CKM Matrix and CP Violation in Standard Model

Transcription

1 CKM Matrix ad Violatio i Stadard Model Measuremet o si2β. Costraits o CKM Lecture 17 Shahram Rahatlou Fisica delle Par,celleElemetari, Ao Accademico

2 Violatio i Itererece betwee Mixig ad Decay βγ Υ(4S) = 0.55 z µ Separate B 0 ad B 0 - e Υ ( 4s) + e B tag Κ B 0 B 0 Coheret BB pair B rec - µ 0 K s - π + µ π + Δt Δ z < βγ > c Δ z B 0 J/ψ K s Ay Eigestate 2

3 Time-Evolutio o B Decays to Eigestates Probability o B 0 > B 0 > > tag > depeds o Dierece Δt betwee decay time o the two B mesos Decay amplitudes 0 A H B,t 0 A H B,t = = Oscillatio parameter q p M = = e M 12 i2β 12 Flavor o taggig eutral B meso: B 0 or B0 Coveiet parameter to describe time evolutio Takes ito accout combied eect o oscillatio ad decay λ q A q A = = η pa pa 3

4 Time-Depedet Decay Rates to Eigestates λ q A q A = = η pa pa Expressio ad complexity o λ depeds o speciic ial states Decay amplitudes A ad A ca be more or less complicated depedig o umber o amplitudes cotributig to total amplitude 4

5 Time-Depedet Asymmetry i Itererece Violatio occurs i q A λ = 1 p A q 1 p = No Violatio A A = 1 i Mixig No Direct Violatio But eve with λ =1 it is suiciet to have Imλ 0 I Stadard Model we expect λ 1 i most o B decays 5

6 Simple Case with λ =1 Φ = β M Very simple expressio or violatig asymmetry Amplitude o asymmetry deied by phase dierece betwee mixig parameter q/p ad ratio o decay amplitudes Complex phase Φ M depeds o speciic ial state Ca probe dieret agles o Uitarity triagle through dieret B decays 6

7 Why do We Need Time Depedece? si ( m B t) + a dδ t = 0 At ϒ(4S): itegrated asymmetry is zero à must do a time-depedet aalysis! This is impossible to do i a covetioal symmetric eergy collider producig ϒ(4S) BB!! 7

8 V I Itererece Betwee Mixig ad Decay B 0 cp 2 B 0 cp 2 0 B A e iϕ B 0 + B 0 cp B 0 + B 0 cp M ie 12 = 2i ϕ M 0 B A e i ϕ 0 0 Neutral B Decays ito ial state accesible by both B & B decays q A This is V whe = 1 ad = 1 ad the parameter o iterest is λ p A V Asymmetry is deied as : a = 0 0 ( Bphys() t ) Γ( Bphys() t ) ( Bphy s() t ) ( Bph ys( t) ) ( 2 ) 1 λ ( Δm t) Γ 2 λ = si - cos Δ B 2 Γ + Γ 1+ λ 1+ λ Whe B decay is domiated by a sigle diagram, λ = 1 a = λ si Im Im η ( Δm t) B qa p A ( mt) B asymm. ca be very large ad ca be clealy related to CKM agles 8

9 Golde Decay Mode B 0 àj/ψk 0 9

10 Golde Decay Mode J/ψ K 0 Tree Pegui:: u,c,t loops A = V V T * T cb cs ccs A =V V P +V V P + V V P * * * P tb ts t cb cs c ub us u * * * Use Uitarity relatio VtbVts + Vcb Vcs + Vub V us to rearrage terms * * A = AT + A P = VcbVcs(Tccs + Pc P) t + VubVu s(pu P) t * * = (VcbV cs) T +(VubVus) P V V 1 ; (V V ) T is the domiat amplitude * ub us Sice VV * cb cs 50 A expect -1 =10 A -2 cb * cs Hece "Platium" mode! 10

11 V I Itererece Betwee Mixig ad Decay: B 0 àj/ψk 0 0 B A e iϕ M ie 12 = 2i ϕ M 0 B A e S i ϕ * * * * * qb AψKS Vt bvtd VV cb cs VV cs cd VtbVtd VcbVcd ψk =- = - S * * * * * pb AψK VV tb td VcbVcs VV cs cd VtbV td VcbV cd λ = e 2i β Im(λ λ ψk S ψk S ) = 1 = si(2β) Γ Γ ( 0 ) t / τ B J/ ψksl, e [ 1 ηsi2βsi( Δmt) ] ( 0 ) t / τ B J/ ψksl, e [ 1+ ηsi2βsi( Δmt) ] Same is true or a variety o B (cc) s ial states λ ψk L = λ ψk η = -1 (+1) or J/ψ K 0 S(L) S 11

