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5. zur Theorie β -Zerfall des Neutrons

5. zur Theorie β -Zerfall des Neutrons. p e J μ W j μ n ν e. V −A weak interaction. 1. universality and 2. CVC. 1. Universality : G F / √ 2 = G μ = G τ =… e and g -charge universality is postulated in Standard Model,

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5. zur Theorie β -Zerfall des Neutrons

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  1. 5. zur Theorie β-Zerfall des Neutrons Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  2. p e JμW jμ n νe V−A weak interaction Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  3. 1. universality and 2. CVC 1. Universality: GF/√2 = Gμ = Gτ =… e and g-charge universality is postulated in Standard Model, is required in Grand Unification. 2.Conservation of weak hadronic Vector Current CVC: hadronic vector coupling = 1: i.e. hadronic vector current: Vμ weak = g·(p γμ n) is conserved, like hadronic el.-magn. current: Vμ el.-m. = e·(p γμ p) is conserved. is required in electro-weak Standard Model Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  4. p e νe p e νe • but neutron decay (q2=0) = + gN f + … • n n • With N = (n, p) and  = (−, 0, + ): • Vμ=Nγμ½τ N + i ∂μ t  + … • is conserved: ∂μVμ=0 • with Isospin operators τ(2×2), t(3×3), … of strong interaction: • CVC in β-decay = conservation of isospin current of strong interact. • Isospin (global) symmetry SU(2)iso: • N' = exp(−i ε·½τ) N leaves Lagrangean L invariant CVC ≡ strong isospin conservation Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  5. 3. PCAC  = gA/gV = 1.27: • axial vector current Aμ= is not conserved: ∂μAμ ≠ 0 • old version (~40 yrs): • pion decay −→μ− +νμ' is axial decay, • has: ∂μAμ~ fm2, with smallm : • → 3. Partial Conservation of Axial-vector Current • applied to neutron decay, this gives • Goldberger–Treiman relation: mNgA = fgN • good to ~10% Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  6. chiral symmetry • "new" version (~20 yrs): • ifgA/gV = 1, then axial hadronic current is conserved: ∂μAμ = 0, • the underlying (global) symmetry is the • chiral symmetry of the strong interaction: • N' = exp(−i η·½τγ5) N leaves Lagrangean L invariant • Chiral symmetry is left-right symmetric: SU(2)L× SU(2)R. • "L" and "R" can be defined only for massless particles, • but nucleons are massive, and as gA/gV≠ 1: • i.e. chiral symmetry is not a good symmetry. • howevergA/gVis nearly 1: There is a chiral symmetry, but it is • spontaneously broken: SU(2)L× SU(2)R → SU(2)iso transition • (probably identical with quark-gluon phase transition). Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  7. σ ↑ <σ>=f example: σ-model • massless fermions, coupling g to: • pions  (pseudoscalar, isotriplet) • and to σ (scalar, isosinglet) • plus quartic terms in , σ: • spontaneous symmetry breaking of chiral symmetry: • fermion mass generation: mN = f g pions  = Goldstones with m = 0 make 's massive by explicit symmetry breaking term in L: then follows automatically: ∂μAμ~ fm2, i.e. f = f , and: mNgA = fgN = Goldberger–Treiman relation  Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  8. predictions for gA/gV • gA enters many other processes: • π-N scattering (Adler-Weisberger relation) • hyperon decay (current algebra relations) • parton model (Björken, Ellis-Jaffe sum rules) • Models: • spin-flavor content of constituent quarks: gA/gV=5/3 • constituent quarks in "bag"-potential: • gA/gV=5/3×radial integral=5/3×0.65=1.09 • QCD calculations on the lattice • (lattice constant a): ←exp. gA/gV Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  9. 4. Weak magnetism • Postulated before advent of Standard Model: • Isovector of hadronic weak current t+, t− • + isovector portion of hadronic el.-magn. current t0 • = isospin triplet (t+, t0, t−) of conserved currents. Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  10. measurement of weak magnetism • either from β-decay asymmetry spectrum (~ 1%-effect): • Problem: statistics, undetected background • or from β-decay difference spectrum (background free): • Problem: statistics, detector function • Today: ~1σ-effect Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  11. 2. Short history of CKM matrixa) 60ies: Suppression of strangeness-changing decays • 1963: 3 quark flavors known: up u • down d • strange s • Observation: Strangeness changing decays of K, Λ, … (ΔS=1) • are suppressed by a factor 20 (w.r.t. ΔS=0): Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  12. b) Cabbibo angle θC • decay rates found such that sin2θC + cos2θC = 1, with: • sin2θC = 0.05, cos2θC = 0.95 (1:20), • sin θC = 0.22, cos θC = 0.97, • θC = 130 = 0.22, • Cabbibo: • quark mixing is 'zero-sum game', • is pure rotation in flavor space, • quark mixing matrix is unitary: Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  13. c) 70ies: more flavors 1970, GIM: "a 4th flavor: charm c, would naturally explain the observed absence of neutral currents in ΔS=0": 1972, KM: "a 3rd generation: bottom b, top t, would naturally incorporate violation of T-invariance via a complex phase φ" with si = sinθi, ci = cosθi, (i=1,2,3, for 1↔2, 1↔3, 2↔3 generation mixing) Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

  14. d) ever since: filling of the CKM matrix Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg

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