1. CP VIOLATION (B-factories) P. Pakhlov (ITEP)

2. 2 The major experiments to explore CP Kaon system: Indirect CP Violation Direct CP Violation Not useful to constrain CKM matrix parameters (too large hadronic uncertainties) Rare K decays to πνν Theoretically very clean modes, but a nightmare for experimentalists: Br ~ 10 –11, two neitrinos. K + → π + νν K L → π 0 νν

3. 3 The major experiments to explore CP D-meson system? Tiny CP violation, due to degenerated unitarity triangle and GIM/CKM suppression EDM of n, p, nuclei? The present ULs are much higher than the SM predictions (however, they are close to many models beyond SM) B-meson system? Large CP violation, Many independent measurements, Simple hadron dynamics, because of heavy b-quark Hadronic uncertainties can be estimated or cancel in appropriate observables. Rare η decays? UL for CP violation in strong interaction Difficult to observe the SM effect, test physics beyond the SM

4. 4 B-mesons What are B mesons? B 0 = d b B + = u b J PC = 0 – + τ = 1.5 × 10 -12 s (ct  450 μm) How are they produced? e + e –  (4S)  B B is the cleanest process (large BB/other cross section; no extra particles) Also at hadron machines: pp  B + B + anything How are they decay? Usually to charm b  c, e.g. B  D  Much rarely to light quarks |b  c| 2  |b  u| 2  100 b q

5. 5 ARGUS and CLEO – pioneers in B-physics Large mixing is observed by ARGUS in 1987 Measurements of |V cb |, |V ub |, |V td | and |V ts |: the UT has comparable sides and therefore angles are not 0 or 180º. Large Br(B  J/  K S ) ~ 10 –3 – very attractive final state All these were good news for physicists: Large mixing – easy to measure CP violation, as interference occurs before B decays CP violation in B can be large Convenient final state The Nature is more favorable to us than we could expect

6. 6 Neutral meson mixing from CKM matrix Equal from CPT invariance Hamiltonian is non-hermitian due to the decay; “Box diagram” It is just a numerical (complex) matrix 2×2: contributes to off- diagonal elements

7. 7 Peculiarity of B-meson system Box diagram Thus, mass (width)-differences are approximated by where Contains weak phase Common CP final states for B 0 and B 0

8. 8 CP violation in B mesons No “K L ” methods applicable! Lifetime difference is tiny (  (B H )-  (B L )/  (B) ~1%): no way to work with a beam of long lived B’s. Semileptonic asymmetry also vanishes. New ideas required! Sanda & Carter (1980): consider a final state f common for both B 0 and B 0 : We arrive at decay rate asymmetry for the B 0 (t=0) and B 0 (t=0) because of interference of two amplitudes with different weak phases The effect is large! Sanda & Carter estimated the asymmetry ~ 0.1 (compare with 0.002 CP violating effects in K L )

9. 9 Interfere B  f CP with B  B  f CP Sanda, Bigi & Carter: × A + × A For B(t=0) = B 0 tree diagram (A) box + tree diagram Calculate t-dependent rates: Remember: |A|=|A|, |p|=|q|

10. 10 B 0  J/  K S taking into account Penguin diagram is difficult to estimate. But we are lucky: it’s amplitude is collinear to those of the tree one. V td V * td dd s bc c J/ψ KSKS bc c dd s KSKS d b t t + Why?

11. 11 B0  π πB0  π π In this case the penguin diagram is not small and has different weak phase: The indirect CP violation ~ S sin(Δm t), where S≠ sin 2α, but sin(2α + some not-negligible phase). There will be direct CP asymmetry ~ A cos(Δm t), V ub dd u b d u π+π+ π–π– V * td d u d u d b t π–π– π+π+ How to take into account this? Wait for the next lecture.

12. 12  (4S) resonance  (4S)  B 0 B 0 / B + B – ~ 50:50 + no extra particles! Coherent BB production in P-wave B-energy is known (B momentum is very low ~ 340MeV A very convenient process to study CP violation in B! bb bound state J PC =1 – – (≡ J PC of photon)  (e + e –  (4S))  1nb Good signal/background ~ 1:3 e + e –  (4S)  B B

13. 13 How to measure CPV at e + e – collider? The source of B mesons is the  (4S), which has J PC = 1 – –. The  (4S) decays to two bosons with J P = 0 –. Quantum Mechanics (application of the Einstein-Rosen-Podosky Effect) tells us that for a C = –1 initial state (Υ(4S)) the rate asymmetry: N = number of events f CP = CP eigenstate (e.g. B 0 →J/ψK S ) f fl = flavor state (particle or anti-particle) (e.g. B 0 → e + X) However, if we measure the time dependence of A we find: Need to measure the time dependence of decays to “see” CP violation using the B’s produced at the  (4S).

14. 14 Asymmetric e + e – collaider CP violation asymmetry vanishes if integrated over Δt from –  to +   kills good idea? No! but requires new idea: Need to reconstruct B-decay vertex: Impossible at symmetric B- factory – we don’t know B’s production point! But possible if  (4S) has a sizeable boost in lab frame We can measure t-dependent asymmetry! Flavor-tag decay (B 0 or B 0 ?) J/  KSKS ee ee zz t=0 Asymmetric energies

15. 15 What‘s required to discover CPV? Produce B mesons! Need accelerator Effectively reconstruct B mesons Correctly determine the flavor of second B Precisely reconstruct the decay vertices Produce a lot of B mesons! Need good accelerator Produce a huge number of B mesons! Need accelerator with record luminosity Need good detector with excellent PID and Vertex very

