The Z, the W, and the Weak Neutral Current

Transcription

1 The Z, the W, and the Weak Neutral Current g L Z = J µ Z 2 cos θ Z µ W J µ Z = r t 3 rl ψ 0 r γµ (1 γ 5 )ψ 0 r 2 sin2 θ W J µ Q t 3 ul = t3 dl = t3 νl = t3 el = 1 2, tan θ W = g /g L NC eff = G F 2 J µ Z J Zµ Primary prediction and test of electroweak unification WNC discovered 1973 (Gargamelle at CERN, HPW at FNAL) W, Z discovered directly 1983 (UA1, UA2) 90 s: Z pole (LEP, SLD), 0.1% P529 Spring,

2 νe νe L νe = G F 2 ν µ γ µ (1 γ 5 )ν µ ē γ µ (g νe V gνe A γ5 )e SM : g νe V sin2 θ W, g νe A 1 2 ν µ e e ν e ν e e Z W Z ν µ e ν e e ν e e P529 Spring,

3 Any gauge model (with lefthanded ν) some g νe V,A Need SM rad. corr. ν e : g νe V,A WCC gνe V,A + 1 Alternative models w. disjoint parameters and perturbations on SM Amplitude-squared (ν(p 1 )e (p 2 ) e (p 3 )ν(p 4 )) 1 2 [ M 2 = 16G 2 F (gv + g A ) 2 p 1 p 2 p 3 p 4 s 1 s 2 s 3 s 4 + (g V g A ) 2 p 1 p 3 p 2 p 4 (g 2 V g2 A )m2 e p ] 1 p 4 P529 Spring,

4 Cross section dσ νµ,ν µ dy = G2 F m ee ν 2π (g νe2 V [ (g νe V g νe2 A )y m e E ν ± gνe A )2 + (g νe V ] gνe A )2 (1 y) 2 where 0 y T e /E ν (1 + m e /2E ν ) 1 For E ν m e σ = G2 F m e E ν 2π [ (g νe V ± gνe A ) (gνe V ] gνe A )2 Flux uncertainties cancel in R σ νµ e/σ νµ e Most precise: CHARM II (CERN) P529 Spring,

5 g V Νe Ν Μ Ν Μ e Ν e e Ν e e A P529 Spring,

6 Deep Inelastic ν Scattering l(k) q l (k ) e ± p e ± X, µ ± p µ ± X, ( ) ν µ p µ X, ( ) ν µ p ( ) ν µ X at Q 2 Mp 2 (or p n, N) WCC: test of QCD, quark model p X Q 2 = q 2 > 0 }{{} lab ν = p q M p k k 2kk (1 cos θ) x = Q 2 2M p ν y = ν E k k k k P529 Spring,

7 ν µ µ ν µ µ ν µ ν µ W + d u W + ū d Z q q p X p X p X Charged current, ( ) ν µ p µ X (Q 2 M 2 W ) d σ ν, ν dk dω = G2 F k 32π 2 k Lµν ν, ν W ν, ν µν L µν ν = Tr [ γ µ (1 γ 5 ) k γ ν (1 γ 5 ) k ] Typeset by FoilTEX 1 = 8 k µ k ν + k µ k ν µν q2 + g 2 + iɛµρνσ k ρ k σ }{{} V A interference P529 Spring,

8 Hadronic tensor (different for e, ν, ν) [ W ν, ν µν = g µν + q ] µq ν W ν, ν ( q 2 1 Q 2, ν ) + 1 [ p M 2 µ p q ] [ q q 2 µ p ν p q q 2 F ν, ν 1 + iɛ µρνσ p ρ q σ 2M ( x, Q 2 ) = MW ν, ν 1 ν, ν 2W3 ( Q 2, ν ) ( Q 2, ν ), F ν, ν 2,3 q ν ] W ν, ν 2 ( Q 2, ν ) ( x, Q 2 ) = νw ν, ν 2,3 ( Q 2, ν ) Approximate scaling (up to QCD corrections): F ν, ν i ( x, Q 2 ) F ν, ν i (x) Cross section predicted to scale as E ν : ν, ν d2 σ cc dxdy = G2 F ME ν π [ xy 2 F ν, ν 1 (x) + (1 y)f ν, ν 2 (x) ± xy(1 y ] ν, ν )F3 (x) 2 P529 Spring,

