Standard Model of Particle Physics SS 2013

Transcription

1 Lecture: Standard Model of Particle Physics Heidelberg SS 13 Registration: Experimental Tests of QED Part 1 1

2 Overview PART I Cross Sections and QED tests Accelerator Facilities + Experimental Results PART II Tests of QED in Particle Decays and Resonances QED Radiative Effects

3 Measurement of Cross Sections ee X - (e e X) + - test predictions of QED 3

4 Measurement of Cross Sections ee X - (e e X) + - test predictions of QED Why is αem=1/137 so small? Breakdown at higher energies? 4

5 Measurement of Cross Sections ee X - (e e X) + - test predictions of QED Why is αem=1/137 so small? Breakdown at higher energies? Reactions depend on center of mass many different accelerators 5

6 Measurement of Cross Sections ee X - (e e X) + - test predictions of QED Why is αem=1/137 so small? Breakdown at higher energies? Reactions depend on center of mass many different accelerators 4 Synchrotron Radiation Law:: E P R large accelerators required for high energies 6

7 List of ee-accelerators 7

8 AdA Accelerator First e+ e- collider ever AdA = Anello di Accumulazione (Frascati/Orsay, ) Energy: 5 MeV Electrons x 5 MeV Positrons 8

9 AdA Accelerator First e+ e- collider ever AdA = Anello di Accumulazione (Frascati, ) Energy: 5 MeV Electrons x 5 MeV Positrons Motivation: Bruno Touschek: excite the dielectric vacuum to create vector mesons (e.g. rho meson predicted to be light!) Note: at that time all new particles had been discovered in hadronic interactions (ie. proton beams)! 9

10 Dielectric Vacuum classical dielectric excited dielectric high energy bare electrical charge shielded by induced dipoles rho-meson bare charge shielded by vacuum polarisation 1

11 AdA Accelerator First e+ e- collider ever AdA = Anello di Accumulazione (Frascati, ) Energy: 5 MeV Electrons x 5 MeV Positrons Motivation: Bruno Touschek: excite the dielectric vacuum to create vector mesons (e.g. rho meson predicted to be light!) Note: at that time all new particles had been discovered in hadronic interactions (ie. proton beams)! Revolutionary concept as the rho-meson is electrically neutral and was predicted to explain (as carrier) strong interactions Remark: Indeed, Touschek was right. The strong force can be tested in e+ e- collisions. But not in AdA (too low luminosity, too low energy) 11

12 AdA Challenges I How to store electrons and positrons? magneto-optical storage ring ( known at this time, synchrotron radiation facilities) cavity 1

13 AdA Challenges I How to store electrons and positrons? magneto-optical storage ring ( known at this time, synchrotron radiation facilities) How to produce positrons? by photon conversions: γ e+ e- ( conversion target) e+ cavity e 13

14 AdA Challenges I How to store electrons and positrons? magneto-optical storage ring ( known at this time, synchroton radiation facilities) How to produce positrons? by photon conversions: γ e+ e- ( conversion target) How to produce the photons (E > 5-1 MeV) Bremsstrahlung from high energetic electrons at target e- N γ e- N using a linear electron accelerator ( also known) e- e+ cavity ee 14

15 AdA Challenges I How to store electrons and positrons? magneto-optical storage ring ( known at this time, synchroton radiation facilities) How to produce positrons? by photon conversions: γ e+ e- ( conversion target) How to produce the photons (E > 5-1 MeV) Bremsstrahlung from high energetic electrons at target e- N γ e- N using a linear electron accelerator ( also known) How to fill the storage ring with electrons and positrons??? place the conversion target inside the storage ring e e- - e + e- e+ ecavity ee 15

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17 AdA Concept e+ ee- e- Electron Injection cavity 3m Positron Injection cavity e- e 17 e+ e-

18 AdA Challenges II How to make electrons and positrons collide? Note: AdA is a single storage ring: electrons and positrons see same optics but in reverse direction B.Touschek: It is guaranteed that an electron and a positron necessarily meet in a single orbit because QED is CP (chargeparity) 18

