Particle Physics II CP violation (also known as Physics of - PowerPoint PPT Presentation

Particle Physics II – CP violation (also known as “Physics of Anti-matter”) Lecture 6 N. Tuning Niels Tuning (1)

Plan 1) Wed 12 Feb: Anti-matter + SM 2) Mon 17 Feb: CKM matrix + Unitarity Triangle 3) Wed 19 Feb: Mixing + Master eqs. + B 0 → J/ ψ K s 4) Mon 9 Mar: CP violation in B (s) decays (I) 5) Wed 11 Mar: CP violation in B (s) and K decays (II) 6) Mon 16 Mar: Rare decays + Flavour Anomalies 7) Wed 18 Mar: Exam postponed... Final Mark: Ø 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 Ø Niels Tuning (2)

Recap L L L L = + + SM Kinetic Higgs Yukawa + u I ⎛ ⎞ ϕ d I I I L Y ( u , d ) d ... − = + W ⎜ ⎟ i Yuk i j L L Rj ⎜ ⎟ 0 ϕ ⎝ ⎠ g g d I I I I I L u W d d W u ... µ − µ + = γ + γ + Kinetic Li Li Li L i µ µ 2 2 Diagonalize Yukawa matrix Y ij I d d ⎛ ⎞ ⎛ ⎞ – Mass terms ⎜ ⎟ ⎜ ⎟ I s V s → ⎜ ⎟ CKM ⎜ ⎟ – Quarks rotate ⎜ ⎟ ⎜ I ⎟ b b – Off diagonal terms in charged current couplings ⎝ ⎠ ⎝ ⎠ m d m u ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ d u L ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ( ) ( ) g g g g d s b , , m s u c t , , m c ... − = + + u Mass ⎜ s ⎟ ⎜ ⎟ ⎜ c ⎟ ⎜ ⎟ L L ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ m b m t W ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ b t R R g g ( ) ( ) L 5 * 5 u W V 1 d d W V 1 u ... µ − µ + = γ − γ + γ − γ + CKM i ij j j i j i µ µ 2 2 d,s,b L L L L = + + SM CKM Higgs Mass Niels Tuning (4)

Why bother with all this? • CKM matrix has origin in L Yukawa Ø Intricately related to quark massed… • Both quark masses and CKM elements show intriguing hierarchy • There is a whole industry of theorist trying to postdict the CKM matrix based on arguments on the mass matrix in L Yukawa … Niels Tuning (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 W d,s,b Niels Tuning (6)

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)

Meson Decays • Formalism of meson oscillations : 0 ( ) P t • Subsequent: decay P 0 à f P 0 à P 0 à f Interference ( ‘ direct ’ ) Decay Interference

Classification of CP Violating effects 1. CP violation in decay 2. CP violation in mixing 3. CP violation in interference Niels Tuning (9)

Classification of CP Violating effects 1. CP violation in decay B K 0 + − Example: → π B K 0 − + → π 2. CP violation in mixing Example: 3. CP violation in interference Example: B 0 → J/ ψ K s N N − 0 0 B f B f → → A ( t ) sin( 2 ) sin( mt ) = = β Δ CP N N + 0 B f 0 → B f → Niels Tuning (10)

Remember! Necessary ingredients for CP violation: 1) Two (interfering) amplitudes 2) Phase difference between amplitudes – one CP conserving phase ( ‘ strong ’ phase) – one CP violating phase ( ‘ weak ’ phase) Niels Tuning (11)

Remember! Niels Tuning (12)

CKM Angle measurements from B d,u decays • Sources of phases in B d,u amplitudes* b � u γ Amplitude Rel. Magnitude Weak phase -i e 1 1 ⎛ ⎞ b à c Dominant 0 ⎜ ⎟ 1 1 1 b à u Suppressed γ ⎜ ⎟ t à d ( x2, mixing) Time dependent -i β 2 β ⎜ e ⎟ 1 1 ⎝ ⎠ *In Wolfenstein phase convention. t � d • The standard techniques for the angles: B 0 mixing + single b � u decay B 0 mixing + single b � c decay Interfere b � c and b � u in B ± decay. Niels Tuning (13)

Classification of CP Violating effects 1. CP violation in decay 2. CP violation in mixing 3. CP violation in interference Niels Tuning (14)

Next… Something completely different? No, just K 1. CP violation in decay 2. CP violation in mixing 3. CP violation in interference

Kaons… • Different notation: confusing! K 1 , K 2 , K L , K S , K + , K - , K 0 • Smaller CP violating effects Ø But historically important! Concepts same as in B-system, so you have a chance to understand… § Niels Tuning (16)

Kaons… • Different notation: confusing! = K 1 , K 2 , K L , K S , K + , K - , K 0 CP eigenstates • Smaller CP violating effects Ø But historically important! Concepts same as in B-system, so you have a chance to understand… § Niels Tuning (17)

