Niels Tuning (1) Topical lectures December 2010 CP violation Hour 3 N. Tuning

Menu TimeTopicSpeaker Monday 13/ – 10.30C, P, CP and the Standard ModelNiels – 11.30CKM matrixNiels – 12.30Flavour mixing in B-decaysNiels – 14.45CP Violation in B-decaysNiels – 15.45CP Violation in B-decaysNiels Niels Tuning (2)

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 (3)

Niels Tuning (4) Dynamics of Neutral B (or K) mesons… No mixing, no decay… No mixing, but with decays… (i.e.: H is not Hermitian!)  With decays included, probability of observing either B 0 or B 0 must go down as time goes by: Time evolution of B 0 and  B 0 can be described by an effective Hamiltonian:

Niels Tuning (5) Describing Mixing… Where to put the mixing term? Now with mixing – but what is the difference between M 12 and  12 ? M 12 describes B 0  B 0 via off-shell states, e.g. the weak box diagram  12 describes B 0  f  B 0 via on- shell states, eg. f=     Time evolution of B 0 and  B 0 can be described by an effective Hamiltonian:

Niels Tuning (6) Solving the Schrödinger Equation Eigenvalues: – Mass and lifetime of physical states: mass eigenstates

Niels Tuning (7) Solving the Schrödinger Equation Eigenvectors: – mass eigenstates

Time evolution Niels Tuning (8) With diagonal Hamiltonian, usual time evolution is obtained:

Niels Tuning (9) B Oscillation Amplitudes For B 0, expect:  ~ 0, |q/p|=1 For an initially produced B 0 or a  B 0 it then follows: (using: with

Niels Tuning (10) Measuring B Oscillations Decay probability B0B0B0B0 B0B0B0B0 Proper Time  For B 0, expect:  ~ 0, |q/p|=1 Examples:

Niels Tuning (11) Compare the mesons: P0P0P0P0 P0P0P0P0 Probability to measure P or P, when we start with 100% P Time  Probability  <><> ΔmΔmx=Δm/Γy=ΔΓ/2Γ K0K s5.29 ns -1 Δm/ Γ S =0.49 ~1 D0D s0.001 fs -1 ~00.01 B0B s0.507 ps ~0 Bs0Bs s17.8 ps ~0.05 By the way, ħ= MeVs x=Δm/ Γ : avg nr of oscillations before decay

Summary (1) Start with Schrodinger equation: Find eigenvalue: Solve eigenstates: Eigenstates have diagonal Hamiltonian: mass eigenstates! (2-component state in P 0 and P 0 subspace)

Summary (2) Two mass eigenstates Time evolution: Probability for |P 0 >  |P 0 > ! Express in M=m H +m L and Δm=m H -m L  Δm dependence

Niels Tuning (14) Let’s summarize … p, q: Δm, Δ Γ: x,y: mixing often quoted in scaled parameters: q,p,M ij, Γ ij related through: with Time dependence (if ΔΓ~0, like for B 0 ) :

Box diagram and Δm

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

Box diagram and Δm: Inami-Lim C.Gay, B Mixing, hep-ex/ B 0 -mixing

Box diagram and Δm: Inami-Lim C.Gay, B Mixing, hep-ex/ B s 0 -mixing

Next: measurements of oscillations 1.B 0 mixing:  1987: Argus, first  2001: Babar/Belle,precise 2.B s 0 mixing:  2006: CDF: first  2010: D0: anomalous ??

B 0 mixing

Niels Tuning (22) B 0 mixing What is the probability to observe a B 0 /B 0 at time t, when it was produced as a B 0 at t=0? –Calculate observable probility *(t) A simple B 0 decay experiment. –Given a source B 0 mesons produced in a flavor eigenstate |B 0 > –You measure the decay time of each meson that decays into a flavor eigenstate (either B 0 orB 0 ) you will find that

B 0 oscillations: –First evidence of heavy top –  m top >50 GeV –Needed to break GIM cancellations B 0 mixing: 1987 Argus Phys.Lett.B192:245,1987

Niels Tuning (24) B 0 mixing: 2001 B-factories You can really see this because (amazingly) B 0 mixing has same time scale as decay – =1.54 ps – m=0.5 ps -1 –50/50 point at m   –Maximal oscillation at 2m  2 Actual measurement of B 0 /B 0 oscillation –Also precision measurement of m!

B s 0 mixing

Niels Tuning (26) B s 0 mixing: 2006

Niels Tuning (27) B s 0 mixing (Δm s ): SM Prediction V ts CKM Matrix Wolfenstein parameterization Ratio of frequencies for B 0 and B s  = from lattice QCD V ts ~ 2 V td ~ 3   Δm s ~ (1/ λ 2 ) Δm d ~ 25 Δm d

Niels Tuning (28) B s 0 mixing (Δm s ): Unitarity Triangle CKM Matrix Unitarity Condition

Niels Tuning (29) B s 0 mixing (Δm s ) Δm s =17.77 ±0.10(stat)±0.07(sys) ps -1 cos(Δm s t) Proper Time t (ps) hep-ex/ BsBs bb b ss st tt W W BsBs g̃BsBs BsBs bb s ss b x x b̃ s̃ g̃

Niels Tuning (30) 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

Meson Decays Formalism of meson oscillations: Subsequent: decay

Notation: Define A f and λ f

Some algebra for the decay P 0  f Interference P0 fP0 fP 0  P 0  f

Some algebra for the decay P 0  f

The ‘master equations’ Interference(‘direct’) Decay

The ‘master equations’ Interference(‘direct’) Decay

Classification of CP Violating effects 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference

Consider f=f : If one amplitude dominates the decay, then A f = A f 3.CP violation in interference Classification of CP Violating effects - Nr. 3: