Particle Physics II CP violation (also known as Physics of Anti-matter ) Lecture 3. N. Tuning. 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 2 Feb: Anti-matter + SM 2) Wed 4 Feb: CKM matrix + Unitarity Triangle 3) Mon 9 Feb: Mixing + Master eqs. + J/ψK s 4) Wed 11 Feb: CP violation in (s) decays (I) 5) Mon 16 Feb: CP violation in (s) decays (II) 6) Wed 18 Feb: CP violation in K decays + Overview 7) Mon 23 Feb: Exam on part 1 (CP violation) Final Mark: if (mark > 5.5) mark = max(exam,.8*exam +.2*homework) else mark = exam In parallel: Lectures on Flavour Physics by prof.dr. R. Fleischer Tuesday + Thrusday Niels Tuning (2)

3 Plan 2 x 45 min 1) Keep track of room! 1) Monday + Wednesday: Start: 9: 9:15 End: 11: Werkcollege: 11: -? Niels Tuning (3)

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5 LSM LKinetic LHiggs LYukawa d I I I LYuk Yi j ( ul, dl ) i d... Rj L g I I g I I u Wd dli WuL 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 LMass d, s, b ms s u, c, t mc c... L L m b b m t t L g 5 g * 5 u W Vij 1 d d WVi 1 u CKM i j j j i R L L L L SM CKM Higgs Mass R Niels Tuning (5)

6 L Charged Currents g I I g I I u W d d W u J W JCC W 2 2 CC Li Li Li Li CC L The charged current term reads: g 1 1 g 1 1 u W d d W u g 5 g * 5 ui WVij 1 d j d j WVi j 1 ui i Vij j j Vji i Under the CP operator this gives: CP g 5 g i * 5 d WVij 1 u u WVij 1 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 (6)

7 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 (7)

8 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 (8)

9 Neutral Meson Oscillations Why? Loop diagram: sensitive to new particles Provides a second amplitude interference effects in -decays b s s b Niels Tuning (9)

10 i Dynamics of Neutral (or K) mesons Time evolution of and can be described by an effective Hamiltonian: t H at () ( t) a( t) b( t) bt () No mixing, no decay No mixing, but with decays (i.e.: H is not Hermitian!) With decays included, probability of observing either or must go down as time goes by: d 2 2 * * at a t b t a t b t bt dt Niels Tuning (1)

11 i Describing Mixing Time evolution of and can be described by an effective Hamiltonian: t H at () ( t) a( t) b( t) bt () Where to put the mixing term? Now with mixing but what is the difference between M 12 and 12? M 12 describes via off-shell states, e.g. the weak box diagram 12 describes f via onshell states, eg. f=p p Niels Tuning (11)

12 Solving the Schrödinger Equation i i M M i t t t i i M12 12 M 2 2 Eigenvalues: Mass and lifetime of physical states: mass eigenstates i i m 2 M12 12 M i i 4 M12 12 M Niels Tuning (12)

13 Solving the Schrödinger Equation i i M M i t t t i i M12 12 M 2 2 Eigenvectors: mass eigenstates p q H p q L i i q p M M 2 2 Niels Tuning (13)

14 Time evolution With diagonal Hamiltonian, usual time evolution is obtained: Niels Tuning (14)

15 Oscillation Amplitudes For an initially produced or a it then follows: (using: t : q t g ( t) g ( t) p p t g ( t) g ( t) q with g () t e For, expect: ~, q/p =1 1 2 p i t i t H L 1 H 2q e 2 L imt t /2 g t e e g imt t /2 t e e mt cos 2 mt isin 2 g t ~ e e 1 1 imt imt 2 2 imt t /2 e e 2 Niels Tuning (15)

16 Decay probability Measuring Oscillations Examples: x q g p g m () t () t X X x m 1 g p g q () t () t m x X X 1 For, expect: ~, q/p =1 t e g t mt 2 2 ~ 1 cos ~ Proper Time Niels Tuning (16)

17 Compare the mesons: Probability to measure P or P, when we start with 1% P P P P P Probability <> Δm x=δm/γ y=δγ/2γ K s 5.29 ns -1 Δm/Γ S =.49 ~1 D s.1 fs -1 ~ s.57 ps ~ s s 17.8 ps ~.5 y the way, ħ= MeVs x=δm/γ: avg nr of oscillations before decay Time Niels Tuning (17)

18 Summary (1) Start with Schrodinger equation: at () () t bt () (2-component state in P and P subspace) Find eigenvalue: Solve eigenstates: p q Eigenstates have diagonal Hamiltonian: mass eigenstates! Niels Tuning (18)

