Weak. interactions. V. Hedberg Weak Interactions 1

Transcription

1 Weak interactions V. Hedberg Weak Interactions 1

2 The electroweak theory y Gauge invariant theories. y y=x 2 A y =x 2 x y =y x =-x x The equation y=x 2 is symmetric or invariant under the transformation A, i.e. it looks the same before and after the transformation. Gauge invariant theories the main equations do not change when a gauge transformation is performed. Requiring gauge invariance deduce the various interactions. V. Hedberg Weak Interactions 2

3 The electroweak theory What is a gauge transformation? Different gauge transformations different interactions. Example: Non-relativistic electromagnetism The equation of motion: for a free non-relativistic particle: i ψ t 1 = ψ Ψ(r,t) 2m where is the wavefunction of the particle and m is its mass. The free particle Schrödinger equation Goal: modify this equation to describes particles that interact electromagnetically. V. Hedberg Weak Interactions 3

4 The electroweak theory Assumption: the new equation should be invariant under a U(1) phase transformation: ψ ψ' = e iqα ψ were α(r,t) is an arbirary continous function and q is the charge of the particle. Result: i ψ t 1 dα ( + iqα) 2mq Ψ 2m dt = new terms ψ' Conclusion: is not a solution to the Schrödinger equation. V. Hedberg Weak Interactions 4

5 The electroweak theory Electromagnetism: A vector potential A and a scalar potential V defined by E = V B = xa d A dt Question: How to add A and V to the Shrödinger equation while keeping it invariant under? ψ where E is the electrical field and B the magnetic field. ψ' = e iqα ψ Introduce interaction: require that the Schrödinger equation is also invariant under a gauge transformation of type A A' = A + α V V' = V V. Hedberg Weak Interactions 5 α t

6 The electroweak theory Result: U(1) phase transformation of the wave function + gauge transformations of A and V is fullfilled by new equation i ψ t = ( qa) + qv Ψ 2m The equation for a non-relativistic particle with charge q moving in an electromagnetic field. The Gauge principle Gauge principle: to keep the invariance condition satisfied it is necessary to add a minimal field to the Schroedinger equation an interaction will have to be introduced. V. Hedberg Weak Interactions 6

7 The electroweak theory The electro weak theory by Glashow, Weinberg and Salam. The EW or GWS model is a quantum field theory for both weak interactions and electromagnetic interactions. w Weak isospin charge I 3 Weak hypercharge Y W Electric charge Q w Q = I 3 + Y W /2 Gauge invariance massless gauge particles W +,W -,W 0, B 0 The gauge particles interact with massless fermions. V. Hedberg Weak Interactions 7

8 The electroweak theory The Higgs field generates mass to gauge bosons and fermions. W + and W - W 0 and B 0 weak radioactive decay not observed experimentally Photon gauge boson for Z 0 the electromagnetic interaction gauge boson for the weak neutral current interaction γ = B 0 cosθ W + W 0 sinθ W Z 0 = B 0 sinθ W + W 0 cosθ W θ W the weak mixing angle a parameter (not predicted). V. Hedberg Weak Interactions 8

9 The electroweak theory Only W-exchange divergent processes infinities e + W - e + W + μ + e - γ W + Non-divergent integrals ν e ν μ e - W - μ Divergent integrals The Z 0 -boson new diagrams cancel out the divergencies e + W - e + Z 0 μ + e + γ μ + e - Z 0 W + e - e - Z 0 μ μ e - e - Z 0 μ μ Non-divergent integrals Divergent integrals V. Hedberg Weak Interactions 9

10 The electroweak theory Coupling constants in EW e, g W and g Z Strength parameters QED: α = 4π e2 1 α s = g s 2 QCD: 137 4π The coupling constants are not independent (in order for all the infinities to cancel out) EW: 4π 4π α W = g W 2 α Z = g Z 2 The unification condition. e/ 8 = g W sinθ W = g Z cosθ W Alternative e = g = sinθ W gcosθ W g= 8 g W g = 8 g Z The weak mixing angle (Weinberg angle) cosθ W = M W M Z V. Hedberg Weak Interactions 10

11 The electroweak theory The strength parameters contribution of different processes (diagrams) to the cross-section. Example: muon-scattering on electrons ν μ + e - μ + ν e Diagrams with increasing complexity can contribute: ν μ g W μ ν μ g W μ g W ν μ g W μ W - W - W + W - e - g W ν e Second order diagram e - g ν e e - W g W g W Sixth order diagram ν e Second order diagram cross section is proportional to a W 2 Sixth order diagram cross section is proportional to a W 6 V. Hedberg Weak Interactions 11

12 The electroweak theory Point-like interactions and low-energy measurements Fermi s theory of weak interactions four-fermion point-like interactions (without W and Z exchange). W bosons are heavy charged current interactions can be approximated by a zero-range interaction at low energy ν μ g W μ ν μ μ W + M W G F e - g W ν e e - ν e Fermi coupling constant (G F ) The strength of the zero-range interactions Relationship between g W and G F : V. Hedberg Weak Interactions 12 G F 2 g2 W = = M2 W 4πα W M2 W next slide

