CP Violation in Kaon Decays

lavi net CP Violation in Kaon Decays A. Pich IFIC, Valencia Workshop on the origins of P, CP and T violation (cpt@ictp) ICTP, Trieste, Italy, July 2 to 5 28

Superweak CP: / Wolfenstein 964 K - K Mixing is the only source of CP / Standard Model CP: / Kobayashi Maskawa 973 d j V i j W u i CP / Quark Mixing d W u, c, t W s d W s u, c, t u, c, t W W s u s d s d u,c,t u,c,t G W G Z, γ s u, c, t d s W d d u q q q q S = 2 S = A. Pich CP Violation in Kaon Decays 2

DIRECT CP VIOLATION η + T(K L π + π ) T(K S π + π ) ε K + ε K ; η T(K L π π ) T(K S π π ) ε K 2 ε K ε K = (2.229 ±.) 3 e i φε K ; φ εk = (43.5 ±.5) Re ( ε ) K ε K 6 { η η + } 2 = (6.5 ± 2.6) 4 4 Re(ε K /ε K ) 23. ± 6.5 NA3 993 7.4 ± 5.9 E73 993 4.7 ± 2.2 NA48 22 2.7 ± 2.8 KTeV 23 A. Pich CP Violation in Kaon Decays 3

Long History of Theoretical Predictions Earlier estimates: ε K /ε K <.2 Ellis-Gaillard-Nanopoulos 76 First LO calculations: ε /ε. Gilman-Wise 79, Guberina-Peccei 8 K K Electroweak penguins: Bijnens-Wise 84, Donoghue et al 86, Buras-Gerard 87 First estimates of isospin breaking: Donoghue et al 86, Buras-Gerard 87, Lusignoli 89 First matrix elements from /N C : Buras-Bardeen-Gerard 87 Heavy top mass: Big cancellation Flynn-Randall 89, Buchalla-Buras-Harlander 9 Paschos-Wu 9, Lusignoli et al 92 NLO short-distance calculation: Re(ε K /ε K ) 7 4 Buras et al 93, Ciuchini et al 93 Modelling matrix elements: Dortmund, Lund, München, Roma, Trieste,... χpt FSI & /N C : Re(ε K /ε K ).7 3 Pallante-Pich, Pallante-Pich-Scimemi Isospin breaking (m u m d, α) Ecker et al, Cirigliano et al 3 Matrix elements at NLO in /N C : Ongoing analytical / lattice effort Amherst, Barcelona, Caltech, CP-PACS, Granada, Lund, Marseille, Montpellier, RBC, Roma,... A. Pich CP Violation in Kaon Decays 4

K 2π ISOSPIN AMPLITUDES A[K π + π ] A e iχ + 2 A 2 e iχ 2 A e iχ = A/2 A[K π π ] A e iχ 2A2 e iχ 2 A 2 e iχ 2 = A3/2 + A 5/2 A[K + π + π ] 3 2 A+ 2 eiχ+ 2 A + 2 e iχ+ 2 = A 3/2 2 3 A 5/2 I = /2 Rule: ω Re (A 2) Re (A ) 22 Strong Final State Interactions: χ χ 2 δ δ 2 45 ε K = i 2 e i (χ 2 χ ) ω { Im (A ) Re(A ) Im (A } 2) Re (A 2 ) A. Pich CP Violation in Kaon Decays 5

S = TRANSITIONS L S= eff W W s u s d s d u,c,t u,c,t G W G Z, γ d u q q q q = G F V ud Vus 2 i C i (µ) Q i (µ) Q = (s α u β ) V A (u β d α ) V A Q 3,5 = (sd) V A q (qq) V A Q 7,9 = 3 2 (sd) V A q e q (qq) V±A Q 6 = 8 q (s Lq R )(q R d L ) Q 2 = (su) V A (ud) V A Q 4 = (s α d β ) V A q (q βq α ) V A Q = 3 2 (s αd β ) V A q e q (q β q α ) V A Q 8 = 2 q e q (s L q R )(q R d L ) A. Pich CP Violation in Kaon Decays 6

