CP Violation. π π. π + K. Stéphane Willocq A4 University of Massachusetts, Amherst

Transcription

1 CP iolation π π π π µ π K µ Stéphane Willocq A4 Univerity of Maachuett, Amhert New Englan Particle Phyic Stuent Retreat Augut 22

2 Outline What i CP iolation? Why i it intereting? Funamental Symmetrie CP iolation in the Stanar Moel Stuie at e e Aymmetric B Factorie S.Willocq (UMa) CP iolation - NEPPSR 22 2

3 What i CP iolation? Obervation that the aw of Phyic are not exactly the ame uner the combine tranformation: Charge conjugation C particle antiparticle Parity P left-hane helicity right-hane helicity CP ymmetry i conerve in trong an electromagnetic interaction BUT weak interaction violate CP ymmetry Manifetation: ifferent ecay rate in K an B meon ecay For example, the ecay rate for K π µ ν µ that for K π µ ν µ (rate aymmetry.3%) i lightly higher than S.Willocq (UMa) CP iolation - NEPPSR 22 3

4 Why i CP iolation Intereting? Phenomenon icovere in 1964 but not yet well unertoo or tete Unertaning of the baryon - antibaryon aymmetry of the Univere require three ingreient: (A. Sakharov, 1967) 1. Baryon number violating reaction occur 2. CP iolation (CP) take place in thee reaction 3. Reaction occur out of thermal equilibrium (Big Bang) Without CP all matter woul have annihilate with antimatter after the Big Bang level of CP neee i much higher than the Stanar Moel can allow Mot extenion of the Stanar Moel provie new ource of CP CP tuie are enitive to New Phyic S.Willocq (UMa) CP iolation - NEPPSR 22 4

5 Funamental Symmetrie (I) Invariance of fiel equation uner certain tranformation Implie exitence of unerlying ymmetry Reult in conervation law (or forbien procee) Example: Invariance uner tranlation in pace Conervation of momentum Invariance uner tranlation in time Conervation of energy Invariance uner phae tranformation Conervation of electric charge There are 3 important icrete ymmetrie: C, P an T S.Willocq (UMa) CP iolation - NEPPSR 22 5

6 Funamental Symmetrie (II) Charge Conjugation C Particle Anti-particle Charge particle not eigentate C e e ± e - Neutral particle are (eigenvalue ±1) C γ γ C π π Strong an electromagnetic interaction are oberve to be invariant uner C S.Willocq (UMa) CP iolation - NEPPSR 22 6

7 Parity P Funamental Symmetrie (III) Reflect a ytem through the origin patial coorinate flippe x -x but angular momentum unchange Particle have intrinic parity P γ γ P π π Parity operation flip helicity tate (left-hane right-hane) helicity: projection of pin vector along irection of motion Strong an electromagnetic interaction conerve P S.Willocq (UMa) CP iolation - NEPPSR 22 7

8 Funamental Symmetrie (I) Time reveral T Revere irection of time t - t Time invariance of a reaction implie equal rate for the time-revere reaction: 27 p Al α 24 Mg Once again, trong an electromagnetic interaction are invariant uner T S.Willocq (UMa) CP iolation - NEPPSR 22 8

9 Funamental Symmetrie () The 3 operation (C,P, an T) are connecte through invariance of combine CPT for all interaction CPT Theorem: all quantum fiel theorie are invariant uner thi combo (any orer) Conequence: particle an antiparticle have ame ma an lifetime particle obey pin tatitic (Fermi or Boe) CP violation implie T violation a well S.Willocq (UMa) CP iolation - NEPPSR 22 9

10 Funamental Symmetrie (I) BUT: weak interaction o NOT conerve either C or P Firt obervation of parity violation in weak ecay of 6 Co (C.S.Wu et al., 1957) Both C an P are completely violate in charge current weak interaction (W couple only to left-hane particle) P µ e ν ν µ e ν ν er µ R R e µ R oberve not oberve e ν er ν µ not oberve Combine CP operation yiel ame muon ecay rate CP µ C e ν er ν µ µ R er ν e ν µ R S.Willocq (UMa) CP iolation - NEPPSR 22 1 µ

