Particle Physics II CP violation. Lecture 3. N. Tuning. (also known as Physics of Anti-matter ) Niels Tuning (1)

Transcription

1 Particle Physics II CP violation (also known as Physics of Anti-matter ) Lecture 3 N. Tuning Niels Tuning (1)

2 Plan 1) Mon 5 Feb: Anti-matter + SM 2) Wed 7 Feb: CKM matrix + Unitarity Triangle 3) Mon 26 Feb: Mixing + Master eqs. + B J/ψK s 4) Wed 28 Feb: CP violation in B (s) decays (I) 5) Mon 12 Mar: CP violation in B (s) and K decays (II) 6) Wed 14 Mar: Rare decays + Flavour Anomalies 7) Wed 21 Mar: Exam Ø Final Mark: if (mark > 5.5) mark = max(exam,.85*exam +.15*homework) else mark = exam Ø In parallel: Lectures on Flavour Physics by prof.dr. R. Fleischer Niels Tuning (2)

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4 L SM = L Kinetic + L Higgs + LYukawa + d I I ϕ I L Yuk = Yi j ( ul, dl) i d... Rj + ϕ L g I µ I g I µ + I = u γ Wµ d + dliγ Wµ ul i Kinetic Li Li Recap W u I d I Diagonalize Yukawa matrix Y ij Mass terms Quarks rotate Off diagonal terms in charged current couplings I d d I s VCKM s I b b W u d,s,b md d mu u L Mass = ( dsb,, ) g ms s ( uct,, ) mc c... L g + g + L g m b b m t t L g 5 g * 5 u µ W Vij ( 1 ) d d µ + = γ µ γ + γ Wµ Vi ( 1 γ ) u CKM i j j j i R L = L + L + L SM CKM Higgs Mass R Niels Tuning (4)

5 L Charged Currents g I µ I g I µ I µ µ = u γ W d + d γ W u = J W + JCC W CC Li µ Li Li µ Li CC µ µ L The charged current term reads: g 1 γ 1 γ g 1 γ 1 γ = u W d + d W u g µ 5 g µ + * 5 = uiγ Wµ Vij ( 1 γ ) d j + d jγ Wµ Vij ( 1 γ ) ui µ µ + i γ µ Vij j j γ µ Vji i Under the CP operator this gives: CP g µ + ( 5 ) g µ i * ( 5 d γ W 1 1 ) µ Vij γ u + uγ Wµ Vij γ d 2 2 CC j i i j A comparison shows that CP is conserved only if V ij = V ij * (Together with (x,t) -> (-x,t)) In general the charged current term is CP violating Niels Tuning (5)

6 CKM-matrix: where are the phases? Possibility 1: simply 3 rotations, and put phase on smallest: Possibility 2: parameterize according to magnitude, in O(λ): W u d,s,b Niels Tuning (6)

7 This was theory, now comes experiment We already saw how the moduli V ij are determined Now we will work towards the measurement of the imaginary part Parameter: η Equivalent: angles α, β, γ. To measure this, we need the formalism of neutral meson oscillations Niels Tuning (7)

8 Neutral Meson Oscillations Why? Loop diagram: sensitive to new particles Provides a second amplitude Ø interference effects in B-decays b s s b Niels Tuning (8)

9 i Dynamics of Neutral B (or K) mesons Time evolution of B and B can be described by an effective Hamiltonian: Ψ= t! H Ψ H = M $ # & " M!#" # $ % hermitian at () Ψ () t = a() t B + b() t B bt () No mixing, no decay! H = M $ # & i! Γ $ " M % 2 # & " Γ %!#" # $!# "# $ hermitian hermitian No mixing, but with decays (i.e.: H is not Hermitian!) è With decays included, probability of observing either B or B must go down as time goes by: d ( 2 2 ( ) ( ) ) ( * * ( ) ( ) ) Γ at ( ) at bt at bt Γ bt ( ) dt + = Γ> Niels Tuning (9)

10 Describing Mixing Time evolution of B and B can be described by an effective Hamiltonian: at () i Ψ= H Ψ Ψ () t = a() t B + b() t B t bt ()! H = M $ # & i! Γ $ " M!#" # $ % 2 # & " Γ!# "# $ % hermitian hermitian! M M $ H = # 12 & i " Γ Γ % $ 12 ' # * " M 12 M & 2 $ * % Γ 12 Γ ' # &!## "## $!## "## $ hermitian hermitian Where to put the mixing term? Now with mixing but what is the difference between M 12 and Γ 12? M 12 describes B B via off-shell states, e.g. the weak box diagram Γ 12 describes B f B via onshell states, eg. f=π + π - Niels Tuning (1)

11 Solving the Schrödinger Equation i i M Γ M Γ i ψ t t t i i M12 12 M Γ Γ 2 2 ( ) = ψ ( ) Eigenvalues: Mass and lifetime of physical states: mass eigenstates i i m 2 M12 12 M Δ = R Γ 12 Γ i i 4 M12 12 M ΔΓ = I Γ 12 Γ Niels Tuning (11)