S = TRANSITIONS L S= eff W W s u s d s d u,c,t u,c,t G W G Z, γ d u q q q q = G F V ud Vus 2 i C i (µ) Q i (µ) Q = (s α u β ) V A (u β d α ) V A Q 3,5 = (sd) V A q (qq) V A Q 7,9 = 3 2 (sd) V A q e q (qq) V±A Q 6 = 8 q (s Lq R )(q R d L ) Q 2 = (su) V A (ud) V A Q 4 = (s α d β ) V A q (q βq α ) V A Q = 3 2 (s αd β ) V A q e q (q β q α ) V A Q 8 = 2 q e q (s L q R )(q R d L ) q > µ : C i (µ) = z i (µ) y i (µ) (V td V ts /V ud V us ) O(α n s t n ), O(α n+ s t n ) [t log (M/m)] (Munich / Rome) A. Pich CP Violation in Kaon Decays 6

S = TRANSITIONS L S= eff W W s u s d s d u,c,t u,c,t G W G Z, γ d u q q q q = G F V ud Vus 2 i C i (µ) Q i (µ) Q = (s α u β ) V A (u β d α ) V A Q 3,5 = (sd) V A q (qq) V A Q 7,9 = 3 2 (sd) V A q e q (qq) V±A Q 6 = 8 q (s Lq R )(q R d L ) Q 2 = (su) V A (ud) V A Q 4 = (s α d β ) V A q (q βq α ) V A Q = 3 2 (s αd β ) V A q e q (q β q α ) V A Q 8 = 2 q e q (s L q R )(q R d L ) q > µ : C i (µ) = z i (µ) y i (µ) (V td V ts /V ud V us ) O(α n s t n ), O(α n+ s t n ) [t log (M/m)] (Munich / Rome) q < µ : ππ Q i (µ) K? Physics does not depend on µ A. Pich CP Violation in Kaon Decays 6

ε K /ε K P (/2) = r i Im(V tsv td ) [ P (/2) P (3/2)] y i (µ) Q i (µ) ( Ω IB ) ; P (3/2) = r ω (Buras et al) y i (µ) Q i (µ) 2 i r = G F ω 2 ε K Re (A ) ; ω = Re (A 2) Re (A ) 22 ; Re (A ) = 3.37 7 GeV A. Pich CP Violation in Kaon Decays 7

ε K /ε K P (/2) = r i Im(V tsv td ) [ P (/2) P (3/2)] y i (µ) Q i (µ) ( Ω IB ) ; P (3/2) = r ω (Buras et al) y i (µ) Q i (µ) 2 i r = G F ω 2 ε K Re (A ) ; ω = Re (A 2) Re (A ) 22 ; Re (A ) = 3.37 7 GeV Q i (µ) Q i vs B i (µ) m t large ε K ε K [ ] MeV 2 { } B (/2) 6 ( Ω IB ).4 B (3/2) 8 m s (2 GeV) Delicate Cancellation. Strong Sensitivity to: m s (quark condensate) Isospin Breaking (m u m d, e.m. effects) Penguin Matrix Elements (χpt corrections) A. Pich CP Violation in Kaon Decays 7

Energy Scale Fields Effective Theory M W W,Z, γ, g τ, µ, e, ν i t, b, c, s, d, u Standard Model OPE < m c γ, g ; µ, e, ν i s, d, u L (n f =3) QCD, L S=,2 eff N C M K γ ; µ, e, ν i π, K, η χpt A. Pich CP Violation in Kaon Decays 8

Weak Currents Factorize at Large N C K π π π W K K π π π O(N 2 C ) O(N C) O() A[K π π ] = A = 2 A 2 No I = 2 enhancement at leading order in /N C A. Pich CP Violation in Kaon Decays 9

