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B mixing: introduction and the case of the B d

B mixing: introduction and the case of the B d. Riccardo Faccini Universita’ di Roma “La Sapienza” Universita’ di Roma3, 4/12/06. What is Mixing?. Mixing occurs every time the eigenstates of the hamiltonian are different from the eigenstates of the decay operator. H = H 0 + H W.

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B mixing: introduction and the case of the B d

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  1. B mixing: introduction and the case of the Bd Riccardo Faccini Universita’ di Roma “La Sapienza” Universita’ di Roma3, 4/12/06

  2. What is Mixing? Mixing occurs every time the eigenstates of the hamiltonian are different from the eigenstates of the decay operator H = H0 + HW Eigenstates of the hamiltonian are a continuum of states Decay final states Undecayed/mixed states

  3. Considering only the subspace with B0 and B0 the hamiltonian becomes NO MORE HERMITIAN! The eigenstates of Heff are Of eigenvalues mL- i GL/2 and mH- i GH/2, respectively. Let us assume the following parametrization and remember the Shroedinger equation

  4. Time evolution Stong interactions produce a B0 which in terms of Heff eigenstates is Analogously for with the evolution of time Interference between two amplitudes with different phase If we can count the and meson present at a given time after the production of a Note: case of the Bd: GL=GH=G

  5. Note: all applies also to the K0-K0 and the D0-D0 system Signs of mixing If no way to measure time Just count how many mixed events you see Otherwise time dependence helps a lot!!! B0phys B0 B0phys B0 No mixing RATES t(ps) t(ps) ASYMMETRY P (B0phys B0) - P (B0phys B0) A(t) = P (B0phys B0) + P (B0phys B0) t(ps) = cos (Δm t)

  6. d s b u c t area~ |Vij|2 CKM Matrix In the Standard Model the complex couplings of the LH quarks and RH antiquarks to the charged weak force carriers (W±) are usually represented in the unitary Cabibbo-Kobayashi-Maskawa (CKM) matrix:

  7. CP Symmetry Discrete symmetries: Charge conjugation: Parity : Time reversal: In the Standard Model CP violation shows up as a complex phase in the CKM matrix NO YES C q L q L W- W+ Vqq´ q´R q´R P q R q R W+ W- V*qq´ q´L q´L NO YES

  8. “The” Unitarity triangle The unitarity condition that gives the most open triangle is Vub*Vud + Vcb*Vcd + Vtb*Vtd= 0 The first and last terms contain the most-off-diagonal elements Vub and Vtd, those with the most significant complex part. It is convenient to divide each term by the middle term so that the base of the triangle has unit length. (r,h) Vtb*Vtd Vcb*Vcd Vub*Vud Vcb*Vcd a b g (1,0) (0,0)

  9. CP cos(Dmt/2) cos(Dmt/2) exp(–2iq) fCP fCP B0 B0 B0 B0 isin(Dm t/2) exp(–2ib)exp(2iq)  isin(Dm t/2) exp(2ib) Mixing and CP in the Standard Model t d b W W B B t d b Vtd* Vtb The mixing diagram has a real part DMd which allows to measure Vtd and a phase (q/p) which probes CP violation The interference between B mixing and decays into a CP eigenstate (accessible to both B0 and B0) provides the cleanest theoretical predictions: with a CP-violating asymmetry  sin 2(b–q). The CKM angle b is associated with the mixing box diagram. The CKM angle q depends on the final state fCP

  10. CP in Oscillations+ Decay Study the oscillation frequency in decay channels common to B0 and B0 (r,h) a g b (0,0) (1,0) Examples

  11. History of mixing The LEP adventure e+e-Zbb (1990-1995) B0B0 oscillations ARGUS (1987) confirmed by CLEO Two B0D*-m+nm decays in the same event e+e-Y(4S)B0B0 Note: B mixing was expected to be a much rarer process because of a lower expected top mass Relative error: 2.8%