13 The electroweak theory A bit of algebra: The unification condition G F 2 = g W M2 W and π α em = g 2 W sinθ gives M2 W W g2 W 2 = = G F πα em 2G 2 F sin θ W M W cosθ W = and M2 M W Z Definition Weinberg angle πα em G 2 F sin θ W = gives M Z 2 = πα em 2G 2 2 F cos θ W sin θ W G Z neutral current coupling constant in the low energy zero-range approximation G Z = g2 Z M2 Z which gives G Z G F 2 2g Z M W 2 2 2g W M Z V. Hedberg Weak Interactions 13 2 = = πα cos 2 θw πα sin 2 θw cos 2 θ W = sin 2 θ W

14 The electroweak theory Measurements of weak interaction rates at low energy G G Z /G F =sin 2 Z and G F (θ W ) 2 sin θ W = 0, 277 ± Measurement of the weak mixing angle predict the masses of the W and Z: M W = 78.3 ± 2.4 GeV/c 2 ; M Z = 89.0 ± 2.0 GeV/c 2 Discovery at CERN of W and Z at predicted masses confirmation that the electroweak theory is correct. V. Hedberg Weak Interactions 14

15 The electroweak theory Modern estimation of the Weinberg angle (from many experiments) 2 sin θ = ± W This value and the previous formulas give: M W = 78.5 GeV/c 2 ; M Z = 89.0 GeV/c 2 while direct measurements give M W = 80.4 GeV/c 2 ; MZ = 91.2 GeV/c 2 The difference is caused by higher-order diagrams (not taken into account in the low- energy formulas) ν μ μ ν μ μ W - W - W - Z 0 b t W - W - e - ν e - V. Hedberg e ν Weak Interactions e 15

16 The electroweak theory Higher-order corrections with top-quarks W measurement of electroweak processes - W - Z predict the top-quark mass 0 ν μ μ ν μ b W - t μ e - W - m t = 170 ± 30 GeV/c 2 ν e e - W - ν e The directly measured mass of the top quark at Fermilab by the CDF experiment gave a value m t = 176 ± 5 GeV/c 2 Perfect agreement with the low-energy prediction! V. Hedberg Weak Interactions 16

17 The W and Z bosons V. Hedberg Weak Interactions 17

18 The W and Z bosons The force carriers in weak interactions are spin-1 bosons (as in QED and QCD) that couple to quarks and leptons. W +, W - and Z 0 Intermediate vector bosons The force carriers of weak interactions W +, W - and Z 0 bosons are very massive particles m W =80.4 GeV and m Z =91.2 GeV Weak interactions have a very short range (2 x 10-3 fm). All observed low-energy weak processes (e.g. β-decay) charged current reactions mediated by W + or W - bosons. Electroweak prediction neutral current reactions caused by the Z 0 boson should exist. V. Hedberg Weak Interactions 18

19 Discovery of the neutral current Accelerator: The Proton Synchrotron (PS) at CERN The PS accelerator: Length = 628 m, Number of magnets = 277, Proton beam energy = 28 GeV Neutrino beams: Step 1. Intense proton beam hits a target Step 2. Charged pions and kaons decay π + μ + +ν μ e + +ν e +ν μ +ν μ. V. Hedberg Weak Interactions 19

20 Discovery of the neutral current Neutral current events was first observed by the Gargamelle experiment at CERN in Film cameras N 2 liquid propane Magnet coils Compressordecompressor system Flash lights Plastic membranes ν Step 1. The liquid propane is at a temperature below its boiling point. Step 2. When the ν enters the propane, its pressure is lowered to make it superheated. Step 3. Charged tracks ionize the propane and these ions create bubbles in the liquid. Step 4. The bubble tracks are photographed by film cameras. V. Hedberg Weak Interactions 20

21 Discovery of the neutral current Elastic and inelastic neutral current reactions possible. ν μ ν μ Ζ 0 h a d r o nucleon n s Main background neutron - nucleon interactions. V. Hedberg Weak Interactions 21

22 Discovery of the neutral current Conversion e + e - γ e - e + γ e - ν μ Bremsstrahlung One of the first neutral current reactions seen by the Gargamelle experiment. V. Hedberg Weak Interactions 22

23 The discovery of the W and Z bosons The accelerator: The Super Proton Synchrotron The W and Z were discovered by the UA1 and UA2 experiments. The SPS accelerator: Length = 6.9 km, Number of magnets = 960, Fixed target = GeV pp-collider = GeV Quadrupol magnet Dipole magnet Cavity V. Hedberg Weak Interactions 23

24 The discovery of the W and Z bosons SPS (CERN) p q g q g q g 450 GeV hadrons hadrons Length: 7 km (960 magnets) Experiments: UA1, UA2 g e q g q g q g 450 GeV p LEP (CERN) e - e + 46 GeV 104 GeV hadrons q Z 0 hadrons 46 GeV 104 GeV Length: 27 km (4184 magnets) Experiments: DELPHI, OPAL, ALEPH, L3 q- The energy of the quarks and gluons carry only a fraction of the proton energy. To produce W- and Z-bosons with a mass of GeV a collider with a beam energy of 270 GeV was needed. The beam energy was later increased to 450 GeV. V. Hedberg Weak Interactions 24

