PHYS 6610: Graduate Nuclear and Particle Physics I H. W. Grießhammer INS Institute for Nuclear Studies The George Washington University Institute for Nuclear Studies Spring 2018 III. Descriptions 4. (Electro-)Weak Interactions: The Glashow-Salam-Weinberg Theory Or: A Theorist’s Theory References: [phenomenology: PRSZR 10, 11, 12, 18.6; Per 7.1-6 – theory: Ryd 8.3-5; CL 11, 12; Per 7, 8, 5.4; most up-to-date: PDG 10-14 and reviews inside listings] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University III.4.0
(a) Weak Phenomenology: Overview The only interaction which has been shown to: – act on all fundamental particles (besides gravity; QED: only charged; QCD: only quarks); – violate each of P , C and CP (i.e. also T ); – change fermion flavours (i.e. violate individual fermion number conservation). – tiny cross sections at low energies: σ typ ∼ 10 − 15 b = 1 fb ; Signatures: – very small rates/long lifetimes: τ typ ∼ [ 10 − 13 ... 10 3 ] s ; (besides parity, duh!) – often “missing” energy & momentum: neutrinos very hard to detect Pauli’s neutrino hypothesis letter: “Dear Radioactive Ladies and Gentlemen, Zürich, Dec. 4, 1930 [. . . ] I have hit upon a desperate remedy to save the "exchange theorem" (1) of statistics and the law of conservation of energy. [. . . ] there could exist electrically neutral particles [. . . ] that have spin 1/2 and obey the exclusion principle and [. . . ] do not travel with the velocity of light. The mass [. . . ] should be of the same order of magnitude as the electron mass [. . . ] Mr Debye [] told me recently in Bruxelles: ‘Oh, It’s better not to think about this at all, like new taxes.’” Same day, private: Today I have done something which you never should do in theoretical physics. I have explained something which is not understood by something which can never be observed. Here a-historic approach: Construct from wealth of present evidence. = ⇒ Step I: Classify wide variety of phenomena into simple categories. PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University III.4.1
Leptonic Processes (Examples) Involve only leptons – rarest but cleanest = ⇒ Use them to develop general theory! µ − → e − + ¯ τ ∼ 10 − 6 s Both violate individual lepton conservation, µ -Decay: ν e + ν µ e − + ν µ → µ − + ν e Charge Transfer: but lepton- family number conserved: ⇒ L µ ( µ − ) = L µ ( ν µ ) = 1 = − L µ ( µ + ) = − L µ ( ¯ = ν µ ) etc. In both, charge is transferred between leptons: Charged-Current interaction (CC) The Z 0 resonance: wide, at √ s = 91 GeV in e + e − → X produces plenty of ν e ¯ ν e , ν µ ¯ ν µ , ν τ ¯ ν τ pairs. = ⇒ Speculate weak process, mediated by J PC = 1 −− boson: Neutral-Current interaction (NC) Determine ν rates indirectly: QED/QCD Γ ν = Γ tot − ( Γ hadr + Γ e µτ ) prediction ���� � �� � line shape calorimeters No decays like ν e ¯ ν µ observed! Γ [ → e + e − ] : Γ [ → µ + µ − ] : Γ [ → τ + τ − ] = 1 : [ 1 . 000 ± 0 . 004 ] : [ 0 . 999 ± 0 . 005 ] [Per 7.2] = ⇒ Weak interaction universal for both neutrinos and charged leptons. ν ν l ] = 165 . 8 MeV . LO decay in HW 5.5: Γ = g 2 M W 1 −− GSW: Γ [ → ν l ¯ 12 π , g → ... GSW theory. Compare to Γ exp = ⇒ [ 2 . 984 ± 0 . 008 ] ν species with M ν ≪ 90 GeV [PDG 2017] ν ν ¯ PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University III.4.2
Semi-Leptonic Processes (Examples) Involve leptons and hadrons – most common, oldest seen. n ( udd ) → p ( uud )+ e − + ¯ ν e τ = [ 880 . 3 ± 1 . 1 ] s Neutron decay [PDG 2012] i.e. d → ue − ¯ ν e = ⇒ Charged Current Exchange: CC d ) → µ + + ν µ , e + + ν e , i.e. quark process similar to proton π + ( u ¯ π decay, e.g. CC s ) → µ + + ν µ , e + + ν e , i.e. u ¯ K + ( u ¯ s → ( s ¯ u ) → ... K decay, e.g. s or u ¯ CC p + p → 2 H + e + + ν e kind of important. . . Solar fusion CC e.g. 60 Co → 60 Ni + e − + ¯ Nuclear β decay ν e Wu 1957: P violated CC e.g. e − + 152 Eu ( J = 0 ) → 152 Sm ( J = 0 )+ γ + ν e Nuclear e − -capture CC Goldhaber 1958: ν helicity measurement All above mutate quark flavours: individual quark-number violated. ⇒ Z 0 ! ν l + A → ν l + X No charged lepton in final state = First Neutral-Current (NC) event [CERN 1973; GSW prediction] NC PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University III.4.3
