6 Bubble Chambers in Charged Particle Beams Conservation Laws The Electron Spiral Electron-Positron Pair An Electron-Positron Tree Charged Particle Decays 17/01/17 F. Ould-Saada 2

3 Like Light wave, Matter wave - carries kinetic energy p²/2m - has a wavelength λ = h/p=2πh c/pc λ (fm)=1.24/p(gev/c) Possibility to study smaller objects possessing finer details - the higher the energy, the smaller the distance - optical microscope: λ γ ~ 200 nm (1 nm = 10-9 m) - electron microscope: λ e ~ nm - high energy accelerator resolves distances down to m!

4 λ = h p = 2π!c pc λ =1fm pc = pc =1TeV λ = pc = 2π!c λ GeV fm 1 fm GeV fm 1000GeV ~ 1.2GeV ~ m ~ am

5 Uncertainty principle ΔxΔp x ~h/2 ΔxΔE~hc/2 To explore dimensions of order Δx energy of E=2ΔE~hc/Δx needed Creation of particles. a process of converting energy into mass based on E=mc 2 80 GeV (W ± ), 91 GeV (Z 0 ), 125 GeV (Higgs), 172 GeV (top quark), Creation and study of new, short leaved particles that only existed just after the Big bang. Accelerator + Detector = Large, time-travel microscope 17/01/17 F. Ould-Saada 5

6 Combination of accelerator, detectors and computers acts as a time travel microscope where researchers hope to shed light on new phenomena à Main Components of an accelerator: - Magnets to bend and focus particle beams - Radio frequency, RF, devices to accelerate them. - Vacuum chamber. à When particles collide, energy is released that is transformed into a shower of new particles. à Particle collision products are photographed by Detectors àcomputers, coupled together in a Grid network, process and analyse the data

7 Linear proton accelerator (1) ion source; (2) accelerating cylindrical electrodes; (3) radio-frequency; (4) vacuum pipe Why does tube length increase for protons and not for electrons? Proton-synchrotron. Pre-accelerator: electrostatic accelerator (1) followed by a linear accelerator (2). Main ring: (3) magnets, (4) accelerating cavity and (5) the straight sections (6) targets, (7) secondary beam lines for experiments 17/01/17 F. Ould-Saada 7

8 Collisions with different particles lead to complementary information: pn, e + e -, ep pp, ppbar, pb pb, νn, νe -, µn, Previous accelerators as preaccelerators Collider vs Fixed Target experiments Collider: LHC pp and PbPb collisions Fixed Target: neutrino beam sent from CERN to Gran Sasso in Italy 730 km away 17/01/17 F. Ould-Saada 8

9 Hadron colliders Discovery machines Fraction of proton momentum carried by quarks and gluons, x, varies large domain of energies investigated simultaneously Potential source of discovery and surprises Electron colliders Precision machines Linear colliders as a solution to the synchrotron radiation problem of circular colliders ep-colliders Exploration and precision Measurement of structure functions 17/01/17 F. Ould-Saada 9

10 N=L.σ N: Distribution of number of events some quantity / observable Distribution measured by detector L: Luminosity - Given by Accelerator σ: Cross-section Predicted by theory Fermi s golden rule dσ = M(i 1,i 2 f 1, f 2,..., f n ) 2 4 (p 1 p 2 ) 2 m 1 2 m 2 2 % ' &' n d 3 p f (2π ) 3 2E f ( * )* (2π )4 δ 4 ( p i p f )S M: matrix element transition probability iàf calculable using Feynman diagram rules Feynman diagrams à process probability by a set of mathematical rules (Feynman rules), derived from underlying quantum field theory 17/01/17 F. Ould-Saada 10

11 Number of collisions N = L. σ (pp X) Luminosity L n. of protons per bunch n. of bunches L = N2 k b f 4πσ x σ y n. of turns per second beam size at IP (σ x,y = 16 µm) Cross-section σ Very small for new processes

12 Large Hadron Collider 27km in circumference, 100 m underground proton bunches with 1000 billion protons circulate nearly at the speed of light : v= c proton bunches collide every 25 / 50 ns: 100µs per round rounds per second energy released enables creation of new particles

13 q Particle collisions at LHC Ø Simulated proton + proton à black hole candidate Ø LHC collides also heavy ions: pb-pb and p-pb q Sensitivity to rare phenomena with small cross sections depends on the luminosity F. Ould-Saada 17/01/17 13

14 45 m ATLAS superimposed to the 5 floors of building m 7000 Tons 17/01/17 F. Ould-Saada 14

