Electroweak Theory: 2

Electroweak Theory: 2 Introduction QED The Fermi theory The standard model Precision tests CP violation; K and B systems Higgs physics Prospectus STIAS (January, 2011) Paul Langacker (IAS) 31

References Slides at http://www.sns.ias.edu/ pgl/talks/ (subject to revision) P. Langacker, The Standard Model and Beyond, (CRC Press, 2010) (especially chapters 6, 7) P. Langacker, Introduction to the Standard Model and Electroweak Physics, [arxiv:0901.0241 [hep-ph]] (TASI 2008) E.D. Commins and P.H. Bucksbaum, Weak Interactions of Leptons and Quarks, (Cambridge, 1983) P. Renton, Electroweak Interactions, (Cambridge, 1990) Precision Tests of the Standard Electroweak Model, ed. P. Langacker (World, 1995) (especially Fetscher and Gerber; Herczog; Deutsch and Quin) K. Nakamura et al. [Particle Data Group], J. Phys. G 37, 075021 (2010)(electroweak and other reviews) STIAS (January, 2011) Paul Langacker (IAS) 32

Previous Lecture QED and the Fermi Theory The Fundamental Forces Quantum Electrodynamics The Weak Interactions The Modern (V A) Form of the Fermi Interaction Muon Decay (leptonic processes) STIAS (January, 2011) Paul Langacker (IAS) 33

This Lecture The Weak Interactions of Hadrons Semi-Leptonic Processes in the Fermi Theory π and K Decays, and the Strong Interactions β Decay and Related Processes Charm (c) Quark and Third Family CKM Universality STIAS (January, 2011) Paul Langacker (IAS) 34

Semi-Leptonic Processes in the Fermi Theory p e ν e H = G F J µ J µ J µ = J l µ + J h µ 2 }{{}}{{} leptonic hadronic Leptonic current e ν e ν e e J l µ = ē γ µ ( 1 γ 5 ) ν e + µγ µ ( 1 γ 5 ) ν µ J µ J µ J µ J µ e ν e Hadronic current n J h ν e e ν e e µ pγ ( ) µ 1 γ 5 n cos θ c + pion, strangeness, etc p e Quark form (p uud, n udd) ν e e ν e g g g J h µ = ūγ µ ( 1 γ 5 ) d = 2ū L γ µ d L W W + STIAS (January, 2011) Paul Langacker (IAS) 35 g

Hadronic current J h µ = ūγ µ ( 1 γ 5 ) d = 2ū L γ µ d L where d = d }{{} V ud CKM +s V us }{{} CKM d cos θ c + s sin θ c sin θ c 0.23 is the Cabibbo angle ( S = 1 vs S = 0) Semi-leptonic: H sl = G F 2 [ J h µ J lµ + J l µ J hµ] Maximal violation of P, C, but CP invariant (for 2 families) P ( V µ A µ ) P 1 = V µ + A µ for g µν = diag(1, 1, 1, 1) Strong interactions (pure V ) conserve P, C (use C, P invariance for matrix elements up to higher order in weak) STIAS (January, 2011) Paul Langacker (IAS) 36

π and K Decays, and the Strong Interactions Charged pion decay π + µ + ν µ (π µ2 ) 99.99% e + ν e (π e2 ) 1.23 10 4 e + ν e π 0 (π e3 ) 1.036 10 8 π beta decay π 0 2γ : 98.8% Electromagnetic γ Color counting via global anomaly π 0 γ STIAS (January, 2011) Paul Langacker (IAS) 37

For π µ ν µ γ µ (p 2 ) ν µ (p 1 ) J h µ = ūγ µ (1 γ 5 ) d cos θ c V µ A µ π 0 γ π (q) M i µ (p 2 ) ν µ (p 1 ) H π (q) = i G F 2 ū µ γ µ (1 γ 5 )v νµ 0 J h µ π (q) 0 J h µ π (q) involves strong interaction bound state hard to calculate (recent: lattice QCD calculation) Typeset by FoilTEX STIAS (January, 2011) Paul Langacker (IAS) 38

However, J h µ is Lorentz vector π 0 γ 0 J h µ π (q) = i } cos {{ θ } c f π q µ µ (p 2 ) convention ν µ (p 1 ) q = p 1 + p 2 is only 4-vector available f π pion decay constant γ Related to pion ūd wave π (q) function (expect f π = O(Λ QCD ) = O(100 MeV)) d ū π f π could depend on q 2, but q 2 = m 2 π = fixed Can show (exercize) that 0 V µ π (q) = 0 using parity invariance (weak P violation already included explicitly to 1 st order strong interaction calculation) STIAS (January, 2011) Paul Langacker (IAS) 39