11 Obervation of CP in the K K ytem Before 1964: Strong interaction flavor eigentate K () an K () are uperpoition of ma eigentate K S an K 1 K S ( K K ) CP K ( K K ) CP -1 2 CP tranform matter antimatter Phyical tate K S an K are eigentate of CP if Hamiltonian i invariant uner CP K K CP K S π π π π π K CP 1 CP 1 τ τ Cronin, Fitch, Chritenon, Turlay (1964): Meaure K Γ( K ecay into CP1 tate Γ( K π π ) all charge moe) (2. ±.4) 1 CP violation in kaon weak ecay Other manifetation of CP alo oberve in kaon ecay but effect are alway mall, e.g. Γ( K Γ( K π π l l ν ) Γ( K ν ) Γ( K π π 3 (3.27 ±.12) 1 l ν ) l ν ) 3 S.Willocq (UMa) CP iolation - NEPPSR 22 11

12 CP iolation in the Stanar Moel (I) How oe the SM account for CP in Kaon ecay? Kobayahi an Makawa (1973) propoe exitence of 3 r family of quark (before icovery of charm an tau) CP originate from an irreucible phae in the quark mixing matrix Quark mixing matrix now calle Cabibbo-Kobayahi-Makawa (CKM) matrix S.Willocq (UMa) CP iolation - NEPPSR 22 12

13 S.Willocq (UMa) CP iolation - NEPPSR CP iolation in the Stanar Moel (II) CKM matrix originate from the fact that weak eigentate are ifferent from quark ma eigentate CKM matrix play an important role in charge current weak interaction (e.g. β ecay n p e ν involve a u tranition) b b b tb t t cb c c ub u u CKM ( ) ( ) with current 1 CK C M C W g H J J M J u c t b µ µ µ µ γ γ

14 CP iolation in the Stanar Moel (III) Propertie of CKM matrix CKM govern probability of quark flavor-changing procee ν e ν µ?? ν τ u c e µ τ lepton quark t b Strength of the quark-flavor changing tranition i etermine by CKM t g t W t gt W t gtb W b Probability t 2.1 t 2.16 tb S.Willocq (UMa) CP iolation - NEPPSR 22 14

15 CP iolation in the Stanar Moel (I) Propertie of CKM matrix How many parameter? 9 complex element 18 parameter (not preicte by the theory) However, (1) CKM i unitary: CKM CKM CKM e.g. t 2 t 2 tb inepenent parameter (2) Quark fiel can be reefine to remove 5 arbitrary phae 4 inepenent parameter 3 angle 1 phae Note: if only 2 familie of quark 2x2 matrix 1 (real) inepenent param no phae an no CP nee at leat 3 familie of quark to get an irreucible phae in the quark mixing matrix S.Willocq (UMa) CP iolation - NEPPSR CKM 1

16 CP iolation in the Stanar Moel () Wolfentein parameterization of CKM matrix u c t u c t ub cb tb λ 2 λ 3 Αλ ( 1 ρ iη) 1 λ 1 2 λ Αλ Αλ ( ρ iη) 2 Αλ O 1 4 ( λ ) λ, A, ρ an η are funamental parameter of the Stanar Moel Expanion in power of λ hierarchy of tranition probabilitie λ u.2196 ±.23 from Kaon ecay rate ( u) A cb / λ ±.41 from B D* l ν ecay & lifetime (b c) ρ.22 ±.1 from global fit to available ata η.35 ±.5 η non-zero phae reponible for CP violation S.Willocq (UMa) CP iolation - NEPPSR 22 16

