CP violation with beautiful baryons

  • Isard Dunietz
Article

Abstract

CP violation can be studied in modes of charmed or bottom baryons when a decay process is compared with its charge-conjugated partner. It can show up as a rate asymmetry and in a study of other decay parameters. Neither tagging nor time-dependences are required to observeCP violation with modes of baryons, in contrast to the conventionalB0 modes. Numerous modes of bottom baryons have the potential to show largeCP-violating effects within the Standard Model. Those effects can be substantial for modes with aD0, which is seen in a final state that can also be fed from a\(\bar D^0 \). For instance, a comparison of theΛbΛCP0 with the\(\bar \Lambda _b \to \bar \Lambda D_{CP}^0 \) process can show sizeableCP violation. HereDCPo denotesCP eigenstates ofD0, which occur at a few percent. Six related processes, such asΛbΛD0,\(\Lambda _b \to \Lambda \bar D^0 \),ΛbΛCP0, and their charge-conjugated counterparts, can extract ϕ, which is the most problematic angle of the unitarity triangle and which is conventionally probed with theBs→ρ0KS asymmetry. HereD0 andD−0 are identified by their charged kaon or lepton. We predictB(ΛbΛD0)∼10−5, thusB(ΛbΛCP0)∼10−7. Under favourable circumstances,CP violation can occur at the few tens of percent level. Thus 102–103ΛbΛCP0 decays start probing ϕ. Tables list many additional modes with typical branching ratios at the 10−5–10−6 level, with large detection efficiencies (in contrast to theDCP0), and with potentially largeCP-violating effects, such as Ξb0→ΛΨ, Λϕ, ΛK*0; Ξb→ΛK(*)−, ΞKs, ΞK*0, Ωb→Ξφ, Ξρ0, ΛK(*)−, ΩKs, ΩK*0.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.H. Christenson, J.W. Cronin, V.L. Fitch, R. Turlay: Phys. Rev. Lett. 13 (1964) 138Google Scholar
  2. 2.
    I.I. Bigi, V.A. Khoze, N.G. Uraltsev, A.I. Sanda: in:CP violation, p. 175. C. Jarlskog (ed.). Singapore: World Scientific 1989Google Scholar
  3. 3.
    J.D. Bjorken: Nucl. Phys. B (Proc. Suppl.) 11 (1989) 325; I.I. Bigi, B. Stech: in Proceedings of the Workshop on High Sensitivity Beauty Physics at Fermilab, Batavia, IL, 1987, p. 239. A.J. Slaughter, N. Lockyer, M. Schmidt (eds.)Google Scholar
  4. 4.
    T.D. Lee, C.N. Yang: Phys. Rev. 108 (1957) 1645Google Scholar
  5. 5.
    J.W. Cronin, O.E. Overseth: Phys. Rev. 129 (1963) 1795Google Scholar
  6. 6.
    W. Koch: in: Analysis of scattering and decay, p. 231. M. Nikolic (ed.). New York, London, Paris: Gordon and Breach 1968Google Scholar
  7. 7.
    T.D. Lee: in: Preludes in theoretical physics, p. 5. A. De-Shalit, H. Feshbach, L. Van Hove (eds.). Amsterdam: North-Holland 1966Google Scholar
  8. 8.
    O.E. Overseth, and S. Pakvasa: Phys. Rev. 184 (1969) 1663.CP-violating effects with strange hyperons have been the subject of many later investigations; see for instance: A. Baltas et al.: Nuovo Cimento 45A (1978) 493; L.-L. Chau, H.-Y. Cheng: Phys. Lett. 131B (1983) 202; T. Brown, S.F. Tuan, S. Pakvasa: Phys. Rev. Lett. 51 (1983) 1823; J.F. Donoghue, S. Pakvasa: Phys. Rev. Lett. 55 (1985) 162; J.F. Donoghue, B.R. Holstein, G. Valencia: Int. J. Mod. Phys. A2 (1987) 319; Phys. Lett. 178B (1986) 319; J.F. Donoghue, X.G. He, S. Pakvasa: Phys. Rev. D34 (1986) 833; G. Bassompierre: Nuovo Cimento 101A (1989) 307; X.G. He, H. Steger, G. Valencia: Phys. Lett. B272 (1991) 411; N. Hamann et al.: Hyperon study working group Report, CERN/SPSLC report, in progressGoogle Scholar
  9. 9.