25 The discovery of the W and Z bosons DELPHI ATLAS UA1 Gargamelle V. Hedberg Weak Interactions 25

26 The discovery of the W and Z bosons The experiment: UA1 Muon chambers Hadronic calorimeter Electromagnetic calorimeter Dipole magnet Drift chamber Tracking detector: Central wire chamber with 0.7 T dipole magnet. Electromagnetic calorimeter: Lead/scintillator sandwich Hadronic calorimeter: Iron/Scintillator sandwich Muon detector: 8 planes of drift chambers. V. Hedberg Weak Interactions 26

27 The discovery of the W and Z bosons Production of W and Z bosons The W and Z bosons are in proton colliders produced by quark-antiquark annihilations: u + d W + d + u W - u + u Z 0 d + d Z 0 p p q q W ±, Z 0 The lifetime of both the W and the Z is about 3 x s they cannot be seen directly in the experiments. V. Hedberg Weak Interactions 27

28 The discovery of the W and Z bosons The decay of W and Z bosons hadronic decays p + p W + + X q + q p + p W - + X q + q p + p Z 0 + X q + q Branching ratio 68% 68% 70% leptonic decays p + p W + + X l + + ν l p + p W - + X l - + ν l p + p Z 0 + X l + + l - Branching ratio 32% e & μ 32% e & μ 6.7% e & μ Cannot be found among all other hadrons produced. The decays to leptons are easy to identify V. Hedberg Weak Interactions 28

29 The discovery of the W and Z bosons Analysis of W-events in UA1 The analysis searched for events with a charged lepton + neutrino A high momentum electron is indicated by the arrow. V. Hedberg Weak Interactions 29

30 The discovery of the W and Z bosons Transverse momentum The transverse momentum and energy of a particle: P T = P sin(θ) E T = E sin(θ) P T θ P L p The angle to the beam E T = P T if the mass of the particle is small since E 2 =P 2 +m 2 The total momentum is zero of all the particles in a collision. Neutrinos are not detectable if the total momentum = 0 the event has missing momentum (or missing energy). V. Hedberg Weak Interactions 30

31 The discovery of the W and Z bosons Analysis of W-events in UA1 The The analysis main was selection looking criteria for events in the with UA1 a W-analysis charged lepton was: and i) A charged electron or muon with a large momentum (>10 GeV/c) ii) This lepton should be emitted at a wide angle to the beam (>5 o ) iii) There should be large missing transverse momentum in the event The expected distribution of the transverse energy of the selected electrons was compared with the measured distribution. Events 20 Measured Distribution Background Subtracted Distribution From the first 148 electron and 47 muon events it was estimated that: = Γ W 65, GeV M W 83, 5 ± 28, GeV Wτν jet-jet Transverse Energy (GeV) V. Hedberg Weak Interactions Simulated Distribution M W =83.5 GeV

32 The discovery of the W and Z bosons Analysis of Z-events in UA1 The analysis was looking for a pair of charged leptons. e - e + V. Hedberg Weak Interactions 32

33 The discovery of the W and Z bosons Invariant mass E 1me The invariant mass of a particle that decays to two other particles: φ Z m zϕ m e m e E 1 E 2 m z 2 = ( P1 + P 2 ) 2 ( 4-vectors ) E 2 m e m z 2 if m=0 = 2 E 1 E 2 ( 1 - cos ϕ) V. Hedberg Weak Interactions 33

34 The discovery of the W and Z bosons Analysis of Z-events in UA1 Main search criteria require pair of electrons or muons with a large transverse energy. The mass distribution of pairs of electrons where each electron Events 8 4 jet-jet background Z 0 candidates has E T >8 GeV Mass (GeV) The first 18 electron pairs and 10 muon pairs in UA1 M Z = 93, 0 ± 14, GeV Γ Z 81, GeV V. Hedberg Weak Interactions 34

35 Precision studies of the W and Z bosons The accelerator: The Large Electron Positron Collider Electrons-positrons collisions in four experiments. Collision energy: 91 GeV 209 GeV Z mass maximum 288 superconducting cavities. V. Hedberg Weak Interactions 35

36 Precision studies of the W and Z bosons Cavity Quadrupol magnet Dipole magnet V. Hedberg Weak Interactions 36

37 Precision studies of the W and Z bosons LEP (CERN) e - e + 46 GeV 104 GeV hadrons q Z 0 Length: 27 km (4184 magnets) Experiments: DELPHI, OPAL, ALEPH, L3 q- hadrons 46 GeV 104 GeV HERA (DESY) e + 30 GeV hadrons γ e + Length: 6 km (1650 magnets) Experiments: H1, ZEUS e 920 GeV q g q g q g p TEVATRON (FERMILAB) p q g q g q g 980 GeV hadrons hadrons Length: 6 km (990 magnets) Experiments: CDF, D0 g e q g q g q g p 980 GeV LHC (CERN) hadrons Length: 27 km ( magnets) Experiments: ATLAS, CMS, LHCb, ALICE V. Hedberg Weak Interactions 37 p q g q g q g 7000 GeV hadrons g e q g q g q g p 7000 GeV

