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Neutrinos & Weak Interactions Lecture 2 Early history of the neutrino Evgueni Goudzovski School of Physics and Astronomy University of Birmingham, United Kingdom [email protected] Feynman diagrams Quantum field theories: interactions between particles proceed discontinuously by exchange of mediator particles. space A+B→C+D A Amplitude of the process (natural units): C ga x virtual “mediator” particle gb B initial state D “how the interaction happened” final state time • ga, gb: the fundamental coupling strengths at the vertices; • Momentum transfer (4-vector): q2 = (pA − pC)2 = (pD − pB)2; • 1/(q2 − mx2): the boson propagator. The reaction rate is proportional to |A|2 1 Electromagnetic processes (1) Force carrier: photon (γ), coupling constant: (α ~ probability assigned to a vertex of a Feynman diagram) Example 1: e+e− annihilation to photons “Perturbative theory”: very precise predictions γ e+ e− e± e+ e− In general, is process of order γ γ γ γ (n≥2) Higher-order electromagnetic processes are suppressed 2 Electromagnetic processes (2) Example 2: Bremsstrahlung e− γ Allowed in the presence of a nucleus (energy-momentum is conserved due to nuclear recoil) Reaction rate: γ e− N N (Z: electric charge of the nucleus) Practical uses: e.g. X-ray generation in medical imaging Example 3: e+e− pair production (photon conversion) is also allowed in the field of a nucleus Reaction rate: The dominant photon interaction at high energies (E>100MeV); Z-dependence is exploited for photon detection (e.g. Pb calorimeter pre-showers) e+ γ γ N e− N 3 The weak charged current Observable in processes: involving neutrinos (no electric/strong charges), or quark flavour change (forbidden by other interactions). Massive force carriers (mW,Z ≈ 90 GeV/c2): limited range (2×10−3 fm). Point (zero-range) approximation is valid in many cases (e.g. for weak decays). The Fermi constant: Example: electron capture p n n g W± propagator (g/mW)2 g e− p νe e− νe 4 Lepton decays (1) Electron (e−) is the lightest charged particle: necessarily stable by conservation of electric charge Allowed decays of charged leptons (conserving energy, lepton flavour and lepton number) µ− (+conjugate decay modes for antileptons) νµ e− W− (Hadronic decays of the tauon are also allowed, e.g. τ−→π−π−π+ντ) νe 0.5 MeV 106 MeV 1.8 GeV 80 GeV low energy regime The decay rate is governed by two parameters: GF and the initial lepton mass m 5 Lepton decays (2) Weak decay rate: dimension: [GeV−4] Lifetime and the total decay rate or width: [GeV−1] [GeV] (lecture 1) Therefore, (“Sargent’s rule”) Lepton universality: All leptons have identical coupling strength to the W± bosons, i.e. K is independent of the mother and daughter lepton types. For example, In agreement with experiment (~0.1% precision) 6 Radioactivity Deflection of α, β, γ rays by magnetic field Radioactive decays (discovered by H. Becquerel, 1896; Nobel Prize 1903): spontaneous emission of ionizing particles by unstable atomic nuclei. B α=4He nucleus γ=photon β=electron (e−) NB: varying curvature Some types of radioactive decay α decay: (A, Z) → (A−4, Z−2) + 4He++ β− decay: (A, Z) → (A, Z+1) + e− β+ decay: (A, Z) → (A, Z−1) + e+ Electron capture: (A, Z) + e− → (A, Z−1) Isomeric transition: (A, Z)* → (A, Z) + γ Proton or neutron emission. (A: mass number; Z: atomic or proton number) 7 Two-body decays Energy-momentum conservation (in terms of 4-momenta): In rest frame of A ( ), pC pB A Momentum conservation: “back-to-back” decay in the A rest frame 4 equations with 4 unknowns a unique solution: if mB≪mA, mC and mA≈mC (relevant for α-decays) ≈ mA − mC (the expression for EC is similar) 8 Three-body decays Various ways to satisfy energy-momentum conservation: momenta of daughters are not uniquely defined. Allowed kinematic range (in the A rest frame): pC A pD pB Momentum conservation: coplanar momenta in A rest frame B is at rest: C and D are back-to-back pD A,B pc “Endpoint”: another back-to-back configuration pC pD A pB For mD=0, the endpoints of the B and C energy spectra are equal to the fixed energy of a 2-body decay A B + C 9 Typical α- and β-decay spectra 210Bi Arbitrary units Arbitrary units α-decay spectra Two-body: (A, Z) → (A−4, Z−2) + 4He++ β-decay spectrum (τ1/2=5 days) (J. Chadwick, 1914) Powerful research tool for early atom exploration (e.g. Rutherford exp’t) 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 α energy, MeV Characteristic discrete lines, as expected for a 2-body decay Electron kinetic energy, MeV Continuous spectra observed for all beta-emitters β-spectrum was measured with two methods: (1) by the deflection in magnetic field; (2) by the produced ionization. Hypothesis 1 (Rutherford & Meitner): electrons from β decay lose energy via secondary interactions with the material of the source. Hypothesis 2: a third unseen particle is emitted. 10 Ellis & Wooster experiment +? 