16. 16 Two B-factories were approved in 1990

17. 17 e + e – Asymmetric B-factories PEP-II BaBar ~1 km in diameter Mt. Tsukuba KEKB Belle SLAC 3.1 x 9GeV 3.5 x 8 GeV stop Apr-2008 Also tau- and charm- factories: 10 9 ττ / cc pairs World highest luminosities L = 2.1 (KEKB) & 1.2 (PEP-II) × 10 34 cm –2 s –1 775(Belle) & 465(BaBar) millions BB-pairs

18. 18 PEP-II at SLACKEKB at KEK Belle BaBar 9GeV (e – )  3.1GeV (e + ) designed luminosity: 3.5  10 33 cm -2 s -1 achieved 10.2  10 33 cm -2 s -1 (3 times larger!) 8GeV (e – )  3.5GeV (e + ) designed luminosity: 10.0  10 33 cm -2 s -1 achieved 21.2  10 33 cm -2 s -1 (2 times larger!) 11 countries, 80 institutes, ~ 600 persons 13 countries, 57 institutes, ~ 400 persons

19. 19 History of 10 years running

20. 20 How to measure CPV at B-factories? Reconstruct the decay of one of the B-mesons’s into a CP eigenstate for example: B  J/  K S Reconstruct the decay of the other B-meson to determine its flavor (“tag”) Partial reconstruction is sufficient Measure the distance (L) between the two B meson decays and convert to proper time need to reconstruct the positions of both B decay vertices  t = L/(  c) Correct for the wrong tag and not perfect vertex resolution Extract CP asymmetry from the dN /d  t distribution: dN/d  t ~ e -  |  t| [1 ±  cp sin2  sin(  m  t)]

21. 21 Step 1: Select B  J/  K S Reconstruct B CP long lived daughter: B  J/  K S  ℓℓ  Check the intermediate masses: M(ℓℓ) ~ M(J/  ); M(  ) ~ M(K S ) Check the mass and ENERGY (a big advantage of B-factories – we know B energy = E beam in the CM system) of J/  K S combination K S decay vertex

22. 22 B-candidate CM energy B-candidate CM momentum Use many other decays B to charmonium (η c, χ c1, ψ’) + K S to increase statistics: These final states have the same (odd) CP eigenvalue They are equally theoretically clean (no penguin uncertainties) They can be reconstructed with the similar high purity B  charmonium K S B  J/  K S

23. 23 Purity 97 % CP odd Purity 59 % CP even B  J/  K L Important to check if the asymmetry flip the sign for the opposite CP eigen value Difficult to detect K L : cτ ~ 15m; only nuclear interactions. p K L information is poor → lower purity Detect nuclear shower in iron: measure direction but not momentum. Use known J/  K L = E beam energy to calculate momentum.

24. 24 Step2: Flavor tagging B0B0 B0B0 D X B0B0 B0B0 Semileptonic decays Hadronic decays X ℓ + ν X ℓ – ν In ~99% of B 0 decays: B 0 and B 0 are distinguishable by their decay products All charged tracks (not associated with the reconstructed B CP ) are from the second B tag in the event: ℓ, K and even  charge provides the information of B tag flavor. |Δt| (ps)

25. 25 Step 3: Vertex reconstruction Use tracks from both B CP and Btag to find out z-coordinate of the two B- decay vertices.

26. 26 B 0 tag _ _ S = sin 2β = 0.65 A=0 Take into account detector effects R : detector resolution w : wrong tag fraction (misidentification of flavor)  (1-2w) quality of flavor tagging They are well determined by using control sample D * lν, D (*) π etc… True Detector smeared Need to solve inverse problem to get true value

27. 27 First Observation: CPV in B 1137 events Asymmetry 2001 [PRL 87,091802(2001)] [PRL 87,091801(2001)] J/ψ K* 0 ( ) Asymmetry Events sin 2β = 0.99 ± 0.14 ± 0.06sin 2β = 0.59 ± 0.14 ± 0.05 32M BB-pairs 31M BB-pairs B 0 tag _

28. 28 The recent Belle result N sig = 7482 J/ψ K S J/ψ K L Phys.Rev.Lett., 98, 031802(2007) sin 2β = 0.642 ± 0.031 ± 0.017 A = 0.018 ± 0.021 ± 0.014 B 0 tag _ N sig = 6512

29. 29 B 0 tag _ Compare CP odd and even final states Asymmetry= –ξ CP sin 2β sin(Δm Δt) B 0 tag _ sin 2β = + 0.643 ± 0.038 A = – 0.001 ± 0.028 sin 2β = + 0.641 ± 0.057 A = – 0.045 ± 0.033

30. 30 The recent BaBar result Phys.Rev. D79, 072009 (2009) sin 2β = 0.687 ± 0.028 ± 0.012 A = 0.024 ± 0.020 ± 0.016

31. 31 There are two solutions for β How to avoid ambiguity? In some B decays the asymmetry is related to cos2β. It is difficult to achieve good accuracy, but even rough measurement allows to exclude the second solution.

32. 32 Other modes that measure sin2β dd d bc c D+D+ D–D– dd d bc c J/ψ π0π0 CP even

33. 33 We have done a great job: CPV violation is observed in the system different from the neutral kaon system. The CPV large (~70%) compared to 0.2% in K 0 decays. The parameter of CPV is measured with great precision (~ 3%) and related to KM parameters without theoretical uncertainties. The angle of UT triangle is measured (without ambiguity) with the precision better than 1º. Can we relax now? Yes, because the time for this lecture is almost over. No, because we have not yet proved that KM anzatz works well.

34. 34 The CM+KM test V ud V * ub V cd V * cb V td V * tb β α γ How to measure other UT angles? sin2β: sin2α: sin2γ: hard experimentally easy One way to test the Standard Model is to measure the 3 sides & 3 angles and check if the triangles closes! How to measure UT sides?