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B Physics and CP Violation

B Physics and CP Violation. Particles and the Universe Lake Louise Winter Institute 16-22 February 2003. Bob Kowalewski University of Victoria. In remembrance of Professor Nate Rodning U. of Alberta (~1957 – 2002). Lecture 1: Why build B factories? Review of CKM

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B Physics and CP Violation

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  1. B Physics and CP Violation Particles and the Universe Lake Louise Winter Institute 16-22 February 2003 Bob Kowalewski University of Victoria Kowalewski - LLWI 2003

  2. In remembrance of Professor Nate Rodning U. of Alberta (~1957 – 2002) Kowalewski - LLWI 2003

  3. Lecture 1: Why build B factories? Review of CKM B production and decay, experimentation Calculational tools: OPE, HQE, HQET |Vub| and |Vcb| Lecture 2: BB oscillations CP violation Rare decays Plan for the lectures Kowalewski - LLWI 2003

  4. Disclaimers • These lectures are pedagogical in nature; as such, I will not necessarily • present the very latest measurements • carefully balance CLEO/Belle/Babar/CDF/LEP… (my own work is on BaBar; it will be obvious!) • Due to time constraints, important topics will be omitted; in particular, • not much will be said about Bs physics • prospects for B studies at hadron machines will not be covered Kowalewski - LLWI 2003

  5. Suggested reading • The following reviews can be consulted for more detailed presentations of the material covered in these lectures: • B Decays and the Heavy Quark Expansion, M. Neubert, hep-ph/9702375 • The Heavy Quark Expansion of QCD, A. Falk, hep-ph/9610363 • Flavour Dynamics: CP Violation and Rare Decays, A. Buras, hep-ph/0101336 • CP Violation: The CKM Matrix and New Physics, Y. Nir, hep-ph/0208080 Kowalewski - LLWI 2003

  6. B decays – a window on the quark sector • The only 3rd generation quark we can study in detail • Investigate flavour-changing processes, oscillationsCKM matrix Cabibbo angle B lifetime, decay CP Asymmetries (phase) BdBd and BsBs oscillations =1 Kowalewski - LLWI 2003

  7. B decays – QCD at the boundary • Mix of large (mb) and small momentum (ΛQCD) scales – a laboratory for testing our understanding of QCD • Large variety of decay channels to study in detail: leptonic, semileptonic, hadronic • High density of states → inclusive measurements (quark-hadron duality) • Vibrant interplay between experiment and theory D B π π Kowalewski - LLWI 2003

  8. CP violation – a fundamental question Pep2 / BaBar But really…why spend ~109 $ on B factories? • Explore CP violation • outside of K0 system • via different mechanisms (direct, mixing, interference) • in many different final states • Test the CKM picture • survey the unitarity triangle • can all measurements be accommodated in this scheme? KEKB / Belle Kowalewski - LLWI 2003

  9. Return on investment PDG 1999 B factories give us • New physics? (high risk) • Determination of unitarity triangle (balanced growth) • Better understanding of heavy hadrons (old economy) PDG 2002 Kowalewski - LLWI 2003

  10. CKM matrix • Kobayashi and Maskawa noted that a 3rd generation results in an irreducible phase in mixing matrix: • Observed smallness of off-diagonal terms suggests a parameterization in powers of sinθC 3 x 3 unitary matrix. Only phase differences are physical, → 3 real angles and 1 imaginary phase Kowalewski - LLWI 2003

  11. d s b u c t Wolfenstein++ parameterization Buras, Lautenbacher, Ostermaier, PRD 50 (1994) 3433. • shown here to O(λ5) where λ=sinθ12=0.22 • Vus, Vcb and Vub have simple forms by definition • Free parameters A, ρ and η are order unity • Unitarity triangle of interest is VudV*ub+VcdV*cb+VtdV*tb=0 • Note that |Vts /Vcb| = 1 + O(λ2) all terms O(λ3) Kowalewski - LLWI 2003

  12. A Unitarity Triangle Choice of parameters:  Rt Ru g b Kowalewski - LLWI 2003

  13. Surveying the unitarity triangle • The sides of the triangle are measured in b→uℓν and b→cℓν transitions (Ru) and in Bd0-Bd0 and Bs0-Bs0 oscillations (Rt) • CP asymmetries measure the angles • Great progress on angles; need sides too! Rt  Ru g b GET A BETTER PICTURE Kowalewski - LLWI 2003

  14. B meson production • Threshold production in e+e- at Y(4S) has advantages: • cross-section ~1.1nb, purity (bb / Σiqiqi) ~ 1/4 • simple initial state (BB in p-wave, no other particles,decay products overlap) • “easy” to trigger, apply kinematic constraints • Role of hadron machines • cross-sections much higher (×102) • Bs are produced • triggering harder, purity (b / Σiqi) ~ (few/103) Kowalewski - LLWI 2003