17 CKM Matrix Unitarity Conition CKM Unitarity require 3 i 1 ( j, k ji CKM λ 2 λ 3 Αλ ( 1 ρ iη) * ki 1,2,3 CKM CKM 1 Αλ an 6 orthogonality conition Repreente by 6 triangle λ 1 2 λ in the complex plane i 1 j Αλ ij 3 Αλ * ik k) 1 ( ρ 1 2 iη) * t t * u u λ 5 * c c ub * c b u * c λ 5 u * c * u ub * c cb λ 2 λ 4 * t tb λ 2 t * c t * c λ 2 λ 4 tb * c b λ 2 * t u t * t b t * u u * u b λ 3 λ 3 tb * u b λ 3 λ λ λ λ λ 3 λ 3 c * c b λ 3 S.Willocq (UMa) CP iolation - NEPPSR 22 17

18 The Unitarity Triangle (I) Unitarity conition between 1 t an 3 r column: u ub c cb Conition i repreente by a triangle with ~equal ie angle α, β, γ are large an are ifferent manifetation of the ingle CP-violating phae α β γ * t tb arg * u ub arg arg * c cb * t t b u c * ub * cb t tb η u * u b c * c b 1 S.Willocq (UMa) CP iolation - NEPPSR γ ρ α t * t b c * c b β

19 CP iolation in the Stanar Moel (I) How oe the CKM phae give rie to CP? Example: compare ecay rate for B π π v. B π π Two iagram contribute: Tree Penguin B f amplitue: B b W T CKM i i Tf T e φ e δ W u b π B u,c,t g u π T P CKM π u u π i i Pf P e φ e δ P φ CKM : weak phae from CKM element involve δ : phae hift ue to trong interaction between final tate particle Decay rate: T P T P CKM CKM CKM S.Willocq (UMa) CP iolation - NEPPSR Relative CKM an trong phae: φckm δ φckm Γ( B f) T P T P T P e e e e f f 2 2 ( φ δ ) T P 2 T P co T T CKM T i i i iδ T P P CKM T P e e e e iφ iδ iφ iδ P P CKM φ φ φ δ δ δ

20 CP iolation in the Stanar Moel (II) How oe the CKM phae give rie to CP? Conier CP-conjugate B f moe B f amplitue: Decay rate: T CKM iφ iδ T T e e f T P CKM iφ iδ P P e e f P ( ) Γ( B f ) T P T P 2T P co φ δ f f CKM Rate are ifferent for B an B ecay A CP Γ( B f ) Γ( B f) 2 T P in φ in δ Γ Γ δ CKM 2 2 ( B f ) ( B f) T P 2 T P co φckm co Thi kin of CP i referre to a irect CP or CP in ecay it require two amplitue with ifferent weak (CKM) an trong phae In general, CP originate from a quantum mechanical interference between amplitue with ifferent phae S.Willocq (UMa) CP iolation - NEPPSR 22 2

21 Why B Factorie? CP iolation in B Decay CP effect expecte to be much larger in ome B ecay moe than thoe oberve in kaon ecay Moe involving quark tranition between 3 r an 1 t familie: t 3 3 Αλ ( 1 ρ i η) an Αλ ( ρ i η) thee element have large imaginary part large weak phae CP phenomenology much richer (many more ecay moe) Some CP meaurement are particularly clean both theoretically an experimentally, e.g., CP in B J/ψ K ecay Opportunity to tet the Stanar Moel in a clean an new way e e- B Factorie operating at SAC (BaBar) an KEK (Belle) ince 1999 haron collier experiment (CDF an D) will alo contribute oon S.Willocq (UMa) CP iolation - NEPPSR ub

22 B B Sytem A in the neutral kaon ytem, Heavy an ight ma eigentate are uperpoition of flavor eigentate B B H p p B B Sytem characterize by ma ifference m m H m with ifference Γ Γ Γ H q q B B Different time evolution for B H an B B B H ( t) ( t) B B H ( t ( t ) ) e e ( im H ( im Γ Γ H / 2) / 2) t t b t W t,t, B B W, t b b, t W W t,t t, b lea to B B ocillation with t,t t,t frequency m (a.k.a. mixing ) m tb t 2 S.Willocq (UMa) CP iolation - NEPPSR 22 22