38 Precision studies of the W and Z bosons Differences between proton and electron colliders. Synchrotron radiation: Total energy loss is proportional to 1/mass 4 Total energy loss is proportional to Total energy loss is proportional to Energy loss in an electron accelerator is times larger. 4 E beam 1/Radius LEP: 344 cavities, accelerating voltage=3630 MV, energy=104 GeV LHC: 16 cavities, accelerating voltage = 16 MV, energy =7000 GeV Beam momentum Magnetic bending field Length of bending field LEP: 0.12 Tesla bending field} LHC: 8.38 Tesla bending field factor 70 V. Hedberg Weak Interactions 38

39 Precision studies of the W and Z bosons The accelerator: The Large Electron Positron Collider Electron-positron collider: Precise measurement of s important! Problem: During 1993 the LEP energy was changing with time! Geological shifts ΔE (MeV) 0-10 Energy calibrations Horizontal Orbit (X ARC ) Lake level fit The water level in lake Geneva Rainfalls and the water table Days V. Hedberg Weak Interactions 39

40 Precision studies of the W and Z bosons Δ E [MeV] 5 November 11 th, 1992 Tides 0 Earth tides caused by the moon :00 3:00 7:00 11:00 15:00 19:00 23:00 3:00 The electron s orbit changes. Δ E [MeV] 5 August 29 th, 1993 October 11 th, mm energy change of 10 MeV :00 13:00 15:00 17:00 19:00 21:00 23:00 18:00 20:00 22:00 24:00 2:00 4:00 6:00 8:00 Daytime V. Hedberg Weak Interactions 40

41 Precision studies of the W and Z bosons acuum Chamber Current Correlation LEP IP3 IP2 SPS IP8 IP1 Lac de CERN Geneve airport 1 km Time V. Hedberg Weak Interactions 41 Bellegarde Beampipe current Trains parasitic currents Currents the magnetic field Mag. field electron s orbit Orbit electron s energy Trains LEP River IP5 La Versoix IP4 IP6 IP7 Lausanne Lake Meyrin Zimeysa Cornavin Geneva Bending B field [Gauss] Voltage on beampipe [V] Voltage on rails [V] RAIL LEP beam pipe LEP NMR Geneve TGV 16:50 16:55 Meyrin Zimeysa

42 Precision studies of the W and Z bosons The DELPHI Experiment Forward Chamber A Barrel Muon Chambers Forward RICH Barrel Hadron Calorimeter Forward Chamber B Scintillators Forward EM Calorimeter Superconducting Coil Tracking detector: Time projection chamber orward Hadron Calorimeter Forward Hodoscope Forward Muon Chambers Surround Muon Chambers High Density Projection Chamber Outer Detector Barrel RICH Small Angle Tile Calorimeter Quadrupole Very Small Angle Tagger Electromagnetic calorimeter: Lead absorber Magnet DELPHI Inner Detector Vertex Detector Time Projection Chamber Beam Pipe Hadronic calorimeter Iron absorber Muon detectors V. Hedberg Weak Interactions 42

43 Precision studies of the W and Z bosons The DELPHI Experiment The DELPHI cavern The Time Projection chamber V. Hedberg Weak Interactions 43

44 Precision studies of the W and Z bosons Studies of the Z-boson Hadronic calorimeter Electromag. calorimeter e + e - Z o e - e+ M a g n e t TPC Cerenkov Cross section Muon spectrometer Collision energy V. Hedberg Weak Interactions 44

45 Precision studies of the W and Z bosons Studies of the Z-boson e + μ - M a g n e t Electromag. calorimeter TPC Hadronic calorimeter Cherenkov Cross section e - Z o μ+ Muon spectrometer Collision energy V. Hedberg Weak Interactions 45

46 Precision studies of the W and Z bosons Studies of the Z-boson Hadronic calorimeter e + τ - Electromag. calorimeter e - Z o τ + M a g n e t TPC Cherenkov Cross section Muon spectrometer Collision energy V. Hedberg Weak Interactions 46

47 The number of neutrino families σ (pb) e + e - Z o Branching ratio ( B ): e- μ - e+ μ+ τ τ - + } ν ν q q Decay width ( Γ ): 0.25 GeV 0.50 GeV 1.74 GeV Center of mass energy (GeV) The total decay width The partial decay widths V. Hedberg Weak Interactions 47 1 τ τ Partial decay width: Γ = B had B ll B νν 25 = = = = 3 10 s Γ had Γ ll Γ νν B Z = = Γ Z Β τ Branching ratio Decay time B had + B ll + B νν Γ had + Γ ll + Γ νν

48 The number of neutrino families Breit-Wigner the muon partial decay widths of the Z 0 σ (pb) σ( e + e - μμ) = 12πM Z Γ ( Z ee )Γ ( Z μμ ) 2 E CM 2 2 E CM M Z + M Z ΓZ Γ Z σ at E Γ( Z 0 cm = M Z give μμ) because then The decay rate to ee The decay rate to μμ M Z σ( e + e - μμ) = The mass of the Z 0 12π Γ ( Z ee )Γ Z μμ ( ) 2 2 M Z Γ Z The total Z 0 decay rate Collision energy - E CM In reality the measurements are a bit more complicated because the measured peaks have to be corrected for initial state radiation (photons radiated off incoming electrons). V. Hedberg Weak Interactions 48