9 σ ν, ν cc = 1 0 dx 1 0 ν, ν d2 σ cc dy dxdy s T /E n [10 Ð38 cm 2 /GeV] [1] NuTeV [5] CDHSW [9] GGM-PS n _ [13] CRS 0.2 [2] CCFR (96) [6] GGM-SPS [10] IHEP-JINR [14] ANL [3] CCFR (90) [7] BEBC WBB [11] IHEP-ITEP [15] BNL-7ft [4] CCFRR [8] GGM-PS n [12] SKAT [16] CHARM E n [GeV] P529 Spring,

10 Simple parton model (without mixing, heavy quarks) F ν 2 (x) = 2xF ν 1 (x) = 2x [d(x) + ū(x)], F ν 3 (x) = 2x [d(x) ū(x)] F ν 2 (x) = 2xF ν 1 (x) = 2x [ u(x) + d(x) ], F ν 3 (x) = 2x [ u(x) d(x) ] Isospin: W ν in W ν ip, W ν ip W ν in, W ν in = 1 2 [ ] W ν ip + W ν in W ν in 5/18 th rule: F 2N F ν 2N = 1 2 (F 2p + F 2n ) ( = F ν 2p + F2n) ν 1 2 ( ) 1 2 x ( u p + d p + ū p + d p) x ( d p + ū p + u p + d p) = 5 18 P529 Spring,

11 Include mixing, m c suppression factors ξ c : d 2 σ cc ν dxdy =2G2 F ME ν {xd [ ] [ ] V ud 2 + V cd 2 ξ c +xs Vus 2 + V π }{{} cs 2 ξ }{{ c } λ d λ s + x (ū + c) (1 y) 2} 2G2 F ME ν π [x (d + s) + x (ū + c) (1 y) 2] d 2 σ cc ν dxdy =2G2 F ME ν π 2G2 F ME ν π [x (u + c) (1 y) 2 + x dλ d + x sλ s ] [ x (u + c) (1 y) 2 + x d ] + x s P529 Spring,

12 Dimuons (extract V cd 2, S V cs 2, ξ c, where S = xs(x)dx): ν( ν)n µ X + c( c) from d, s c (s, d)µ + ν µ, c ( s, d)µ ν µ P529 Spring,

13 νq νq (Mainly Deep Inelastic) WNC: test of electroweak standard model L νhadron = G F 2 ν γ µ (1 γ 5 )ν i [ ɛl (i) q i γ µ (1 γ 5 )q i + ɛ R (i) q i γ µ (1 + γ 5 )q i ] Standard model ɛ L (u) sin2 θ W ɛ R (u) 2 3 sin2 θ W ɛ L (d) sin2 θ W ɛ R (d) 1 3 sin2 θ W P529 Spring,

14 Deep inelastic ( ) ν µ N ( ) ν µ X l(k) l (k ) d 2 σ NC νn dx dy = 2G2 F M pe ν { π [ ɛl (u) 2 + ɛ R (u) 2 (1 y) 2] (xu + xc ξ c ) p q X + [ ɛ L (d) 2 + ɛ R (d) 2 (1 y) 2] (xd + xs) + [ ɛ R (u) 2 + ɛ L (u) 2 (1 y) 2] (xū + x c ξ c ) + [ ɛ R (d) 2 + ɛ L (d) 2 (1 y) 2] (x d + x s)} (ɛ L (i) ɛ R (i) for ν) P529 Spring, Typeset by FoilTEX 1

15 WNN/WCC ratios measured to 1% or better by CDHS and CHARM (CERN) and CCFR (FNAL) (many strong interaction, ν flux, and systematic effects cancel) For isoscalar targer (N p = N n ); ignoring s, c and third family sea; ignoring c threshold correction (ξ c = 1) R ν σnc νn σνn CC R ν σnc νn σνn CC g 2 L + g2 R r g 2 L + g2 R r g 2 L ɛ L(u) 2 + ɛ L (d) sin2 θ W sin4 θ W g 2 R ɛ R(u) 2 + ɛ R (d) sin4 θ W r σνn CC/σCC νn measured (r 1/3 for q/q 0) P529 Spring,