23 3 Clae of CP iolation (I) Nee 2 amplitue with ifferent phae tructure contributing to the ame ecay 3 ifferent way to achieve thi: 1) CP violation in ecay (a.k.a. irect CP violation) B f 2 B f 2 nee f f H H B B 1 two amplitue with ifferent weak phae & ifferent trong phae e.g. compare BR(B K π ) an BR(B K π ) but trong phae are not known 2) CP violation in mixing (a.k.a. inirect CP violation) B B 2 B f B 2 f q nee 1 p Nee relative phae between ma an with part of mixing matrix CP-violating aymmetrie expecte to be mall in Stanar Moel S.Willocq (UMa) CP iolation - NEPPSR 22 23

24 3 Clae of CP iolation (II) 3) CP violation in interference between ecay with an without mixing B 2 f B f 2 B B f B B f Final tate f i a CP eigentate (e.g. J/ψ K or π π ) arg q f H B p f H B nee to have CP (no trong phae neee!) which can happen even if q p f H B 1 an f H B only nee weak phae aymmetrie can be large & o NOT require unknown trong phae mall theoretical uncertaintie in ome cae (e.g. J/ψ K ) mot promiing way to tuy CP via meaurement of the angle α, β, γ S.Willocq (UMa) CP iolation - NEPPSR

25 CP iolation in B J/ψ K Decay (I) Conier B ecay into CP eigentate Interference between amplitue for ecay with an without mixing Γ ( B f ) 1 Im( λ ) in m t Γ( B f ) 1 Im( λ ) in m t λ f CP B mixing q p f f B H H B B f CP f B b B mixing cb * W c B c c J/ψ K f f CP K q p * tb tb t * t e i2β β : weak (CKM) phae from B mixing B b W t tb * * t tb W t t b cb * W c c c J/ψ K K S.Willocq (UMa) CP iolation - NEPPSR 22 25

26 CP iolation in B J/ψ K Decay (II) Expect large CP aymmetry a J/ ψ K Γ(B J/ψ K ) Γ(B J/ψ K ) ( t) Γ(B J/ψ K ) Γ(B J/ψ K ) in 2β in m Stanar Moel fit yiel in 2β.75 ±.9 S.Mele, PRD59, (1999) Small branching ratio t True Aymmetry BR(B J/ψ K ) (8.9 ±1.2) x 1-4 BR(J/ψ l l ) (5.9 ±.1) x 1-2 combine BR 1-4 for e & µ moe Nee to recontruct J/ψ e e, µ µ an K π π (account for etector an election efficiency ~5%) Require very large ample of B meon t / τ S.Willocq (UMa) CP iolation - NEPPSR 22 26

27 e e B Factorie GOA: Prouce 3-1 million B B event/year to tuy CP violation in B ecay via e e - ϒ(4) B B (5%) B B (5%) High ignal-to-backgroun ratio σ bb / σ haron.22 with σ bb 1.5 nb Clean event <# track> 11 & able to recontruct π an γ No fragmentation prouct (low combinatorial backgroun) Strong kinematical contraint (p ϒ(4) an p B* ) for backgroun uppreion S.Willocq (UMa) CP iolation - NEPPSR 22 27

28 ϒ(4) B B B CP B B ytem in coherent 1 tate B an B evolve IN PHASE alway one B an one B until one of them ecay B tag B B ϒ(4) t tag t CP at time t t tag t tag Other B continue to evolve until it ecay at time t t CP Conier other B ecay into CP eigentate f CP If B tag i B at time t tag then probability to oberve other B ecay into f CP i Γ t [ 1 Im( λ ) m t] 1 f Γ e f in 4 CP with t t CP -t tag if B tag i B at time t tag then f 1 4 Γ e Γ t [ 1 Im( λ ) in m t] f CP S.Willocq (UMa) CP iolation - NEPPSR 22 28

