Embedding of non-simple Lie groups, coupling constant relations and non-uniqueness of models of unification
- 19 Downloads
Abstract
A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) ⇔ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin2ϑ=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons likeE 6, while addition of extra charged fermion singlets can reduce the value of sin2 ϑ to 1/4. We point out that at the present time the models of grand unification are far from unique.
Keywords
Coupling constant relations embedding in higher symmetries Weinberg-Salam model grand unified theories Shmushkevich relations Weinberg angle neutral currents Schur’s lemma graded Lie groupsPreview
Unable to display preview. Download preview PDF.
References
- Bajaj J K and Rajasekaran G 1979Pramana 12 397ADSGoogle Scholar
- Bajaj J K and Rajasekaran G 1980a Madras Univ. Preprint MUTP-79/13 to be published inPramāna Google Scholar
- Bajaj J K and Rajasekaran G 1980bPramana 14 411ADSGoogle Scholar
- Bajaj J K and Rajasekaran G (1980c) Madras University PreprintGoogle Scholar
- Dydak 1979 as quoted by J. Ellis CERN TH-2723Google Scholar
- Fairlie D 1979Phys. Lett. B82 97ADSGoogle Scholar
- Fritzsch H and Minkowski P 1975Ann. Phys. (NY) 93 193CrossRefADSMathSciNetGoogle Scholar
- Georgi H and Glashow S L 1974Phys. Rev. Lett. 32 438CrossRefADSGoogle Scholar
- Georgi H and Weinberg S 1978Phys. Res. D11 1313Google Scholar
- Glashow S L 1961Nucl. Phys. 22 579CrossRefGoogle Scholar
- Gupta V and Mani H S 1974Phys. Rev. D10 1310ADSGoogle Scholar
- Gürsey F 1978 Spring-Verlag lecture notes in Physics, Vol. 94, p 508Google Scholar
- Kac V G 1977Adv. Math. 26 8MATHCrossRefGoogle Scholar
- Khare A, Mani H S and Ramachandran G 1979 Preprint, IP-BBSR/79-13Google Scholar
- Macferlane A J, Mukunda N and Sudarshan E C G 1964J. Math. Phys. 5 576CrossRefADSGoogle Scholar
- Marshak R E and Sudarshan E C G 1961Introduction to elementary particle physics (New York: Interscience)MATHGoogle Scholar
- Neeman Y 1979Phys, Lett. B81 190ADSMathSciNetGoogle Scholar
- Neeman Y and Thierry-Mieg J 1979 Tel Aviv Preprint TAUP 727-79Google Scholar
- Pandit L K 1976Pramana 7 291ADSCrossRefGoogle Scholar
- Pati J C 1979 Technical Reprt. No. 80-003, Univ. of MarylandGoogle Scholar
- Pati J C and Salam A 1973Phys. Rev. D8 1240ADSGoogle Scholar
- Rittenberg V 1978 inGroup theoretical methods in physics Proc. VI. Int. Conf. (Tubingen 1977). eds. O. Kramer and A Riekcers, Springer-Verlag Lectures Notes in Physics 79, Berlin-Heidelberg, New YorkGoogle Scholar
- Salam A 1968Elementary particle theory ed N Svartholm (Stockholm: Almquist and Wiksells) p. 367Google Scholar
- Schecter J and Ueda Y 1973Phys. Rev. D8 484ADSGoogle Scholar
- Weinberg S 1967Phys. Res. Lett. 19 1264CrossRefADSGoogle Scholar
- Weinberg S 1972Phys. Rev. D5 1962ADSGoogle Scholar