Physics of Antimatter Lecture 6 N Tuning Niels

Physics of Anti-matter Lecture 6 N. Tuning Niels Tuning (1)

Plan 1) Mon 3 Feb: Anti-matter + SM 2) Wed 5 Feb: CKM matrix + Unitarity Triangle 3) Mon 10 Feb: Mixing + Master eqs. + B 0 J/ψKs 4) Wed 12 Feb: CP violation in B(s) decays (I) 5) Mon 17 Feb: CP violation in B(s) decays (II) 6) Wed 19 Feb: CP violation in K decays + Overview 7) Mon 24 Feb: Mini-project (MSc. V. Syropoulos) Ø Wed 26 Feb: Exam Ø Final Mark: 2/3*Exam + 1/6*Homework + 1/6*Mini project Ø In March: 7 Lectures on Flavour Physics by prof. dr. R. Fleischer Niels Tuning (2)

Recap W u. I d. I Diagonalize Yukawa matrix Yij – Mass terms – Quarks rotate – Off diagonal terms in charged current couplings W u d, s, b 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): W u d, s, b 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)

Meson Decays • Formalism of meson oscillations: • Subsequent: decay P 0 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 Example: 2. CP violation in mixing Example: 3. CP violation in interference Example: B 0→J/ψKs 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) 2 amplitudes 2 phases Niels Tuning (11)

Remember! 2 amplitudes 2 phases Niels Tuning (12)

CKM Angle measurements from Bd, u decays • Sources of phases in Bd, u amplitudes* Amplitude Rel. Magnitude b c Dominant 0 b u Suppressed γ t d (x 2, mixing) Time dependent b u Weak phase 2β *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)

Other ways of measuring sin 2β • Need interference of b c transition and B 0 – B 0 mixing • Let’s look at other b c decays to CP eigenstates: All these decay amplitudes have the same phase (in the Wolfenstein parameterization) so they (should) measure the same CP violation Niels Tuning (15)

CP in interference with B φKs • Same as B 0 J/ψKs : • Interference between B 0→f. CP and B 0→f. CP – For example: B 0→J/ΨKs and B 0→ J/ΨKs – For example: B 0→φKs and B 0→ φKs Amplitude 1 Amplitude 2 + e-iφ Niels Tuning (16)

CP in interference with B φKs: what is different? ? • Same as B 0 J/ψKs : • Interference between B 0→f. CP and B 0→f. CP – For example: B 0→J/ΨKs and B 0→ J/ΨKs – For example: B 0→φKs and B 0→ φKs Amplitude 1 Amplitude 2 + e-iφ Niels Tuning (17)

Penguin diagrams Nucl. Phys. B 131: 285 1977 Niels Tuning (18)

Penguins? ? The original penguin: A real penguin: Our penguin: Niels Tuning (19)

Funny Flying Penguin Dead Penguin Super Penguin: Penguin T-shirt: Niels Tuning (20)

The “b-s penguin” B 0 J/ψKS Asymmetry in SM B 0 φKS “Penguin” diagram: ΔB=1 … unless there is new physics! s b μ μ • New particles (also heavy) can show up in loops: – Can affect the branching ratio – And can introduce additional phase and affect the asymmetry Niels Tuning (21)

Hint for new physics? ? d B d b s c c • Ks J/ψ sin 2βb ccs = 0. 68 ± 0. 03 sin 2β d d B ? b ~~ g, b, …? • t s s s Ks φ sin 2βpeng = 0. 52 ± 0. 05 sin 2βpeng S. T’Jampens, CKM fitter, Beauty 2006 Niels Tuning (22)

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, KL, KS, 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 (24)

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 KL (BNL Cosmotron) 1960 : Dm = m. L-m. S measured from regeneration 1964 : Discovery of CP violation (Cronin & Fitch) 1970 : Suppression of FCNC, KL - 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: e’/e ≠ 0 (KTe. V and NA 48) From G. Capon Niels Tuning (25)

Intermezzo: CP eigenvalue • Remember: – P 2 = 1 (x -x x) – C 2 = 1 (ψ ψ ψ ) – 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 > • CP eigenstates: |KS> = p| K 0> +q| K 0> |KL> = p| K 0> - q| K 0> ( S(K)=0 L(ππ)=0 ) |Ks> (CP=+1) |KL> (CP=-1) → p p (CP= (-1)(-1)l=0 =+1) → p p p (CP = (-1)(-1)l=0 = -1) Niels Tuning (26)

Decays of neutral kaons • Neutral kaons is the lightest strange particle 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) →pp (CP= (-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) →ppp (CP = (-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 (27)

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 – 1 = 0. 89 x 10 -10 sec – 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… K 1 decay early (into pp) Pure K 2 beam after a while! (all decaying into πππ) ! Initial K 0 beam Niels Tuning (28)

The Cronin & Fitch experiment Essential idea: Look for (CP violating) K 2 pp 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 ppp decay they will generally not point along the beam line Niels Tuning (29)

