IntroductionIntroductionIntroduction tototo NeutrinoNeutrinoNeutrino InteractionInteractionInteraction PhysicsPhysicsPhysics NUFACT08NUFACT08NUFACT08 SummerSummerSummer SchoolSchoolSchool 11-13 June 2008 Benasque, Spain Paul Soler ReferencesReferences 1. K Zuber, “Neutrino Physics”, Institute of Physics Publishing, 2004. 2. C.H. Kim & A. Pevsner “Neutrinos in Physics and Astrophysics”, Harwood Academic Publishers, 1993. 3. K. Winter (editor), “Neutrino Physics”, Cambridge University Press (2 nd edition), 2000. 4. R.N. Mohapatra, P.B. Pal, “Massive Neutrinos in Physics and Astrophysics”, World Scientific (2 nd edition), 1998. 5. H.V. Klapdor-Kleingrothaus & K. Zuber, “Particle Astrophysics”, Institute of Physics Publishing, 1997. 6. K. McFarland, Neutrino Interaction Physics, lectures at SUSSP61, St Andrews, June 2006, (To be published in Proceedings SUSSP61, Taylor & Francis, 2008). Neutrino Interaction Physics 2 NUFACT08 Summer School ContentsContents 1. History and Introduction 2. Neutrino Electron Scattering 3. Neutrino Nucleon Deep-Inelastic Scattering 4. Quasi-elastic, Resonant, Coherent and Diffractive Scattering 5. Nuclear Effects Neutrino Interaction Physics 3 NUFACT08 Summer School 1. History and Introduction 1.1 Fermi Theory 1.2 Neutrino discovery 1.3 Parity violation and V-A theory 1.4 Neutral currents 1.5 Standard model neutrino interactions Neutrino Interaction Physics 4 NUFACT08 Summer School 1.11.1 FermiFermi theorytheory ofof betabeta decaydecay (1932)(1932) Existence of a point-like four fermion interaction (Fermi , 1932): − n e − n → p + e +ν e p ν e Lagrangian of the interaction: G L(x) = − F [φ (x)γ µφ (x)][φ (x)γ φ (x)] 2 p n e µ ν −5 −2 GF = Fermi coupling constant = .1( 16637 ± .0 00001 )×10 GeV Gamow-Teller interaction when final spin different to initial nucleus: GF i L(x) = − ∑[φ p (x)Γ φn (x)][φe (x)Γiφν (x)]+ h c.. 2 i Possible interactions: Γi = ,1 γ 5 ,γ µ ,γ 5γ µ ,σ µν = S, P,V , A,T Neutrino Interaction Physics 5 NUFACT08 Summer School FirstFirst neutrinoneutrino crosscross --sectionsection calculationcalculation Bethe-Peierls (1934): calculation of first cross-section for inverse beta reaction + or − using Fermi theory ν e + p → n + e ν e + n → p + e −44 2 νe σ ≈ 5×10 cm for E(ν ) = 2 MeV Accurate to factor 2 σ b Conversion from natural units: hc =197 3. MeV ⋅ fm p 2 −27 2 2 Cross-section: multiply by (hc) = .0 3894 ×10 GeV ⋅cm Mean free path of antineutrino in water: 1 λ = ≈ 5.1 ×10 21 cm ≈1600 light − years nσ num. free protons N n = ≈ 2 A ρ volume A 2 ×6×10 23 In water: n = = 7.6 ×10 22 cm −3 18 Probability of interaction: L L P =1− exp − ≈ = 7.6 ×10 −20 (m water )−1 λ λ Need very intense source of antineutrinos to detect inverse beta reaction. Neutrino Interaction Physics 6 NUFACT08 Summer School 1.21.2 NeutrinoNeutrino discoverydiscovery (1956)(1956) + Reines and Cowan detect ν e + p → n + e in 1953 (Hanford) (discovery confirmed 1956 in Savannah River): – Detection of two back-to-back γs from prompt signal e +e- ->γγ at t=0. – Neutron thermalization: neutron