49 The number of neutrino families The fitted parameters: M Z = ± GeV/c 2 Γ Z = ± GeV Γ( Z 0 hadrons) = ± GeV Γ( Z 0 l + l - ) = ± GeV Neutrinos cannot be measured in the experiments. Γ Z = Γ( Z 0 hadrons) + 3Γ( Z 0 l + l - )+ N ν ΓZ 0 ν l ν l N ν Γ Z 0 ν l ν l = ± GeV Number of neutrinos Decay width to neutrinos V. Hedberg Weak Interactions 49

50 The number of neutrino families Measurement: Calculation: Γ Z 0 ν l ν l N ν ΓZ 0 ν l ν l = GeV = GeV N ν = ± N=2 N=3 N=4 DELPHI Z 0 to hadrons No restrictions on N ν in SM LEP three types of light neutrinos Energy, GeV V. Hedberg Weak Interactions 50

51 Precision studies of the W and Z bosons Studies of the W-boson W bosons were produced in pairs. e + W + e - γ / Z o W - e + e- The signature: ν e W + W - e + e- qq qq qq lν lν lν 46% 44% 11% A WW-event with 4 jets V. Hedberg Weak Interactions 51

52 Precision studies of the W and Z bosons Studies of the W-boson Step 1. Select WW-pair events The mass distribution of jet-pairs Step 2. Calculate the W-mass ϕ 2 Μ W = ( _ ) Μ W 2 P + q P q qq qq 46% ϕ _ = 2 E E ( 1 - cos ) q if m q= 0 ( 4-vectors ) Μ W = GeV Μ W = GeV q 2 (UA1) (LEP) events / 2 GeV/c 2 DATA 250 WW (Mw = 80.35) 200 ZZ QCD W mass [ GeV/c 2 ] V. Hedberg Weak Interactions 52

53 Charged current reactions V. Hedberg Weak Interactions 53

54 W and Z reactions Leptonic reactions Hadronic reactions Charge current reactions l l + - q q g W W W V qq g W Neutral current reactions l g Z l l - gz l + q g Z q Z 0 Z 0 Z 0 V. Hedberg Weak Interactions 54

55 Charged current reactions Charged current reactions are mediated by a W. ν μ Purely leptonic processes: μ - e - + ν e + ν μ μ W - e - ν e Purely hadronic processes: Λ π + p Λ s u d W - u u d p d u π Λ e - d s u W - d u d u u π p W - Semileptonic reactions: n p + e - + ν e n d d u u d p V. Hedberg Weak Interactions u 55 ν e

56 Leptonic charged current reactions All the electromagnetic interactions eight basic interactions: e - γ e e - e - e - γ γ e + The basic vertex for electron-photon interactions. Leptonic weak interaction described by basic vertices: ν l l - ν l l + The two basic vertices for W-lepton interactions.. W ± W ± V. Hedberg Weak Interactions 56

57 Leptonic charged current reactions Eight basic charged current reactions from two basic W vertices: ν l ν l l - + W + W + l + l + W + + ν l W + ν l l + + ν l W + W + l + ν l l + W - W + ν l l - W - W - + l + ν l W - l - + ν l l - l - ν l W - ν l l + ν l l - ν l vacuum l - + ν l + W + W + l + + ν l + W - vacuum W - ν l l + V. Hedberg Weak Interactions 57

58 Leptonic charged current reactions Weak interactions conserve lepton numbers: L e, L μ, L τ Feynman diagrams: 1) at each vertex, there is one arrow pointing in and one out 2) the lepton indices l are the same on both lines. ν e e - e - e - Allowed: W ± ν e W + W - ν e Forbidden: ν μ W ± e ν μ e - e - W + W - ν μ V. Hedberg Weak Interactions 58

59 Leptonic charged current reactions The weak strength parameter: α W α W is the same at all leptonic vertices (it does not depend on lepton type) Example: The decay rate of W to e+ν Estimation from theory Γ( W eν) α W M W α W 80 GeV Measurement Γ( W eν) 0.2 GeV α W =0.003 Compare with the electromagnetic strength parameter: α em =0.007 V. Hedberg Weak Interactions 59

60 Leptonic charged current reactions Why is the weak interaction so weak if α W and α em is of a similar size? Compare the decay of charged and neutral pions: Electromagnetic decay { u π 0 u Lifetime = 8 x 10 s γ γ -17 π { d u Weak decay W - Lifetime = x 10 s -17 (Lifetime of a real W = x 10 s) ν μ μ- -17 CONCLUSION: Apparent weakness large W and Z masses V. Hedberg Weak Interactions 60

61 W and Z reactions Leptonic reactions Hadronic reactions Charge current reactions l l + - q q g W W W V qq g W Neutral current reactions l g Z l l - gz l + q g Z q Z 0 Z 0 Z 0 V. Hedberg Weak Interactions 61