The Cronin & Fitch experiment Essential idea: Look for K 2 pp decays 20 meters away from K 0 production point Decay pions Incoming K 2 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 pp decay) Niels Tuning (30)

The Cronin & Fitch experiment Essential idea: Look for K 2 pp decays 20 meters away from K 0 production point Decay pions Incoming K 2 beam Result: an excess of events at Q=0 degrees! • CP violation, because K 2 (CP=-1) changed into K 1 (CP=+1) K 2 pp decays (CP Violation!) K 2 ppp decays Note scale: 99. 99% of K ppp decays are left of plot boundary Niels Tuning (31)

Nobel Prize 1980 "for the discovery of violations of fundamental symmetry principles in the decay of neutral K mesons" The discovery emphasizes, once again, that even almost self evident principles in science cannot be regarded fully valid until they have been critically examined in precise experiments. James Watson Cronin 1/2 of the prize University of Chicago, IL, USA b. 1931 Val Logsdon Fitch 1/2 of the prize Princeton University Princeton, NJ, USA b. 1923 Niels Tuning (32)

Cronin & Fitch – Discovery of CP violation • Conclusion: weak decay violates CP (as well as C and P) – But effect is tiny! (~0. 05%) – Maximal (100%) violation of P symmetry easily follows from absence of right-handed neutrino, but how would you construct a physics law that violates a symmetry just a tiny little bit? • Results also provides us with convention-free definition of matter vs anti-matter. – If there is no CP violation, the K 2 decays in equal amounts to p+ e- e (a) p- e+ e (b) – Just like CPV introduces K 2 ππ decays, it also introduces a slight asymmetry in the above decays (b) happens more often than (a) – “Positive charge is the charged carried by the lepton preferentially produced in the decay of the long-lived neutral K meson” Niels Tuning (33)

Intermezzo: Regeneration • Different cross section for σ(p K 0) than σ(p K 0) o Elastic scattering: same o Charge exchange : same o Hyperon production: more for K 0 ! strong interactions: must conserve strangeness leave little free energy – unlikely! • What happens when KL-beam hits a wall ? ? • Then admixture changes…: |KL> = p| K 0> - q| K 0> Regeneration of KS ! • Could fake CP violation due to KS→π+π-… Niels Tuning (34)

KS and KL Usual (historical) notation in kaon physics: Modern notation used in B physics: Regardless of notation: KL and KS are not orthogonal: Niels Tuning (35)

Three ways to break CP; e. g. in K 0→ π+π- Niels Tuning (36)

Classification of CP Violating effects 1. CP violation in decay 2. CP violation in mixing 3. CP violation in interference Niels Tuning (37)

Time evolution Niels Tuning (38)

B-system 2. CP violation in mixing K-system CPLEAR, Phys. Rep. 374(2003) 165 -270 Ba. Bar, (2002) CPLear (2003)

B-system 2. CP violation in mixing Ba. Bar, (2002) K-system NA 48, (2001) L(e) = (3. 317 0. 070 0. 072) 10 -3 Niels Tuning (40)

B-system 3. Time-dependent CP asymmetry B 0→J/ψKs Ba. Bar (2002) Niels Tuning (41)

B-system 3. Time-dependent CP asymmetry K-system K 0→π-π+ B 0→J/ψKs ~50/50 decay as Ks and KL + interference! K 0 _ K 0 p+p- rate asymmetry Ba. Bar (2002) CPLear (PLB 1999)

The Quest for Direct CP Violation Indirect CP violation in the mixing: Direct CP violation in the decay: ’ A fascinating 30 -year long enterprise: “Is CP violation a peculiarity of kaons? Is it induced by a new superweak interaction? ” Niels Tuning (43)

B system 1. Direct CP violation B 0→K+π- B 0→K-π+ K system K 0→π-π+ K 0→π0π0 Different CP violation for the two decays Some CP violation in the decay! ε’≠ 0 Niels Tuning (44)

Niels Tuning (45)

Hints for new physics? 1) sin 2β≠sin 2β ? d B d b ~~ g, b, …? t s s s Ks φ 2) ACP (B 0 K+π-)≠ACP (B+ K+π0) ? 4 th generation, t’ ? 3) βs≠ 0. 04 ? 4) P(B 0 s→ B 0 s) ≠ P(B 0 s← B 0 s) Niels Tuning (46)

Present knowledge of unitarity triangle Niels Tuning (47)

“The” Unitarity triangle • We can visualize the CKM-constraints in (r, h) plane

Present knowledge of unitarity triangle

I) sin 2β

I) sin 2β

II) ε and the unitarity triangle: box diagram CP violation in mixing

II) ε and the unitarity triangle: box diagram

II) ε and the unitarity triangle: box diagram Im(z 2)=Im( (Rez+i. Imz)2)=2 Rez. Imz

II) ε and the unitarity triangle ρ Niels Tuning (55)

III. ) |Vub| / |Vcb| • Measurement of Vub – Compare decay rates of B 0 D*-l+ and B 0 p-l+ – Ratio proportional to (Vub/Vcb)2 – |Vub/Vcb| = 0. 090 ± 0. 025 – Vub is of order sin(qc)3 [= 0. 01]