12 Solving the Schrödinger Equation i i M Γ M Γ i ψ t t t i i M12 12 M Γ Γ 2 2 ( ) = ψ ( ) Eigenvectors: mass eigenstates B = p B + q B H B = p B q B L i i q p= M Γ M Γ 2 2 Niels Tuning (12)

13 Time evolution With diagonal Hamiltonian, usual time evolution is obtained: Niels Tuning (13)

14 ψ B Oscillation Amplitudes For an initially produced B or a B it then follows: (using: ( t) : q B ( t) = g () t B + g () t B p + p B ( t) = g () t B + g () t B q + with g ± () t = e For B, expect: ΔΓ ~, q/p =1 1 2 p ( H L ) B = B + B 1 B = B B 2q ( H L ) iω t iω t ± e 2 + ( ) imt Γt /2 g+ t = e e g ( ) imt Γt /2 t = e e Δmt cos 2 Δmt i sin 2 ( ) g t ; ~ e e ± 1 1 iδ mt + iδmt 2 2 imt Γt /2 e ± e 2 Niels Tuning (14)

15 B Decay probability Measuring B Oscillations Examples: q g p g + () t () t Δm x = Γ B l ν X + l l ν X + l x B B B àb B àb Δm Γ 1 g + p g q () t () t Δm x? > Γ B l ν X + l l ν X + l B 1 For B, expect: ΔΓ ~, q/p =1 Γt e g± t ± Δm t 2 2 ( ) ; ~ 1 cos( ) Proper Time à Niels Tuning (15)

16 Compare the mesons: Probability to measure P or P, when we start with 1% P P àp P àp Probability à <τ> Δm x=δm/γ y=δγ/2γ K s 5.29 ns -1 Δm/Γ S =.49 ~1 D s.1 fs -1 ~.1 B s.57 ps ~ B s s 17.8 ps ~.5 By the way, ħ= MeVs x=δm/γ: avg nr of oscillations before decay Time à Niels Tuning (16)

17 Summary (1) Start with Schrodinger equation: at () ψ () t = bt () (2-component state in P and P subspace) Find eigenvalue: Solve eigenstates: ψ p = ± ± q Eigenstates have diagonal Hamiltonian: mass eigenstates! Niels Tuning (17)

18 Summary (2) Two mass eigenstates Time evolution: P () t Probability for P > à P >! Express in M=m H +m L and Δm=m H -m L à Δm dependence

19 Summary p, q: BH = p B + q B BL = p B q B Δm, ΔΓ: x,y: mixing often quoted in scaled parameters: i i m 2 M12 12 M Δ = R Γ 12 Γ i i 4 M12 12 M ΔΓ = I Γ 12 Γ Δm x= y= Γ ΔΓ 2Γ q,p,m ij,γ ij related through: q M Γ i = p M Γ i /2 /2 Δmt t cos( Δ mt) = cos = cos x Γ τ τ Time dependence (if ΔΓ~, like for B ): q B ( t) = g () t B + g () t B p + p B ( t) = g () t B + g () t B q + with ( ) imt Γt /2 g+ t = e e g ( ) imt Γt /2 t = e e Δmt cos 2 Δmt i sin 2 Niels Tuning (19)

20 Personal impression: People think it is a complicated part of the Standard Model (me too:-). Why? 1) Non-intuitive concepts? Imaginary phase in transition amplitude, T ~ e iφ Different bases to express quark states, d =.97 d +.22 s +.3 b Oscillations (mixing) of mesons: K > K > 2) Complicated calculations? 3) Many decay modes? Beetopaipaigamma ( B f ) A ( ) 2 f g+ t λ g ( t) 2 ( λg+ ( t) g ( t) ) Γ + + R 2 ( ) ( ) 2 1 ( ) 2 2 B f Af g+ t g t g 2 λ 2 + ( t) g ( t) Γ + + R λ λ PDG reports 347 decay modes of the B -meson: Γ 1 l + ν l anything ( 1.33 ±.28 ) 1 2 Γ 347 ν ν γ < CL=9% And for one decay there are often more than one decay amplitudes ( ) Niels Tuning (2)

21 Describing Mixing Time evolution of B and B can be described by an effective Hamiltonian: M 12 describes B B via off-shell states, e.g. the weak box diagram Γ 12 describes B f B via onshell states, eg. f=π + π - Niels Tuning (21)

22 Box diagram and Δm Inami and Lim, Prog.Theor.Phys.65:297,1981 Δ m = m m = P H P P H P P H PL H H L L Niels Tuning (22)

