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

Plan Mon 5 Feb: Anti-matter + SM Wed 7 Feb: CKM matrix + Unitarity Triangle Mon 26 Feb: Mixing + Master eqs. + B0J/ψKs Wed 28 Feb: CP violation in B(s) decays (I) Mon 12 Mar: CP violation in B(s) and K decays (II) Wed 14 Mar: Rare decays + Flavour Anomalies Wed 21 Mar: Exam Final Mark: if (mark > 5.5) mark = max(exam, 0.85*exam + 0.15*homework) else mark = exam In parallel: Lectures on Flavour Physics by prof.dr. R. Fleischer Niels Tuning (2)

Recap uI W dI u W d,s,b Diagonalize Yukawa matrix Yij Mass terms Quarks rotate Off diagonal terms in charged current couplings u d,s,b W Replace the derivative with the covariant derivative introducing the force carriers: gluons, weak vector bosons and photon. The constants g_s, g and g’ are the corresponding coupling constants of the gauge particles. Niels Tuning (4) 4

Charged Currents In general the charged current term is CP violating The charged current term reads: Under the CP operator this gives: (Together with (x,t) -> (-x,t)) A comparison shows that CP is conserved only if Vij = Vij* In general the charged current term is CP violating Niels Tuning (5) 5

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): u d,s,b W Niels Tuning (6)

This was theory, now comes experiment We already saw how the moduli |Vij| 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)

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

Dynamics of Neutral B (or K) mesons… Time evolution of B0 and B0 can be described by an effective Hamiltonian: No mixing, no decay… No mixing, but with decays… (i.e.: H is not Hermitian!) With decays included, probability of observing either B0 or B0 must go down as time goes by: Niels Tuning (9)

Describing Mixing… Time evolution of B0 and B0 can be described by an effective Hamiltonian: Where to put the mixing term? Now with mixing – but what is the difference between M12 and G12? M12 describes B0  B0 via off-shell states, e.g. the weak box diagram G12 describes B0fB0 via on-shell states, eg. f=p+p- Niels Tuning (10)

Solving the Schrödinger Equation Eigenvalues: Mass and lifetime of physical states: mass eigenstates The physical particles are the eigenstates of the Hamiltonian. Solve the eigenvalues lambda by putting det (H11-lambda*I) = 0 This you can not see here. You just have to sit down and *do* it. Niels Tuning (11)

Solving the Schrödinger Equation Eigenvectors: mass eigenstates The physical particles are the eigenstates of the Hamiltonian. Solve the eigenvalues lambda by putting det (H11-lambda*I) = 0 This you can not see here. You just have to sit down and *do* it. Niels Tuning (12)

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

B Oscillation Amplitudes For an initially produced B0 or a B0 it then follows: (using: with For B0, expect: DG ~ 0, |q/p|=1 These formula’s just follow from substitution. No magic. Note that in the last step g_ gets a 90 degree phase ! ~ Niels Tuning (14)

Measuring B Oscillations For B0, expect: DG ~ 0, |q/p|=1 Examples: ~ B0B0 Decay probability Use cos^2 (dmt/2) = 0.5 * (1 + cos(dmt)) > Proper Time  Niels Tuning (15)

Probability to measure P or P, when we start with 100% P Compare the mesons: Probability to measure P or P, when we start with 100% P P0P0 P0P0 <> Δm x=Δm/Γ y=ΔΓ/2Γ K0 2.6 10-8 s 5.29 ns-1 Δm/ΓS=0.49 ~1 D0 0.41 10-12 s 0.001 fs-1 ~0 0.01 B0 1.53 10-12 s 0.507 ps-1 0.78 Bs0 1.47 10-12 s 17.8 ps-1 12.1 ~0.05 Probability  By the way, ħ=6.58 10-22 MeVs x=Δm/Γ: avg nr of oscillations before decay Time  Niels Tuning (16)

Summary (1) Start with Schrodinger equation: Find eigenvalue: Solve eigenstates: Eigenstates have diagonal Hamiltonian: mass eigenstates! (2-component state in P0 and P0 subspace) Niels Tuning (17)

Summary (2) Two mass eigenstates Time evolution: Probability for |P0>  |P0> ! Express in M=mH+mL and Δm=mH-mL  Δm dependence

Time dependence (if ΔΓ~0, like for B0): Summary p, q: Δm, ΔΓ: x,y: mixing often quoted in scaled parameters: q,p,Mij,Γij related through: Time dependence (if ΔΓ~0, like for B0): with Niels Tuning (19)

