Standard Model of Particle Physics SS 2013

Transcription

1 ecture: Standard Model of Particle Physics Heidelberg SS 013 (Weak) Neutral Currents 1

2 Contents Theoretical Motivation for Neutral Currents NC Processes Experimental Discovery Measurement of the Weinberg Angle NC Fermion couplings

3 Recap: Weinberg-Salam Theory eft handed fermions (doublets): ψ1 = ψ = Right handed fermions (singlets): ψ3 = νe νμ μ ντ τ (e ) ( ) ( ) ν e, R νμ, R er μ R ντ, R τr ( ) ( ) ( ) u d ur dr c s cr sr t b tr br Gauge Transformations: Yj τ ψ j (x) ψ j (x)=exp(i α ( x) ) exp(iβ(x) ) ψ j ( x) SU() τ: Pauli matrices U(1) Yj: hypercharge Smallest gauge group representation with >1 gauge boson is SU(): W, W representated by τ±= 1 ( τ 1±i τ ) additional W3 field represented by: τ3 ( 4th gauge boson) + - 3

4 Recap: Weinberg-Salam Theory eft handed fermions (doublets): ψ1 = ψ = Right handed fermions (singlets): ψ3 = νe νμ μ ντ τ (e ) ( ) ( ) ν e, R νμ, R er μ R ντ, R τr ( ) ( ) ( ) u d c s ur dr cr sr t b tr br Gauge Transformations: Yj τ ψ j (x) ψ j (x)=exp(i α ( x) ) exp(iβ(x) ) ψ j ( x) SU() τ: Pauli matrices U(1) Yj: hypercharge Note: SU() fields W1, W, W3, and U(1) field B (hypercharge) correspond to massless bosons! fields W3 (V-A coupling) and B (hypercharge) can/do mix! 4

5 Electroweak Symmetry Breaking cos θw sin θw W 3 Z = A sin θw cos θw B () ( )( ) ( ) ( )( ) W3 cos θw sin θw Z = B sin θw cos θw A 1 Y ew = g j W 3 + g ' j B 3 symmetry breaking 1 Y elm = g j sin θw A + g ' j cos θw A 1 3 Y NC = g j cos θw Z g ' j sin θw Z 3 5

6 Electromagnetic Interaction 1 elm = g j sin θw A + g ' j Y cos θw A 3 eft-handed Current: ( 1 0 Pauli matrix τ3: τ 3 = 0 1 ) 1 D ) j = (U U D 3 isospin up isospin down Hypercharge Current: U + Y doublet D D + Y singlet D R DR Y ψ = Y doublet U jy = ψ only down component here (leptons)! Photon field: vector current and coupling to electric charges: Gell-Mann Nishijima 1 Y 3 j elm = j + j Q = I + 1 Y 1. e = g sin θw = g ' cos θw D D R D R (e,μ,τ). eptons: Y doublet = 1, Y singlet = j elm = D 3. Quarks: Y doublet = 1 4, Y u singlet =, Y d singlet =

7 Weak Neutral Current 1 Y NC = g j cos θw Z g ' j sin θw Z 3 Z f i g γμ 1 (C C A γ5 ) cos θw V ( g cos θw cos θw ) ( j NC )μ =Ψ γμ Q f sin ΘW ' μ ( j NC ) =Ψ e γ C A= CV = 7 ) 1 [c (1 γ5 )+ c R (1+ γ5 )] Ψ e cr= e ( g sin θw cos θw I 3= 1/ I 3=+ 1/ 1/ Q f sin ΘW + 1/ Q f sin ΘW c = no pure V-A coupling for non-zero Weinberg angle! g' sin θw = μ Q f sin ΘW ' 1 (C V C A γ 5 )Ψ e I 3= 1/ I 3 =+ 1/ 1/ + 1/ 1/ ' Q f sin ΘW + 1/' Q f sin ΘW

8 Unitarity in SU() Gauge Group Recall: divergent behavior at high energies νe e σ (νμ e μ ν e ) G F s four-fermion interaction νμ μ fixed by introducing the W-boson νe e σ (νμ e μ ν e ) G F W± νμ W-exchange 8 μ

9 Unitarity in SU() Gauge Group Fermion W-boson Scattering W+ e+ σ (e e + W 0 W 0+ ) G F s νe divergent high energy behavior of longitudinal (J3=0) spin component e.g. W-pair production W- e- fixed by introducing the Z boson (predicted by non-abelian SU()) W+ e σ (e e W W ) G Z0 F e- triple gauge coupliing W- General Rule (1970, t'hooft, Veltmann): UV-divergences vanish only in gauge invariant theories 9

10 Neutrino-Nucleon Scattering Experiments 10

11 Experimental Discovery of NC in early 70ties bubble chambers where used to study particle interactions Principle: take pictures! superheated fluid de/dx piston hydrogen, freon (fluorocarbon) boiling charged particle fast expansion reconstruction of all charged particles! problem: low repetition rate, difficult analysis 11

12 BEBC principle iquid = hydrogen 1

13 BEBC (CERN, ) Heidelberg -Saclay-CERN 6.3 million photographs 13

14 BEBC (CERN, ) Heidelberg -Saclay-CERN 3.7m 6.3 million photographs 14

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16 Neutrino-Proton Scattering (Charged Current) 16

17 Gargamelle iquid: freon (CF3Br). 17

18 Cross Section of Experiment 18

19 Eleastic Neutral Current νe νe 19

20 Discovery of Neutral Currents Hasert et al. 0

21 Classification of Inelastic Events dangerous background from neutrons n? 1

22 Hadronic neutral current reaction

23 NC/CC Ratio Neutrino-Nucleon Scattering Anti-neutrino Beam 3

24 R-Measurements in Gargamelle Neutrino-Nucleon Scattering NC event in every ~1000th film 4

25 Signatures in CHARM Experiment Drift Chambers: charged currents neutral currents 5

26 Neutrino-Electron Scattering and similar for anti-neutrinos possible to determine couplings and Weinberg angle from different reactions 6

27 epton Couplings C A= CV = I 3 = 1/ I 3 =+ 1/ 1/ + 1/ 1/' Q f sin ΘW + 1/' Q f sin ΘW compilation of several experiments (Wu) 7

28 Deep Inelastic Neutrino-epton Scattering and Weinberg Angle Geweniger 1984: 8

29 orentz Invariant Kinematics of the Deep Inelastic Scattering Process The virtuality of the exchanged photon is given by: p' positron θ Q = q = ( p p ') p positron 1 4 sin / q Relative energy loss (inelasticity): qp ν y = = Eν pp γ / Z-boson xp N nucleon relative fraction of parton momentum: q Q x = = q P Sy with cms energy: S = pp 9

30 HERA NC (CC) Cross Sections propagator effect Difference between e+p and e-p cross section due to electroweak (cv, ca) Z-boson couplings MW,Z ~ 100 GeV 30

31 DIS Structure Functions at HERA Deep Inelastic Scattering for e±p described by: ~ ~ Generalised functions F and F3: with Structure Functions F and F3: 31

32 Summary Neutral Currents = Virtual exchange of Z-boson discovered with the Gargamelle experiment in 1973 Electroweak Symmetry Breaking: Triplet field W couples to left handed particles (V-A) Singlet field B couples to hypercharge parity violation fields W3 and B are broken into Z and A field The Photon field is massless and parity conserving (V-coupling) The Z-field has V and A couplings depending on fermion type Electroweak Symmetry Breaking needs Higgs field to explain masses of W and Z particles mw mz = 90GeV cos θw Masses of W and Z particles ~ 100 GeV, precise determination in resonant production (EP Wednesday) 3

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