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20 AdA Challenges II How to make electrons and positrons collide? Note: AdA is a single storage ring: electrons and positrons see same optics but in reverse direction B.Touschek: It is guaranteed that an electron and a positron necessarily meet in a single orbit because QED is CP (chargeparity) If a ring collider works, then CP(T) invariance of QED is confirmed!!! Note: CP(T) invariance says that a positron can be regarded as an electron traveling in reverse time direction. Touschek was right, in a very short time AdA was commissioned and electron-positron collisions were observed much more than just a technical (engineering) achievement!

21 AdA Challenges III How to measure that electron-positron collisions take place? How many collisions? Definition of Luminosity Measurement (source factor) R=Lσ Relation between rate of events and cross section of process e- e + 1

22 Luminosity Measurement in Ring Collider: N1 and N and beam cross section A are unknown and have to be precisely measured difficult N1 N f L= 4π A More simple ansatz use reference process(es): e+ e- e+ eultrarelativistic approx. (Bhabha 1936) e+ e- γ γ annihilation process (Compton-like) Both processes are forward peaked! t-pole

23 Bhabha Scattering ( dσ + u + t s + u u + α (e e e e ) = + + dω s st s t annihilation scattering ) interference annihilation diagram scattering diagram q μ s=qμ qμ s-pole from photon propagator t=qμ qμ t-pole from photon propagator 3

24 Photon Pair Production ( dσ + u +t α (e e γ γ) = dω s tu 4 )

25 Photon Pair Production dσ + u t α (e e γ γ) = + dω s t u ( qμ μ t=q qμ 5 ) t-pole from electron propagator

26 Photon Pair Production dσ + u t α (e e γ γ) = + dω s t u ( qμ μ t=q qμ ) t-pole from electron propagator u-pole from crossed diagram 6

27 Sketch of Luminosity Measurement rate R1 γ / e- rate R e+ γ/e Measurement: rates R1 and R (in counts/s) + e- luminosity detector Use: R = L σdetector L = R/ σdetector σ Detector = Detector dσ dω dω acceptance calculation is an experimental task! σdetector is the observed cross section total cross cross section 7

28 Background for Luminosity Measurement rate R1 γ / e- I1(e-) I(e+) γ / e+ background (BG) rate R Problem: beam induced background, e.g. electron-rest gas scattering) Ansatz: R1 R1 = a 1 I 1 + b I 1 I = I 1 (a 1+ b I ) lumi R = a I + b I 1 I = I (a + b I 1 ) BG BG lumi I 8

29 The Big e e Accelerators + - SPEAR (Stanford Positron Electron Accelerator Ring) at SLAC ( ), s1/=3-8 GeV, Discovery of the Charm Quark PETRA (Positron Electron Tandem Ringanlage) at DESY ( ), s1/=38 GeV, Discovery of Gluon-Jets TRISTAN at KEK, Japan ( ) s1/=5-64 GeV (discovery of the desert ) Large Electron-Positron Collider, Geneva (1988-): s1/=9 GeV (LEP I, Z-factory), s1/= GeV (LEP II, WW factory) Stanford Linear Accelerator at SLAC, Stanford ( ) s1/=9 GeV (SLC, Z-factory) 9

30 SPEAR at SLAC Stanford Positron Electron Accelerator Ring ( ), s1/=3-7 GeV, Discovery of the J/Psi Discovery of the Charm Quark Ψ (S) J / Ψ π π e e π π

31 Quark-Pair Production Resonant Rho production later e+ c- e e c c+ - z=/3 e e- similar to muon-pair production dσ + α q u + t (e e c c ) = dω s s ( c ) 31

32 PETRA at DESY Positron Electron Tandem Ring Anlage ( ), s1/=38 GeV, Discovery of Gluon Jets predicted by QCD!!! 3

33 Tasso at PETRA QED Test: Bhabha scattering 33

34 Total Muon Pair Production C.S. derivation: d t u = dt s s s t u= m i (only two independent) u =t s t s d t s ts = 4 dt s 3 3 t s ts 4 /3s s s3 = s = = 4 4 3s s s 34

