Standard Model of Particle Physics SS 2012

Transcription

1 Lecture: Standard Model of Particle Physics Heidelberg SS 212 Flavour Physics I + II 1

2 And the winner is Congratulations! Prize 2

3 Examination Who needs a grade for this lecture (e.g. Erasmus students)? Oral examination (3 minutes) at July 24th, morning Please contact me or Werner Rodejohann to fix the time 3

4 Contents PART I Determination of the CKM Matrix CP Violation in Kaon system CP violation in the B-system PART II Search for Flavor Violating Neutral Currents (Lepton Flavor Violation) Search for Lepton/Baryon Number Violation PART III (W.R) Massive Neutrinos 4

5 CKM Matrix Definition: Experimental values: no theory prediction! (Particle Data Group 212) 5

6 CKM Matrix Standdard Parameterisation (Euler Angles): 6

7 CKM Matrix Wolfenstein Parameterisation: note that η and ρ are phase convention dependent, η and ρ not 7

8 CKM Matrix Wolfenstein Parameterisation: note that η and ρ are phase convention dependent, η and ρ not Experimental values: no theory prediction! 8

9 Experimental Determination of CKM Matrix Elements Vus: Kaon decay: fk /fπ = ±.7 K μ ν μ- - - π μ ν - - = s u d u s u form-factor ν theory uncertainties due to Kaon/Pion formfactors mostly cancel Vus =.2252 ±.9. Vus: Tau decay: τ- τ νkx form-factor u LEP, Barbar, Belle combined: Vus =.228 ±.39 s ν 9

10 D - Decays Vcd: D-meson decay: D K- lν D π- lν = c s u u c s, d c d ν l- CLEOc + Belle combined: Vcd =.229 ±.6 ±.24 from CLEOc arxiv

11 Neutrino Scattering Vcd: from neutrino (antineutrino) scattering ν μone muons W d u ν μμ + Vcd d W c W + ν two muons from CDHS, CCFR, CHARM II and CHORUS experiments: Vcd =.23 ±.11. d 11

12 DS - Decays Vcs: from DS decays s μ- c ν u u c s, d DS lν Vcs: from D decays D K lν - combined CLEOc, Belle, Babar: Vcs = 1.6 ±.23 ν l- 12

13 B and Top Decays Determination of Vub and Vcb from B-decays Vub: B Xu lν Vub = (4.15 ±.49) 1 3 Vcb: inclusive and exclusive B decays Vcb = (4.9 ± 1.1) 1 3. Vtd: Vts: Both difficult to determine from top decays with high precision instead use trick 13

14 B and BS oscillations B B oscillations W+ b t d b d d b testing Vtd s testing Vts b t t b s s W t W- W testing Vtd BS BS oscillations W+ b t d W t W- t s b testing Vts W t b by measuring time dependence of oscillations: Vtd = (8.4 ±.6) 1 3, Vts = (42.9 ± 2.6)

15 Result Fitting the four free parameters to the experimental results yields (global fit): Representation using the Wolfenstein parameterisation (only 4 parameters!) V 12 V 21 λ 2 V V λ V 13 V 31 λ (mystery!) As η (ñ ) the CKM matrix violates CP-invariance! However, CP-violation is too small to explain observed matter-antimatter asymmetry in universe 15

16 CP Violation and the Consequences u l - Wb γ b c γ c b d W- ν W+ c c b W+ l+ u ν d If CP-violated, the above final states do not occur with same rate! Direct CP-Violation: different partial decay widths for particles and antiparticles Might explain observed baryon asymmetry in universe if in addition baryon-number violating process exists 16

17 CP violation in the Kaon system first discovered here! K K oscillations W+ s u,c,t u,c,t s d W u,c,t d W d s W- d u,c,t s Transition Amplitude: (V ud ) (V us ) f (mu) + (V cd ) (V cs ) f (mc )+ (V td ) (V ts ) f (mt ) CKM elements of antifermions are complex conjugated if δ13= (Vtd) then CP is conserved: K T K K T K if δ13<> (Vtd) then CP is violated: K T K = K T K 17

18 Kaon Physics (reminder) Quarkmodel: K = d s K = d s Both states can be experimentally distinguished. Different cross sections with matter (strong interactions): + K p K p, K η + K p K p, Λ π Weak Interactions (oscillations): Define CP invariant (hypothetical) states: K 1 = K 2 = ( K + K ) CP K 1 = K 1 ( K K ) CP K 2 = + K 2 Physical States: KL π ππ KS π π K L K 1 K S K 2 CP= -1 CP= Δ M =M L M S O(1 8 τ( K L )=5 1 s 1 τ( K S )=.9 1 s very small mass difference! MeV ) 18