Rate ( ) 2 Γ(π µν) = G2 F cos2 θ c f 2 π 8π m2 µ m π 1 m2 µ }{{} m 2 π matrix element }{{} phase space Experiment: τ π ± 2.60 10 8 s G F 1.17 10 5 GeV 2 from µ lifetime cos θ c 0.975 from superallowed β decay f π 130.4(2) MeV 0.93 m π STIAS (January, 2011) Paul Langacker (IAS) 40

e/µ ratio Γ(π eν) Γ(π µν) = m2 e m 2 µ ( m 2 π m 2 e m 2 π m2 µ ) 2 (1 + O(α) ) }{{} rad. corr. = 1.28 10 4 (1 + O(α)) = 1.24 10 4 Experiment: (1.230(4)) 10 4 V A favors h l = 1 2 Angular momentum forces wrong π helicity ν l Amplitude suppressed by m l /E l l STIAS (January, 2011) Paul Langacker (IAS) 41

Kaon decays ( S = ±1) K + µ + ν µ (K µ2 ) 63.4% f K /f π e + ν e (K e2 ) 1.6 10 5 µ + ν µ π 0 (K µ3 ) 3.3% universality test e + ν e π 0 (K e3 ) 5.0% universality test π + π 0 (K 2π ) 20.9% nonleptonic π + π + π (K 3π ) 5.6% π + π 0 π 0 (K 3π ) 1.8% STIAS (January, 2011) Paul Langacker (IAS) 42

K is also pseudoscalar, related to π by flavor SU(3) f K = kaon decay constant 0 J h µ K (q) = i } sin {{ θ } c f K q µ convention In SU(3) limit f K = f π However, SU(3) typically broken by 20-30% Γ(K µν) = G2 F sin2 θ c 8π f 2 K m2 µ m K ( 1 m2 µ m 2 K ) 2 Observed rate + sin θ c 0.226 from K l3 or hyperon decay: f K 155.5(8) MeV 1.19f π (20% SU(3) breaking) STIAS (January, 2011) Paul Langacker (IAS) 43

Pion beta decay (π e3 ), π ± π 0 e ± ( ) ν e M = i G F 2 ū e γ µ (1 γ 5 )v νe π 0 (p 2 ) J h µ π (p 1 ) Parity: only vector current V µ cos θ cūγ µ d contributes Lorentz invariance: only two momenta, p 1,2 in hadronic matrix element π 0 (p 2 ) V µ π (p 1 ) = cos θ c [f + (q 2 )(p 1µ +p 2µ )+f (q 2 )(p 1µ p 2µ )] f ± (q 2 ) are form factors, which can depend on q 2 (p 2 p 1 ) 2 STIAS (January, 2011) Paul Langacker (IAS) 44

Are f ± (q 2 ) totally unknown because of strong interactions? No! Symmetry rescues us. Strong interactions almost invariant under global SU(2) isospin symmetry (broken at 1% level by electromagnetism and by m d m u few MeV 0) V µ / cos θ c ūγ µ d is generator of isospin π 0 (p 2 ) V µ π (p 1 ) = cos θ c [f + (q 2 )(p 1µ +p 2µ )+f (q 2 )(p 1µ p 2µ )] If isospin were exact, f + (0) = 2. Also, µ V µ = 0 f (q 2 ) = 0 (cf non-renormalization of electric charge) STIAS (January, 2011) Paul Langacker (IAS) 45

Conserved vector current (CVC): ūγ µ d, dγ µ u and 1 2 (ūγ µu dγ µ d) (isovector part of J elm µ = 1 2 (ūγ µu dγ µ d) + 1 6 (ūγ µu + dγ µ d)) are related by isospin and have same form factors (Was hypothesis. Natural in quark model.) Ademollo-Gatto theorem: corrections to f + (0) from isospin breaking are second order 10 3 (negligible) For π e3, = m π + m π 0 4.6 MeV can neglect p 2 p 1 term and take f + (q 2 ) f + (0) = 2. Γ(π ± π 0 e ± ( ) ν e ) G2 F cos2 θ c f + (0) 2 5 60π 3 Including /m π, m e /, rad: Γ 0.399(1)s 1 (exp: 0.3980(24) s 1 ) STIAS (January, 2011) Paul Langacker (IAS) 46