IV. ) Δmd and Δms • Δm depends on Vtd • Vts constraints hadronic uncertainties

Present knowledge of unitarity triangle Niels Tuning (58)

Hints for new physics? 1) sin 2β≠sin 2β ? d B d b ~~ g, b, …? t s s s Ks φ 2) ACP (B 0 K+π-)≠ACP (B+ K+π0) ? 4 th generation, t’ ? 3) βs≠ 0. 04 ? 4) P(B 0 s→ B 0 s) ≠ P(B 0 s← B 0 s) Niels Tuning (59)

More hints for new physics? 5) εK ? § Treatment of errors… § Input from Lattice QCD BK § Strong dependence on Vcb Niels Tuning (60)

More hints for new physics? 6) Vub: 2. 9σ ? ? BR(B+→τυ)=1. 68 ± 0. 31 10 -4 Predicted: 0. 764± 0. 087 10 -4 (If f. Bd off, then BBd needs to be off too, to make Δmd agree) ? |Vub| avg from semi-lep |Vub| from fit From: H. Lacker, and A. Buras, Beauty 2011, Amsterdam |Vub| from B→τν Niels Tuning (61)

A. Buras, Beauty 2011: Niels Tuning (62)

A. Buras, Beauty 2011: Niels Tuning (63)

Standard Model: 25 free parameters Elementary particle masses (Me. V): me 0. 51099890 m 105. 658357 m 1777. 0 m e < 0. 000003 m < 0. 19 m < 18. 2 mu 3 mc 1200 mt 174000 md 7 ms 120 mb 4300 Electro-weak interaction: e(0) m. W m. Z m. HH 1/137. 036 80. 42 Ge. V 91. 188 Ge. V >114. 3 Ge. V CMS Strong interaction: s(m. Z) 0. 117 quark mixing (4) u’ d’ = s’ Vijq u d s neutrino mixing (4) e = Vijl 1 2 3 LHCb Niels Tuning (64)

The CKM matrix • Couplings of the charged current: b Wg. Vub u • Wolfenstein parametrization: • Magnitude: • Complex phases: Niels Tuning (65)

The CKM matrix • Couplings of the charged current: 1) 2) • Wolfenstein parametrization • Magnitude: 3) • Complex phases: Niels Tuning (66)

The CKM matrix • Couplings of the charged current: • Wolfenstein parametrization: • Magnitude: • Complex phases:

Remember the following: • CP violation is discovered in the K-system • CP violation is naturally included if there are 3 generations or more – 3 x 3 unitary matrix has 1 free complex parameter • CP violation manifests itself as a complex phase in the CKM matrix • The CKM matrix gives the strengths and phases of the weak couplings • CP violation is apparent in experiments/processes with 2 interfering amplitudes with different strong and weak phase – Often using “mixing” to get the 2 nd decay process • Flavour physics is powerful for finding new physics in loops! – Complementary to Atlas/CMS Niels Tuning (68)

Remember the following: • CP violation is discovered in the K-system • CP violation is naturally included if there are 3 generations or more – 3 x 3 unitary matrix has 1 free complex parameter • CP violation manifests itself as a complex phase in the CKM matrix • The CKM matrix gives the strengths and phases of the weak couplings • CP violation is apparent in experiments/processes with 2 interfering amplitudes with different strong and weak phase – Often using “mixing” to get the 2 nd decay process • Flavour physics is powerful for finding new physics in loops! – Complementary to Atlas/CMS Thank you Niels Tuning (69)

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 ~ eiφ § Different bases to express quark states, d’=0. 97 d + 0. 22 s + 0. 003 b § Oscillations (mixing) of mesons: |K 0> ↔ | K 0> 2) Complicated calculations? 3) Many decay modes? “Beetopaipaigamma…” – PDG reports 347 decay modes of the B 0 -meson: • Γ 1 l+ νl anything • Γ 347 ν ν γ ( 10. 33 ± 0. 28 ) × 10− 2 <4. 7 × 10− 5 CL=90% – And for one decay there are often more than one decay amplitudes… Niels Tuning (70)

Backup Niels Tuning (71)

SLAC: LINAC + PEPII Linac HER LER PEP-II accelerator schematic and tunnel view

Coherent Time Evolution at the (4 S) PEP-2 (SLAC) B-Flavor Tagging Exclusive B Meson Reconstruction Vertexing & Time Difference Determination Niels Tuning (73)

LHCb: the Detector • High cross section • LHC energy • • Large acceptance • • p. T of B-hadron • η of B-hadron Large boost of b’s Trigger • • b’s produced forward Small multiple scattering • • Bs produced in large quantities ↓ Low p. T Leptons + hadrons (MUON, CALO) Particle identification (RICH)

Measuring the Quark Couplings W q Vq’q • Measure the CKM triangle to unprecedented precision • Measure very small Branching Ratios q’ The well known triangle: β CP phases: γ α γ β Niels Tuning (75)