Electroweak Theory: 5 - PDF Free Download

Electroweak Theory: 5 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) 162

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) 163

Previous Lecture The Z, the W, and the Weak Neutral Current The Weak Neutral Current Renormalization and Radiative Corrections The W and Z The Z Pole and Beyond Triple Gauge Vertices Global Analysis of the Standard Model and Beyond STIAS (January, 2011) Paul Langacker (IAS) 164

This Lecture The CKM Matrix and CP Violation The CKM Matrix CP Violation and the Unitarity Triangle The Neutral K and B Systems STIAS (January, 2011) Paul Langacker (IAS) 165

The Cabibbo-Kobayashi-Maskawa (CKM) matrix Charge-raising current J µ W = ( ν e ν µ ν τ )γ µ (1 γ 5 ) V = A u L Ad L e µ τ + (ū c t)γ µ (1 γ 5 )V Mismatch between weak and quark masses, and between A u,d L, which relate weak and mass eigenstates d s b V = unitary 3 angles and 1 phase after removing unobservable overall phases of fields V V = V V = I STIAS (January, 2011) Paul Langacker (IAS) 166

Magnitudes of elements (PDG) V = V ud V us V ub V cd V cs V cb V td V ts V tb V ij = 0.9742 0.226 0.0036 0.226 0.973 0.042 0.0087 0.041 0.9991 V ud from superallowed β decay; V us from K l3 V cd,cs from c decay and from c production (dimuons) in νn V cb,ub from b c and b u decay rates (theory uncertainties) V td,ts,tb from B 0 B 0 mixing, t b, unitarity STIAS (January, 2011) Paul Langacker (IAS) 167

Various exact parametrizations consistent with unitarity V = 1 0 0 0 c 23 s 23 c 13 0 s 13 e iδ 0 1 0 c 12 s 12 0 s 12 c 12 0 0 s 23 c 23 s 13 e iδ 0 c 13 0 0 1 where c ij cos θ ij, s ij sin θ ij s 12 sin θ C 0.23, s 13 s 23 s 12 ; δ = CP phase Want to test unitarity V V = V V = I. Apparent violation would signal new physics. ( V V ) = V 11 ud 2 + V us 2 + V ub 2 = 1? (Universality) ( V V ) 31 = V ub V ud + V cb V cd + V tb V td = 0? Unitarity triangle: each complex number in ( V V ) is a vector in 31 complex plane. Should sum to zero, i.e., form triangle. STIAS (January, 2011) Paul Langacker (IAS) 168

V ub V α ud V tb V td γ β Vcb V cd ( ρ, η) α ρ + i η 1 ρ i η γ β (0, 0) 1 (1, 0) The unitarity triangle ( ρ, η) α ρ + i η Vcb V cd 1 ρ i η γ β (0, 0) 1 (1, 0) Divide each side by (well-measured) Overconstrain by redundant tests Sides by (CP -conserving) rates, e.g., b u decay rate, B 0 B 0 mixing Angles by CP violating effects CP area (Jarlskog invariant): J = Im (V us V cb V ub V cs ) A2 λ 6 η Deviation: extra family, fermion mixing, new sources of CP -violation (e.g., SUSY loops), new FCNC interactions (extended Higgs, Z ) STIAS (January, 2011) Paul Langacker (IAS) 169

The Wolfenstein parametrization. sin θ C 0.226 Empirical expansion in λ Simple to remember and work with V = 1 λ 2 /2 λ Aλ 3 (ρ iη) λ 1 λ 2 /2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 A 0.81 from b c decay rate; (ρ, η) real, expected O(1) Vertices of triangle at (0, 0), (1, 0), and ( ρ, η), where ρ = ρ(1 λ 2 /2), η = η(1 λ 2 /2) Each constraint determines allowed region in ρ, η plane STIAS (January, 2011) Paul Langacker (IAS) 170

1.5 1.0 excluded area has CL > 0.95 sin 2'! excluded at CL > 0.95 #m d & #m s V ub determined by rate for exclusive or inclusive b ulν (theory uncertainties) ) 0.5 0.0-0.5 $ K " V ub V ub & % SL! " ' " #m d ( V ub V ud ) 2 /( V cb V cd ) 2 = ρ 2 + η 2 radius 2 of circle centered at (0, 0) -1.0 CKM f i t t e r ICHEP 10! $ K sol. w/ cos 2' < 0 (excl. at CL > 0.95) -1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 (CKMFITTER: http://ckmfitter.in2p3.fr/) ( STIAS (January, 2011) Paul Langacker (IAS) 171