Weak Currents Factorize at Large N C K π π π W K K π π π O(N 2 C ) O(N C) O() A[K π π ] = A = 2 A 2 No I = 2 enhancement at leading order in /N C Multiscale problem: OPE N C ( ) log MW µ Short-distance logarithms must be summed 3 4 A. Pich CP Violation in Kaon Decays 9

Weak Currents Factorize at Large N C K π π π W K K π π π O(N 2 C ) O(N C) O() A[K π π ] = A = 2 A 2 No I = 2 enhancement at leading order in /N C Multiscale problem: OPE N C ( ) log MW µ Short-distance logarithms must be summed 3 4 Large χpt logarithms: FSI N C ( ) log µ M π 3 2 Infrared logarithms must also be included [δ I O(/N C ), δ δ 2 45 ] A. Pich CP Violation in Kaon Decays 9

CHIRAL PERTURBATION THEORY (χpt) Expansion in powers of p 2 /Λ 2 χ : A = n A(n) (Λ χ 4πF π.2 GeV) Amplitude structure fixed by chiral symmetry Short-distance dynamics encoded in low-energy couplings (LECs) A. Pich CP Violation in Kaon Decays

CHIRAL PERTURBATION THEORY (χpt) Expansion in powers of p 2 /Λ 2 χ : A = n A(n) (Λ χ 4πF π.2 GeV) Amplitude structure fixed by chiral symmetry Short-distance dynamics encoded in low-energy couplings (LECs) O(p 2 ) χpt: δ = δ 2 = A /2 = 2 F π (G 8 + ) 9 G 27 (MK 2 M2 π) A 3/2 = 9 F π G 27 (M 2 K M2 π ) ; A 5/2 = A. Pich CP Violation in Kaon Decays

CHIRAL PERTURBATION THEORY (χpt) Expansion in powers of p 2 /Λ 2 χ : A = n A(n) (Λ χ 4πF π.2 GeV) Amplitude structure fixed by chiral symmetry Short-distance dynamics encoded in low-energy couplings (LECs) O(p 2 ) χpt: δ = δ 2 = A /2 = 2 F π (G 8 + ) 9 G 27 (MK 2 M2 π) A 3/2 = 9 F π G 27 (M 2 K M2 π ) ; A 5/2 = Loop corrections (χpt logarithms) unambiguously predicted LECs can be determined at N C A. Pich CP Violation in Kaon Decays

O(p 2,e 2 p ) χpt Q = diag ( 2 3, 3, ) 3 L S= 2 = G 8 F 4 λl µ L µ +G 27 F (L 4 µ23 L µ + 2 ) 3 L µ2l µ 3 +e 2 F 6 G 8 g ew λu QU G R G F 2 V ud V us g R { ; L µ = iu D µu ; λ 2 λ 6 i7 ; U exp i } 2 Φ/F A /2 = { ( 2F π G 8 [(MK 2 Mπ) 2 2 ) 3 3 ε(2) 2 ] 3 F π 2 e 2 (g ew + 2 Z) + } 9 G 27 (MK 2 Mπ) 2 A 3/2 = 2 3 F π {( 5 3 G 27 + 2 ) } ε (2) G 8 (MK 2 M2 π ) F π 2 e2 G 8 (g ew + 2 Z) 3 A 5/2 = ; δ = δ 2 = ε (2) = ( 3/4) (m d m u)/(m s ˆm). ; Z (M 2 π ± M2 π )/(2 e2 F 2 π ).8 A. Pich CP Violation in Kaon Decays

O(p 2,e 2 p ) χpt ; N C g 8 = ( 3 5 C 2 2 ) ( ) q q (µ) 2 5 C + C 4 6 L 5 Fπ 3 C 6 (µ) F 3 π g 27 = 3 5 (C 2 + C ) ( ) q q (µ) 2 [ e 2 g 8 g ew = 3 C 8 (µ) + 6 ] 9 C 6(µ) e 2 (K 9 2K ) G R G F 2 V ud Vus g (R = 8, 27) R q q (µ) F 3 π = M 2 K (m s + m d )(µ)f π { } 8M2 K Fπ 2 (2L 8 L 5 ) + 4M2 π Fπ 2 L 5 A. Pich CP Violation in Kaon Decays 2