29 ϒ(4) B B Different time evolution for B (t t tag ) f CP an B (t t tag ) f CP ecay Aymmetry epen on t t CP t tag (NB: t can be > or < ) Decay Probability.5.4 True Aymmetry f- f f f- t / τ t/τ ϒ(4) ret frame: B meon prouce nearly at ret p B * 34 Me/c avg itance travele before ecay <*> 3 µm (given τ B 1.55 p) S.Willocq (UMa) CP iolation - NEPPSR Symmetric e e collier (e.g. CESR) oe not allow time recontruction Nee unequal beam energie to boot ϒ(4) ytem an meaure t

30 S.Willocq (UMa) CP iolation - NEPPSR 22 3

31 PEP-II B SAC E(e ) 3.1 Ge an E(e ) 9. Ge βγ.55 <> 26 µm Peak luminoity 3. x 1 33 cm -2-1 (eign) 4.6 x 1 33 cm -2-1 (achieve) Number of bunche 8 Poitron current 1775 ma, Electron current 16 ma IP beam ize 15 µm in x, 5 µm in y S.Willocq (UMa) CP iolation - NEPPSR 22 31

32 PEP-II B SAC S.Willocq (UMa) CP iolation - NEPPSR 22 32

33 BABAR SAC Collaboration SAC July 22 9 Countrie 76 Intitution 55 Phyicit July 22 S.Willocq (UMa) CP iolation - NEPPSR 22 33

34 BABAR PEP-II Superconucting Coil (1.5T) Silicon ertex Tracker (ST) e (3.1 Ge) e - (9. Ge) Drift Chamber (DCH) Cherenkov Detector (DIRC) CI Calorimeter (EMC) Intrumente Flux Return (IFR) S.Willocq (UMa) CP iolation - NEPPSR 22 34

35 in 2β (Blin) Analyi at BaBar 1. Fully recontruct B ecay to CP eigentate (eigenvalue η CP ±1) 2. Determine B or B flavor of the other (tagging) B meon 3. Recontruct ecay vertice of both B meon z z CP z tag < z> 26 µm t z / (γ β c) SIGNED! 4. Extract in 2β with unbinne maximum likelihoo fit (value hien to avoi bia) Α F e Υ ( 4) F ( t) F ( t) ( t) -ηcp( D in 2β ) (in m t) F ( t) F ( t) CP ( ) 1 Γ t t t ± 4 Γe CP β [ 1± ( η ) Din 2 in m t] R( ) Experimental effect: Dilution D (1 2w) an reolution function R( t) σ(in 2β) 1 / (N ε tag D 2 ) 1/2 S.Willocq (UMa) CP iolation - NEPPSR e B H B z tβγc B B D π υ µ µ µ µ π K π π

36 Excluive B Recontruction (I) Exploit two kinematical contraint: Beam energy ubtitute ma m E p *2 *2 ES beam Brec reolution ~ 2.6 Me/c 2 ominate by beam energy prea m ES Signal region m ES : [m B -3σ, m B 3σ] E: [ -3σ, 3σ] Energy ifference E * * E Brec E beam reolution ~1-4 Me epening on ecay moe E (Me) uppre backgroun from other B ecay E m ES (Ge/c2 ) S.Willocq (UMa) CP iolation - NEPPSR 22 36

37 Excluive B Recontruction (II) Full recontruction of B ecay into CP-o eigentate: η CP -1 B J/ψ K J/ψ e e, µ µ B ψ(2) K ψ(2) e e, µ µ, J/ψ π π B χ c1 K χ c1 J/ψ γ B η c K η c K K π, K K π with K π π (an π π for J/ψ moe) CP-even eigentate: η CP ignal caniate, purity 94% BEE J/ψ K 988 ignal caniate, purity 55% B J/ψ K CP-mixe eigentate: B J/ψ K* (K* K π ) S.Willocq (UMa) CP iolation - NEPPSR 22 37