  12. The B Factories B0 e+ e- Y(4S) B0 Since J(Y)=1 and J(B)=0 and the B0 mesons have to obey the bose-einstein statistics Two B mesons with opposite flavour are produced in a coherent state

  13. PEP-II &KEK-B Lint: 391 fb-1 Lint: 680 fb-1

  14. The Detectors WARNING : All future detector descriptions refer to BaBar

  15. Experimental Technique B-Flavor Tagging II 0 B tag D III B Meson Reconstruction I Accurate and unbiased measurement of the vertices  Allows time dependent analyses!!! Several techniques to reconstruct a lot of B mesons: look for states that better discriminate between B0 and anti-B0

  16. B meson reconstruction • Identification of a lepton  leptonic • Identification of BD*ln, D*p (D*D0ps) via the reconstruction of the lepton/p and pspartial reconstruction • Fully reconstructed BDX purity efficiency tagging

  17. Effect of tagging and resolution B0 B0 or B0 B0 UNMIXED B0 B0 or B0 B0 MIXED Perfect reconstruction Mistake tagging with probability w (=22% in figure) Resolution on Dz, sDz(=170 mm in figure)

  18. Tagging BUT : cascade events can mimic opposite tag • Cleanest tag is to require a lepton • Only 10% of events per lepton • In case of clean reconstruction dirtier tags can be used b quarks are tagged by negatively charged leptons. e- or m- e- or m- W+ W- anti-c quark n n W- anti-b quark (Q = +1/3) anti-s quark (Q = +1/3) b quark (Q = -1/3) c quark (Q = +2/3) Effective efficiency:

  19. BREC direction BREC Vertex BREC daughters Interaction Point Beam spot BTAG direction TAG Vertex TAG tracks, V0s Vertexing Algorithm If one of the two Bs is fully reco’d the full kinematics can be exploited: * good resolution (sDz~180mm) * limited bias from D lifetimes s~70 mm ~0.1 mm s~180 mm ~1cm Otherwise only one track per side is used (typically the two leptons) * reasonable core resolution but … * … very long tail from D lifetimes  larger systematics

  20. Dilepton mixing Use BD(*)ln decay both to reconstruct and to tag  reconstruct only the charged lepton Pros: extremely high stat cons: high, irreducible backgrounds B+B-, continuum lots of parameters in simultaneous fit cascade, resolution, mistags, fractions,… dependency on sDz and lack of control samples

  21. Only true signal Unmixed DMd(ps-1) Mixed Belle 32M BB~ (Unmixed-Mixed) /(Unmixed+Mixed)

  22. Exploring fundamental symmetries Removing assumptions on CP(T) symmetries Define: CP symmetry  p=q CPT symmetry  z=0

  23. T/CP/CPT in B0 mixing BaBar hep-ex/0603053 40% reduction in s(q/p) 80% reduction in s(Im(z)) First Measurement of Re(z)! after before NP ? Constraints on New Physics from |q/p| SM SM

  24. Partially reconstructed B decays Look for BD*p or D*ln D*D0p BaBar Belle Pros: very high stat cons: relatively high background, particles leaking in tag side

  25. Best single measurement! DMd(ps-1)

  26. Fully reconstructed semileptonic B decays Reconstruct one of the Bs with the decay Neutrino not reconstructed Pion easy to identify (soft) Pros: relatively clean sample and high stat cons: same as pros … Ideal size and purity for the first simultaneous fit to lifetime and DMd!!!

  27. Higher due to simultaneous measurement of tB DMd(ps-1)

  28. Fully reconstructed hadronic B decays hadronic decays Neutral B Mesons Belle Pros: clean sample, efficient tagging cons: low stat Dominant sys: vertex reconstruction

  29. (Unmixed-Mixed) /(Unmixed+Mixed) Belle DMd(ps-1)

  30. Summary of results Relative error on world average: 1%

  31. Constraints on the Unitarity Triangle Current knowledge of the unitarity triangle Regardless of all exp efforts the constraint on the unitarity triangle is not very stringent … … but mixing has been critical to constrain the angles!

  32. backup

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