Personal impression: People think it is a complicated part of the Standard Model (me too:-). Why? Non-intuitive concepts? Imaginary phase in transition amplitude, T ~ eiφ Different bases to express quark states, d’=0.97 d + 0.22 s + 0.003 b Oscillations (mixing) of mesons: |K0> ↔ |K0> Complicated calculations? Many decay modes? “Beetopaipaigamma…” PDG reports 347 decay modes of the B0-meson: Γ1 l+ νl anything ( 10.33 ± 0.28 ) × 10−2 Γ347 ν ν γ <4.7 × 10−5 CL=90% And for one decay there are often more than one decay amplitudes… Niels Tuning (20)

Describing Mixing Time evolution of B0 andB0 can be described by an effective Hamiltonian: M12 describes B0  B0 via off-shell states, e.g. the weak box diagram G12 describes B0fB0 via on-shell states, eg. f=p+p- Niels Tuning (21)

Box diagram and Δm Inami and Lim, Prog.Theor.Phys.65:297,1981 Niels Tuning (22)

Box diagram and Δm Niels Tuning (23)

Box diagram and Δm: Inami-Lim K-mixing C.Gay, B Mixing, hep-ex/0103016

Box diagram and Δm: Inami-Lim B0-mixing C.Gay, B Mixing, hep-ex/0103016

Box diagram and Δm: Inami-Lim Bs0-mixing C.Gay, B Mixing, hep-ex/0103016

Next: measurements of oscillations B0 mixing: 1987: Argus, first 2001: Babar/Belle, precise Bs0 mixing: 2006: CDF: first 2010: D0: anomalous ?? Niels Tuning (27)

B0 mixing Niels Tuning (28)

B0 mixing What is the probability to observe a B0/B0 at time t, when it was produced as a B0 at t=0? Calculate observable probility Y*Y(t) A simple B0 decay experiment. Given a source B0 mesons produced in a flavor eigenstate |B0> You measure the decay time of each meson that decays into a flavor eigenstate (either B0 orB0) you will find that Exercise idea: compare tau, dm of K0 and B0 Niels Tuning (29) 29

B0 mixing: 1987 Argus B0 oscillations: First evidence of heavy top  mtop>50 GeV Needed to break GIM cancellations NB: loops can reveal heavy particles! Phys.Lett.B192:245,1987 Niels Tuning (30)

B0 mixing: t quark GIM: c quark B0 mixing pointed to the top quark: K0→μμ pointed to the charm quark: ARGUS Coll, Phys.Lett.B192:245,1987 GIM, Phys.Rev.D2,1285,1970 … d s μ b d

B0 mixing: 2001 B-factories You can really see this because (amazingly) B0 mixing has same time scale as decay t=1.54 ps Dm=0.5 ps-1 50/50 point at pDm  t Maximal oscillation at 2pDm  2t Actual measurement of B0/B0 oscillation Also precision measurement of Dm! Exercise idea: compare tau, dm of K0 and B0 Niels Tuning (32) 32

Bs0 mixing Niels Tuning (33)

Bs0 mixing: 2006 Niels Tuning (34) 34

Bs0 mixing (Δms): SM Prediction CKM Matrix Wolfenstein parameterization Vts Ratio of frequencies for B0 and Bs Vts ~ 2 Vtd ~3  Δms ~ (1/λ2)Δmd ~ 25 Δmd  = 1.210 +0.047 from lattice QCD -0.035 Niels Tuning (35)

Bs0 mixing (Δms): Unitarity Triangle CKM Matrix Unitarity Condition Niels Tuning (36) 36

Bs0 mixing (Δms) cos(Δmst) Proper Time t (ps) Δms=17.77 ±0.10(stat)±0.07(sys) ps-1 hep-ex/0609040 - - Bs b s t W g̃ x b̃ s̃ - - cos(Δmst) - - - Proper Time t (ps) Niels Tuning (37)

Bs0 mixing (Δms): New: LHCb t W g̃ x b̃ s̃ LHCb, arXiv:1304.4741 Niels Tuning (38)

Bs0 mixing (Δms): New: LHCb Ideal resolution Tagging, Acceptance LHCb, arXiv:1304.4741 Niels Tuning (39)

Mixing  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 (40)

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

Notation: Define Af and λf Niels Tuning (42)

Some algebra for the decay P0  f Interference P0 f P0P0 f Niels Tuning (43)

Some algebra for the decay P0  f Niels Tuning (44)

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

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

Classification of CP Violating effects CP violation in decay CP violation in mixing CP violation in interference Niels Tuning (47)

What’s the time? Niels Tuning (48)