The strong coupling constant: Its theoretical derivation from a geometric approach to hadron structure
Since more than a decade, abi-scale, unified approach to strong and gravitational interactions has been proposed, that uses the geometrical methods of general relativity, and yielded results similar to “strong gravity” theory's. We fix our attention, in this note, on hadron structure, and show that also the strong interaction strength αS, ordinarily called the “(perturbative) coupling-constant square”, can be evaluated within our theory, and found to decrease (increase) as the “distance”r decreases (increases). This yields both the confinement of the hadron constituents (for large values ofr) and their asymptotic freedom (for small values ofr inside the hadron): in qualitative agreement with the experimental evidence. In other words, our approach leads us, on a purely theoretical ground, to a dependence of αS onr which had been previously found only on phenomenological and heuristic grounds. We expect the above agreement to be also quantitative, on the basis of a few checks performed in this paper, and of further work of ours on calculating meson mass spectra.
Key wordsstrong coupling constant strong gravity bi-scale theories general relativity geometrical methods
Unable to display preview. Download preview PDF.
- 1.See, e.g., P. Caldirola, M. Pavšič and E. Recami,Nuovo Cimento B 48 (1978) 205;Phys. Lett A66 (1978) 9;Lett Nuovo Cimento 24 (1979) 565. See also E. Recami and P. Castorina,ibid. 15 (1976) 357; A. Italiano and E. Recami,ibid. 40 (1984) 140; E. Recami,Found. Phys. 13 (1983) 341.Google Scholar
- 2.E. Recami,Prog. Part. Nucl. Phys. 8 (1982) 401; E. Recami, J.M. Martínez, and V. Tonin-Zanchin,Prog. Part. Nucl. Phys. 17 (1986) 143; E. Recami and V. Tonin-Zanchin,Phys. Lett. B 177 (1986) 304;B 181 (1986) E416; “Particelle elementari quali micro-universi,” inDove va la scienza, F. Selleri and V. Tonini, eds. (Dedalo, Bari, 1990). See also E. Recami inOld and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology, A. van der Merwe, ed. (Plenum, New York; 1982), p. 377; V. Tonin-Zanchin, M. Sc. thesis (UNICAMP, Campinas, S.P., 1987).Google Scholar
- 3.See,e.g., A. Italianoet al., Hadronic J. 7 (1984) 1321, and references therein; E. Recamiet al., Hadronic J. 14 (1991) 441.Google Scholar
- 4.V. Tonin-Zanchin, E. Recami, J.A. Roversi, and L.A. Brasca-Annes, “Regge-like relations for stable (non-evaporating) black holes,”Found Phys. Lett. 7 (1994); E. Recami and V.T. Zanchin,Nuovo Saggiatore 8 (2) (1992) 13.Google Scholar
- 5.See,e.g., A. Salam and J. Strathdee,Phys. Rev. D 8 (1978) 4598; A. Salam, inProceedings 19th International Conf. High Energy Physics (Tokyo, 1978), p.937;Ann. N. Y. Acad. Sc. 294 (1977) 12; K.P. Sinha and C. Sivaram,Phys. Rep. 51 (3) (1979), S.S. De,Int. J. Theor. Phys. 25 (1986) 1125; D. Sijacki and Y. Ne'eman,Phys. Lett. B 247 (1990) 571.Google Scholar
- 6.See,e.g., C.W. Misner, K.S. Thome, and J.A. Wheeler,Gravitation (Freeman, San Francisco, 1973), Sec. 25.2, pp. 650 et seq.Google Scholar
- 7.Cf.,e.g., L. Landau and E. Lifshitz,The Classical Theory of Fields (Addison-Wesley, Reading. 1971); Ya.B. Zeldovich and I.D. Novikov,Stars and Relativity (Chicago, 1971), p.93; F. Markley,Am. J. Phys. 41 (1973) 45; J. Jaffe and I. Shapiro,Phys. Rev. D 6 (1974) 405; A.P. Lightman, W.H. Press, R.H. Price, and S.A. Teukolski,Problem book in relativity and gravitation (Princeton University Press, Princeton, 1975), p.405; G. Cavalleri and G. Spinelli,Phys. Rev. D 15 (1977) 3065.Google Scholar
- 8.See,e.g., B. Barbiellini and G. Barbiellini, “Unificazione delle forze fondamentali,” Report LNF-86/20(R) (Frascati, 1986); M.R. Pennington, “A new ABC of QCD,” Report (Rutherford Appleton Laboratory, September 1983).Google Scholar
- 9.See,e.g., H.-J. Behrendet al., Phys.Lett. B 183 (1987) 400; see also .Google Scholar
- 10.E. Recami and V. Tonin-Zanchin, work in progress.Google Scholar