  15. Y(4S) experiments • e+e- → Y(4S) → B+B- or B0B0; roughly 50% each • B nearly at rest (βγ ~ 0.06) in 4S frame; no flight info • Asymmetric beam energies boost into lab: (βγ)4S ~0.5 on peak off peak (q=u,d,s,c) 2mB Kowalewski - LLWI 2003

  16. Requirements • High luminosity (need 108 B or more); this means L~1033-34/cm-2s-1, 30-100 fb-1/year • Measure Δt = tB1-tB2 (need to boost Y(4S) in lab, use silicon micro-vertex detectors to measure Δz) • Fully reconstruct B decays with good efficiency and signal/noise (need good track and photon resolution, acceptance) • Determine B flavour (need to separate ℓ, π, K over ~full kinematic range) Kowalewski - LLWI 2003

  17. PEP-II and KEK-B Kowalewski - LLWI 2003

  18. B factories: KEK-B and PEP-II Belle BaBarLmax (1033/cm2/s)8.3 4.6 best day (pb-1) 434 303 total (fb-1) 106 96 • Both B factories are running well: Belle Kowalewski - LLWI 2003

  19. B factory detectors • Belle and BaBar are similar in performance; some different choice made for Cherenkov, silicon detectors • Slightly different boost, interaction region geometry CsI (Tl) BaBar DIRC e+ (3.1 GeV) Belle e- (9 GeV) IFR SVT DCH Kowalewski - LLWI 2003

  20. So e+e-→bb… then what? Kowalewski - LLWI 2003

  21. b quark decay b quark decay c e νeb • Charged-current Lagrangian in SM: • Since mb<< MW, effective 4-fermion interaction is • CKM suppressed → long lifetime ~ 1.5ps ×3 for color Kowalewski - LLWI 2003

  22. b u Leptonic < 10-4, 7,11τ, μ, e Tree-level decays single hadronic current; reliable theory Semileptonic ~ 26% Hadronic ~ 73% Theoretical preductions tend to have large uncertainties Vub, helicity suppressed Colour-suppressed: Charmonium! Kowalewski - LLWI 2003

  23. Loop decays –significant due to large mt , sensitive to new physics b→sg: O(10-2) γ,Z b→s(d)ℓℓ: O(10-6) b→sγ: O(10-4) B0 → B0: (B0→B0)/ B0 = 0.18 Kowalewski - LLWI 2003

  24. B hadron decay • QCD becomes non-perturbative at ΛQCD ~ 0.2 GeV, and isolated b quarks do not exist. • How does QCD modify the weak decay of b quark? • Bound b quark is virtual and has some “Fermi momentum” – this was the basis of the parton (valence) model of B decay • Parton model had some successes, but did not provide quantitative estimates of theoretical uncertainties. • Modern approach – use the operator product expansion to separate short- and long-distance physics Xhνe e B Kowalewski - LLWI 2003

  25. Operator Product Expansion • The heavy particle fields can be integrated out of the full Lagrangian to yield an effective theorywith the same low-energy behaviour (e.g. V-A theory) • The effective action is non-local; locality is restored in an expansion (OPE) of local operators of increasing dimension ( ~1/[Mheavy]n ) • The coefficients are modified by perturbative corrections to the short-distance physics • An arbitrary scale μ separates short- and long-distance effects; the physics cannot depend on it Kowalewski - LLWI 2003

  26. OPE in B decays • The scale μ separating short/long distance matters not … except in finite order calculations  • typically use ΛQCD << μ ~ mb << MW; αS(mb) ~ 0.22 • Wilson coefficients Ci(μ) contain weak decay and hard-QCD processes • The matrix elements in the sum are non-perturbative • Renormalization group allows summation of terms involving large logs (ln MW/μ) → improved Ci(μ) Kowalewski - LLWI 2003

  27. Heavy Quarks in QCD • There is no way to avoid non-perturbative effects in calculating B hadron decay widths • Heavy Quarks have mQ >> ΛQCD (or, equivalently, Compton wavelengthλQ << 1/ΛQCD) • Since λQ << 1/ΛQCD, soft gluons (p2 ~ ΛQCD) cannot probe the quantum numbers of a heavy quark → Heavy Quark Symmetry Kowalewski - LLWI 2003

  28. Heavy Quark Symmetry • For mQ→∞ the light degrees of freedom decouple from those of the heavy quark; • the light degrees of freedom are invariant under changes to the heavy quark mass, spin and flavour • SQ and Jℓ are separately conserved. • The heavy quark (atomic nucleus) acts as a static source of color (electric) charge. Magnetic (color) effects are relativistic and thus suppressed by 1/mQ • HQ symmetry is not surprising - different isotopes of a given element have similar chemistry! Kowalewski - LLWI 2003