15 Let s build ATLAS in ~ 1 minute F. Ould-Saada 17/01/17 15

16 A real event in a detector F. Ould-Saada 17/01/17 16

17 CMS: 2900 physicists 184 Institutions 38 countries 550 MCHF LHCB 700 physicists 52 Institutions 15 countries 75 MCHF ALICE; 1000 physicists 105 Institutions 30 countries 150 MCHF and 3 smaller experiments TOTEM LHCf MoEDAL ATLAS : 3030 Physicists 174 Institutions 38 countries 550 MCHF

18 Mission of ALICE Investigating the QGP in the LHC energy regime Comparison of Pb+Pb, p+pb to p+p collisions Tomographic studies using selected hard probes (neutral mesons, direct photons, charged hadrons), medium modifications of spectra (RAA) and correlations due to parton energy loss in QGP. Jet-flow separation. Collective properties and dynamics explored through anisotropic flow and thermal photon spectra 17/01/17 F. Ould-Saada 18

19 Pb Heavy ion collisions Pb π + p π -

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21 Particle identification through de/dx measured de/dx signal versus magnetic rigidity, together with the expected curves for negatively-charged particles (Bethe-Block formula). inset panel: Time Of Flight mass measurement which provides additional separation between 3 He and 4 He for tracks with p/z>2.3gev/c. 21

22 Fixed target pp collision Fraction of available energy transformed into mass New particle produced Quantum numbers conserved: baryon and lepton numbers, electric charge, Strong processes Electromagnetic processes Weak processes 17/01/17 F. Ould-Saada 22

23 new particle π 0 produced Electric charge, baryonic number conserved 4-momentum: p i =(E i,p i ) Lorentz-invariant (c=1): p 2 =E 2 -p 2 =m 2 s=(p 1 +p 2 ) 2 = (E 1 +E 2 ) 2 (p 1 +p 2 ) 2 Practice! p * 1 =(E* 1,p* ), p * 2 =(E* 2,-p* ) s=e cm =(E * 1 +E* 2 ) = 2Tcm +2m p s thr = 2m p +m π T cm thr= m π /2=67.5 MeV p 1 =(E 1,p 1 ), p 2 =(m 2,0) s=(e 1 +m 2 ) 2 -p 12 =m 12 +m 22 +2E 1 m 2 s=4m p2 +2T lab m p T lab thr =(s thr -4m p 2 )/2m p =280 MeV =((2m p +m π ) 2-4m p2 )/2m p 17/01/17 F. Ould-Saada 23

24 Time-of-flight spectrometer Primary proton beam interacts with target B charged particles emitted at an angle α are counted with counter C1, separated in momentum with magnet M and again counted with C22 Angle β depends on p/q (momentum/electric charge) Time used by every particle to travel distance l= C 11MC 2 is measured: t=l/v 2 m = p/v = p t / l è given p and l, time depends only on mass Special relativity: m=0 vs m#0: p = mvγ β = v / c = l / tc t = l c Δt = l v l c = l 1 c β 1 = l c m2 + p2 c 2 1+η 2 η 1 ; η = p mc Work out numerical example p. 59! 17/01/17 F. Ould-Saada 24

25 Time distribution for e, π, K, p P=1GeV/c ; l = 10m ; equal proportions Mass distribution of particles produced in the forward direction in pn collisions at 26 GeV analysed with a time-offlight spectrometer. Beam of 2 GeV/c 25

26 F=qvB=mv 2 /R è p=qbr è P(GeV/c)=0.30 R(m) B(T) Simulation of a particle track in a hydrogen bubble chamber (B=2 T) Only ionisation a) 330 MeV/c electron b) 470 MeV/c proton c) sagitta=ab 2 /8R c) AB=50cm, B=2T P=1GeV/c à r=1.67m, s=2cm ; p= 10GeVàs=2mm 26

27 Electron spiral track B=0.12T P(MeV/c)=3.6 R(cm) v~c very high (small number of bubbles ) m very small: small radius e constantly looses E/p à radius smaller 17/01/17 F. Ould-Saada 27

28 e + e - pair production e + (e - )àγ γ+nàe + e - +N Also possible: γe - à(e + e - )e - 17/01/17 F. Ould-Saada 28

29 A single bubble chambre photo 4 new particles: K +, π +, µ +, e +, K + π + π 0 π + µ + ν µ µ + e + ν e ν µ Note importance of kinematics and conservation laws a: 2-body decay b: 3 body decay ++ 17/01/17 F. Ould-Saada 29

30 K + π + π + π π + µ + ν µ ; π µ ν µ µ + e + ν e ν µ ; µ e ν e ν µ 3 charged particles 1 charged + 1 neutral 1 charged + 2 neutrals π- outside plane, µ- decay not visible 17/01/17 F. Ould-Saada 30

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