210Bi β-decay spectrum Ethermal Emean=0.39MeV (Cambridge, 1927) 210Bi 210Po = 83p + 127n + 83e = 84p + 126n + 84e Assume a two-body decay. Convert from the atomic mass to the mass of a nucleus: Ee = (m(210Bi)−83me) − (m(210Po)−84me) 210Bi) − m(210Po) + m , = m( e Emax=1.16MeV Eekin = Ee − me = = m(210Bi) − m(210Po) = 1.16 MeV. Electron kinetic energy, MeV A calorimetric measurement by Ellis and Wooster: average thermal energy emitted per 210Bi decay is Ethermal = (0.34±0.03) MeV. “a striking confirmation of the hypothesis that the continuous spectrum is emitted as such from the nucleus” [Nature 119 (1927) 563] Eendpoint ≈ E2-body: the third daughter, if any, is light. 11 The postulation of the neutrino Problems with β-decay in 1920s: Continuous rather than discrete beta-spectrum (the “energy crisis”): Niels Bohr’s proposal: energy conservation is valid only statistically (!) Angular momentum non-conservation: β-decay never changes nuclear spin by ½. At the same time, spins of n, p, e− were known to be ½. ½ → ½ + ½ (?) n → p + e−: Proposal by Wolfgang Pauli (4th December 1930): a new light spin-½ particle produced with the electron, escaping detection. 210Bi → 210Po + e− + νe n → p + e− + νe (called “neutron” by W.Pauli in 1930; renamed “neutrino” by E.Fermi in 1933) 12 Further evidence for the neutrino (Powell, Fowler, Perkins; 1949) e± “kink” Discoveries made by the Bristol group (Powell et al.) in the late 1940s by photographic emulsion method: apparent momentum non-conservation (A) µ± (B) π± “kink”: escaping neutrino (now known to be a neutrino in case A, and two neutrinos in case B) 13 Nuclear reactors as νe sources Nuclear fission: splitting of a nucleus into smaller nuclei. Discovered by Otto Hahn in 1938 (Nobel Prize for Chemistry 1945). n An example of a neutron-induced fission reaction: + 200 MeV 92p+144n 98p+138n ~106 times greater than in chemical reactions Neutron production: chain reaction First nuclear reactor: December 1942, University of Chicago. First atomic bomb: July 1945, New Mexico, US. Effectively, 6 neutron to proton conversions: 140Ce 94Zr Antineutrino production rate in a reactor: (typical modern commercial reactor power is ~1 GW) n Fν / Pth ~ 6 / 200 MeV = 6 / (200×1.602×10−13 J) ~ 1020 s−1GW−1. n Nuclear reactors and bombs: first artificial high intensity antineutrino sources 14 Neutrinos or anti-neutrinos? Chart of nuclides 238U 208Pb Neutron-to-proton ratio grows as a function of atomic number. Reason: mutual Coulomb repulsion of the protons. Examples: 16O = 8p + 8n; 94Zr = 40p + 54n; 208Pb = 82p + 126n; 238U = 92p + 146n; 94Zr N(n)/N(p)=1 N(n)/N(p)=1.35 N(n)/N(p)=1.54 N(n)/N(p)=1.59 Nuclear fission necessarily leads to neutron-to-proton conversion. By electric charge and lepton flavour conservation, anti-neutrino production: 8O 15 Inverse beta-decay Beta decays: (mn > np: free neutron is unstable, τ = 882 s) (proton is stable; decay occurs within nuclei) Neutrinos are created in beta-decays. Could they be absorbed in the reverse process? (recall bremsstrahlung and photon conversion ) Crossing symmetry: antiparticles are equivalent to particles going backwards in time. Inverse beta decay (IBD): related to beta-decays by crossing symmetry IBD: production of charged particles (e±). A possible tool for indirect (anti)neutrino detection. 16 Reactor νe detection via IBD Energy threshold for : (see lecture 1) Antineutrinos/fission Reactor νe energy spectra Detection rate Flux Eth Antineutrino energy, MeV Cross-section Antineutrino energy, MeV 17 Interaction cross-section Number of “interaction centres” in a volume: n: density of the “interaction centres” [cm–3] Area S The fraction of area covered by interaction centres: (=probability for an incoming particle to interact) Thickness ∆L σ: geometrical cross-section of an interaction centre [cm2] Fluence : the number of particles that intersect a unit area [cm−2] The number of reactions per interaction centre: Differential equation for the fluence Φ: 18 Beam attenuation ; Beam attenuation law: Mean free path: [ (cm–3×cm2)−1 = cm ] Physical meaning of the mean free path: A beam is attenuated by a factor of e=2.71 over the mean free path 19 Neutrino interaction cross-section Elastic scattering: Dimensional estimate assuming : (ECM is the only available Lorentz-invariant scale parameter) Dimensional analysis: Energies in the CM frame (ECM) and the lab frame (Eν) Therefore, [see lecture 1]: 20 The numerical result Natural units: [unit: GeV−2] Practical units: [Unit: GeV−2 × (GeV×cm)2 = cm2] The cross-section has a linear energy-dependence Numerically, 21 scattering cross-section We expect: σ(1 MeV) ~ 10−43 cm2, σ(1 GeV) ~ 10−40 cm2 in agreement with data! 10−37 cm2 10−40 cm2 10−43 cm2 1 MeV 1 GeV arXiv:1305.7513 Neutrino energy, eV 22 Neutrino mean free path Mean free path of a typical reactor/solar (~1 MeV) (anti)neutrino in rock: n: density of protons [cm−3]. ρ: density of matter [g cm−3]. About half of the nucleons are protons. (~ distance to α Canis Minoris) Consider a ~1 MeV neutrino produced in the Solar core. Probability of interaction before leaving Sun: (average Solar density = 1.4 g/cm3) Low energy neutrinos are direct probes into the Sun’s (and Earth’s) interior (but not into neutron stars) 23