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

20 Summary p, q: H p q L p q Δm, ΔΓ: x,y: mixing often quoted in scaled parameters: i i m 2 M12 12 M i i 4 M12 12 M x m y 2 q,p,m ij,γ ij related through: q M i p M i /2 /2 m t t cos( mt) cos =cos x Time dependence (if ΔΓ~, like for ): q t g ( t) g ( t) p p t g ( t) g ( t) q with imt t /2 g t e e g imt t /2 t e e mt cos 2 mt isin 2 Niels Tuning (2)

21 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? eetopaipaigamma f A 2 f g t g t 2 g t g t f Af g t g 2 t 2 g t g t PDG reports 347 decay modes of the -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 (21)

22 Describing Mixing Time evolution of and can be described by an effective Hamiltonian: M 12 describes via off-shell states, e.g. the weak box diagram 12 describes f via onshell states, eg. f=p p Niels Tuning (22)

23 ox diagram and Δm Inami and Lim, Prog.Theor.Phys.65:297,1981 m m m P H P P H P P H PL H H L L Niels Tuning (23)

24 ox diagram and Δm Niels Tuning (24)

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

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

27 ox diagram and Δm: Inami-Lim s -mixing C.Gay, Mixing, hep-ex/1316

28 Next: measurements of oscillations 1. mixing: 1987: Argus, first 21: abar/elle, precise 2. s mixing: 26: CDF: first 21: D: anomalous?? Niels Tuning (28)

29 mixing Niels Tuning (29)

30 Niels Tuning (3) mixing What is the probability to observe a / at time t, when it was produced as a at t=? Calculate observable probility *(t) A simple decay experiment. Given a source mesons produced in a flavor eigenstate > You measure the decay time of each meson that decays into a flavor eigenstate (either or ) you will find that ) cos( 1 2 ) ) ( ( ) cos( 1 2 ) ) ( ( / / mt e t prob mt e t prob t t ) cos( ) ( ) ( ) ( ) ( t m t N t N t N t N

31 mixing: 1987 Argus oscillations: Phys.Lett.192:245,1987 First evidence of heavy top m top >5 GeV Needed to break GIM cancellations N: loops can reveal heavy particles! Niels Tuning (31)

32 mixing: t quark GIM: c quark mixing pointed to the top quark: ARGUS Coll, Phys.Lett.192:245,1987 K μμ pointed to the charm quark: GIM, Phys.Rev.D2,1285,197 b d d b d s μ μ

33 mixing: 21 -factories You can really see this because (amazingly) mixing has same time scale as decay =1.54 ps m=.5 ps -1 5/5 point at pm Maximal oscillation at 2pm 2 Actual measurement of / oscillation Also precision measurement of m! N N ( t) ( t) N N ( t) ( t) cos( mt) Niels Tuning (33)

34 s mixing Niels Tuning (34)

35 s mixing: 26 Niels Tuning (35)

36 s mixing (Δm s ): SM Prediction V CKM CKM Matrix Vud Vus Vub Vcd Vcs Vcb Vtd Vts V tb Wolfenstein parameterization / 2 A ( i) / 2 A O( ) 3 2 A (1 i) A 1 V ts Ratio of frequencies for and s V ts V ts m m s d m m s d f f 2 s 2 d s d V V ts td 2 2 m m s d 2 V V ts td 2 2 V ts ~ 2 V td ~ 3 Δm s ~ (1/λ 2 )Δm d ~ 25 Δm d V ts = from lattice QCD -.35 Niels Tuning (36)

37 s mixing (Δm s ): Unitarity Triangle CKM Matrix Unitarity Condition V ud V * ub V cd V * cb V td V * tb V V V 1 td tb td V V V V cd * * cb ts cd Niels Tuning (37)

38 cos(δm s t) s mixing (Δm s ) N ( t) N ( t) N ( t) N ( t) cos( mt) Δm s =17.77 ±.1(stat)±.7(sys) ps -1 hep-ex/694 s b s t s W W s t b s b s b g s x x s g b s b s Proper Time t (ps) Niels Tuning (38)

39 s mixing (Δm s ): New: LHCb N ( t) N ( t) N ( t) N ( t) cos( mt) s b s t s W W s t b s b s b g s x x s g b s b s LHCb, arxiv: Niels Tuning (39)

40 Tagging, resolution s mixing (Δm s ): New: LHCb N ( t) N ( t) N ( t) N ( t) cos( mt) Ideal LHCb, arxiv: Niels Tuning (4)

41 Mixing CP violation? N: 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 (41)

42 Meson Decays Formalism of meson oscillations: P () t Subsequent: decay Niels Tuning (42)

43 Notation: Define A f and λ f Niels Tuning (43)

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

45 Some algebra for the decay P f Niels Tuning (45)

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

47 The master equations ( direct ) Decay Interference Niels Tuning (47)

48 Classification of CP Violating effects 1. CP violation in decay 2. CP violation in mixing 3. CP violation in interference Niels Tuning (48)

49 What s the time? Niels Tuning (49)

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