12 Time-Depedet Asymmetry with a Perect Detector Perect measuremet o time iterval t=δt Perect taggig o B 0 ad B 0 meso lavors For a B decay mode such as B 0 ψks with λ =1 B 0 B 0 Asymmetry A si 2β V A ( t) =si2 si ( m t) 12

13 Charmoium+K 0 Sample or BABAR ( 02) η = 1 modes 1506 sigal cadidates, purity 94% η = 1 modes S S 0 + ( 2 ) l l + B J/ψK { ππ } B J/ψK { ππ } B ψ S { or J/ψπ π }K B χ { J/ψγ}K B { KK }K 0 0 c1 S 0 0 ηc π S 0 S η =+ 1 mode B 0 0 J/ψK L 988 sigal cadidates, purity 55% BABAR 81.3 b 1 (ater taggig & vertexig) 13

14 Calibratio with Flavor eigestates Cotrol Sample with o expected asymmetry B 0 B 0 0 ( ) + + B D π /ρ /a + 1 si2β = ± times larger tha sigal 14

15 Observatio o Violatio (BaBar 2001) si2β = ± B 0 B 0 B 0 à J/ψ K S B 0 à ψ(2s) K S B 0 à χ c K S B 0 à η c K S 15

16 BABAR Result or si2β (July 2002) η = -1 η = +1 si2β = ± si2β = ± ± (stat) (syst) 16

17 Updated (ICHEP04) si2β results rom Charmoium Modes 0 ( cc ) KS ( odd) modes 0 ( cc ) KL ( eve) modes b o peak or 227 M BB pairs 7730 evets (tagged sigal) Limit o direct V si 2β = ± ± λ C = = ± ± λ cc K + cc K S L 17

18 Belle Results o si2β rom Charmoium Modes BàψK S Sample Belle M BB pairs C si 2β = ± ± λ = = ± ± λ New Belle value lower tha i 03 si 2β = ± ± but still cosistet with BaBar 04 18

19 Violatio i B Decays Firmly Established 19

20 Lessos From si2β Measuremet With B 0 J/ψK 0 I 2001, large Violatio i B system was observed i this mode by BaBar ad Belle. First istace o V outside the Kao system. First istace o a V eect which was O(1) i cotrast with the Kao system Coirms the 1972 cojecture o Kobayashi & Maskawa. Excludes models with approximate symmetry (small V). I 2007 si2β became a precisio measuremet (5%) ad agrees well with the costraits i the ρ-η plae rom measuremets o the CKM magitudes (will be discussed i tomorrow s lecture) Appears ulikely to id aother O(1) source o V eterprise ow moves towards lookig or correctios rather tha alteratives to SM/CKM picture Focus ow shits to measuremets o time-depedet asymmetries i rare B decays domiated by Pegui diagrams i the SM ad where New Physics could cotribute to the asymmetries 20

21 Costraits o Uitarity Triagle rom Measuremets o CKM Elemets ad CKM Agles 21

22 V V V V ud us ub = V V V CKM cd cs cb V V V td ts tb V CKM = 1 λ 2 /2 λ Aλ 3 ( ρ iη ) λ 1 λ 2 /2 Aλ 2 Aλ 3 (1 ρ iη) Aλ O ( λ4) e 1 1 -iβ e -i γ 22

23 Determiatio o CKM Elemets rom Measuremets CKM Fitter UTit 23

24 B d mixig + V i K mixig (ε K ) ε ~ η(1 ρ) K 24

25 Add V ub / V cb 25

26 + B S Mixig costrait 26

27 + Si2β 27

28 + α costrait 28

29 All measuremets cosistet, apex o (ρ,η) well deied + γ measuremet 29

30 Uitarity Triagle ater All Costraits Icludes costraits rom all CKM-related measuremets 30

31 Impact o Agle Measuremets o CKM Fit Measuremets o agles domiate the costrait o the UT apex! 31

32 All costraits Status o UT i 2007 Oly agles rom B ad ε K rom Kaos 32