Tests of the Electroweak Theory

Tests of the Electroweak Theory History/introduction Weak charged current QED Weak neutral current Precision tests Rare processes CP violation and B decays Neutrino mass FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 56

Announcements e-mail questions to carena@fnal.gov or pgl@fnal.gov (between lectures) Slides and video at http://theory.fnal.gov/academiclectures.html Today in Curia II; others in One West FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 57

References (mainly weak neutral current/z-pole) E.D. Commins and P.H. Bucksbaum, Weak Interactions of Leptons and Quarks, (Cambridge Univ. Press, Cambridge, 1983) P. Renton, Electroweak Interactions, (Cambridge Univ. Press, Cambridge, 1990) P. Langacker, M.-X. Luo and A. K. Mann, High precision electroweak experiments, Rev. Mod. Phys. 64, 87 (1992) Precision Tests of the Standard Electroweak Model, ed. P. Langacker (World Scientific, Singapore, 1995) S. Eidelman et al. [Particle Data Group], Phys. Lett. B 592, 1 (2004) (Electroweak review, J. Erler and PL) LEP Electroweak Working Group: http://www.cern.ch/lepewwg/ FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 58

Prediction of SU(2) U(1) The Weak Neutral Current g2 + g 2 ( ) L = J µ Z sin θ W B µ + cos θ W W 3 µ 2 g = J µ Z 2 cos θ Z µ W Neutral current process and effective 4-fermi interaction for Q M Z FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 59

Neutral current: J µ Z = [ū0 ml γµ u 0 ml d 0 ml γµ d 0 ml + ν0 ml γµ ν 0 ml ] ē0 ml γµ e 0 ml m = m 2 sin 2 θ W J µ Q [ūml γ µ u ml d ml γ µ d ml + ν ml γ µ ν ml ē ml γ µ ] e ml 2 sin 2 θ W J µ Q Flavor diagonal: Same form in weak and mass bases because fields which mix have same charge GIM mechanism: c quark predicted so that s L could be in doublet to avoid unwanted flavor changing neutral currents (FCNC) at tree and loop level Parity violated but not maximally: first term is pure V A, second is V FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 60

Effective 4-fermi interaction for Q 2 M 2 Z : L NC eff = G F 2 J µ Z J Zµ Coefficient same as WCC because G F 2 = g2 8M 2 W = g2 + g 2 8M 2 Z WNC discovered 1973: Gargamelle at CERN, HPW at FNAL Tested in many processes: νe νe, νn νn, νn νx (pure Z); e D ex, atomic parity violation, e + e, pp (γ Z interference) WNC, W, and Z are primary test/prediction of electroweak model FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 61

Results before the LEP/SLD era Global Analysis more information than individual experiments caveat: exp./theor. systematics, correlations Model-independent fits Unique νq, νe, eq SM correct to first approximation Contrived imitators out Limits on small deviations FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 62

QCD evolved structure functions Radiative corrections necessary (sin 2 θ W defns) sin 2 θ W =.230 ±0.007, m t < 200 GeV Unique fermion reps. (wnc + wcc) t and ν τ exist Grand unification Ordinary SU(5) excluded; consistent with SUSY GUTS and perhaps even the first harbinger of supersymmetry Stringent limits on new physics Z, exotic fermions, exotic Higgs, leptoquarks, 4-F operators FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 63

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 1.16637(1) 10 5 GeV 2 ) α = 1/137.03599911(46) (but must extrapolate to M Z ) M Z (or sin 2 θ W ) FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 64

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 = 1 2 + 2 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 FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 65

On-shell : s 2 W 1 M W 2 = 0.22306 (33) M Z 2 (ZFITTER: D. Y. Bardin et al., hep-ph/9908433) + most familiar + simple conceptually large m t, M H dependence from Z-pole observables mixed QCD-EW artificially large depends on SSB mechanism awkward for new physics Z-mass (only running α) : s 2 M Z = 0.23108 (8) + most precise (no m t, M H dependence) + simple conceptually m t, M H reenter when predicting other observables mixed QCD-EW artificially large depends on SSB mechanism awkward for new physics FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 66

MS : ŝ 2 Z = 0.23122 (15) (GAPP: J. Erler, hep-ph/0005084) + based on coupling constants (almost minimal counterterms) + convenient for GUTs + also used for QCD mixed QCD-EW smaller + usually insensitive to new physics + Z asymmetries independent of m t, M H value runs with Q 2 ; usually quote value at M Z theorists definition; not simple conceptually usually determined by global fit reduced sensitivity to m t, M H effective (Zf f vertex): s 2 l = 0.23152 (14) + simple + Z asymmetries independent of m t, M H phenomenological; exact definition in computer code different for each f hard to relate to non Z-pole observables FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 67

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 FNAL Typeset (December by FoilTEX 6, 2005) Paul Langacker (Penn/FNAL) 1 68

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). Also, 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 H Z Z FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 69 G

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 FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 70

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 Any gauge model (with lefthanded ν) corresponds to some g νe V,A g νe WCC V,A gνe V,A + 1 for ν e from Alternative models w. disjoint parameters and perturbations on SM (Amaldi et al, PR D36, 1385 (1987)) FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 71