Kaons… • Different notation: confusing! K 1 , K 2 , K L , K S , K + , K - , K 0 Mass/lifetime eigenstates • Smaller CP violating effects Ø But historically important! Concepts same as in B-system, so you have a chance to understand… § Niels Tuning (18)

Kaons… • Different notation: confusing! K 1 , K 2 , K L , K S , K + , K - , K 0 Flavour eigenstates • Smaller CP violating effects Ø But historically important! Concepts same as in B-system, so you have a chance to understand… § Niels Tuning (19)

Neutral kaons – 60 years of history 1947 : First K 0 observation in cloud chamber ( “ V particle ” ) 1955 : Introduction of Strangeness ( Gell-Mann & Nishijima ) K 0 , K 0 are two distinct particles ( Gell-Mann & Pais ) … the θ 0 must be considered as a "particle mixture" exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes, and that no more than half of all θ 0 's undergo the familiar decay into two pions. 1956 : Parity violation observation of long lived K L ( BNL Cosmotron ) 1960 : Δ m = m L -m S measured from regeneration 1964 : Discovery of CP violation ( Cronin & Fitch ) 1970 : Suppression of FCNC, K L à µµ - GIM mechanism/charm hypothesis 1972 : 6-quark model; CP violation explained in SM ( Kobayashi & Maskawa ) 1992-2000 : K 0 , K 0 time evolution, decays, asymmetries ( CPLear ) 1999-2003 : Direct CP violation measured: ε ’ / ε ≠ 0 ( KTeV and NA48 ) Niels Tuning (20) From G.Capon

Intermezzo: CP eigenvalue Remember: • – P 2 = 1 (x à -x à x) – C 2 = 1 ( ψ � ψ � ψ ) – è CP 2 =1 CP | f > = ± | f > • Knowing this we can evaluate the effect of CP on the K 0 • CP| � K 0 > = -1| K 0 > CP| K 0 > = -1| � K 0 > Mass/Lifetime eigenstates: almost CP eigenstates! • |K S > = p| K 0 > +q|K 0 > |K L > = p| K 0 > - q|K 0 > ( S( K )=0 � L( ππ )=0 ) |K s > (CP=+1) → π π (CP= (-1)(-1)(-1) l=0 =+1) |K L > (CP=-1) → π π π (CP = (-1)(-1)(-1)(-1) l=0 = -1) Niels Tuning (21)

Decays of neutral kaons • Neutral kaons is the lightest strange particle à it must decay through the weak interaction • If weak force conserves CP then – decay products of K 1 can only be a CP=+1 state , i.e. |K 1 > (CP=+1) → π π (CP= (-1)(-1)(-1) l=0 =+1) ( S( K )=0 � L( ππ )=0 ) – decay products of K 2 can only be a CP=-1 state, i.e. |K 2 > (CP=-1) → π π π (CP = (-1)(-1)(-1)(-1) l=0 = -1) • You can use neutral kaons to precisely test that the weak force preserves CP (or not) – If you (somehow) have a pure CP=-1 K 2 state and you observe it decaying into 2 pions (with CP=+1) then you know that the weak decay violates CP… Niels Tuning (22)

Designing a CP violation experiment • How do you obtain a pure ‘ beam ’ of K 2 particles? – It turns out that you can do that through clever use of kinematics • Exploit that decay of K into two pions is much faster than decay of K into three pions – Related to fact that energy of pions are large in 2-body decay – τ 1 = 0.89 x 10 -10 sec – τ 2 = 5.2 x 10 -8 sec (~600 times larger!) • Beam of neutral Kaons automatically becomes beam of |K 2 > as all |K 1 > decay very early on… Pure K 2 beam after a while! K 1 decay early (into ππ ππ ) (all decaying into πππ ) ! Initial K 0 beam Niels Tuning (23)

The Cronin & Fitch experiment Essential idea: Look for (CP violating) K 2 à ππ decays 20 meters away from K 0 production point Decay of K 2 into 3 pions Incoming K 2 beam If you detect two of the three pions of a K 2 � πππ πππ decay they will generally not point along the beam line Niels Tuning (24)

The Cronin & Fitch experiment Essential idea: Look for K 2 à ππ decays 20 meters away from K 0 production point Decay pions Incoming K2 beam If K 2 decays into two pions instead of three both the reconstructed direction should be exactly along the beamline (conservation of momentum in K 2 � ππ ππ decay) Niels Tuning (25)

The Cronin & Fitch experiment Essential idea: Look for K 2 à ππ decays 20 meters away from K 0 production point Decay pions K 2 � ππ ππ decays Incoming K 2 beam (CP Violation!) K 2 � πππ πππ decays Result: an excess of events at Θ =0 degrees! • CP violation, because K 2 (CP=-1) Note scale: 99.99% of K � πππ decays changed into K 1 (CP=+1 ) are left of plot boundary Niels Tuning (26)