capture in Cd, emission of late γs <t>~ 20 ms γ γ γ Scintillator γ n e + H2O + CdCl 2 γ Scintillator ν Publication Science 1956: σσσ= 6 x10 -44 cm 2 ±±± 25% (within 5% expected) 1956: parity violation discovery increases theory cross-section: σσσ=(10 ±±±1.7)x10 -44 cm 2 Reanalysis data in 1960: σσσ= (12+7-4) x10 -44 cm 2 Nobel prize Reines 1995 4200 l scintillator Neutrino Interaction Physics 7 NUFACT08 Summer School 1.31.3 ParityParity violationviolation andand VV --AA Parity violation in weak decays postulated by Lee & Yang in 1950 Parity violation confirmed through forward-backward asymmetry of polarized 60 Co ( Wu , 1957). 60 60 * − Co → Ni + e +ν e More electrons emitted in direction opposite to 60 Co spins, implying maximal parity violation r r r r σ ⋅ p P σ ⋅(− p) Helicity operator: H = r → r = −H p p Projects spin along direction of motion Neutrino Interaction Physics 8 NUFACT08 Summer School 1.31.3 ParityParity violationviolation andand VV --AA Goldhaber, Grodzins, Sunyar (1958) measure helicity of neutrino from K capture of 152 Eu: 152 − − 152 * − Eu 0( ) + e → Sm 1( ) +ν e 152 Sm * 1( − )→152 Sm * 0( + ) +γ pγ=-pν σγ=-σν Hγ=Hν Asymmetry of photon spectrum in magnetic field determines helicity of νe: H (ν e ) = −1⇒ H (ν e ) = +1 Neutrinos are “left-handed” Antineutrinos are “right-handed” Neutrino Interaction Physics 9 NUFACT08 Summer School 1.31.3 ParityParity violationviolation andand VV --AA Left and right handed projection operators: 1 1 ν = Pν = 1( −γ )ν ν = P ν = 1( +γ )ν L L 2 5 R R 2 5 0 1 2 3 Chirality operator: γ 5 = iγ γ γ γ same as helicity operator for massless neutrinos ( E=p ). γ 5ν L = Hν L = −ν L γ 5ν R = Hν R = +ν R If only νL interact and ν_____R do not interact, then Γi have to transform as: eΓiν → ()()PLe Γi PLν = ePRΓi PLν 1 1 V : P γ µP = γ µ ()1− γ A :P γ µγ P = − γ µ ()1− γ R L 2 5 R 5 L 2 5 The only possible coupling is V-A, due to maximal parity violation in weak interactions ( Feynman, Gell-Mann , 1958): GF µ LV −A = − [φ pγ 1( − g Aγ 5 )φn ][φeγ µ 1( −γ 5 )φν ]with g A = − .1 2573 ± .0 0028 2 (determined empirically) Neutrino Interaction Physics 10 NUFACT08 Summer School 1.41.4 NeutralNeutral currentscurrents Two types of weak interaction: charged current (CC) and neutral current (NC) from electroweak theory of Glashow, Weinberg, Salam. 0 W ± Z First example of NC observed in 1973, inside the Gargamelle bubble chamber filled with freon (CF 3Br): no muon! ν µ ν µ Z 0 N X ν µ + N →ν µ + X Neutrino Interaction Physics 11 NUFACT08 Summer School 1.51.5 StandardStandard ModelModel NeutrinoNeutrino InteractionsInteractions Lagrangian for electroweak interactions: g L = i [j(+)W µ + j (−)W µ + ]+ i[g cos θ j )3( − g sin' θ j (Y )2/ ]Z µ + int 2 µ µ W µ W µ )3( (Y )2/ µ + i[]g sin θW jµ + g'cos θW jµ A 1st term: charged current interactions (W +, W - exchange) 2nd term: neutral current interactions (Z 0 exchange) 3rd term:electromagnetic interactions (photon exchange) Electron charge: e = g sin θW = g'cos θW e.m. )3( (Y )2/ rd 3 term: ej µ = e( jµ + jµ ) (neutrinos only