The ATLAS Experiment and the CERN Large Hadron Collider

Transcription

1 The ATLAS Experiment and the CERN Large Hadron Collider HEP101-4 February 20, 2012 Al Goshaw 1

2 HEP 101 Today Introduction to HEP units Particles created in high energy collisions What can be measured in the ATLAS detector? Basics of relativistic mechanics Measuring particle properties with the application of relativistic mechanics See the HEP101 web site for lectures and other information about the Duke LHC research groups: 2

3 HEP units of measurement As in any branch of science, the first barrier to carrying out quantitative calculations is to understand the units being used. We use the Standard International system of units, but scale them to be more convenient for the description of elementary particles and their interactions. Length 1 fermi (fm) = m ( the size of a proton is ~ 1 fm) Area 1 barn (b) = m 2 ( typical cross sections are in mb, µb, nb, pb) Energy 1 ev = 1.60x10-19 J ( typical energies MeV, GeV, TeV) Mass Mc 2 in GeV (shorthand M in GeV/c 2 ) For a proton Mc 2 ~ 1.0 GeV. For an electron Mc 2 ~ 0.5 MeV. Momentum Pc in GeV (shorthand p in GeV/c) 3

4 HEP units of measurement Some handy conversion factors c = 3.00 x fm/s h = 6.58 x GeV s h c = GeV fm (h c) 2 = GeV 2 mb All these units are SI-based as they ultimately refer to the the standards of length, mass and time to be the meter, kilogram and second. 4

5 Particles created in high energy collisions Some elementary particles are stable and do not decay: protons and the anti-matter partner anti-protons electrons and the anti-matter partner positrons neutrinos photons Others are unstable but decay with long lifetimes: neutrons decay to p + e - + ν e muons decay to e - + ν e + ν µ pions decay to µ - + ν µ These are so long-lived that they travel many meters before decaying and can be observed directly in particle detectors. 5

6 Particles created in high energy collisions Many important elementary particles decay so quickly that they do not travel distances that are measurable by particle detectors: The weak force carriers. Example decays are: Z -> µ + + µ - W -> µ + + ν µ The top quark: t -> W + + b quark The Higgs boson (decay modes depend on its mass): H -> W + + W + if high mass H -> b + b or two photons if low mass (now favored) 6

7 Particles created in high energy collisions What can be measured for stable and long-lived particles? 1. The particle s momentum from the curvature in in a known magnetic field. Use the detailed particle path measured in the tracking detectors that were described last lecture. 2. The particle s energy using the total energy deposit in the calorimeters described last lecture. 3. The particle type and therefore mass using the signature left in the tracking/calorimeter/muon detectors. The properties of very short lived particles can be measured from their decay products as discussed below. 7

8 Measuring stable and long-lived particles measure the momentum of protons, electrons, muons, charged pions, measure the energy of neutral particles ( photons, neutrons, ) in calorimeters identify the type of particle by how it interacts with detector components 8 8

9 Studying short-lived particles For very short lived particles only the stable decay products are detected: Z and W bosons, top quarks, excited states of protons, Higgs bosons, Z -> µ + µ - W -> e ν top -> W b -> e ν b 9

10 Z boson production with decay to µ + µ - 10

11 Z boson production with decay to e + e - 11

12 W boson production with decay to e + ν 12

13 Et=37 GeV e e γ Et=30 GeV γ e Et=51 GeV M(e,e) =91.2 GeV e e γ e Graduate Seminar September

14 A top pair production candidate One W decays to an electron, the other to a muon Event display of an top pair e-mu dilepton candidate with two b-tagged jets. The electron is shown by the red track pointing to the green calorimeter cluster in the 3D view, and the muon by the long red track intersecting the muon chambers. The two b-tagged jets are shown by the purple cones, whose sizes are proportional to the jet energies. 14 Tom LeCompte, ANL 14

15 A lead-lead nuclear collision 15

16 γ e + e - conversions 2009 data p T (e + ) = 1.75 GeV, 11 TRT high-threshold hits p T (e - ) = 0.79 GeV, 3 TRT high-threshold hits e + e- γ conversion point R ~ 30 cm (1 st Silicon strip layer) 16 16

17 Relativistic Kinematics 17

18 Single Particle Kinematics Consider the motion of a point particle in an inertial reference frame. m = particle s rest mass v = d r /dt t and r measured by clocks and meter sticks at rest in O τ = time measured by a clock carried by m x O y r(t) m v(t) z Define β = v /c and γ = 1/ 1 - β 2 Then: p = γ β mc E = γ mc 2 = K + mc 2 Also t = γ τ (time dialation) For any free particle note that E 2 = (pc) 2 + (mc 2 ) 2 18

19 Four vectors The location of a particle can be specified by a four component vector X µ = ( ct, x, y, z ) = (ct, r ) where µ is an index 0,1,2,3 specifying the vector component. Other examples of 4-vectors are: 4-velocity U µ = d X µ /d τ = γ ( c, v ) 4-momentum P µ = m U µ = m γ ( c, v ) = (E/c, p ) 4-force F µ = d P µ /d τ = ( γ/c de/dt, γ d p /dt ) 19

20 Algebra of four vectors Some notation: contravariant 4-vector V µ = (v o, +v ) covariant 4-vector V µ = (v o, -v ) Define a scalar product: V 2 = V V = V µ V µ = V µ V µ = v o 2 - v 2 ( the sum over repeated indices is implied) Some examples: P 2 = (E/c) 2 - p 2 = (mc) 2 U 2 = γ 2 c 2 - γ 2 v 2 = c 2 It is convenient to introduce a metric tensor: V µ = g µν V ν V 2 = V µ g µν V ν g µν = g µν =

21 Lorentz transformations The kinematic quantities describing a point particle can be transformed between inertial reference frames. A simple example is a boost along one axis (say the z axis). Let β o = v o /c and γ o = 1/ 1 - β o 2 Any 4-vector V in O has a value V when measured in O. V µ = L µ ν Vν where the L µ ν are the elements of a boost matrix R b. R b = γ o 0 0 -β o γ ο β o γ o 0 0 γ o 21

22 Lorentz transformations For example find the momentum and energy of this particle when measured in the reference frame O p,e m Use the boost matrix R b as given on the previous page: P µ = L µ ν Pν p x = p x p y = p y p z = γ o (p z - β o E/c ) E /c = γ o (E/c - β o p z ) 22

23 Applications of relativisitic kinematics Calculate a particle s mass from its decay products: M -> m 1 + m 2 Measure energy and momentum of m 1 and m 2 and then calculate the mass of M. To fix these ideas work 3 homework problems (given in the lecture). END LECTURE 4 23