62 Hadronic charged current reactions In weak hadronic interactions, constituent quarks emit or absorb W or Z bosons. Examples: d u π W - g W e - Λ d s u W - d u u p n d d u g ud ν e d u π Neutron β-decay. u d u p Λ s u d W - u u d p The dominant quark diagrams for Λ decay V. Hedberg Weak Interactions 62

63 Hadronic charged current reactions ASSUMPTION: Lepton-quark symmetry i.e. corresponding generations of quarks and leptons have identical weak interactions. ν e e - u d Interactions will then only take place within a family! ν μ μ - c s ν τ τ - t b u d u d c s c s ν l l - g ud g ud g cs g cs g W ν l l + g W W ± W ± W ± W ± W ± W ± The W-quark vertices for the first two generations, assuming lepton-quark symmetry. The W-lepton vertices. V. Hedberg Weak Interactions 63

64 Hadronic charged current reactions Experimental tests of the assumption of lepton-quark symmetry. Some weak reactions should be allowed and some should be forbidden if lepton-quark symmetry is true: π μ + ν μ du μ + ν μ K - μ + ν μ su μ + ν μ π K - { { d u s u V. Hedberg Weak Interactions 64 W - Different families Measurements of these decays give: π μ + ν μ Branching ratio = τ = 2.6 x 10-8 s K - μ + ν μ Branching ratio = τ = 1.2x 10-8 s W - ν μ μ- ν μ μ- Allowed Not Allowed CONCLUSION: Quarks from different generations can participate in charged current interactions!

65 Hadronic charged current reactions Cabibbo quark mixing in order to explain kaon decays. Quark mixing scheme d- and s-quarks participate in weak interactions via the linear combinations: d' = dcosθ C + ssinθ C s' = dsinθ C + scosθ C where θ C is called the Cabibbo angle. The quark-lepton symmetry applies to doublets like u and c d' s' The ud W vertex interpreted as a sum of the udw and usw vertices: u g W W ± d u g ud + W ± d u g us W ± s g ud =g W cosθ C g us =g W sinθ C V. Hedberg Weak Interactions 65

66 Hadronic charged current reactions The quark mixing hypothesis more W-quark vertices: u d g ud g W cosθ C u g ud d g W cosθ C c s c s g cs g cs g W cosθ C g W cos θ C W ± W ± W ± W ± u s u s c g d c d us g cd g W sinθ C g us g W sinθ C g W sinθ C gcd g W sinθ C W ± W ± W ± W ± Within a generation: Between generations: g ud = g cs = g W cosθ C g us = g cd = g W sinθ C V. Hedberg Weak Interactions 66

67 Hadronic charged current reactions Measurements of the Cabibbo angle. The Cabibbo angle has to be measured. Comparing the decay rates of π μ + ν μ with K - μ + ν μ Γ( K - μ - ν μ ) Γπ ( - μ - ν μ ) g2 us g2 ud tan 2 θ C = θ C = 12.7 ± 0.1 The coupling constants within and between generations: g W g W cos θ C sinθ C = = 0, 98g W 0, 22g W V. Hedberg Weak Interactions 67

68 Hadronic charged current reactions Charmed particle decays. Particles with charm quarks almost always give a strange particle in the final state because other decays are Cabibbo supressed: l ν l l ν l g W g W W + g W + g c W cos θ C c W sin θ C s The suppression factor is: d g cd = tan 2 θ g2 C = cs θ C = 12, 6 Neutrino scattering experiments The charmed quark couplings g cd and g cs θ C = 12 ± 1 V. Hedberg Weak Interactions 68

69 Weak interactions and the third generation Two generation quark mixing can be written in matrix form: cos d' θ = C s' sinθ C sinθ C cosθ C d s This means that the following weak transitions are favoured: u d And that the following weak transitions are surpressed: u C d s Charge conservation forbids the following charged current transitions: u Charge = 2/3 Charge = -1/3 d with transitions within C s C s V. Hedberg Weak Interactions 69 u and c d' s'

70 Weak interactions and the third generation The c-quark was predicted from lepton-quark symmetry Discovered in experiments in Discovery of the τ lepton and the b-quark The sixth quark was predicted to complete the symmetry Top quark was discovered in 1994 The third generation gives rise to the Cabibbo-Kobayashi- Maskawa (CKM) matrix V αβ : g αβ = g W V αβ V d' ud V us V ub s' = V cd V cs V cb b' V td V ts V tb d s b α=u,c,t β=d,s,b V. Hedberg Weak Interactions 70

71 Weak interactions and the third generation Weak transitions can now take place between: u d = V ud d+v us s+v ub b c s = V cd d+v cs s+v cb b t b = V td d+v ts s+v tb b If the mixing between the b and t quarks with lighter quarks can be neglected the CKM-matrix is reduced to: V ud V us V ub V cd V cs V cb V td V ts V tb cosθ C sinθ C 0 sinθ C cosθ C If V ub, V cb, V td and V ts are not small The two-generation mixing model would not work V. Hedberg Weak Interactions 71

72 Weak interactions and the third generation V ub =V cb =V td =V ts =0 b - quarks t-quark decay only to b-quarks b-quark is stable (since it cannot decay to u- or c-quarks) Not true Semileptonic decays of b-quarks to u- and c-quarks observed! The observed decay rate is proportional to the squared couplings: gub 2 V ub 2 gw 2 = u V. Hedberg Weak Interactions 72 b W - g W V g ub g W ub l - ν l