couple to W ± and Z 0) Neutrino Interaction Physics 12 NUFACT08 Summer School S.M.S.M. interactionsinteractions (cont)(cont) A) Neutrino electron interaction g (+) µ (−) µ + g (Z ) µ e.m Lint = i [jµ W + jµ W ]+ i jµ Z + iej µ 2 2cos θW 1 j (+) =ν γ e = ν γ 1( −γ )e Where: µ e,L µ L 2 e µ 5 1 j (−) = e γ ν = eγ 1( −γ )ν µ L µ e,L 2 µ 5 e (Z ) )3( 2 e.m jµ = (2 jµ − sin θW jµ ) = 2 =ν e,Lγ µν e,L − eLγ µ eL + 2sin θW eγ µ e = 1 1 = ν γ 1( −γ )ν − eγ 1( −γ )e + 2sin 2 θ eγ e 2 e µ 5 e 2 µ 5 W µ 1 ⇒ j(Z ) = ν γ 1( −γ )ν + eγ (g − g γ )e µ 2 e µ 5 e µ V A 5 1 1 With: g = − + 2sin 2 θ g = − V 2 W A 2 Neutrino Interaction Physics 13 NUFACT08 Summer School S.M.S.M. interactionsinteractions (cont)(cont) B) Quark weak interactions g (+) µ (−) µ + g (Z ) µ e.m Lint = i [jµ W + jµ W ]+ i jµ Z + iej µ 2 2cos θW 1 Where: j (+) = uγ 1( −γ )d µ 2 µ 5 1 j (−) = dγ 1( −γ )u µ 2 µ 5 (Z ) jµ = uγ µ (Au − Buγ 5 )u + dγ µ (Ad − Bdγ 5 )d With: 1 4 1 A = − sin 2 θ B = u 2 3 W u 2 1 1 2 2 A = − + sin θ Bd = − d 2 3 W 2 Neutrino Interaction Physics 14 NUFACT08 Summer School S.M.S.M. interactionsinteractions (cont)(cont) After introducing Higgs field and spontaneous symmetry breaking: 2 2 4 LHiggs = − Dµφ − µ φ − λ φ Masses: mH = 2λv 2 gv 2 m ± g 2 m ± = W W = = cos θ 2 2 2 W mZ 0 g + g' g 2 + g'2 m 0 = v Z 2 − /1 2 Vacuum expectation value: v = ( 2GF ) ≈ 246 GeV Effective Hamiltonian: g 2 g 2 H = j (+)µ j (−) + h.c. + j (Z )µ j (Z ) = eff 2 []µ 2 2 µ 4mW 8mZ cos θW G = F [2 j(+)µ j (−) + h c.. + j(Z )µ j(Z ) ] 2 µ µ Neutrino Interaction Physics 15 NUFACT08 Summer School S.M.S.M. interactionsinteractions (cont)(cont) The vector boson masses are then predicted: G g 2 e2 4πα F = = = α = /1 137 .036 2 2 2 2 2 2 8mW 8mW sin θW 8mW sin θW mW = 80 .450 ± .0 058 GeV Masses: 2 m = 91 .1876 ± .0 0021 GeV 2 37 .2805 Z mW = sin θ 2 W sin θW = .0 22280 ± .0 00035 Need radiative corrections: 37 .2805 mW = /1 2 sin θW 1( − ∆r ) with ∆r ≈ .0 03630 ± .0 0011 for m t = 172 7. GeV mH = 117 GeV yields : mW = 80 51. ± 11.0 GeV Neutrino Interaction Physics 16 NUFACT08 Summer School 2. Neutrino Electron Scattering 2.1 Charged current 2.2 Neutral current 2.3 Interference charged and neutral current 2.4 Mass suppression 2.5 Number of neutrinos Neutrino Interaction Physics 17 NUFACT08 Summer School 2.12.1 NeutrinoNeutrino --electronelectron CCCC scatteringscattering − − Only charged current: ν µ + e →ν e + µ (Inverse Muon Decay) − GF µ ν µ µ H = [ν γ 1( − γ )µ][eγ 1( − γ )ν ] eff 2 µ 5 µ 5 e − s = p + p 2= 2m E (in LAB ) W ( ν µ e ) e ν µ t = q 2 = −Q2 = p − p 2 − ( ν µ µ ) Inelasticity variable e ν e p ⋅ p − p E − E (0<y<1) e ( ν µ µ ) ν µ µ Total spin J=0 y = = (in LAB ) p ⋅ p E e ν µ ν µ dσ (ν e− ) G 2 m 4 s G 2 m 4 CC µ = F W ⇒ σ (ν e− ) = F W dQ 2 2 2 2 2 CC µ ∫ 2 2 2 dQ dy π (Q + mW ) 0 π (Q + mW ) Total cross-section (ignoring mass terms): Measurement CHARM-II: 2 2 E − GF s 2GF me − −41 2 σ (ν e ) ≈ = E (in LAB ) σ(ν µe ) = ().1 651 ± .0 093 ×10 cm CC µ ν µ 1GeV π π (cross-section proportional to energy!) 2 2 2GF me ()hc Eν Eν hc = 197 33.