Hadronic Processes (Examples) Involve only hadrons – window to QCD. K 0 ( d ¯ s ) → π + ( u ¯ d )+ π − ( ¯ s → ¯ K decay ud ) , i.e. ¯ d + u ¯ u CC τ ∼ 10 − 10 s Λ 0 ( uds ) → p ( uud )+ π − ( ¯ Λ ( 1405 ) decay ud ) CC Research Frontier: Hadronic flavour-conserving parity-violation (HFCPV), e.g. pp → pp N N P -wave (parity − ) S -wave (parity + ) N N One of the least-explored sectors of the Standard Model: GW theory: hgrie • What is the weak part of the nuclear force? (US, EU Long Range Plans) 1 • Z 0 (NC) as Inside-Out Probe of non-perturbative QCD: qq correlations at ∼ 0 . 002fm M W PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University III.4.4
What we find – and what not (Examples) Neutral & Charged Current Exchanges with J PC = 1 −− , like for photon : Produced as resonances in annihilations and other processes: e + e − ( √ s = 90GeV ) → Z 0 , e + e − ( √ s = 160GeV ) → W + W − ; u → Z 0 , u ¯ d → W + . and in NN or N ¯ N collisions also resonances from u ¯ = ⇒ Try gauge theory of gauge bosons with charges ± 1 , 0 ? Not Seen Seen Interpretation → e − + p ν e + n → e − + p ν e + n / ¯ neutrino is not anti-neutrino, L e ( ν e ) = − L e ( ¯ ν e ) → e + + n ν µ + p → µ + + n ν µ + p / e -neutrino is not µ - neutrino, but. . . → e − + X ν µ + A → µ − + X ν µ + A / no interactions across lepton families � ν e � � ν µ � � ν τ � = ⇒ Natural grouping into lepton families: , , µ τ e PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University III.4.5
(b) Weak Interactions Violate Parity Reminder Fermion Helicity & Chirality [QFT and TCP chapters] h = + 1 parallel: right-handed Helicity h = � σ · � p : E spin component longitudinal to � p h = − 1 anti-parallel: left-handed For m = 0 , indentical to chirality : eigenvalues of spinors with respect to γ 5 : γ 5 ϕ RL = ± ϕ RL Projectors: P RL : = 1 2 ( 1 ± γ 5 ) , i.e. P RL ϕ = ϕ RL , P 2 RL = P RL , P RL P LR = 0 , P R + P L = 1 parity Parity transformation: � σ axial, � p polar = ⇒ Ph ± = h ∓ = ⇒ �� �� ϕ R � � p + g � E − gA 0 + � σ · ( � A ) Recall Lagrangean m ϕ † R , ϕ † : L p − g � E + gA 0 − � σ · ( � A ) ϕ L m of QED in chiral basis ⇒ Gauge field does not mix chiralities; only mass term does: ∝ ( 1 − β ) = 1 − | � p | = . E PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University III.4.6
Electron Helicity from Nuclear β Decay (CC Event) 60 Co → 60 Ni + e − + ¯ ν e First: Wu 1957 (prompted by theorists Lee/Yang 1956) � B � = � e z defines quantisation axis θ π−θ µ and e − spin � for 60 Co spin � σ e . Expectation: e − emission uniform if parity conserved . µ : ˆ p , ˆ Reflection on plane perpendicular to � P � µ → � P � p → − � µ Result: Intensity I ( θ ) � = I ( π − θ ) , and emission of e − more likely against 60 Co spin , matches dependence on initial e − -polarisation P : I ( θ ) = 1 + P � σ e · � p e = 1 + P β e cos θ E e and data compatible with P = − 1 . = ⇒ Parity violated, electron emitted with h e = − 1 , m e � = 0 explains spin-flip observed in detector. [Per 7.6 after Koks/van Klinken 1976] Similar for µ + → e + + ν e + ¯ ν µ : P ( e + ) = + 1 . Both confirmed in cornucopia of systems. PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University III.4.7
Neutrino Helicity from Nuclear Capture (CC event) cf. [PRSZR 18.6, Per 7.6] First: e − + 152 Eu ( J = 0 ) → 152 Sm ( J = 0 )+ γ + ν e Goldhaber 1958 J z conservation: photon spin ( J = 1 ) parallel to electron spin ( J = 1 2 ), antiparallel to ν spin ( J = 1 2 ). = ⇒ Detect photon spin to know ν helicity (mag. quantum m e = m γ + m ν ). ⇐ = found in experiment never found in experiment [Mar] L , ν L and e + ⇒ All evidence suggests: only e − = R , ¯ ν R interact weakly in CC events: Maximal Parity Violation PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University III.4.8
(c) Philosophy of the Glashow-Salam-Weinberg Model (d) GSW for One Lepton Family (e) Dynamical Gauge Boson Mass Generation Nobel 2013 The Higgs-Kibble-Englert Mechanism: A U ( 1 ) Example See Landau-Ginzburg Theory of Superconductivity PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University III.4.9
Recommend
More recommend