Standard model g νe V 1 2 + 2 ( sin2 θ W ρ νe 1 2 + 2ˆκ ) νe ŝ 2 Z g νe A ( ) 1 ρ 2 νe 1 2 Dominant m t dependence ρ 1 + ρ t ρ t 3G F m 2 t /8 2π 2 = 0.00935(m t /172.7 GeV) 2 ˆκ 1 (MS ) κ 1 + ρ t / tan 2 θ W (on shell) Including small effects, ρ νe = 1.0127 and ˆκ νe = 0.9965 (MS ) FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 72

Cross section (exercize) 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 )2 + 1 3 (gνe V ] gνe A )2 Flux uncertainties cancel in R σ νµ e/σ νµ e Most precise: CHARM II (CERN) FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 73

g V -1.0-0.8-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.3 0.6 ν e µ reactor ν e (LANL) e all -1.0-0.8-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 g A FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 74

Deep Inelastic ν Scattering l(k) l (k ) e ± p e ± X, µ ± p µ ± X, ( ) ν µ p ( ) ν µ X at Q 2 Mp 2 ( ) ν µ p µ X, (or p n, N) q Test of QCD, quark model p X Q 2 = q 2 > 0 }{{} 2kk (1 cos θ) lab ν = p q M p k k x = Q 2 2M p ν y = ν E k k k k FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 75

WCC: ( ) ν µ N µ X (N = p, n, or nucleus) d 2 σ CC νn dx dy d 2 σ CC νn dx dy = 2G2 F M pe ν π = 2G2 F M pe ν π [ xd λd + xs λ s + x(ū + c)(1 y) 2] [ x(u + c)(1 y) 2 + x d λ d + x s λ s ] d(x, Q 2 ) d(x) d quark density in N (slow Q 2 QCD evolution) λ i = V ui 2 + V ci 2 ξ c (i = d, s), where ξ c (m c ) is kinematic c-quark suppression (ξ c 1 at high energy) Test of QCD Dimuons: ( ) ν µ N µ X + c( c) with c( c) s( s)µ ±( ) ν µ allow extraction of V cd, ξ c, s V cs 2 FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 76

Muon Neutrino and Anti-Neutrino Charged-Current Total Cross Section 0 10 20 30 50 100 150 200 250 300 350 1.0 1.0 0.8 νn 0.8 σ T /E ν [10 38 cm 2 / GeV] 0.6 0.4 0.2 νn [1] CCFR (96) [6] BEBC WBB [2] CCFR (90) [7] GGM-PS ν [3] CCFRR [8]. GGM-PS ν [4] CDHSW [9] IHEP-JINR [5] GGM-SPS [10] IHEP-ITEP [11] SKAT [12] CRS [13] ANL [14] BNL-7ft [15] CHARM 0.6 0.4 0.2 0.0 0 10 20 30 50 100 E ν [GeV] 150 200 250 300 0.0 350 Figure 40.9: σ T /E ν, for the muon neutrino and anti-neutrino charged-current total cross section as a function of neutrino energy. The error bars include FNAL both (December statistical6, and 2005) systematic errors. The straight lines are the averaged Paul valueslangacker over all energies (Penn/FNAL) as measured by the 77 experiments in Refs. [1 4]: = 0.677 ± 0.014 (0.334 ± 0.008) 10 38 cm 2 /GeV. Note the change in the energy scale at 30 GeV. (Courtesy W. Seligman and M.H. Shaevitz, Columbia University, 2001.)

WNC: ( ) ν µ N ( ) ν µ X 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 (leading: ρ 1 + ρ t, κ 1, λ 0) ɛ L (u) 1 2 2 3 sin2 θ W ρ NC νn ɛ L (d) 1 2 + 1 3 sin2 θ W ρ NC νn ɛ R (u) 2 3 sin2 θ W ρ NC νn ɛ R (d) 1 3 sin2 θ W ρ NC νn ( 1 ) 2 2 3ˆκ νn ŝ 2 Z ( 1 2 + 1 3ˆκ νn ŝ 2 Z ( 2 ) 3ˆκ νn ŝ 2 Z ( ) 1 3ˆκ νn ŝ 2 Z + λ ul ) + λ ur + λ dr + λ dl FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 78

Deep inelastic ( ) ν µ N ( ) ν µ X 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 ) + [ 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) FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 79

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 and c and third family; and ξ c = 1 (exercize) 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) 2 1 2 sin2 θ W + 5 9 sin4 θ W g 2 R ɛ R(u) 2 + ɛ R (d) 2 5 9 sin4 θ W r σνn CC/σCC νn measured (r 1/3 for q/q 0) FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 80

0.4 0.2 0.2 0.1 0.3 ε L (d) (u) 0.0-0.2 1.0 0.7 ε R (d) (u) 0.0-0.1 0.0-0.4 0.4 0.0-0.2-0.4-0.2 0.0 0.2 0.4 ε L (u) -0.2-0.1 0.0 0.1 0.2 ε R (u) FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 81

Most precise sin 2 θ W before LEP/SLD: s 2 W 0.233 ± 0.003 (exp) ± 0.005 (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 FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 82

Recent NuTeV (FNAL) analysis minimizes m c uncertainty Obtains s 2 W = 0.2277 ± 0.0016 (insensitive to m t, M H ), 3σ above current global fit value 0.2231(3) New Physics (e.g., Z, ν-mixing)? QCD effect, e.g., isospin breaking; s s asymmetry (wrong sign?); NLO QCD or EW corrections? FNAL (December 6, 2005) Paul Langacker (Penn/FNAL) 83