Notes

(1) Limits from hadroproduction experiments depend on assumptions about heavy-hadron production cross sections; the limits quoted here are based on collisions where the cross section is presumably well known. For a recent review see L. W. Jones, Rev. Mod. Phys. 49, 717 (1977).

(2) S. Wolfram, Phys. Lett. B (to be published). See also related studies by Ya. B. Zeldovitch, L. B. Okun', and S. B. Pikel'ner, Usp. Fiz. Nauk 87, 113 (1965) [Sov. Phys.---Usp. 8, 702 (1966)]; B. W. Lee and S. Weinberg, Phys. Rev. Lett. 39, 165 (1977); D. A. Dicus, E. W. Kolb, and V. L. Teplitz, ibid. 39, 168 (1977).

(3) S.D. Drell and T.-M. Yan, Ann. Phys. (N.Y.) 66, 578 (1971); for a more recent treatment see E. L. Berger, invited talk at the Vanderbilt Conference, 1978 (unpublished); C. Quigg, Rev. Mod. Phys. 49, 297 (1977).

(4) S. W. Herb et al., Phys. Rev. Lett. 39, 252 (1977) and references therein.

(5) We use the quark distribution functions of Ref. 6 and a gluon distribution function proportional to .

(6) J. Babcock, D. Sivers, and S. Wolfram, Phys. Rev. D 18, 162 (1978).

(7) S. Hayakawa, Cosmic Ray Physics (Wiley, New York, 1969), p. 349; also the model of M. Hillas (private communication from E. W. Kellermann).

(8) Muon-electron pairs produced in collisions may be used as a signal for charm production. This source will undoubtedly swamp any signal in this channel due to heavier hadronic flavors; our calculations indicate that the background to charm from production will also be negligible (less than ). This result is in agreement with previous similar calculations, for example, those of R. Bhattacharya, J. Smith, and A. Soni, Phys. Rev. D 13, 2150 (1976).

(9) P. F. Smith and A. H. Spurway, Rutherford Laboratory Report No. R1-73-023 (unpublished). These values are based on integration over the lifetime of the oceans.

(10) H. J. Rose, private communication.

(11) Bound states of two heavy quarks (such as the ), however, should and do have cross sections significantly smaller than hadrons containing light quarks.

(12) G. B. Yodh, University of Maryland report 1978 (unpublished).

(13) Unlike ionization losses, strong-interaction losses are caused by only a small number of interactions, which are rather inelastic. The fluctuations of the ranges of about the mean will therefore be much larger.

(14) There have been reports of delayed particle production in cosmic rays. See S. C. Tonwar, S. Naranan, and B. V. Sreekantan, J. Phys. A 5, 569 (1972) and references therein, and J. A. Goodman, R. W. Ellsworth, A. Ito, J. R. MacFall, F. Sidhan, R. E. Streitmatter, S. C. Tonwar, P. R. Vishwanath, and G. B. Yodh, Bull. Am. Phys. Soc. 23, paper No. 511 (1978).

(15) R. H. Cahn, Phys. Rev. Lett. 40, 80 (1978).

(16) The scheme of M. Kobayashi and K. Maskawa [Prog. Theor. Phys. 49, 652 (1973)] could not accommodate such a long-lived state. A lifetime sec would require such a new hadron to have a mixing angle significantly smaller than the Cabbibo angle.

previous