19 K Oscillations Kaons at rest: i M L t e i M S t e K L (t ) = K L () e K S (t ) = K S () e Γ L t /2 ΓS t /2 oscillation decay =i t Hamilton operator: H eigenvalues: H= ( i M S Γ S 2 i M L Γ L 2 ) Oscillations: 1 A (t ) = K (t ) K () = K L (t ) K S (t ) K L ()+ K S () 4 1 Γ t Γ t 1/ 2(Γ +Γ )t P(t )= A (t ) A (t ) = ( e +e 2cos(Δ M t ) e ) 4 L S L S with Δ M =M L M S 19

20 Kaon Oscillations and Regeneration 5% KS and KL 1% KL 2 (1/2)2

21 Discovery of CP Violation Christensen at al. (1964) BR(K L π+ π ) = (Nobel Prize Cronin and Fitch 198) very small CP-violating effects in Kaon system Question: CP violation in decay or KL or in mixing? 21

22 How to measure CP violation? Single CKM matrix element is not enough: CKM: 3 V td = A λ (1 ρ i η) Example top decay: (Wolfenstein parameterisation) t dw (e.g. LHC, difficult!) B(t d W ) V td2 = A 2 λ 6 [(1 ρ)2+η2 ] complex phase not visible! Complex phase can only be measured in interference processes: Three possibilities: direct CP Violation CP violation in mixing interference between decays with and without mixing 22

23 CP transformation Consider CP violating (weak) process i f: +i ϕ CP ai = e a i +i ϕ CP a f = e a f i i weak f A f = af O ai it follows if [O,CP]= f transition amplitudes: i weak f A f = a f O a i +i(ϕ ϕ ) A f = e Af f 23 i

24 CP transformation Consider CP violating (weak) process i f: +i ϕ CP ai = e a i +i ϕ CP a f = e a f i i weak f f i transition amplitudes: A f = af O ai weak f A f = a f O a i +i(ϕ ϕ ) A f = e Af it follows if [O,CP]= f i If quarks involved, there is an additional QCD phase shift: QCD i weak s weak QCD f i +i(θ+ϕ ) A f = n e f s +i(θ ϕ ) A f = n e i i strong interaction (strong phase shift θ) is CP invariant! 24

25 I. Direct CP violation Definition A f / A f 1 not possible with single process as exp(ix) =1 (see previous page) Superposition of two processes: like a classical double slit experiment s i f s +i(θ1 +ϕ 1) A f = n1 e A f = n1 e +i(θ1 ϕ1 ) + n2 e A f 2 = n21+n22 +2 n1 n2 cos((θ1 θ2)+(ϕ1 ϕ2 )) A f 2 = n21+n22+2 n 1 n2 cos((θ1 θ2) (ϕ1 ϕ2)) +i(θ2 +ϕ2 ) A f / A f 1 if ϕ1 ϕ2 and θ1 θ2 +i(θ2 ϕ 2) + n2 e 25

26 I. Direct CP violation Definition A f / A f 1 not possible with single process as exp(ix) =1 (see previous page) Superposition of two processes: like a classical double slit experiment s i f s +i(θ1 +ϕ 1) A f = n1 e A f = n1 e +i(θ1 ϕ1 ) + n2 e A f 2 = n21+n22 +2 n1 n2 cos((θ1 θ2)+(ϕ1 ϕ2 )) A f 2 = n21+n22+2 n 1 n2 cos((θ1 θ2) (ϕ1 ϕ2)) +i(θ2 +ϕ2 ) A f / A f 1 if ϕ1 ϕ2 and θ1 θ2 +i(θ2 ϕ 2) + n2 e 26

27 I. Direct CP violation Definition A f / A f 1 not possible with single process as exp(ix) =1 (see previous page) Superposition of two processes: like a classical double slit experiment s i f A f 2 = n21+n22 +2 n1 n2 cos((θ1 θ2)+(ϕ1 ϕ2 )) A f 2 = n21+n22+2 n 1 n2 cos((θ1 θ2) (ϕ1 ϕ2)) s +i(θ1 +ϕ 1) A f = n1 e A f = n1 e +i(θ1 ϕ1 ) + n2 e +i(θ2 +ϕ2 ) A f / A f 1 if ϕ1 ϕ2 and θ1 θ2 +i(θ2 ϕ 2) + n2 e Can be measured in decays of charged and neutral particles! + example: δ L = + Γ( K L l ν l π ) Γ( K L l ν l π ) Γ( K L l + ν l π ) + Γ( K L l ν l π + ) 3 δ L = (3.32±.6) 1 (experiment) Note: total decay width is not affect by CP violation (would violate CPT) 27

28 Example KL Decays d π- K s u W+ K L 1 2 ν l+ ( K + K ) d W- π- t K s u ν different weak and QCD phases! 28 l+

29 Direct CP Violation in Charged Meson Decay B K ρ u B - ρ u b W V*ub s - K- u Vus u B K - s b - V*tb Vts t u W- u ρ different weak and QCD phases! 29 huge!

