CKM Matrix and CP Violation in Standard Model

Transcription

1 CKM Matrix and CP Violation in Standard Model CP&Viola,on&in&Standard&Model&& Lecture&15& Shahram&Rahatlou& Fisica&delle&Par,celle&Elementari,&Anno&Accademico& &

2 Measurement of V ub and V cb V! Vud Vus Vub " # $ = V V V # V V V $ CKM cd cs cb % 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 2 1 ' ( ) * 61

3 V cb Exclusive 62

4 V cb from B 0 D ( ) lν Decays Differential measurement of B(B 0 D * lν) allows for the extraction of V cb through the expression: d dw Γ 2 2 Vcb F G ( w) ( w) w= v v = Form factor of B D * transition Known kinematic factor HQET and LQCD provide calculation at zero recoil B D m + m q B * D 2mm B D * In reality the formula is slightly more complicated: 0! " 2 # 2 2 % 1 2wr + r F 2 ( w) G( w) = ha ( w) w 1( w+ 1) ( 2& 1 2 ' % + &) ( 1 r) '* 2-2 w 1. " w 1#,% 11+R1 ( w) ( 1 R2 ( w) ) 0 3 w+ 14 ) & 1 r * ' %5 M where r= M D B * F"1 for w"1 63

5 B 0 D ( ) lν Decays l + ν B 0 π D 0 D * 64

6 D + D 0 mass difference! D 0 mass: 1864 MeV! D* mass: 2010 MeV D * D 0 π! Fixed momentum for soft pion! Only experimental resolution 65

7 Angular Variables for B 0 D ( ) lν Selection! Angle between D* and lepton Background Signal! Angle between B 0 and the D*l system! From kinematic quantities since B direction not measured Background Signal 66

8 Extraction of V cb Measurement: Determine number of B 0 D l + ν candidates as function of w Obtain h A1 (w) V cb distribution Fit differential spectrum and extrapolate to w=1 In BaBar: ( ) h (1) V = 35.5 ± 0.3 ± 1.6 A cb stat syst 1 h A 55,000 Decays ( w = 1) = BABAR and using h A 1( w = 1) = Hashimoto et al. PRD 66, (LQCD) 1.5 V cb = (38.7 ± 0.3stat ± 1.7syst ±.3A1 1 ) 10 3 w 67

9 V ub Inclusive 68

10 V ub from Inclusive Semileptonic B Decays Inclusive charmless semileptonic B decays, B X u lν, allow for the measurement of V ub V BB ( Xl u ν )1.61ps = (1 ± ± ) b τ ub OPE m B Theoretically relatively simple, but hadronization effects and Fermi motion of b quark non-perturbative parametrizations (Shape Function, SF) affected by large uncertainties Experimentally challenging, because B X c lν background (60 times higher) separated in limited region of phase space extrapolation to full phase space introduces uncertainties 69

11 Lots of Theory Needed as Input for Interpretation 70

12 V ub inclusive from m X and recoil ν D 0 π + π Y(4S) Reco ed Missed π + l - ν # Background B X c lν separated using invariant mass of the X system (M X ) # Full reconstruction of one B meson to improve signal/background ratio # Look for semileptonic decay on the recoil side 71

13 Fully Reconstructed B Mesons with Leptons in Recoil Fully reconstruct as many decay modes as possible on one side On the other side use lepton identification to clean up the sample: p*>0.5 GeV for electrons p*>0.8 GeV for muons 72

14 Kinematic Variables Useful for V ub 73

15 M x to separate b clν from b ulν B D*lν B D*lν B D**lν reconstructed B πlν B ρlν B ηlν reconstructed About 60-80% of signal for M X < M D 74

16 q 2 Spectrum 75

17 Lepton spectrum in Semileptonic Decays! Cascade (secondary) leptons have lower momentum! Requirement on momentum of leptons provides good separation between signal and cascade leptons! Higher end of the spectrum mostly from decays mediated by Vub! Lighter hadrons allows more momentum for leptons 76

18 hep-ex/ V ub inclusive from m X vs q 2 Results vary slightly depending on particular calculation or experimental input to shape functions Uncertainty dominated by theory! 77

19 Asymmetric Universe of Matter! Universe is very empty but in a biased way n n baryon photons N(anti-baryon) N(baryon) ! Absence of anti-nuclei amongst cosmic rays in our galaxy! Absence of intense γ ray emission due to annihilation of distant galaxies in collision with antimatter galaxies! The early universe believed to have equal amount of matter and anti-matter! What happened to the anti-matter?! CP Violation is one of the three ingredients required to generate such an asymmetry after the Big Bang (A. Sakharov, 1967)! Baryon-number violating processes! Non-equilibrium state during expansion! C and CP Violation 2

20 C and P Symmetries and Fundamental Interactions! Parity, P s v P s v C s v p v e e e +! Parity reflects a system through the origin. Converts right-handed coordinate systems to left-handed ones.! Vectors change sign but axial vectors remain unchanged! x x, L L! Charge Conjugation, C p v! Charge conjugation turns a particle into its anti-particle! e + e, K K +, γ γ p v 3

21 CP Symmetry, particles and anti-particles! CP symmetry transforms a particle in its anti-particle CP! CP is violated IF particles and anti-particles behave differently! 4

