Particle Physics II CP violation (also known as Physics of Anti-matter ) Lecture 3 N. Tuning Niels Tuning (1)
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)
Plan 2 x 45 min 1) Keep track of room! 1) Monday + Wednesday: Start: 9: 9:15 End: 11: Werkcollege: 11: -? Niels Tuning (3)
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... 2 2 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... 2 2 CKM i j j j i R L L L L SM CKM Higgs Mass R Niels Tuning (5)
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 2 2 2 2 2 2 g 5 g * 5 ui WVij 1 d j d j WVi j 1 ui 2 2 5 5 5 5 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)
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)
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)
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)
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)
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)
Solving the Schrödinger Equation i i M M12 12 2 2 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 12 12 2 2 i i 4 M12 12 M 12 12 2 2 Niels Tuning (12)
Solving the Schrödinger Equation i i M M12 12 2 2 i t t t i i M12 12 M 2 2 Eigenvectors: mass eigenstates p q H p q 12 12 12 12 L i i q p M M 2 2 Niels Tuning (13)
Time evolution With diagonal Hamiltonian, usual time evolution is obtained: Niels Tuning (14)
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)
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)
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 2.6 1-8 s 5.29 ns -1 Δm/Γ S =.49 ~1 D.41 1-12 s.1 fs -1 ~.1 1.53 1-12 s.57 ps -1.78 ~ s 1.47 1-12 s 17.8 ps -1 12.1 ~.5 y the way, ħ=6.58 1-22 MeVs x=δm/γ: avg nr of oscillations before decay Time Niels Tuning (17)
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)
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
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 12 12 2 2 i i 4 M12 12 M 12 12 2 2 x m y 2 q,p,m ij,γ ij related through: q M i p M i 12 12 12 12 /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)
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 2 2 2 f A 2 f g t g t 2 g t g t 2 2 1 2 2 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 <4.7 1 5 CL=9% And for one decay there are often more than one decay amplitudes Niels Tuning (21)
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)
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)
ox diagram and Δm Niels Tuning (24)
ox diagram and Δm: Inami-Lim K-mixing C.Gay, Mixing, hep-ex/1316
ox diagram and Δm: Inami-Lim -mixing C.Gay, Mixing, hep-ex/1316
ox diagram and Δm: Inami-Lim s -mixing C.Gay, Mixing, hep-ex/1316
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)
mixing Niels Tuning (29)
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
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)
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
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)
s mixing Niels Tuning (34)
s mixing: 26 Niels Tuning (35)
s mixing (Δm s ): SM Prediction V CKM CKM Matrix Vud Vus Vub Vcd Vcs Vcb Vtd Vts V tb Wolfenstein parameterization 2 3 1 / 2 A ( i) 2 2 4 1 / 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 = 1.21 +.47 from lattice QCD -.35 Niels Tuning (36)
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)
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)
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:134.4741 Niels Tuning (39)
Tagging, resolution s mixing (Δm s ): New: LHCb N ( t) N ( t) N ( t) N ( t) cos( mt) Ideal LHCb, arxiv:134.4741 Niels Tuning (4)
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)
Meson Decays Formalism of meson oscillations: P () t Subsequent: decay Niels Tuning (42)
Notation: Define A f and λ f Niels Tuning (43)
Some algebra for the decay P f P () t Interference P f P P f Niels Tuning (44)
Some algebra for the decay P f Niels Tuning (45)
The master equations ( direct ) Decay Interference Niels Tuning (46)
The master equations ( direct ) Decay Interference Niels Tuning (47)
Classification of CP Violating effects 1. CP violation in decay 2. CP violation in mixing 3. CP violation in interference Niels Tuning (48)
What s the time? Niels Tuning (49)