30 II. CP violation in mixing oscillations of neutral mesons measure time dependent decay width + d Γ / dt ( M l X ) d Γ/ dt ( M l X ) A osc = d Γ / dt ( M l + X ) + d Γ/ dt ( M l X ) δc = A osc time dependent charge asymmetry K K oscillations ± K l ν l π 3

31 III. Interference Decay + Mixing B interference between decay without mixing and decay with mixing f oscillation neutral final state B Γ( B (t ) f ) Γ ( B (t ) f ) AΓ = Γ( B (t ) f ) + Γ ( B (t ) f ) Note, in Kaon system all three kinds of CP violating effects were discovered! It took about 4 years of measurements and theory to fully understand this subject! 31

32 Quantitative Description of KL state assume that KL is not a pure K1 state: K L = 1 ( (1+ϵ) K ϵ + (1 ϵ) K ) ε describes CP odd admixture K L = K S = 1 ( K 1 + ϵ K 2 ) 2 1+ ϵ 1 ( ϵ K 1 + K 2 ) 2 1+ ϵ mixing causes oscillations which are time dependent affects in contrast to direct CP violation pure CP eigenstates Decompose into mixing and direct CP violation effect η± = + + π π T K L π π T K S = ϵ + ϵ with + π π T K 1 ϵ = + π π T K 2 mixing direct 32

33 KS and KL Interference δc = A osc Experimental Result: η± = (2.333±.1) 1 η± ϵ 3 CP violation mainly due to mixing! What about ε? 33

34 KS and KL Interference δc = A osc Experimental Result: η± = (2.333±.1) 1 η± ϵ 3 CP violation mainly due to mixing! consistent with type II CP violation result of 3 δc =2 ℜ(ϵ) = (3.33±.14) 1 time dependent charge asymmetry K K oscillations What about ε? ± K l ν l π 34

35 Direct CP Violation in K ππ Decays What about ε? Idea: mixing effects are in the K - anti-k system direct CP violation is decay specific look into different decays! η = ϵ+ π π T K L π π T K S = ϵ 2 ϵ note different sign and factor By measuring Kaon decays into charged and neutral pions with high precision ε can be measured: 4 (1988) ℜ(ϵ / ϵ) = (33±11) 1 4 (2) ℜ(ϵ / ϵ) = (16.7±2.6) 1 35

36 Summary Kaon Physics Decay K l ± νl π direct CP violation discovered + ± K l ν l π + Γ(K L l νl π ) Γ(K L l ν l π ) δl = Γ(K L l + νl π ) + Γ(K L l ν l π + ) 3 (experiment) δ L = (3.32±.6) 1 and CP violation in mixing + Decay K π π,π π CP violation in mixing ϵ = (2.228±.11) 1 3 and tiny direct CP violation 4 ℜ(ϵ / ϵ) = (16.7±2.6) 1 36

37 Unitarity Trigangle one of six possible unitarity triangles define angles α, β, γ 37

38 Kaon Constraints Relation between CP violating ε parameter and CKM matrix elements: S is Inami-Lim function leads to bands (hyperbola) in η-ρ plane: next slide 38

39 Summary of experimental Results 39

40 Babar Detector PEP-C Accelerator, Stanford 4

41 Belle Detector KEK, Japan 41

42 B-Oscillations at B-factories Exploit different beam energies: 42 + E(e )>E (e )

43 Classification of B-decays always two identical flavours interfering diagrams 43

44 sin 2β clearly non zero! 44

45 Summary of experimental Results 45

46 B-Mixing Formalism Oscillations: ( ) ( )( M (t) M () M 11 i Γ1 /2 M 12 = M 21 M 22 i Γ2 /2 M () M (t) ) Linear combination of low and high mass eigenstate slightly different convention c.t. the more historic Kaon conventions both have been measured for B and Bs 46

47 Classification of CP Violation I. Direct CP-violation A f / A f 1 II. CP-violation in mixing q/ p 1 III. CP-violation in decay with and without mixing q A f ℑ(λ f )= p Af asymmetry often called S CP-eigenstate 47

48 CP Violation in B J/ψ K mixing effect in B-sector is much larger than in K-sector! 48

49 Correlation Direct versus Mixing large direct CP violation! small CP violation in mixing 49

50 Summary B-Asymmetry Parameters I. Direct CP-violation is large II. CP-violation in mixing is very small! Sensitive to new BSM physics! III. CP-violation in decay with and without mixing 5

51 Summary of experimental Results All measurements very consistent! No sign of non-ckm CP violation 51

52 Summary The CKM Matrix elements are determined from a global fit to precision measurements The CKM matrix is tested to be unitary and has a non-zero CP violating phase CP violation can be measured in particle decays if at least two diagrams with different strong and weak phases interfere CP violation shows up in decays and mixing (oscillations) In Kaon system CP violation in mixing dominates In B-system CP violation in direct decays dominates CP violation in hadron decays explained by CKM matrix 52

53 53