73 Weak interactions and the third generation b - quarks The most precise measurements at present V ub 0, 004 and V cb 0, 04 The CKM-matrix becomes V ud V us V ub cosθ C V cd V cs V cb V td V ts V tb sinθ C 0004, sinθ C cosθ C 004, , 022, 0, , 0, , V. Hedberg Weak Interactions 73

74 Weak interactions and the third generation The top quark The top quark is much heavier than even the W-bosons and it can decay by W + W + W + t g td 0 t g ts 0 t g ts = g W d s b g td and g ts are close to zero the only significant decay mode: t W + b rate proportional to α W g2 W 4π = 0, 0042 Estimation of the decay width of the top (Γ α W m t 1 GeV) 25 very short lifetime τ t 4 10 s V. Hedberg Weak Interactions 74

75 The discovery of the top quark The accelerator: The Tevatron Type Bending field Length Collision energy Tevatron: pp-collider 4.5 T 6.3 km 1960 GeV SPS: pp-collider 1.8 T 6.9 km 900 GeV LHC: pp-collider 8.4 T 27 km GeV Superconducting magnets CDF ν p 900 GeV 150 GeV Main injector Tevatron V. Hedberg Weak Interactions 75

76 The discovery of the top quark The accelerator: The Tevatron The Tevatron accelerator was put under the old main ring which was used as a pre-accelerator. Dipole magnet Old main ring Magnet coil The Tevatron V. Hedberg Weak Interactions 76

77 The discovery of the top quark The experiment: The Collider Detector at Fermilab =0 =1 Muon system Solenoid magnet Silicon Vertex Detector Drift chamber Electromagn. Calorimeter Had. Calorimeter V. Hedberg Weak Interactions 108 Lead/Scintillator Iron/Scintillator V. Hedberg Weak Interactions 77

78 The discovery of the top quark The experiment: CDF V. Hedberg Weak Interactions 78

79 The discovery of the top quark Particle Lifetime Decay Decay Decay Length Place Measurement W, Z, top 3-4x10-13 ps 0 Beampipe Not possible π 0 ( γγ) ps 0.025μm Beampipe Not possible τ 0.3 ps 90μm Beampipe Microvertex Charm: D 0 /D +- /D s ps μm Beampipe Microvertex Bottom: B 0 /B +- /B s / 1.5 ps 450μm Beampipe Microvertex K s ( ππ) 80 ps 2.7cm Tracker Tracker K ,000 ps 3.7m Tracker Not possible π K L ( πππ) μ ( eν e ν μ ) Compare particles decay length 30,000 ps 7.8m No decay Not possible 50,000 ps 16 m No decay Not possible 2,000,000 ps 659 m No decay Not possible V. Hedberg Weak Interactions 79

80 The discovery of the top quark Production of top-quarks In proton-antiproton colliders, pairs of top quarks are mostly produced by quark-antiquark annihilation: q + q g t + t p p q q g t t V. Hedberg Weak Interactions 80

81 The discovery of the top quark The decay of top-quarks l + The most likely decay of a top quark is to a b quark and to a W. t W + b ν l t W - b q q The W can decay to leptons or hadrons The final state is a complex mix of jets and leptons. p + p V. Hedberg Weak Interactions 81 t + t + X W - + b W + + b l - + ν l { q + q l + + ν l { q + q

82 The discovery of the top quark After a selection of likely top event plot mass distribution of the top-candidates. A large background component Extract the top mass: Expected Signal Expected Background M t = 176 ± 5 GeV Latest results: M t = 173 ± 1GeV V. Hedberg Weak Interactions 82

83 Neutral current reactions V. Hedberg Weak Interactions 83

84 W and Z reactions Leptonic reactions Hadronic reactions Charge current reactions l l + - q q g W W W V qq g W Neutral current reactions l g Z l l - gz l + q g Z q Z 0 Z 0 Z 0 V. Hedberg Weak Interactions 84

85 Neutral current reactions The basic vertices with W bosons: - Conserved lepton numbers - Not conserved quark flavour (quark mixing) The basic vertices with Z bosons: - Conserved lepton numbers - Conserved quark flavour (no quark mixing) ν l l - ν l l + q q ν l ν l l - l + q q g W g W g W cosθ C g W sinθ C g Z g Z g Z W ± W ± W ± Z 0 Z 0 Z 0 The basic W vertices The basic Z vertices V. Hedberg Weak Interactions 85

86 Neutral current reactions In processes in which a photon can be exchanged, a Z 0 boson can be exchanged as well: ν l ν l l - l + q q g Z g Z g Z Z 0 γ, Z 0 γ, Z 0 Example: e + e - μ + μ has two dominant contributions e + μ e + μ e - γ μ + e - Z 0 μ + V. Hedberg Weak Interactions 86