    M. Bander, D. Silverman, A. Soni: Phys. Rev. Lett. 43 (1979) 242Google Scholar
  10. 10.
    H. Simma, G. Eilam, D. Wyler: Nucl. Phys. B352 (1991) 367Google Scholar
  11. 11.
    J.-M. Gérard, W.S. Hou: Phys. Lett. B253 (1991) 478; Phys. Rev. D43 (1991) 2909Google Scholar
  12. 12.
    H. Simma, D. Wyler: Phys. Lett. B272 (1991) 395Google Scholar
  13. 13.
    M. Kobayashi, T. Maskawa: Prog. Theor. Phys. 49 (1973) 652Google Scholar
  14. 14.
    M. Gronau, D. London: Phys. Lett. B253 (1991) 483Google Scholar
  15. 15.
    M. Gronau, D. Wyler: Phys. Lett. B265 (1991) 172Google Scholar
  16. 16.
    I. Dunietz: Phys. Lett. B270 (1991) 75Google Scholar
  17. 17.
    I. Dunietz: in: B Decays, p. 393. S. Stone (ed.). Singapore: World Scientific 1992Google Scholar
  18. 18.
    I. Dunietz, A. Snyder: Phys. Rev. D43 (1991) 1593; see especially the longer version, SLAC report, SLAC-PUB-5234, 1990 (unpublished)Google Scholar
  19. 19.
    I. Dunietz, H. Quinn, A. Snyder, W. Toki and H.J. Lipkin: Phys. Rev. D43 (1991) 2193Google Scholar
  20. 20.
    J.M. Soares: Nucl. Phys. B367 (1991) 575Google Scholar
  21. 21.
    R. Aleksan, I. Dunietz, B. Kayser: Z. Phys. C—Particles and Fields 54 (1992) 653Google Scholar
  22. 22.
    R. Aleksan, I. Dunietz, B. Kayser, F. Le Diberder: Nucl. Phys. B361 (1991) 141Google Scholar
  23. 23.
    A.B. Carter, A.I. Sanda: Phys. Rev. Lett. 45 (1980) 952; Phys. Rev. D23 (1981) 1567; L. Wolfenstein: Ann. Rev. Nucl. Part. Sci. 36 (1986) 137; I.I. Bigi, A.I. Sanda: Phys. Lett. B211 (1988) 213Google Scholar
  24. 24.
    E.D. Commins, P.H. Bucksbaum: Weak interactions of leptons and quarks. Cambridge: Cambridge University Press 1983; W. Koch: [6]; G. Källén: Elementary particle physics. Reading: Addison-Wesley 1964Google Scholar
  25. 25.
    The example of 143-1 as a way to measure the decay parameters is reviewed here. The decay parameters α, β, γ for the 143-2 process can be extracted from the angular distribution of the subsequent 143-3 decay, as follows: 143-4, 143-5, 143-6. 143-7. Here 143-8 and 143-9 denote the 143-10 polarization and the known decay parameter for 143-11, respectively. In the definition of the angles 143-12 is the emission direction ofp in the Λ rest frame, and the 143-13 are defined in the 143-14 rest frame as 143-15, 143-16, 143-17. The emission direction of Λ in the 143-18 rest frame is denoted by Â. The azimuthal dependence has been integrated out in the intensities 143-19. From 143-20 and the known 143-21, the decay parameter α can be extracted. The initial polarization can be measured from modes with much larger data samples than the very rare exclusive modes of interest in this work, which have potentially largeCP-violating effects. Thus, β and γ can be obtained from the measured intensities 143-22 and 143-23. Although this footnote uses a nonrelativistic framework, the relations remain true for particles in relativistic motion when an elaborate procedure of boosts is applied, see W. Koch: [6]Google Scholar
  26. 26.
    For a review see: J. Lach: Fermilab report, 1991, FERMILAB-Conf-91/200Google Scholar
  27. 27.
    A. De Rujula et al.: in: Proc. of LHC Workshop (Aachen 1990), Vol. II, p. 201. G. Jarlskog, D. Rein (eds.). CERN 90-10Google Scholar
  28. 28.
    M. Jacob, G.C. Wick: Ann. Phys. (N.Y.) 7 (1959) 404; W. Koch: [6]Google Scholar
  29. 29.