K 0 K 0 mixing Strong interactions conserve strangeness (S K = S Λ = 1, S K = 1) K 0 = d s K 0 = ds CP K 0 = η K K 0 CP K 0 = η K K0 K 0 and K 0 are states relevant to strong interaction processes, e.g., π p K 0 Λ allowed, but π p K 0 Λ ( Λ = sdu ) Choose quark (or meson) phases so that η K = 1 STIAS (January, 2011) Paul Langacker (IAS) 172

s u, c, t d K 0 W W K 0 d u, c, t s However, WCC can violate strangeness and lead to K 0 K 0 mixing at second order M ( ) MK 0 M 12 M12 M K 0 s W d K 0 u, c, t u, c, t K 0 d W s M K 0 = M K 0 by CP T tiny M 12 important Need GIM m c 1.5 GeV predicted Typeset by FoilTEX 1 Severe constraint on tree-level Z, FCNC Higgs 2 families real M 12 eigenstates K 0 1,2 = K0 K 0 2 K S,L m = m K2 m K1 = 2M 12 G2 F 6π 2m2 c V cd 2 V cs 2 f 2 K m KB K 3.5 10 6 ev (regeneration) STIAS (January, 2011) Paul Langacker (IAS) 173

Assume CP is conserved CP violation CP K 0 = K 0 CP K 0 = K 0 CP K 0 1,2 = CP K0 K 0 2 = ±K 0 1,2 CP π + π = + π + π CP π 0 π 0 = + π 0 π 0 for J = 0 CP 3π = 3π for J = Q = 0 Thus, K S K 0 1 2π (τ S = 8.9 10 11 s); K L K 0 2 3π (τ S = 5.1 10 8 s) Fitch-Cronin (1964): observed K L 2π with B(K L 2π) 3 10 3 CP STIAS (January, 2011) Paul Langacker (IAS) 174

CP violation and phases CP violation requires complex observable phases Some phases unobservable: only overall phase of amplitude; can absorb in phase of state Need interference between amplitudes, e.g., diagrams involving all three families Phase in CKM can generate Im M 12 0. Effect small due to small mixings even if CKM phase large s u, c, t d K 0 W W K 0 d u, c, t s s W d K 0 u, c, t u, c, t K 0 d W s Typeset by FoilTEX STIAS (January, 2011) Paul Langacker (IAS) 175

Toy example H eff = M K 0 K 0 K 0 }{{} K 0, K 0 mass + M 12 ( e 2iϕ K 0 K 0 + e 2iϕ K 0 K 0) }{{} complex mixing mass (indirect) + a ( e iβ K 0 + e iβ K 0) ππ }{{} complex decay amplitude (direct) Absorb e 2iϕ by K 0 e iϕ K 0 and K 0 e iϕ K 0 H decay eff ( = a e i(β ϕ) K 0 + e i(β ϕ) K 0 ) ππ = 2 a cos(β ϕ) K0 K 0 }{{ 2 } K S Observable CP by phase difference β ϕ +i sin(β ϕ) K0 + K 0 2 } {{ } K L ππ STIAS (January, 2011) Paul Langacker (IAS) 176

Actual K L,S system; amplitude ratios η + A(K L π + π ) A(K S π + π ) = ɛ + ɛ η 00 A(K L π 0 π 0 ) A(K S π 0 π 0 ) = ɛ 2ɛ Difference because two isospin amplitudes for 2π, I = 0 (large) and I = 2 (small) ɛ from mixing (indirect) and CP in I = 0 amplitude (small) ɛ from difference in I = 0 and I = 2 phases (direct suppressed) Experiment: ɛ = 2.229(12) 10 3 Re(ɛ /ɛ) = 1.65(26) 10 3 (CERN, FNAL) STIAS (January, 2011) Paul Langacker (IAS) 177

Physical states CP parameters K L = p K 0 + q K 0 = ɛ K0 1 + K0 2 1 + ɛ 2 K S = p K 0 q K 0 = K0 1 + ɛ K0 2 1 + ɛ 2 p q 1 + ɛ 1 ɛ ɛ = ɛ }{{} mixing 2ɛ = i e i(δ 2 δ 0 ) }{{} strong + i ImA 0 ReA 0 }{{} I=0 decay ReA 2 ReA 0 }{{} 0.045 [ ImA2 ImA ] 0 } ReA 2 {{ ReA 0 } I=0,2 mismatch STIAS (January, 2011) Paul Langacker (IAS) 178

Box diagrams ɛ box Im(V ts V td)f (m t, m c, angles, QCD) η [(1 ρ)f 1 + F 2 ] s u, c, t d K 0 W W K 0 d u, c, t s Hyperbola in ( ρ, η) plane 1.5 1.0 excluded area has CL > 0.95! sin 2' excluded at CL > 0.95 #m d & #m s s W d K 0 u, c, t u, c, t K 0 d W s 0.5 $ K " #m d ) 0.0-0.5 " V ub V ub & % SL! ' " Typeset by FoilTEX -1.0 CKM f i t t e r ICHEP 10! $ K sol. w/ cos 2' < 0 (excl. at CL > 0.95) -1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 ( STIAS (January, 2011) Paul Langacker (IAS) 179