87 Neutral current reactions Estimation of the cross-section for the photon- and Z-exchange process in e + e - collisions at low energy: α σ γ σ 2 Z G Z ECM E CM where E cm is the collision energy. The photon exchange process will dominate at low energies. At E cm =M z this low-energy approximation fails and the Z 0 peak is described by the Breit-Wigner formula: σ( E CM ) C M 2 = E 2 CM E CM M 2 2 where M is the mass of the resonance + M 2 Γ 2 and Γ its decay width. V. Hedberg Weak Interactions 87

88 Neutral current reactions σ (pb) e + μ e + μ e - γ μ + e - Z 0 α 2 σ( ee μμ) 2 2 σ γ E 2 σ Z G Z E μ + = 2 12πM Z Γ ( Z0 ee)γ( Z 0 μμ) E CM 2 2 E CM M Z + M Z ΓZ Γ Z M Z Center of mass energy (GeV) V. Hedberg Weak Interactions 88

89 Test of flavour conservation That flavour is conserved at a Z 0 vertex can be verified by experiments. Example: measurement of the decay rate of charged kaons K + s u W + ν μ μ + u π 0 K + π 0 + μ + + ν μ K + s u Z 0 ν l ν l d u π + K + π + + ν l + ν l The measured upper limit on the ratio of the decay rate of these two processes was Γ( K + π + + ν l + ν l ) l Γ K + π 0 μ + < 10 7 ( + + ν μ ) until experiment E787 came along... V. Hedberg Weak Interactions 89

90 Test of flavour conservation The BNL experiment E787 was a fixed target experiment. It used a K + beam created by 24 GeV protons from the AGS. AGS E787 g-2 muon storage ring AGS to RHIC Linac Booster AGS Experimental Area Tandem Van de Graaff The 800 m long AGS has 240 magnets. V. Hedberg Weak Interactions 90

91 Test of flavour conservation E787 (b) K + π + + ν l + ν l 50 c el Calorimetero to veto on photons ge Scintillators ck π + Drift Target T chambers Scintillators Calorimeter Tracking SC CsI Calorimeter Endcap to veto on photons Veto K + beamm 0.8 GeV CMaterial B4 to slow down Kaons Drift chamber Target Scintillating fibers V. Hedberg Weak Interactions 91 T Target Kaons stopped in a target made of scintillating fibers The decay of the K+ at rest was then studied. The momentum, energy and range of the particle from the decay was measured.

92 Test of flavour conservation After many years of running two candidate events for K + π + + ν l + ν l were found. Drift chamber hits Scintillators Scintillating fibers Target The result from these two events were: Γ( K + π + + ν l + ν l ) l Γ( K + π 0 + μ + + ν μ ) = , 10 0, = 10 V. Hedberg Weak Interactions 92

93 Test of flavour conservation Explanation: second-order charged current reactions and not neutral current processes: + K u s u u u u u π + + K + π + u K π + d s c d s t d w w w w w w l l l ν ν ν ν ν ν The t-d vertex in the third diagram set limits on the V td element in the CKM matrix 0, 007 < V td < 0, 030 V. Hedberg Weak Interactions 93

94 The Higgs boson Experimental data agrees extremely well with predictions of the gauge invariant electroweak theory. Gauge invariance the gauge bosons have zero mass. True for photons in QED and gluons in QCD but not for W and Z. A new scalar field called the Higgs field is introduced to generate mass to the W and Z bosons as well as fermion masses. Associated with the field is a new spin 0 particle called the Higgs boson. The theory predicts how the Higgs boson couples to other particles but do not predict its mass. V. Hedberg Weak Interactions 94

95 The Higgs boson Unusual characteristic of the Higgs field a non-zero value φ 0 in vacuum (i.e. the field is not zero in its groundstate). φ 0 Non-zero vacuum expectation value The vacuum is populated with massive Higgs bosons When a gauge field interacts with the Higgs field it acquires mass. V. Hedberg Weak Interactions 95

96 The Higgs boson The interaction with the Higgs field W and Z bosons obtain masses with the ratio given by cosθ W = M W M Z Fermions acquire mass by interacting with the Higgs boson: f H 0 g Hff The coupling constant depends on the fermion mass. 2 g Hff = 2G F m f 2 f Photons and gluons do not interact with the Higgs boson. V. Hedberg Weak Interactions 96

97 Search for the Higgs boson at LEP LEP 2: Higgs production by Higgs strahlung: e + + e - H 0 + Z 0 e + e - Z o* H 0 Z o bb ττ WW gg cc 74% 8% 8% 6% 4% qq νν ee μμ ττ 70% 20% 3% 3% 3% Most of the Higgs events would have 4 jets in the final state. Two of these should be coming from b-quarks. V. Hedberg Weak Interactions 97

98 Search for the Higgs boson at LEP ALEPH reported a couple of Higgs candidates at 115 GeV DELPHI, L3 and OPAL had no signal. All data added together no discovery. LEP was turned off in DELPHI, L3 ALEPH, OPAL The DELPHI experiment put a limit on the Higgs mass of: M H > 114 GeV/c 2 V. Hedberg Weak Interactions 98

99 Search for the Higgs boson at LEP The measurement of many electroweak parameters at LEP global fit with the Higgs mass as a free parameter. χ 2 Quantifies how good the fit is Perfect fit m H = GeV -5 V. Hedberg Weak Interactions 99