O(p 2,e 2 p ) χpt ; N C g 8 = ( 3 5 C 2 2 ) ( ) q q (µ) 2 5 C + C 4 6 L 5 Fπ 3 C 6 (µ) F 3 π g 27 = 3 5 (C 2 + C ) ( ) q q (µ) 2 [ e 2 g 8 g ew = 3 C 8 (µ) + 6 ] 9 C 6(µ) e 2 (K 9 2K ) G R G F 2 V ud Vus g (R = 8, 27) R q q (µ) F 3 π = M 2 K (m s + m d )(µ)f π { } 8M2 K Fπ 2 (2L 8 L 5 ) + 4M2 π Fπ 2 L 5 Equivalent to standard calculations of B i µ dependence only captured for Q 6,8 A. Pich CP Violation in Kaon Decays 2

O [ p 4, (m u m d )p 2,e 2 p 2] χpt Nonleptonic weak Lagrangian: O(G F p 4 ) L (4) weak = i G 8 N i F 2 Oi 8 + i G 27 D i F 2 Oi 27 + h.c. Electroweak Lagrangian: O(G F e 2 p 2 ) L EW = e 2 i G 8 Z i F 4 O EW i + h.c. O(e 2 p 2 ) Electromagnetic + O(p 4 ) Strong: K i, L i K ππ, ππγ Inclusive, DAPHNE A. Pich CP Violation in Kaon Decays 3

A (X) n = a (X) n [ + L A (X) n ] + C A (X) n O(p 4 ) χpt Loops: Large correction NLO in /N C L A (8) /2 =.27 ±.5 +.47 i ; L A (27) /2 =.2 ±.6 +.47 i ; L A (27) 3/2 L A (g) /2 =.27 ±.5 +.47 i ; L A (g) 3/2 =.4 ±.5.2 i =.5 ±.2.2 i Pallante-Pich-Scimemi A. Pich CP Violation in Kaon Decays 4

A (X) n = a (X) n [ + L A (X) n ] + C A (X) n O(p 4 ) χpt Loops: Large correction NLO in /N C L A (8) /2 =.27 ±.5 +.47 i ; L A (27) /2 =.2 ±.6 +.47 i ; L A (27) 3/2 L A (g) /2 =.27 ±.5 +.47 i ; L A (g) 3/2 =.4 ±.5.2 i =.5 ±.2.2 i Pallante-Pich-Scimemi 2 All local O(p 4 ) couplings fixed at N C C A (X) n Small correction to O(p 2 ) results A. Pich CP Violation in Kaon Decays 4

A (X) n = a (X) n [ + L A (X) n ] + C A (X) n O(p 4 ) χpt Loops: Large correction NLO in /N C L A (8) /2 =.27 ±.5 +.47 i ; L A (27) /2 =.2 ±.6 +.47 i ; L A (27) 3/2 L A (g) /2 =.27 ±.5 +.47 i ; L A (g) 3/2 =.4 ±.5.2 i =.5 ±.2.2 i Pallante-Pich-Scimemi 2 All local O(p 4 ) couplings fixed at N C C A (X) n Small correction to O(p 2 ) results 3 Isospin Breaking: O [ (m u m d )p 2,e 2 p 2] Sizeable corrections Cirigliano-Ecker-Neufeld-Pich A. Pich CP Violation in Kaon Decays 4

A (X) n = a (X) n [ + L A (X) n ] + C A (X) n O(p 4 ) χpt Loops: Large correction NLO in /N C L A (8) /2 =.27 ±.5 +.47 i ; L A (27) /2 =.2 ±.6 +.47 i ; L A (27) 3/2 L A (g) /2 =.27 ±.5 +.47 i ; L A (g) 3/2 =.4 ±.5.2 i =.5 ±.2.2 i Pallante-Pich-Scimemi 2 All local O(p 4 ) couplings fixed at N C C A (X) n Small correction to O(p 2 ) results 3 Isospin Breaking: O [ (m u m d )p 2,e 2 p 2] Sizeable corrections 4 Re(g 8 ), Re(g 27 ), χ χ 2 fitted to data Cirigliano-Ecker-Neufeld-Pich A. Pich CP Violation in Kaon Decays 4