K l3 decays: K + l + ν l π 0, K 0 l + ν l π, etc π 0 (p 2 ) V µ K + (p 1 ) = V us [f K+ + (q2 )(p 1µ +p 2µ )+f K+ (q2 )(p 1µ p 2µ )] Large energy release. Cannot neglect q 2 dependence of form factors or f term Can measure them (linear or quadratic approximation) from decay distributions, but need f+ K+ K0 (0) and f+ (0) V µ are SU(3) generators 2 f K + + (0) f K0 + (0) 1 + O(ɛ2 ) where ɛ 20% is typical SU(3) breaking (Ademollo-Gatto) Estimates of O(ɛ 2 ): lattice and chiral perturbation theory V us = 0.2255(19) sin θ c (most precise determination of CKM element weak universality) STIAS (January, 2011) Paul Langacker (IAS) 47

β Decay and Related Processes n pe ν e neutron (N, Z) (N 1, Z + 1)e ν e nuclear (heavy) (N, Z) (N + 1, Z 1)e + ν e nuclear (light, e.g., Sun) l p nν l atomic e or µ capture ν e n e p, ν e p e + n inverse β decay Σ ± Λe ± ν e ( ν e ), Σ nl ν l, hyperon decays H = G F 2 V ud ēγ µ (1 γ 5 )ν e ūγ µ (1 γ 5 )d + HC V ud cos θ c STIAS (January, 2011) Paul Langacker (IAS) 48

Radiative corrections divergent in Fermi theory, finite in SU(2) U(1) Nuclear filter: V µ (Fermi transition), A µ (Gamow-Teller transition), or both relevant Superallowed: 0 + i 0+ f in same isomultiplet Pure Fermi transition 0 + f ūγ 0d 0 + i = 1 + O(δ2 ), where δ = isospin breaking (Ademollo-Gatto). Corrections tiny but critical. Best determination of V ud = 0.97418(27) STIAS (January, 2011) Paul Langacker (IAS) 49

Neutron β decay p ūγ µ (1 γ 5 )d n = ū p γ µf 1 (q 2 ) + iσ µν 2m qν f 2 (q 2 ) γ µ γ 5 g 1 (q 2 ) σ µνγ 5 ū p γ µ (g V g A γ 5 )u n }{{} weak magnetism 2m qν g 2 (q 2 ) }{{} G odd + q µ f 3 (q 2 ) }{{} vanishes by CVC q µ γ 5 g 3 (q 2 ) }{{} induced pseudoscalar(µ) u n q = p p p n, g V 1 + O(δ 2 ) g A 1, since no symmetry prevents large strong interaction effect (Adler-Weisberger estimate: g A = O(1.24)) STIAS (January, 2011) Paul Langacker (IAS) 50

n lifetime G 2 F V 2 ud m5 e (g2 V + 3g2 A ) Asymmetries w.r.t. n polarization, e ν correlation (e.g., ILL (Grenoble)) g A /g V = 1.2695(29) STIAS (January, 2011) Paul Langacker (IAS) 51

Charm (c) Quark and Third Family c quark (1974) restores quark-lepton symmetry and suppresses K 0 K 0 mixing (GIM) ( ) ( ) J e µ = ( ν e ν µ )γ µ (1 γ 5 d ) µ + (ū c)γ µ (1 γ 5 )V Cabibbo s V Cabibbo = ( ) cos θc sin θ c sin θ c cos θ c c sl + ν l (cos θ c ), c dl + ν l (sin θ c ) V Cabibbo unitary, V V = V V = I STIAS (January, 2011) Paul Langacker (IAS) 52

Third family (τ, ν τ, t, b) J µ = ( ν e ν µ ν τ )γ µ (1 γ 5 ) V CKM = e µ τ V ud V us V ub V cd V cs V cb V td V ts V tb +(ū c t)γ µ (1 γ 5 ) V CKM }{{} unitary 1 λ λ3 λ 1 λ 2 λ 3 λ 2 1 d s b λ = sin θ c Mixing with third family small Heavy quark and lepton decays (τ ν τ l ν l, τ ν τ π, t bl + ν l, ) CP violating phase in V CKM (unremovable) Analogous leptonic mixing matrix required when m ν relevant STIAS (January, 2011) Paul Langacker (IAS) 53

CKM Universality Universality of quark and lepton couplings (required by gauge theory) and unitarity of CKM relate µ, β, K l3, and b ul ν l Measure G F V ui. Divide by G F from µ decay V ui Universality: j=dsb V uj 2 = 1 experiment: V ud 2 }{{} β + V us 2 }{{} + V ub }{{} 2 K l3 negligible = 0.9999(10) Severe constraint on new interactions, W R, W L W R fermion-exotic mixing, neutrino-exotic mixing mixing, V uj 2 1.04 without radiative corrections! Only finite and meaningful in full SU(2) U(1) gauge theory STIAS (January, 2011) Paul Langacker (IAS) 54