35 Myon Pair Production 4 85nb e e = 3s s PETRA accelerator (DESY) 35

36 Quark-Pair Production Difficulty: quarks and anti-quarks are experim. difficult to distinguish s t= (1 cos θ) s u= (1±cos θ) s t +u = (1+cos θ) e+ different signs for quarks and antiquarks quarks and antiquarks averaged! c- e+ e- c c- TASSO (1984) z=/3 e e- similar to muon-pair production dσ + α q u + t (e e c c ) = dω s s ( c ) 36

37 Tristan Collider at KEK : s1/=5-64 GeV Search for the top in the desert 37

38 QED Tests in e e collisions + - Feynman diagram Possible tests: universality of charges (leptons, quarks,...) energy dependence of coupling ( running ) test of perturbation theory Lorentz structure of coupling propagator effect new physics test crossing symmetries ( gauge invariance) 38

39 Measurement of Rhad Test of Quark Charges e + e hadrons R= + + e e μ μ onset of quark thresholds 39

40 Crossing Symmetries dσ + u t α (e e γ γ) = + dω s t u ( ) e- γ e- γ t t s u dσ s u α (γe γe ) = + dω s u s ( ) 4

41 The Low Energy Limit Electromagnetic coupling at low energy: q μ Q= t= (qμ qμ ) Thompson scattering cross section 8π 8 π α λc σt = = 3 π 3 re ( ) used to determine 41 α

42 The Low Energy Limit Electromagnetic coupling at low energy: e μ Q = t= (q qμ ) m Thompson scattering cross section e 8π 8 π α λc σt = = 3 π 3 re ( ) not dependent on energy! Used to determine α General cross section: e* dσ s u α (γ e γ e ) = + dω s u s ( ) two terms 4

43 Running of alphaem α(q=)=1/137 α(q=9 GeV )=1/18 self-energy corrections alpha is not a constant! vertex corrections dressed charge! measure em. coupling for different (high) energies search for new physics effects at mass scale Λ d σ (QED) dσ s = 1+ dω dω Λ ( 43 )

44 Lorentz-Structure of Electromagnetic Interaction From Maxwell Equations: ν μ μ ν A ( x) = e J (x) in QED: j V = (conservation of currents) electromagnetic interaction described by vector currents! Also true at high energies? Vector Current: V scalar coupling: ψ λ=ψ j = Axial-vector Current: pseudoscalar coupling: 5 j A = γ5 ψ λ=ψ lead in general to different angular distributions! 44

45 LEP Collider biggest electron-positron collider with up to GeV centre of mass 4 experiments: ALEPH, DELPHI, L3, OPAL LEP1: Z-factory LEP: WW factory 45

46 LEP Regime Processes: e+ e- Z e+ e- W+ W- at LEP energies radiative and electroweak effects play an important role! 46

47 International Linear Collider 5 GeV electrons x 5 GeV positrons 47

48 Backup 48

49 Fermion-Fermion Scattering particle-particle (here electron-proton) scattering external leg lowest oder perturbation theory: leading order graph (Born) 49

50 Gamma Matrices I Gamma matrices γμ are chosen such that γ is hermitian while γk (k=1,,3) are anti-hermitian (γ) = γ, (γ)μ = 1, (γk) = -(γk), (γk)μ = -1 (k=1,,3) We define γ5 as the hermitian matrix: γ5 = i γ γ1 γ γ3, (γ5) = 1, The 4x4 gamma matrices can be represented by (representation where γ is diagonal): k =, k k 1 =, 1 1 = 1 5 (note several representations exist) With the x Pauli matrices: 1 = 1, 1 = i i 3= 1. 1 Gamma matrices anti-commute: γi γk + γk γi = 5 for i k

51 Gamma Matrices II 1 = = i i = i i 5 = = (in other representations g5 is diagonal ) 51

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