ε K ε K [ ] 5 MeV 2 { } B (/2) 6 ( Ω eff ).4 B (3/2) 8 m s (2 GeV) Delicate Cancellation. Strong Sensitivity to: m s (quark condensate) m s (2 GeV) = 5 ± 2 MeV Isospin Breaking (m u m d, α) Ω eff =.6 ±.8 Penguin Matrix Elements χpt Loops (FSI): B (/2) 6, (.35 ±.5) ; B(3/2) 8, Cirigliano-Ecker-Neufeld-Pich (.54 ±.2) A. Pich CP Violation in Kaon Decays 5

ε K ε K [ ] 5 MeV 2 { } B (/2) 6 ( Ω eff ).4 B (3/2) 8 m s (2 GeV) Delicate Cancellation. Strong Sensitivity to: m s (quark condensate) m s (2 GeV) = 5 ± 2 MeV Isospin Breaking (m u m d, α) Ω eff =.6 ±.8 Penguin Matrix Elements χpt Loops (FSI): B (/2) 6, Re ( ε /ε ) = (.35 ±.5) ; B(3/2) 8, Cirigliano-Ecker-Neufeld-Pich (.54 ±.2) ( ) +9 9 ± 2 µ 6 ms ± 6 /NC 4 Pallante-Pich-Scimemi (updated) Exp. world average: Re(ε /ε) = (6.5 ± 2.6) 4 A. Pich CP Violation in Kaon Decays 5

ε K ε K [ ] 5 MeV 2 { } B (/2) 6 ( Ω eff ).4 B (3/2) 8 m s (2 GeV) Delicate Cancellation. Strong Sensitivity to: m s (quark condensate) m s (2 GeV) = 5 ± 2 MeV Isospin Breaking (m u m d, α) Ω eff =.6 ±.8 Penguin Matrix Elements χpt Loops (FSI): B (/2) 6, Re ( ε /ε ) = (.35 ±.5) ; B(3/2) 8, Cirigliano-Ecker-Neufeld-Pich (.54 ±.2) ( ) +9 9 ± 2 µ 6 ms ± 6 /NC 4 Pallante-Pich-Scimemi (updated) Exp. world average: Re(ε /ε) = (6.5 ± 2.6) 4 Challenge: Control of subleading /N C corrections to χpt couplings A. Pich CP Violation in Kaon Decays 5

ˆ ε /ε = Im (V ts V td ) [ P (/2) P (3/2)] 4 Im (V ts V td ) P(/2) 5 4 BEIJING LUND MARS V. Cirigliano 3 2 VAL DORTMUND TRIESTE TAIPEI ROMA MUNICH RBC CP-PACS MONTP 5 5 2 25 3 4 Im (V tsv td ) P (3/2) Q i I from original calculations Ω eff Updated A. Pich CP Violation in Kaon Decays 6

ELECTROWEAK PENGUINS contribute at O(p ) (m q, p ) e 2 g 8 g ew F 6 = 6 C 7 (µ) O (µ) 2 C 8 (µ) O 2 (µ) N C 3 C 8(µ) qq(µ) 2 O (µ) (s L γ µ d L )( d R γ µ s R ) ; O 2 (µ) (s L s R )( d R d L ) M 8 (GeV 3 ) KPdR FGdR 4 CDGM CDGM 3 BGP Narison DGGM 99 Large Nc.5 2. 2.5 3..5.. T T I A C E L RBC 3 BGLLMPS 5 BGHHLR 6 CP PACS 3 M 8 (2π) I=2 Q 8 (µ ) K mq=p= = 8 F 3 O 2(µ ) µ = 2 GeV M 8 N C 2 F 3 qq(µ ) 2 2M 4 K F 3 (m s + m q ) 2 (µ )F 2 π A. Pich CP Violation in Kaon Decays 7