23 Box diagram and Δm Niels Tuning (23)

24 Box diagram and Δm: Inami-Lim K-mixing C.Gay, B Mixing, hep-ex/1316

25 Box diagram and Δm: Inami-Lim B -mixing C.Gay, B Mixing, hep-ex/1316

26 Box diagram and Δm: Inami-Lim B s -mixing C.Gay, B Mixing, hep-ex/1316

27 Next: measurements of oscillations 1. B mixing: Ø 1987: Argus, first Ø 21: Babar/Belle, precise 2. B s mixing: Ø 26: CDF: first Ø 21: D: anomalous?? Niels Tuning (27)

28 B mixing Niels Tuning (28)

29 B mixing What is the probability to observe a B /B at time t, when it was produced as a B at t=? Calculate observable probility Ψ*Ψ(t) t / τ e prob( B ( t) B ) 1+ cos( Δmt) 2 t / τ e prob( B ( t) B ) 1 cos( Δmt) 2 A simple B decay experiment. ( ) ( ) Given a source B mesons produced in a flavor eigenstate B > You measure the decay time of each meson that decays into a flavor eigenstate (either B or B ) you will find that N N B B B B ( t) ( t) + N N B B B B ( t) ( t) = cos( Δm t) Niels Tuning (29)

30 B mixing: 1987 Argus B oscillations: Phys.Lett.B192:245,1987 First evidence of heavy top à m top >5 GeV Needed to break GIM cancellations NB: loops can reveal heavy particles! Niels Tuning (3)

31 B mixing: t quark GIM: c quark B mixing pointed to the top quark: ARGUS Coll, Phys.Lett.B192:245,1987 K µµ pointed to the charm quark: GIM, Phys.Rev.D2,1285,197 b d d s d b μ μ

32 B mixing: 21 B-factories You can really see this because (amazingly) B mixing has same time scale as decay τ=1.54 ps Δm=.5 ps -1 5/5 point at πδm τ Maximal oscillation at 2πΔm 2τ Actual measurement of B / B oscillation Also precision measurement of Δm! N N B B B B ( t) ( t) + N N B B B B ( t) ( t) = cos( Δm t) Niels Tuning (32)

33 B s mixing Niels Tuning (33)

34 B s mixing: 26 Niels Tuning (34)

35 B s mixing (Δm s ): SM Prediction V CKM = CKM Matrix Vud Vus Vub Vcd Vcs Vcb Vtd Vts V tb Wolfenstein parameterization λ / 2 λ Aλ ( ρ iη) = λ 1 λ / 2 Aλ + O( λ ) 3 2 Aλ (1 ρ iη) Aλ 1 V ts V ts V ts Ratio of frequencies for B and B s 2 Δm V s mbs f BBs ts mbs 2 V = = ξ 2 Δm m f B V m V d Bd 2 Bs 2 Bd Bd td Bd ts td 2 2 V ts ~ λ 2 V td ~λ 3 à Δm s ~ (1/λ 2 )Δm d ~ 25 Δm d V ts ξ = from lattice QCD -.35 Niels Tuning (35)

36 B s mixing (Δm s ): Unitarity Triangle CKM Matrix Unitarity Condition V ud V * ub + V V * + V V * cd cb td tb = V V V 1 td tb = td V V V V cd * * cb ts cd Niels Tuning (36)

37 B s mixing (Δm s ) N () t N () t B B B B N () t + N () t B B B B = cos( Δm t) Δm s =17.77 ±.1(stat)±.7(sys) ps -1 cos(δm s t) hep-ex/694 B s - b t - s - - W W B s s t b B s x - b b s s - g g s s b b x - B s Proper Time t (ps) Niels Tuning (37)

38 B s mixing (Δm s ): New: LHCb N () t N () t B B B B N () t + N () t B B B B = cos( Δm t) B s b s t s W W B s t b B s b s b g s x x s g b s b B s LHCb, arxiv: Niels Tuning (38)

39 B s mixing (Δm s ): New: LHCb N () t N () t B B B B N () t + N () t B B B B = cos( Δm t) Ideal Tagging, resolution LHCb, arxiv: Niels Tuning (39)

40 Mixing à CP violation? NB: Just mixing is not necessarily CP violation! However, by studying certain decays with and without mixing, CP violation is observed Next: Measuring CP violation Finally Niels Tuning (4)

41 Meson Decays Formalism of meson oscillations: P () t Subsequent: decay Niels Tuning (41)

42 Notation: Define A f and λ f Niels Tuning (42)

43 Some algebra for the decay P à f P () t Interference P àf P àp àf Niels Tuning (43)

44 Some algebra for the decay P à f Niels Tuning (44)

45 The master equations ( direct ) Decay Interference Niels Tuning (45)

46 The master equations ( direct ) Decay Interference Niels Tuning (46)

47 Classification of CP Violating effects 1. CP violation in decay 2. CP violation in mixing 3. CP violation in interference Niels Tuning (47)

48 What s the time? Niels Tuning (48)

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