  29. Heavy Quark symmetry group • The heavy quark spin-flavour symmetry forms an SU(2Nh) symmetry group, where Nh is the number of heavy quark flavours. • In the SM, t and b are heavy quarks; c is borderline. • No hadrons form with t quarks (they decay too rapidly) so in practice only b and c hadrons are of interest in applying heavy quark symmetry • This symmetry group forms the basis of an effective theory of QCD: Heavy Quark Effective Theory Kowalewski - LLWI 2003

  30. Heavy Quark Effective Theory • The heavy quark is almost on-shell: pQ=mQv+k, where k is the residual momentum, kμ << mQ • The velocity v is ~ same for heavy quark and hadron • The QCD Lagrangian for a heavy quark can be rewritten to emphasize HQ symmetry: • In Q rest frame, h(H) correspond to upper(lower) components of the Dirac spinor Q(x) Kowalewski - LLWI 2003

  31. HQET Lagrangian • The first term is all that remains for mQ→∞; it is clearly invariant under HQ spin-flavour symmetry • The terms proportional to 1/mQare • the kinetic energy operator OKfor the residual motion of the heavy quark, and • the interaction of the heavy quark spin with the color-magnetic field, (operator OG) • The associated matrix elements are non-perturbative; however, they are related to measurable quantities Kowalewski - LLWI 2003

  32. Non-perturbative parameters • The kinetic energy term is parameterized by λ1= <B|OK|B>/2mB • The spin dependent term is parameterized by λ2= -<B|OG|B>/6mB • The mass of a heavy meson is given by The parameter Λ arises from the light quark degrees of freedom and is defined by Λ = limm→∞(mH – mQ) Kowalewski - LLWI 2003

  33. Phenomenological consequences The spin-flavour symmetry relates b and c hadrons: • SU(3)Flavour breaking:m(Bs) - m(Bd) = Λs – Λd + O(1/mb); 90±3 MeVm(Ds) - m(Dd) = Λs – Λd + O(1/mc); 99±1 MeV • Vector-pseudoscalar splittings: (→ λ2 ~0.12 GeV)m2(B*) - m2(B) = 4λ2+O(1/mb); 0.49 GeV2m2(D*) - m2(D) = 4λ2+O(1/mc); 0.55 GeV2 • baryon-meson splittings:m(Λb) - m(B) - 3λ2/2mB+ O(1/mb2);312±6 MeVm(Λc) - m(D) - 3λ2/2mD+ O(1/mc2); 320±1 MeV Kowalewski - LLWI 2003

  34. Exclusive semileptonic decays D*νe e B • HQET simplifies the description of BXceνdecays and allows better determinations of |Vcb| • Consider the (“zero recoil”) limit in which vc=vb (i.e. when the leptons take away all the kinetic energy) • If SU(2Nh) were exact, the light QCD degrees of freedom wouldn’t know that anything happened • For mQ→∞ the form factor can depend only on w=vb·vc (the relativistic boost relating b and c frames) • This universal function is known as the Isgur-Wise function, and satisfies ξ(w= 1) = 1. Kowalewski - LLWI 2003

  35. BD*eν form factors • The HQET matrix element for BD*eν decays is • The form factors hV … are related in HQET: • ξ must be measured; predicted relations can be tested! Kowalewski - LLWI 2003

  36. Determination of |Vcb| • The zero-recoil point in BD(*)eνis suppressed by phase space; the rate vanishes at w=1, requiring an extrapolation from w>1 to w=1. includes radiative and HQ symmetry-breaking corrections, and Luke’s theorem Kowalewski - LLWI 2003

  37. Current status of |Vcb| from B→D*eν • Measurements of the rate at w=1 are experimentally challenging due to • limited statistics: dΓ/dw(w=1) = 0 • softness of transition π from D*→D • extrapolation to w=1 • Current status (PDG 2002): 5% error Kowalewski - LLWI 2003

  38. Tests of HQET • Predicted relations between form factors can be used to test HQET and explore symmetry-breaking terms • The accuracy of tests at present is close to testing the lowest order symmetry-breaking corrections – e.g. the ratio of form factors  / for B→Deν / B→D*eν is Kowalewski - LLWI 2003

  39. Exclusive charmlesssemileptonic decays πνe e B • HQET is not helpful in analyzing BXueνdecays in order to extract |Vub| • The decays B0→π+ℓ-ν and B→ρℓ-ν have been observed (BF ~ 2×10-4); large backgrounds from e+e-→qq events • Prospects for calculating the form factor in B→πℓν decay on the Lattice are good; current uncertainties are in the 15-20% range on |Vub| • Not yet very constraining Kowalewski - LLWI 2003