CP / Charge Asymmetry in K ± (3π) ± Decays T(u,v) 2 + g u + h u 2 + k v 2 + u (s 3 s )/m 2 π ; v (s s 2 )/m 2 π ; s (s + s 2 + s 3 )/3 ; s i (p K p πi ) 2 ; 3 = odd π NA48/2: A g g+ g g + + g = (.5 ± 2.) 4 π ± π + π (.8 ±.9) 4 π ± π π Theory: A π± π + π g = (.24 ±.2) 4 ; A π± π π g = (. ±.7) 4 (Gámiz-Prades-Scimemi) A. Pich CP Violation in Kaon Decays 8

K πν ν T F(Vis V id, m2 i ) ( ν MW 2 L γ µ ν L ) π s L γ µ d L K s d s d W u; c; t u; c; t W W l Z Br(K + π + ν ν) = (8. ±.) A 4 [ η 2 + (.4 ρ) 2] Br(K L π ν ν) = (2.8 ±.4) A 4 η 2 Buras et al Long-distance contributions are negligible A(K L π ν ν) Direct CP / BNL-E787: few events! Br(K + π + ν ν) = (.47.89 +.3 ) KEK-E39a: Br(K L π ν ν) < 2. 7 (9% CL) New Experiments Needed A. Pich CP Violation in Kaon Decays 9

SUMMARY Qualitative understanding of ε /ε within the Standard Model Quantitative prediction using the /N C expansion and χpt Large chiral corrections generated by infrared logarithms Detailed analysis of isospin breaking corrections Good agreement with experiment Re ( ε /ε ) = (but large uncertainties) ( 9 ± 2 µ +9 6 ms ± 6 /NC ) 4 Challenge: Control of subleading /N C corrections to χpt couplings On-going theoretical efforts using both analytical & lattice tools A. Pich CP Violation in Kaon Decays 2

BACKUP SLIDES A. Pich CP Violation in Kaon Decays 2

Isospin Breaking in ε /ε ǫ K ω + { Im A () Re A () { Im A () ω + Re A () ( ) ImA 2 + + f 5/2 ReA () 2 } ( Ω eff ) ImAemp 2 Re A () 2 } ω ReA 2 ReA = ω + ( + f5/2 ) ; ω + ReA+ 2 ; Ω IB = ReA () ReA ReA () 2 Im A non emp 2 ImA () Cirigliano-Ecker-Neufeld-Pich α = α 2 LO NLO LO NLO Ω IB.7 5.9 ± 4.5 8. ± 6.5 22.7 ± 7.6.4.4 ±.5 8.7 ± 3. 8.4 ± 3.6 f 5/2 8.3 ± 2.4 Ω eff.7 6.3 ± 4.5 9.3 ± 5.8 6. ± 7.7 Ω eff =.6 ±.8 Ω IB f 5/2 Ω π η IB =.6 ±.3 A. Pich CP Violation in Kaon Decays 22

ELECTROWEAK PENGUINS contribute at O(p ) (m q, p ) e 2 g 8 g ew F 6 = 6 C 7 (µ) O (µ) 2 C 8 (µ) O 2 (µ) N C 3 C 8(µ) qq(µ) 2 O (µ) (s L γ µ d L )( d R γ µ s R ) ; O 2 (µ) (s L s R )( d R d L ) These D=6 vacuum condensates appear in the left-right correlator: Π µν LR (q) 2i d 4 x e iqx T(L µ (x), R ν () ) ( g µν q 2 + q µ q ν) Π LR ( q 2 ) υ a 2.5 2.5.5 -.5 - ALEPH τ (V,A, I=) ν τ parton model/perturbative QCD.5.5 2 2.5 3 3.5 Mass 2 (GeV/c 2 ) 2 Π LR (Q 2 ) = dt ImΠ LR(t) π t + Q 2 = Õ2n+4 2 (Q 2 ) n+2 n= }{{}}{{} Data QCD OPE [ lim Q 2 Q6 Π LR (Q 2 ) = 4πα s 4 O 2 + 2 ] O N C O dq 2 Q D Π LR (Q 2 ) A. Pich CP Violation in Kaon Decays 23

