Standard Model of Particle Physics SS 2013

Transcription

1 Lecture: Standard Model of Particle Physics Heidelberg SS 2012 Experimental Tests of QED Part 2 1

2 Overview PART I Cross Sections and QED tests Accelerator Facilities + Experimental Results and Tests PART II Tests of QED in Particle Decays QED Radiative Effects (Bremsstrahlung, Higher Order Processes) 2

3 Electromagnetic Decay of Pion Pion is the lightest hadron (meson) consists of u and d quarks (isospin triplet) No strong or weak decay possible Can the electromagnetic decay of the pion be described by QED? Complication: quarks are involve large QCD corrections! Solution: introduce pion form factor e+ pion 1 π = ( u u d d ) 2 0 Pion formfactor e- (measured from pion lifetime) 3

4 Test Pion Branching Ratios dominant decay: B(π0 γγ) = % radiative decay: B(π0 e+e- γ) = % 2-prong decay: B(π0 e+e-) = 6.46 x 10-8 Can QED describe this surprisingly small branching ratio? Vector Currents: j μ elm μ = v (x) γ u(x) e+ Vector currents conserve helicity. Resulting spin should be J(π0)=1 But pion is a Pseudo-scalar J(π0)=0 contradiction helicity suppression pion e- Resulting suppression factor: Polarisation of helicity state is given by fermion velocity: λ = ±β per photon/fermion vertex m2q m2e 1 1 (1 β2q )(1 β2e ) = = γ q γ q mπ for right/left chiralities no scalar couplings! 4 ~

5 QED Radiative Effects Bremsstrahlung Higher Order Processes Experimentally very important: can be exploited for measurements (luminosity, radiative returns) but can also disturb measurements! 5

6 QED First Order Corrections p1 p2 p1 k k p2 p1 p' p' initial state radiation (ISR) Fermion propagator: ISR: p2 final state radiation (FSR) 1 1 = p ' 2 m2 ( p1 k )2 m = = p 1 k 2 E e E γ (1 cos θ) ( p1 k) m p1 +k 2 p 1 k m 1 1 = p ' 2 m2 ( p2 +k)2 m2 (if mass small) Singularities: photon emission under zero degrees θ 0 soft photon E 0 γ FSR: similar ISR + FSR: interference term shows no singularity (wide angle scattering) 6

7 QED First Order Corrections Singularities are not allowed in (renormalisable) gauge theories and have to cancel Singularity from soft and collinear Bremsstrahlung cancel with virtual vertex corrections in QED real corrections (Bremsstrahlung) α 2 α 2 virtual correction: interference of LO diagram and vertex correction ~ α2 compensates singularities from Bremsstrahlung α α 7 3

8 Electron-Proton Collider HERA Ee = 26.7 GeV Ep= 920 GeV 8

9 Proton Parton Densities 9

10 proton E=920 GeV electron E=27.5 GeV ep e X (neutral current) 10

11 Kinematics Scattering Process The virtuality of the exchanged photon is given by: p' Q 2 = q 2 = ( p p ') 2 p 1 4 sin / 2 θ electron q Energy transfer (in Proton-rest frame): photon = E Elektron E Elektron ' Energy of photon-proton system (hadronic final state): W = mp proton 11

12 Lorentz Invariant Kinematics of Deep Inelastic Scattering Process The virtuality of the exchanged photon is given by: p' Q 2 = q 2 = ( p p ') 2 p 1 4 sin / 2 q Relative energy loss (inelasticity): y = ν E Elektron θ electron qp = pp photon xp P proton relative fraction of parton momentum: q2 Q2 x = = 2q P sy with cms energy: s = 2pP 12

13 proton E=920 GeV electron E=27.5 GeV 13

14 Determination of Luminosity? 14

15 Reference Process Need process with large cross section Bethe Heitler Process: e p ep γ Bremsstrahlung-Process with large cross section (~ 1 barn)! electron electron proton proton Note, the proton stays intact (elastic)! the cross section can only be given for a minimum photon energy! (infrared singularity) 15

16 Radiative Effects in ElectonProton Scattering Bremsstrahlung proportional to ( p k ) m Bremsstrahlung effects are large for particles with low mass Electron mass: me = MeV Proton mass: mp = 938 GeV heavy radiation! Radiation is large if 1. photon is soft 2. photon is emitted collinear Photons can be emitted from 1. incoming electron (initial state radiation, ISR) 2. outgoing electron (final state radiation, FSR) 16