22 Weak Interactions and Symmetry Violation! P and C are good symmetries of the strong and electromagnetic interactions! Parity violation observed in 1957! Asymmetry in β decays of 60 Co 60 Ni + e + ν! Electrons produced mostly in one hemisphere C.S.Wu! Charge-conjugation violation 1958! Only left-handed neutrinos and right-handed anti-neutrinos! CP believed to be a good symmetry, but 5

23 A Shocker : Weak Interaction Violates Parity! 1956 Observation of a spatial asymmetry in the β-decay electrons from 60 Co 60 Ni + e + ν C.S.Wu Cold 60 Co inside a Solenoidal B Field 60 Co nuclei spin aligned with B field direction 60 Co undergoes β decay.electron emitted Measure electron intensity w.r.t B field dir. Result:Electrons preferentially emitted in opposite spin direction v e I( θ) = 1 - cos θ c B θ V e asymmetry of intensity " Weak interaction violated Parity 6

24 CP Violation in Kaons! CP conservation implies CP = +1 CP = 1! CP violation in kaons observed in % of the time!! No theoretical explanation! 7

25 Observation of CP Violation in Kaons 8

26 Complex Coupling Constants and CP Violation Generic interaction lagrangian with vector and axial fields a, b: real constants c: complex constant Lagrangian after CP transformation Lagrangian invariant under CP IF AND ONLY IF c=c*! c must be real 9

27 Reminder Kobayashi-Maskawa Mechanism of CP Violation 1972 Two Young Postdocs at that time!! Proposed a daring explanation for CP violation in K decay:! CP violation appears only in the charged current weak interaction of quarks! There is a single source of CP Violation Complex Quantum Mechanical Phase δ ΚΜ in inter-quark coupling matrix! Need at least 3 Generation of Quarks (then not known) to facilitate this! CP is NOT an approximate symmetry, δ ΚΜ 1, it is MAXIMALLY violated! 10

28 quark decay q q gv qp anti-quark decay gv * qp W p W + p CKM Matrix Revisited V! Vud Vus Vub " # $ = V V V # V V V $ CKM cd cs cb V CKM % td ts tb &! -iγ 1 1 e " # $ V # $ CKM # -i β e 1 1 $ & ' $ 1 λ 2 /2 λ Aλ 3 ( ρ iη ) % ' ( = ' λ 1 λ 2 /2 Aλ 2 ( ' ( Aλ 3 (1 ρ iη) Aλ 2 1 ' ( ) * + O ( λ4) Only Source of CP Violation in SM CP Violation built in the Standard Model through Kobayashi-Maskawa Mechanism! Only one complex phase! All CP violating effects in SM related to each other B and K decays CP Violating phenomena are cause by the same complex phase 11

29 Unitarity of CKM Matrix VV = VV = 1! All rows and columns must be orthonormal! 3 conditions for diagonal elements! 6 conditions for off-diagonal elements Magnitude of each term Only condition with comparable size of all pieces and involving b decays 12

30 Unitarity Triangles Unitarity condition of CKM Matrix " orthonormality of rows & columns VV* = δ ; VV* = δ ij ik jk ij kj ik ( i= uct,, ) ( i= d, sb, ) three conditions are interesting for understanding SM predictions for CP violation Each relation requires sum of three complex quantities to vanish " can be represented in the complex plane as a triangle " known as Unitarity Triangles With the knowledge of V ij magnitudes, its instructive to draw the triangles 13

31 Three Unitarity Triangles Drawn to Common Scale ds sb One side is much shorter than the other two" triangle collapses on a line db All sides of comparable length ( λ 3 ) " All angles are large Experimentally hard to measure small numbers easier to measure larger numbers as in (c) 14

32 CKM Unitarity Triangle in B Decays V V + V V + V V = ud ub cd cb td tb 0 Angles of Unitarity Triangle! V V * " α= φ arg # td tb $, 2 # V V * $ #& ud ub $ ' Rescaling, aligning! V V * " β = φ arg # cd cb $, 1 # V V * $ #& td tb $ '! V V * " γ = φ arg# ud ub $ 3 # V V * $ #& cd cb $ ' All lengths involve b decays Large CP Asymmetries predicted, UT angles 15

33 Measuring Complex Phase of CKM Matrix! Branching fractions and lifetimes sensitive to magnitude of CKM elements! Decay probabilities usually include V ij 2! We looked for decays involving only one CKM element to make interpretation of experimental result possible! Complex phase of CKM is a relative phase between matrix elements! We need processes with interference of two different CKM elements iα A = Ae 1 A 2 tot = iβ 1 2 A = A + B + ABe + ABe tot Be A = A + A Sensitive to phase difference! i( α β) i( α β) 16

34 CP Violation! CP violation can be observed by comparing decay rates of particles and antiparticles Γ( a f) Γ( a f) CP Violation! The difference in decay rates arises from a different interference term for the matter vs. antimatter process. Analogy to double-slit experiment: source A 1 A 2 Classical double-slit experiment: Relative phase variation due to different path lengths: interference pattern in space A 1 A 1 A 2 A 2 17

35 CP Violation in B Meson System Identify B final states which are arrived at by two paths B A 1 A 2 B A 1 A 2 In B system, B É B oscillation provides one path with the other path(s) come from weak decay of B hadron ± In B system no oscillation possible, 2 (or more) amplitudes must come from different weak decay of B B Meson is heavy many final states, multiple paths. 2 classes of B decays come into play: Tree spectator decay like Penguin FCNC loop diagrams with u,c,t 18