38 Caniate for B J/ψ K with J/ψ e e an K π π S.Willocq (UMa) CP iolation - NEPPSR 22 38

39 Caniate for for BB J/ψ J/ψK K withj/ψ J/ψ e e e an KK π π π S.Willocq (UMa) CP iolation - NEPPSR 22 39

40 Flavor Tagging (I) e e Υ ( 4) B H B Nee to tag B or B flavor of other (B tag ) meon B B z tβγc D π υ µ µ µ µ π K π π B CP B tag B CP ha flavor oppoite that of B tag at t t tag Examine all charge particle in the event not inclue in B CP reco Ingreient: epton charge (B l X v. B l X ) Kaon charge (b c tranition B K X v. B K X) Slow pion charge (B D* X low π ) Cacae lepton charge S.Willocq (UMa) CP iolation - NEPPSR 22 4

41 Flavor Tagging (II) Tag performance extracte irectly from ata: recontruct one B ecay to flavor eigentate D* l ν l, D ( * ) π,d ( * ) ρ, tag the ret of the event an meaure both mitag rate w an m Metho ε tag (%) w(%) Q(%) epton 9.1 ± ± ±.3 Kaon I Kaon II 16.7 ± ±.3 1. ± ± ± ±.4 Effectivene Q ε (1 2w) 2 ε D 2 Incluive 2. ± ± ±.3 All 65.5 ± ±.7 S.Willocq (UMa) CP iolation - NEPPSR 22 41

42 Proper Time Difference t z / (γ β c) Meaure ecay vertex poition for B CP an B tag along boot irection e - B tag B CP e B CP vertex: * Geometric & kinematic fit σ z ~ 65 µm z B tag vertex: * Fit remaining track * Ue beam pot contraint * Iterate to remove trk with large χ 2 (minimize bia from charm ecay) * Inclue reultant K trajectory an B CP momentum vector σ z ~ 11 µm ominate z reolution introuce δz ~ 25 µm bia from charm S.Willocq (UMa) CP iolation - NEPPSR 22 42

43 in 2β Meaurement BaBar 88 x 1 6 BB pair: in 2β.741±.67 ( tat) ±.33 ( yt) η CP -1 η CP 1 S.Willocq (UMa) CP iolation - NEPPSR 22 43

44 in 2β Meaurement with epton Tag Only 22 lepton-tagge η f -1 event 98% purity 3.3% mitag rate 2% better t reolution in2β. 79 ±. 11 S.Willocq (UMa) CP iolation - NEPPSR 22 44

45 Worl in 2β Meaurement Worl average in 2β.734 ±.55 In excellent agreement with value etermine inirectly from other B an K ecay meaurement: in 2β.75 ±.9 S.Mele, PRD59, (1999) S.Willocq (UMa) CP iolation - NEPPSR 22 45

46 CP iolation in ecay: Search for CP violation in charmle B ecay (b u or b tranition) meaure ecay rate aymmetry A CP Γ( B Γ( B No evience for irect CP yet Uncertaintie at the 5-4% level (imilar reult from CEO an BEE) Mot precie for B K π with CP iolation in Decay f ) Γ( B f ) Γ( B A.12 ±.5 (tat) CP B f ) f ) ±.16 (yt) f 2 B f S.Willocq (UMa) CP iolation - NEPPSR

47 CP iolation in mixing: CP iolation in Mixing Meaure aymmetry in emileptonic ecay a S Γ ν Γ ν 1 q/ p Γ( B l X) Γ( B l X) 1 q/ p ( B l lx) ( B l lx) νl νl Rate of wrong ign lepton (from mixing) BaBar: a S.5 ±.12(tat) ±.14(yt) q / p.998 ±.6(tat) ±.7(yt) Conitent with mall preicte violation B B 2 B f B 2 f t (p) S.Willocq (UMa) CP iolation - NEPPSR Same-ign Dilepton Aymmetry BABAR

48 The Unitarity Triangle (II) Without in 2β, ρ an η poorly contraine by exp t (large theory uncertaintie) ub A λ 3 (ρ iη) B X u l ν ecay (b u) t A λ 3 (1 ρ iη) B B ocill. freq. ( t) CP in Kaon ecay ε K meaurement ( c) All contraint are conitent with one another GOA: Stringent tet of SM via precie meaurement of the ie an angle of the unitarity triangle S.Willocq (UMa) CP iolation - NEPPSR 22 48