n f /N C Correction to QCD PENGUIN (m q ) Im(g 8 ) = Im[C 6 (µ)] ( q α q β q 2 { ) g αβ W DGRR ( q 2 ) = 6L 5 ( qq F 3 ) 2 + 8n f 6π 2 F 4 (Hambye-Peris-de Rafael 3) dq 2 Q D 2 W DGRR (Q 2 ) dω q d 4 x d 4 y d 4 z e iqx T [ ( s L q R )(x) ( q R d L )() ( d R γ αu R )(y) (ū R γ α s R )(z) ] con } -. -.2 -.3 -.4 -.5 -.6 2 n (z f z W µ had. ) DGRR Available theoretical information: (very poor) [ lim Q 2 W DGRR (Q 2 ) = F4 ( ) ] πα s qq 2 Q 2 6Q 2 6L 5 F 3 lim Q 2 W DGRR (Q 2 ) = Q 2 ( ) { qq 2 F 2 F 2 8Q 2 ( L 5 5 ) } 2 L 3 -.7 2 3 4 z Big enhancement ( 3) claimed Infrared unstability from pion pole: Large non-factorizable contribution claimed before Q ǫ dq 2 Q 2 + mπ 2 2 ǫ m ǫ π (Bardeen et al, Bijnens-Prades) A. Pich CP Violation in Kaon Decays 24

Phenomenological K ππ Fit Cirigliano-Ecker-Neufeld-Pich PDG + KLOE 2 [Γ(K S π + π (γ)/γ(k S π π )] LO-IC LO-IB NLO-IC NLO-IB Re g 8 5.9 ±. 5. ±. 3.67 ±.4 3.65 ±.4 Re g 27.294 ±..27 ±..297 ±.4.33 ±.4 χ χ 2 (48.6 ± 2.6) (48.5 ± 2.6) (48.6 ± 2.6) (54.6 ± 2.4) IC [m u m d = α = ] ; IB [m u m d, α ] ππ ππ: δ δ 2 = (47.7 ±.5) Colangelo Gasser Leutwyler Before KLOE 2 (χ χ 2 ) LO IC = 57 A. Pich CP Violation in Kaon Decays 25

UNITARITY TRIANGLE CONSTRAINTS η f i t t e r.6 Summer 27.5.4.3.2 excluded area has CL >.95 γ sin2β ε K m d α m s & m d ε K sol. w/ cos2β < (excl. at CL >.95) α CKM γ. γ V α ub β -.4 -.2.2.4.6.8 ρ A. Pich CP Violation in Kaon Decays 26

Future Kaon Initiatives CERN-SPS Rare K decays LFV Chiral dynamics Φ factory Hadron xsec K S decays, interferometry U-7 Frequent K decays J-PARC Λ Ξ hypernuclei K Rare Decay A. Ceccucci NA48/2 2 kaon decays P-326 (NA48/3) > 3 kaon decays Δ[Br(K + π + νν)] ~. Flavour Physics A. Pich Super B 27

Plans for K + π + νν J-PARC: LoI ; plans to use the BNL-E949 detector CERN: P-326 ; about 8 SM events in two years Plans for K L π νν KEK: E39a ; data taking completed (three runs) Present limit < 2. -7 9% CL (% of Run- data) Aims to reach the Grossman-Nir bound (~ -9 ) J-PARC: proposal (>2) Step I: E39a detector at J-PARC ~ SM sensitivity Step II: New detector & dedicated beam-line ~ SM events CERN: would need an upgraded proton complex Flavour Physics A. Pich Super B 27

K. Komatsubara K L π l + l Plenty of Room for New Physics Flavour Physics A. Pich Super B 27