# Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 1 5. zur Theorie β-Zerfall des Neutrons.

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Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 1 5. zur Theorie β-Zerfall des Neutrons

Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 2 V−A weak interaction p e J μ W j μ n ν e

Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 3 1. universality and 2. CVC 1. Universality: G F /√2 = G μ = G τ =… 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: V μ weak = g·(p γ μ n) is conserved, like hadronic el.-magn. current: V μ el.-m. = e·(p γ μ p) is conserved. is required in electro-weak Standard Model

Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 4 CVC ≡ strong isospin conservation p e ν e p e ν e but neutron decay (q 2 =0) = + g  N  f  + … n n With N = (n, p) and  = (  −,  0,  + ): V μ =  N γ μ ½τ N + i ∂ μ  t  + … is conserved: ∂ μ V μ =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

Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 5 3. PCAC = g A /g V = 1.27: axial vector current A μ = is not conserved: ∂ μ A μ ≠ 0 old version (~40 yrs): pion decay  − → μ − + ν μ ' is axial decay, has: ∂ μ A μ ~ f  m  2, with small m  : → 3. Partial Conservation of Axial-vector Current applied to neutron decay, this gives Goldberger–Treiman relation:m N g A = f  g  N good to ~10%

Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 6 chiral symmetry "new" version (~20 yrs): if g A /g V = 1, then axial hadronic current is conserved: ∂ μ A μ = 0, the underlying (global) symmetry is the chiral symmetry of the strong interaction: N' = exp(−i η·½τ γ 5 ) 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 g A /g V ≠ 1: i.e. chiral symmetry is not a good symmetry. however g A /g V is 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).

Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 7 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:m N = f g pions  = Goldstones withm  = 0 make  's massive by explicit symmetry breaking term in L: then follows automatically: ∂ μ A μ ~ f m  2, i.e. f = f , and: m N g A = f  g  N = Goldberger–Treiman relation  σ ↑ =f

Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 8 predictions for g A /g V g A 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: g A /g V =5/3 constituent quarks in "bag"-potential: g A /g V =5/3×radial integral=5/3×0.65=1.09 QCD calculations on the lattice (lattice constant a): ←exp. g A /g V

Schleching 2/2008Präzisionsphysik 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 t 0 = isospin triplet (t +, t 0, t − ) of conserved currents.

Schleching 2/2008Präzisionsphysik 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

Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 11 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): weak decay examples quark description rate 14 O (0 + → 0 + )u → d + e + + ν e ' G μ 2 cos 2 θ C n → p e ν π − → π 0 e ν d → u + e − + ν e ' G μ 2 cos 2 θ C K − → π 0 e ν Λ → p e ν s → u + e − + ν e 'G μ 2 sin 2 θ C μ → e ν ν−Gμ2Gμ2 2. Short history of CKM matrix a) 60ies: Suppression of strangeness-changing decays

Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 12 b) Cabbibo angle θ C decay rates found such that sin 2 θ C + cos 2 θ C = 1, with: sin 2 θ C = 0.05, cos 2 θ C = 0.95 (1:20), sin θ C = 0.22, cos θ C = 0.97, θ C = 13 0 = 0.22, Cabbibo: quark mixing is 'zero-sum game', is pure rotation in flavor space, quark mixing matrix is unitary:

Schleching 2/2008Präzisionsphysik 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 3 rd generation: bottom b, top t, would naturally incorporate violation of T-invariance via a complex phase φ" with s i = sinθ i, c i = cosθ i, (i=1,2,3, for 1↔2, 1↔3, 2↔3 generation mixing)

Schleching 2/2008Präzisionsphysik mit Neutronen/5. Theorie n-Zerfall Neutron Decay St.Petersburg 14 d) ever since: filling of the CKM matrix

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