16 ε L (d) (u) ε R (d) (u) ε L (u) ε R (u) P529 Spring,

17 Most precise sin 2 θ W before LEP/SLD: s 2 W ± (exp) ± (m c ) Must correct for N n N p ; s(x), c(x), ξ c, QCD, third family mixing, W/Z propagators, radiative corrections, experimental cuts Can separate ɛ i (u)/ɛ i (d) by p and n targets, e.g., bubble chamber (less precise) Error dominated by charm threshold (m c in ξ c ) Can reduce sensitivity using Paschos-Wolfenstein ratio R = σnc νn σnc νn σνn CC σcc νn g 2 L g2 R 1 2 sin2 θ W P529 Spring,

18 Weak-Electromagnetic Interference Low energy: Z exchange much smaller than Coulomb, but observe V A (parity-violating) and A A (parity conserving) effects High energy: γ and Z may be comparable (propagator effects) Observables Polarization (charge) asymmetries in ed ex (SLAC), µc µx (CERN); e e Møller (SLAC); low energy elastic or quasielastic (Mainz, Bates, CEBAF) Atomic parity violation in Cs (Boulder, Paris) and other atoms Cross sections and FB asymmetries in e + e l l, q q, b b (SPEAR, PEP, DORIS, TRISTAN, LEP II) FB asymmetries in pp e + e (CDF, D0) P529 Spring,

19 Parity-violating e-hadron L eq = G F 2 i [ C1i ē γ µ γ 5 e q i γ µ q i + C 2i ē γ µ e q i γ µ γ 5 q i ] Standard model C 1u sin2 θ W C 2u sin2 θ W C 1d sin2 θ W C 2d sin2 θ W P529 Spring,

20 Atomic parity violation Axial e, vector nucleon currents lead to potential V ( r e ) G F 4 2 Q W δ 3 ( r e ) σ e v e c + HC Weak charge Q W = 2 [C 1u (2Z + N) + C 1d (Z + 2N)] Z(1 4 sin 2 θ W ) N Measure in 6S 7S transition (S P wave mixing) Cs is very simple atom; radiative corrections now under control P529 Spring,

21 0.18 C1 u C1 d Mainz e Be Bates ec SLAC ed Q W Cs Q W Th PVES u 1 d P529 Spring,

22 A FB SPEAR MARK I PEP HRS MAC MARK II PETRA CELLO JADE MARK J PLUTO TASSO TRISTAN LEP AMY TOPAZ VENUS e + e! " µ + µ! #s [GeV] (J. Mnich, Phys. Rep. 271, 181) 10. Electroweak model and constraints on new physics 15!"$)!"$'% L3 e + e l + l, hadrons below/above Z-pole SLAC E158 Polarized Møller Asymmetry e e asymmetry, P 90% sin 2 θ eff (Q) = (13) W (Q 2 = GeV 2 ) *+, $ θ ' (µ)!"$'(!"$''!"$'$!"$'!"$&%!"$&( -. / /43 ν*+,- Future: Q W EAK (JLAB): polarized ep, s !"$&'!"$&$ CD556E -F4<G 5617# :4;<=>?,!"$&!"$$% 4@AB8 859!"!!!#!"!!#!"!#!"# # #! #!! #!!! #!!!! µ!"#$%& (Running ŝ 2 Z in MS scheme) P529 Spring,

23 as the ɛ R, are strongly correlated and non-gaussian, so that for implementations we recommend the parametrization using g 2 i and θ i = tan 1 [ɛ i (u)/ɛ i (d)], i = L or R. The analysis of more recent low energy experiments in polarized electron scattering performed in Ref. 123 is included by means of the two orthogonal constraints, cos γ C 1d sin γ C 1u =0.342 ± and sin γ C 1d + cos γ C 1u = ± , where tan γ In the SM predictions, the uncertainty is from M Z, M H, m t, m b, m c, α(m Z ), and α s. Quantity Value SM Correlation ɛ L (u) ± (1) ɛ L (d) ± (1) nonɛ R (u) (1) Gaussian ɛ R (d) g 2 L ± (2) g 2 R ± θ L 2.48 ± (1) 0.24 θ R gv νe ± (3) 0.05 ga νe ± (1) C 1u + C 1d ± (1) C 1u C 1d ± (3) C 2u + C 2d 0.21 ± C 2u C 2d ± (5) Q W (e) = 2 C 2e ± (5) defined in Eqs. (1.11) (1.14) are given in Table 1.9 along with the predictions of the P529 SM. The agreement is very good. (The ν-hadron results without the NuTeV data can be Spring, 2013 found in the 1998 edition of this Review, and the fits using the original NuTeV data in the edition.) The off Z pole e + e results are difficult to present in a model-independent