17 Radiative Poles Neglecting the small electron mass, the poles become: Af p ' k Ai p k ISR FSR Note ISR reduces the available center of mass energy s 1/2 17

18 calculated jet direction Initial State Radiation? 18

19 calculated jet direction Energy E conserved and momentum p conserved E-pz conserved E-pz (proton)=0 E-pz (electron) = 2 x 26.7 GeV 19

20 Kinematic Reconstruction of ISR radiative ISR tail 20

21 Photondetector at H1 photon detector 21

22 Initial State Radiation? 22

23 electron photon? Inner Drift Chamber operational? Final State Radiation? 23

24 electron photon? Inner Drift Chamber operational? Final State Radiation? 24

25 Question: Final State Radiation? collinear photon can not be resolved! 25

26 Radiative Poles Neglecting the small electron mass, the poles become: Ai p k Af p' k ISR FSR Note ISR reduces the available center of mass energy s 1/2 There is a third pole (Compton events / Wide Angle Bremsstrahlung): Ac 1 = (energy is transferred from the proton to the electron line) 2 2 ( p p' k) q Final state electron and photon have large opening angles and are pt balanced 26

27 electron e* electron pole proton proton 27

28 Bethe Heitler Process diagram: electron electron poles proton proton Cross section is largest if electron and photon are scattered (emitted) at small angle (Compton and ISR/FSR poles combined) Electron and photon go down the beampipe and are not registered in the central detector 28

29 Luminosity Measurement at HERA dedicated electron and photon detectors photon detector electron detector 29

30 H1 Luminosity Detectors Method: measure coincidence signal 30

31 Coincidence Technique Photon Energy Electron Energy 31

32 Data Monte Carlo Comparison Photon Detector Energy 32

33 Principle of Luminosity Measurement Integration of the instantaneous luminosity: Relation between Photon counts, Bethe-Heitler cross section and integrated Luminosity 33

34 Breakdown of Systematic Errors Pileup Correction 34

35 Effect of Pileup Nγ is average number of photons per collision 35

36 QED Compton Analysis 2nd method: electron electron Ac 1 = 2 2 ( p p ' k ) q pole proton proton 36

37 QED Compton Event 37

38 QED Compton Events Back-to-Back Topology: 38

39 Radiative Corrections to Compton Events! Bremsstrahlung! 39

40 Uncertainties to Compton Analysis total systematic error [in percent]: =

41 Bremsstrahlung in Charged Currents ν e ν e W W ν e W Neutrinos are note seen in detector and create missing pt 41

42 Radiative Charged Current Events and W-W-γ Coupling The W-boson is electrically charged and can also radiate photons! It is possible to test anomalous couplings 42

43 Charged Current Event with Bremsstrahlung 43

44 Radiative Corrections in CC events rad. correction Higher order leading logarithmic QED corrections to deep inelastic ep scattering at very high energies have significant impact on the kinematic reconstruction These logarithmic QED corrections come from multiple photon emissions systematic error of precision measurements 44 J. Kripfganz, H.-J. Möhring, H. Spiesberger

45 Higher Order Processes at HERA 45

46 Alpha Processes at HERA 4 e+ p e+ X μ+ μ 46

47 Alpha Processes at HERA 4 e+ p X e+ e+ e- 47

48 Exploitation of ISR 48

49 Exploitation of ISR ISR reduces the center of mass energy of the actual hard interaction This can be used to extend the kinematic phase space to lower energies Q 2 = q 2 = ( p p ' ) 2 allows to access smaller values of Q2 which could not be reached otherwise! 49

50 Exploitation of ISR ISR reduces the center of mass energy of the actual hard interaction This can be used to extend the kinematic phase space to lower energies Q 2 = q 2 = ( p p ') 2 allows to access smaller values of Q2 which could not be reached otherwise! 50

51 Radiative Returns Z-boson are resonantly produced in e+ e- collisions at resonance (mz ~91 GeV) For s1/2 > mz the radiative return allows a return to the resonance: e+ e- Z γ This effect can be large, e.g. at LEP 51

52 DELPHI Radiative Return Event at LEP photon Z-boson 52

53 Measurement of Radiative Return radiative returns are extemely important! incl. radiative return no radiative return 53

54 Radiative Return at KLEO (Daphne) e+ e- collider at s1/2 = 1 GeV rho resonance + omega resonance e+ e- π+ π- γ 54

55 Radiative Returns at Barbar e+ e- collider at s1/2 = 10 GeV e+ e- p p- γ 55

56 56