    J. Seguinot, T. Ypsilantis: CERN report, 1991, CERN-LAA/PI/91-004Google Scholar
  30. 30.
    C.O. Dib, I. Dunietz, F.J. Gilman, Y. Nir: Phys. Rev. D41 (1990) 1522Google Scholar
  31. 31.
    J.L. Rosner: in: B Decays, p. 312. S. Stone (ed.). Singapore: World Scientific 1992; M. Schmidtler, K.R. Schubert: Z. Phys. C—Particles and Fields 53 (1992) 347Google Scholar
  32. 32.
    New physics could introduceCP-violating effects between Λb→ΛD0 and its charge-conjugated counterpart, and between\(\Lambda _b \to \Lambda \bar D^0 \) and its counterpart. We thank L. Lavoura for pointing this out to usGoogle Scholar
  33. 33.
    The unlikely scenario requires equality between the Λb→ΛD0 and\(\Lambda _b \to \Lambda \bar D^0 \) rates. It would cause a much suppressed rate in either Λb→ΛDCP0 or\(\bar \Lambda _b \to \bar \Lambda D_{CP}^0 \), which would show up as a largeCP-violating rate asymmetry. Finally, no suppression in rate would occur when theD 0 is seen in modes with the oppositeCP-parityGoogle Scholar
  34. 34.
    The non-factorizable graphs are absent in the 6 relevant processes of Ξb→ΞD0 and Ωb→ΩD0, because no valenceu-quark exists in the initialb-flavoured baryonGoogle Scholar
  35. 35.
    For a definition of colour-allowed and colour-suppressed processes see, for instance: M. Bauer, B. Stech, M. Wirbel: Z. Phys. C—Particles and Fields 34 (1987) 103Google Scholar
  36. 36.
    A. Yagil: talk presented at La Thuile, 1992Google Scholar
  37. 37.
    C. Albajar et al.: Phys. Lett. B273 (1991) 540Google Scholar
  38. 38.
    M. Neubert et al.: Heidelberg report, HD-THEP-91-28, 1991, to be published in Heavy Flavours, A.J. Buras, M. Lindner (eds.)Google Scholar
  39. 39.
    J.L. Rosner: Phys. Rev. D42 (1990) 3732; Enrico Fermi Institute report, EFI 90-80, 1990, presented at Snowmass 90Google Scholar
  40. 40.
    T. Mannel, W. Roberts, Z. Ryzak: Nucl. Phys. B355 (1991) 38; Phys. Lett. B255 (1991) 593Google Scholar
  41. 41.
    N. Isgur, M.B. Wise: Nucl. Phys. B348 (1991) 278; H. Georgi: Nucl. Phys. B348 (1991) 293Google Scholar
  42. 42.
    Particle Data Group, J.J. Hernández et al.: Phys. Lett. B239 (1990) 1Google Scholar
  43. 43.
    D. Izatt et al.: Nucl. Phys. B199 (1982) 269Google Scholar
  44. 44.
    The leptonic width is given by\(\Gamma _{ee} = \frac{{4\pi }}{3}\left( {\frac{4}{9}} \right)\frac{{\alpha ^2 }}{{m_\psi }}f_\psi ^2 \), where the electromagnetic fine structure constant is α≈1/137Google Scholar
  45. 45.
    M. Danilov: review talk of heavy flavour physics (non-LEP) given at the Joint International Lepton-Photon Symposium & Europhysics Conference on High Energy Physics, CERN, Geneva, Switzerland, 1991Google Scholar
  46. 46.
    L. Wolfenstein: Phys. Rev. D43 (1991) 151Google Scholar
  47. 47.
    M.A. Shifman, A.I. Vainshtein, V.I. Zakharov: Phys. Rev. D18 (1978) 2583; S. Bertolini, F. Borzumati, A. Masiero: Phys. Rev. Lett. 59 (1987) 180; N.G. Deshpande et al.: Phys Rev. Lett. 59 (1987) 183; B. Grinstein, R. Springer, M.B. Wise: Nucl. Phys. B339 (1990) 269; A. Ali, C. Greub: Phys. Lett. B259 (1991) 182; Z. Phys. C—Particles and Fields 49 (1991) 431Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Isard Dunietz
    • 1
  1. 1.Theory DivisionCERNGeneva 23Switzerland

Personalised recommendations