Abstract
The weak phase γ is conventionally probed by theB s→ρ 0 mode. The predicted rate is tiny. Even if aB s→ρ 0 K s rate difference could be established, it would not be clear that sin 2γ had been measured, because amplitudes with other weak phases may contribute significantly. Non-CP eigenstates, such asB s →D ± s K ∓, have a two-fold advantage overB s→ρ 0 K s. Their rates are orders of magnitude above that forB s→ρ 0 K s, and they probe theCP-violating phase γ, without any contamination from other weak phases. Detailed time-dependent studies of non-CP eigenstates remove possible final-state phases and extract the weak phase γ.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Kobayashi, T. Maskawa: Prog. Theor. Phys. 49 (1973) 652
For a general reference see, for instance: I. Bigi, V.A. Khoze, N.G. Uraltsev, A.I. Sanda: in: CP Violation, p. 175, C. Jarlskog (ed.) Singapore: World Scientific 1989
L.L. Chau, W.-Y. Keung: Phys. Rev. Lett. 53 (1984) 1802; J.D. Biorken: private communication; Fermilab report, 1988 (unpublished); C. Jarlskog, R. Stora: Phys. Lett. B 208 (1988) 268
R. Aleksan, J. Bartelt, P.R. Burchat, A. Seiden: Phys. Rev. D39 (1989) 1283
R. Aleksan, I. Dunietz, B. Kayser, F. Le Diberder: Nucl. Phys. B361 (1991) 141
M. Gronau, D. London: Phys. Rev. Lett. 65 (1990) 3381
M. Gronau, D. London: Phys. Lett. B 253 (1991) 483
M. Gronau, D. Wyler: Phys. Lett. B 265 (1991) 172; I. Dunietz: Phys. Lett B270, 75 (1991); CERN report, CERN-TH-6239/91, to be published in “B decays,” S. Stone (ed.); CERN report, CERN-TH-6240/91, in progress
D. Du, I. Dunietz, Dan-di Wu: Phys. Rev. D34 (1986) 3414; I. Dunietz, J.L. Rosner: Phys. Rev. D34 (1986) 1404
We have not applied the helicity formalism in order to disentangle the various helicity amplitudes for those processes, but it can be done in principle. The formalism is straightforward and can be found in: M. Jacob, G.C. Wick: Ann. Phys. 7 (1959) 404; G. Valencia: Phys. Rev. D39 (1989) 3339; B. Kayser, M. Kuroda, R.D. Peccei, A.I. Sanda: Phys. Lett. 237B (1990) 508; I. Dunietz, H. Quinn, A. Snyder, W. Toki, H. Y. Lipkin: Phys. Rev. D43 (1991) 2193; G. Kramer, W.F. Palmer: DESY report, DESY 91-072 (1991)
C. Jarlskog: Phys. Rev. Lett. 55 (1985) 1039; Z. Phys. C—Particles and Fields 29 (1985) 491; O.W. Greenberg: Phys. Rev. D32 (1985) 1841; Dan-di Wu: Phys. Rev. D33 (1986) 860; D. Du, I. Dunietz, D.-d. Wu: Phys. Rev. D34 (1986) 3414; J.D. Bjorken, I. Dunietz: Phys. Rev. D36 (1987) 2109; I. Dunietz: Ann. Phys. 184 (1988) 350
C.O. Dib, I. Dunietz, F.J. Gilman, Y. Nir: Phys. Rev. D41 (1990) 1522. See also: P. Krawczyk et al.: Nucl. Phys. B307 (1988) 19; C.S. Kim, J.L. Rosner, C.-P. Yuan: Phys. Rev. D42 (1990) 96; J.L. Rosner: Enrico Fermi Institute report, 1991, to be published in B decays, S. Stone (ed.)
For a definition of colour-allowed and colour-suppressed modes see, for instance: M. Bauer, B. Stech, M. Wirbel: Z. Phys. C—Particles and Fields 34 (1987) 103
J.D. Bjorken: Lectures presented at the 18th Annual SLAC Summer Institute on Particle Physics, Stanford, 1990, SLAC report, SLAC-PUB-5389, 1990
There are cases when the phase γ itself can be unambiguously determined. For instance, consider sinγ at its lower predicted range, say sinγ∼0.1. Then cosγ≈±1. The unambiguous determination of γ requires in addition to a non-vanishing measurement of sinγ, the sign of cosγ (see (2.17)). A small lifetime inequatlity ΔΛ probably allows the measurement of cosγ with a much larger error than can be obtained for sinγ. That may still prove sufficient for measuring the sign of cosγ
M. Bauer, B. Stech, M. Wirbel: Z. Phys. C—Particles and Fields 34 (1987) 103
J.D. Bjorken: Nucl. Phys. B (Proc. Suppl.) 11 (1989) 325
J.L. Rosner: Phys. Rev. D42 (1990) 3732; Enrico Fermi Institute report, EFI 90-80, 1990, presented at Snowmass 90
T. Mannel, W. Roberts Z. Ryzak: Phys. Lett. B259 (1991) 359; Phys. Rev. D44 (1991) 18
M. Neubert et al.: Heidelberg report, HD-THEP-91-28, 1991, to be published in “Heavy Flavours,” A.J. Buras, M. Lindner (eds.)
A. Szczepaniak, E.M. Henley, S.J. Brodsky: Phys. Lett. B243 (1990) 287
M.J. Dugan, B. Grinstein: Phys. Lett. B255 (1991) 583
For the |V ub >/V cb | measurements see: R. Fulton et al., CLEO Coll.: Phys. Rev. Lett. 64 (1990) 16; H. Albrecht et al., ARGUS Coll.: Phys. Lett. 234B (1990) 409. For branching rates see; D. Bortoletto et al., CLEO Coll.: Cornell report, 1991, CLNS 91/1102, to be published in Phys. Rev. D; H. Schröder, ARGUS Coll.: Proceedings of the 25th International Conference on High Energy Physics, Singapore, K.K. Phua, Y. Yamaguchi (eds); D.L. Kreinick, CLEO Coll.: Proceedings of the 1989 Int. Symp. on Lepton and Photon Interactions at High Energies, 1989, Stanford Univ., M. Riordan (ed.), Singapore: World Scientific 1990. An updated overview can be found in 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, 1991
Neglecting, for argument's sake, a final-state phase difference for non-CP eigenstates and contaminations from other weak phases for theCP eigenstates
B. Grinstein: private communication
D. Bortoletto, S. Stone: Phys. Rev. Lett. 65 (1990) 2951
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Aleksan, R., Dunietz, I. & Kayser, B. Determining theCP-violating phase γ. Z. Phys. C - Particles and Fields 54, 653–659 (1992). https://doi.org/10.1007/BF01559494
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01559494