ɛ from direct CP violation (i.e., in decay amplitudes) Believed dominated by penguin diagrams (A 0 enhanced) Re(ɛ /ɛ) = 1.65(26) 10 3 η Roughly consistent with SM, but large theory uncertainty s W u, c, t d G(Z, γ) d d STIAS (January, 2011) Paul Langacker (IAS) 180

B 0 B 0 mixing CLEO, LEP, Tevatron, BaBar (SLAC), BELLE (KEK), LHCb Strong interaction states B 0 d = d b B 0 d = db = CP B 0 d B 0 s = s b B 0 s = sb = CP B0 s Mixed by second order weak (box diagrams) B Hi = p i B 0 i + q i B 0 i, i = d, s B Li = p i B 0 i q i B 0 i where p i q i = 1 ɛ i 1+ ɛ i and ɛ i = iimm i 12 / m i 1 ( m i m Hi m Li = 2 M i 12 ) STIAS (January, 2011) Paul Langacker (IAS) 181

Observe m i m Hi m Li = 2 M i 12 by B0 B 0 oscillations (cf ν oscillations). eg., suppose initial state tagged as B 0 i ψ(0) = B 0 i = 1 2p i ( BLi + B Hi ) ψ(τ ) 1 ( ) B Li e im L τ i + B Hi e im H i τ 2p i ( ) mi τ cos 2 B 0 i + i sin ( mi τ 2 ) qi p i B 0 i Measure m i by time dependence (or integral) of decays, using b cl ν l (from B 0 ); b cl + ν l (from B 0 ) m d = 0.507(5) ps 1 3.3 10 4 ev (1 ρ) 2 + η 2 m s = 17.77(12) ps 1 0.012 ev 1 (QCD correlated theory error reduced in m d / m s ) STIAS (January, 2011) Paul Langacker (IAS) 182

1.5 excluded at CL > 0.95 excluded area has CL > 0.95! 1.0 #m d & #m s sin 2' 0.5 #m d $ K " ) 0.0-0.5 " V ub V ub & % SL! ' " -1.0 CKM f i t t e r ICHEP 10! $ K sol. w/ cos 2' < 0 (excl. at CL > 0.95) -1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 (CKMFITTER group: http://ckmfitter.in2p3.fr/) ( STIAS (January, 2011) Paul Langacker (IAS) 183

The CP asymmetries in B decays Many CP asymmetries to determine angles of unitarity triangle, but QCD uncertainties Cleanest: breaking) B 0 ( B 0 ) f, where f CP eigenstate (up to CP CP f = ± f η f f e.g., f = J/ψK S, π + π, ρk S Let B 0 (τ ) be time-evolution of state tagged as B 0 at τ = 0, and similarly for B 0 (τ ) STIAS (January, 2011) Paul Langacker (IAS) 184

CP -odd asymmetry where a f (τ ) = Γ(B0 (τ ) f) Γ( B 0 (τ ) f) Γ(B 0 (τ ) f) + Γ( B 0 (τ ) f) = (1 λ 2 ) cos( m τ ) 2 Imλ sin( m τ ) (1 + λ 2 ) λ = p q }{{} mixing Ā A }{{} decay Usually confused by sum over diagrams, with (CP -conserving) strong phases (final state interactions) and (CP -violating) CKM phases A = α A α e iδ α e iϕ α Ā = η f α A α e iδ α }{{} strong e iϕ α }{{} CKM STIAS (January, 2011) Paul Langacker (IAS) 185

Golden modes, B J/ψK S,L (only one significant diagram no strong interaction uncertainty) ψ c c W b s B 0 K 0 d d λ = ( V tb V td ) V tb V }{{ td } B B mixing ( V cs V cb ) V cs V }{{ cb } decay, 1 Imλ = ± sin 2β, λ = 1 BaBar, Belle: sin 2β = 0.681(25) STIAS (January, 2011) Paul Langacker (IAS) 186 Typeset by FoilTEX 1

Many other modes studied, including charmless u π + d B π + π W Tree-level only: λ = sin 2α However, competition from significant penguin theory uncertainty (isospin) Penguin-dominated, b s ss, e.g., B φk S (hint of discrepancy in sin 2β?) SM loops; may be significant new physics from tree (FCNC Z, extended Higgs) or enhanced supersymmetric loops (large tan β) Recent CDF, D0 B s asymmetries? B 0 B 0 b d W u, c, t b G d b Typeset by FoilTEX B 0 G d W u, c, t d u ū d ū d π + π s s s d π φ K 0 STIAS (January, 2011) Paul Langacker (IAS) 188

Stringent tests of CKM universality, unitarity triangle CP violation well studied in K and B sector Tests electroweak loops, renormalization, QCD corrections Strong interaction challenges largely overcome Constraints on new physics However, addition CP violation required for baryogenesis STIAS (January, 2011) Paul Langacker (IAS) 189