  40. Inclusive Decay Rates • The inclusive decay widths of B hadrons into partially-specified final states (e.g. semileptonic) can be calculated using an OPE based on: • HQET - the effects on the b quark of being bound to light d.o.f. can be accounted for in a 1/mb expansion involving familiar non-perturbative matrix elements • Parton-hadron duality – the hypothesis that decay widths summed over many final states are insensitive to the properties of individual hadrons and can be calculated at the parton level. Kowalewski - LLWI 2003

  41. Parton-Hadron Duality • One distinguishes two cases: • Global duality – the integration over a large range of invariant hadronic mass provides the smearing, as in e+e-→hadrons and semileptonic HQ decays • Local duality – a stronger assumption; the sum over multiple decay channels provides the smearing (e.g. b→sγ vs. B→Xsγ). No good near kinematic boundary. • Global duality is on firmer ground, both theoretically and experimentally Kowalewski - LLWI 2003

  42. Heavy Quark Expansion • The decay rate into all states with quantum numbers f is • Expanding this in αS and 1/mb leads towhere λ1 and λ2 are the HQET kinetic energy and chromomagnetic matrix elements. • Note the absence of any 1/mb term! free quark Kowalewski - LLWI 2003

  43. Inclusive semileptonic decays X νe e B • The HQE can be used for both b→u and b→c decays • The dependence on mb5must be dealt with; in fact, an ambiguity of order ΛQCDexists in defining mb. Care must be taken to correct all quantities to the same order in αS in the same scheme) • The non-perturbative parameters λ1 and λ2 must be measured: λ2~0.12 GeV from B*-B splitting; λ1 from b→sγ, moments in semileptonic decays, … Kowalewski - LLWI 2003

  44. The upsilon expansion1 • The mb appearing in the HQE is the pole mass; it is infrared sensitive (changes at different orders in PT) • Instead, one can expand both Γ(B→Xf) and mY(1S) in a perturbation series in αS(mb) and substitute mY(1S) for mb in Γ(B→Xf) – this is the upsilon expansion • There are subtleties in this – the expansion must be done to different orders in αS(mb) in the two quantities • The resulting series is well behaved and gives 1 Hoang, Ligeti and Manohar, hep-ph/9809423 4% error Kowalewski - LLWI 2003

  45. Semileptonic B decay basics • BF(B→Xℓ-ν) ~ 10.5% • Γ(b→cℓ-ν) is about ~60 times Γ(b→uℓ-ν) (not shown) • Leptons from the cascade b→c→ℓ+ have similar rate but softer momentum spectrum, opposite charge b→ℓ- b→ℓ+ Kowalewski - LLWI 2003

  46. |Vcb| from inclusive s.l. B decays • ΓSL = τB×BFSL≅ Γ(B→Xcℓν) ∝ |Vcb|2 • Using (from PDG2002)τ(B0) = 1542±16 fs, τ(B+) = 1674±18 fs, BF(B→Xcℓν) = (10.38±0.32)%along with the aforementioned theoretical relation, |Vcb| = (40.4±0.5exp±0.5±0.8th)·10-3 • Compatible with D*ℓν result; 3rd best CKM element Knowledge of λ1, λ2 higher orders in mb, αS Kowalewski - LLWI 2003

  47. Determination of |Vub| • The same method (ΓSL) can be used to extract |Vub|. • Additional theoretical uncertainties arise due to the restrictive phase space cuts needed to reject the dominant B→Xceν decays • Traditional methods usesendpoint of lepton momentumspectrum; acceptance ~10%leading to large extrapolationuncertainty Kowalewski - LLWI 2003

  48. b→callowed mX2 b→callowed b→callowed Better(?) methods for determining |Vub| • invariant mass q2 of ℓν pair (acceptance ~20%, requires neutrino reconstruction) B0→Xuℓ-ν • mass mx recoiling against ℓν (acceptance ~70%, but requires full reconstruction of 1 B meson) B→Xuℓ-ν Kowalewski - LLWI 2003

  49. Shmax (GeV2) Shape function • The Shape function, i.e. the distribution of the b quark mass within the B • Some estimators (e.g., q2) are insensitive to it reject accept reject accept Kowalewski - LLWI 2003

  50. Measuring non-perturbative parameters and testing HQE mb and λ1 can be measured from • Eγ distribution in b→sγ • moments (mX, sX, Eℓ, EW+pW) in semileptonic decays • Comparing values extractedfrom different measurementstests HQE • This is currently an area ofsignificant activity λ1 mb/2→Λ Kowalewski - LLWI 2003

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