49 The Unitarity Triangle (III) We can now check the conitency of the CKM picture of CP Compare contraint from: 1. CP in the kaon ytem (ε K ) 2. CP in b cc (e.g. B J/ψ K ) 3. ub an t from b u ecay rate an B mixing frequency η _ 1 Excellent conitency between the ifferent obervable CKM matrix provie coherent framework (o far ) -1 ε K in2β 1 ρ _ S.Willocq (UMa) CP iolation - NEPPSR 22 49

50 The Unitarity Triangle (I) Poible ituation in 27 howing inconitency between the meaurement of the ie an of the angle of the triangle: Aume uncertaintie of 3% in cb, 1% in ub, <1% in m an m Aume uncertaintie of 1% in in 2β, 5 o in α an 1 o in γ Inconitency between contraint might look like: S.Willocq (UMa) CP iolation - NEPPSR 22 5

51 Summary CP iolation: New winow into the Stanar Moel of Particle Phyic, relevant to matter-antimatter aymmetry of the Univere, enitive to New Phyic CKM quark mixing matrix for 3 familie of quark contain an irreucible phae that inuce CP violation in weak charge current interaction B Factorie have oberve (large) CP violation for the firt time outie of the neutral kaon ytem (B J/ψ K ecay) Current ata i in excellent agreement with the CKM picture of CP Probing of the SM continue with larger ata ample at the B Factorie an begin at the Fermilab Tevatron S.Willocq (UMa) CP iolation - NEPPSR 22 51

52 Aitional Slie S.Willocq (UMa) CP iolation - NEPPSR 22 52

53 CP iolation in the Stanar Moel (I) (Electroweak) Stanar Moel: Three familie of quark an lepton arrange in left-hane oublet an right-hane inglet u ν, e e, u R, R, e R for 1 t family ocal gauge invariance uner U(1) Y SU(2) ymmetry group yiel electromagnetic an weak interaction Fiel equation (agrangian) ecribe electromagnetic ( EM ), charge current weak ( CC ), an neutral current weak ( NC ) interaction, alo Yukawa interaction between Higg fiel φ an fermion ( Y to provie ma to the fermion) S.Willocq (UMa) CP iolation - NEPPSR 22 53

54 S.Willocq (UMa) CP iolation - NEPPSR CP iolation in the Stanar Moel (II) Higg coupling to fermion: For the firt family we have Note: eparate term for up-type quark (Q 2/3 e) an own-type quark (Q -1/3 e) After pontaneou ymmetry breaking, we obtain quark ma term φ φ φ φ φ φ ν φ φ φ,,, where.. * c e R c u R R e Y u Q e h c u Q g Q g e g ( ) ( ) R D R U Y b M b t c u M t c u ~ ~ quark ma

55 S.Willocq (UMa) CP iolation - NEPPSR CP iolation in the Stanar Moel (III) Quark ma matrice: In general, ma matrice are not iagonal Nee to iagonalize thoe with matrice up an own Reefine quark eigentate to get ( ) ( ) R own R D own R up R U up Y b M b t c u M t c u quark ma M U M D ~ an ~ ( ) ( ) R D R U Y b M b t c u M t c u quark ma

56 S.Willocq (UMa) CP iolation - NEPPSR CP iolation in the Stanar Moel (I) Charge-current Weak Interaction: Reefinition of quark ma eigentate ha non-trivial conequence: Eigentate for weak interaction (,, b ) are linear combination of ma eigentate (,, b): Unitary tranformation matrix i Cabibbo-Kobayahi-Makawa (CKM) mixing matrix ( ) ( ).. ' ' ' h c W b t c u g h c W b t c u g own up CC γ γ µ µ µ µ b b b tb t t cb c c ub u u CKM own up CKM