24 Input Parameters for Weak Neutral Current and Z-Pole Basic inputs SU(2) and U(1) gauge couplings g and g ν = 2 0 φ 0 0 (vacuum of theory) Higgs mass M H (value unknown) (enters radiative corrections) Heavy fermion masses, m t, m b, (phase space; radiative corrections) strong coupling α s (enters radiative corrections) Trade g, g, ν for precisely known quantities G F = 1 2ν 2 from τ µ (G F (5) 10 5 GeV 2 ) α = 1/ (51) (but must extrapolate to M Z ) M Z (or sin 2 θ W ) P529 Spring,

25 Definitions of sin 2 θ W Several equivalent expressions for sin 2 θ W at tree-level sin 2 θ W = 1 M 2 W sin 2 θ W cos 2 θ W = M 2 Z πα 2GF M 2 Z on shell Z mass sin 2 θ W = g 2 g 2 + g 2 MS g Ze+ e V = sin2 θ W effective Each can be basis of definition of renormalized sin 2 θ W related by calculable, m t M H dependent, corrections of O(α)) (others P529 Spring,

26 Radiative Corrections γ QED corrections to W or Z exchange γ No vacuum polarization or box diagrams Finite and gauge invariant Depend on kinematic variables and cuts calculate for each experiment γ P529 Typeset by FoilTEX Spring,

27 Electroweak at multiloop level (include W, Z, γ) self-energy vertex box (quadratic) m t and (logarithmic) M H dependence from W W, ZZ, Zγ self-energies (SU(2)-breaking); m t from Zb b vertex Z(γ) t(b) Z W t W b W b b t b t(b) b t t W W H H Typeset by FoilTEX 1 Z Z P529 Spring,

28 Z(γ) Z W G α s fromt(b) QCD vertices and mixed QCD-EW H b H H Mixed QCD-EW (e.g., self-energies and vertices, fermion masses) Awkward in on-shell G mixed Typeset by FoilTEX Typeset by FoilTEX 1 P529 Spring,

29 The W and Z Masses and Decays On-shell scheme, s 2 W 1 M 2 W /M 2 Z M W = A 0 s W (1 r) 1/2 M Z = M W c W c 2 W = 1 s2 W, A 0 = (πα/ 2G F ) 1/2 = (8) GeV r rad. corrections relating α, α(m Z ), G F, M W, and M Z r 1 α ρ t ˆα(M Z ) tan }{{} 2 + small }{{ θ W} (11) artificially large ρ t 3 G F m 2 ( t 8 = m t 2π GeV ) 2 P529 Spring,

30 Modified minimal subtraction (M S) scheme M W = A 0 ŝ Z (1 ˆr W ) 1/2 M Z = M W ˆρ 1/2 ĉ Z ˆr W 1 α + small ˆα(M Z ) }{{} (11) ˆρ G F m 2 t + small 8 2π 2 }{{} ρ t P529 Spring,

31 The W decay width Γ(W + e + ν e ) = G F M 3 W 6 2π ± 0.07 MeV Γ(W + u i d j ) = CG F MW 3 6 2π V ij 2 ( ± 0.22) V ij 2 MeV 1, leptons C = 3 }{{} color ( 1 + α s(m W ) π ) α2 s α3 π 2 s 80.0 α4 π 3 s, quarks π 4 Also, QED, mass; g 2 M W /4 2 G F M 3 W absorbs running α Γ W ± GeV (SM) Experiment (LEP,CDF, D0): Γ W = ± GeV P529 Spring,