Left-Right symmetric fermions and sterile neutrinos from complex split biquaternions and bioctonions Vatsalya Vaibhava1 and Tejinder P. Singhb2 aIndian Institute of Technology Kanpur, 208016, India bTata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
[email protected],
[email protected] ABSTRACT In this article we investigate the application of complex split biquaternions and bioctonions to the standard model. We show that the Clifford algebras Cl(3) and Cl(7) can be used for making left- right symmetric fermions. Hence we incorporate right-handed neutrinos in the division algebras based approach to the standard model. The right-handed neutrinos, also known as sterile neutrinos, are a potential dark-matter candidate. We discuss the left-right symmetric fermions and their phenomenology using the division algebra approach. We describe the gauge groups associated with the left-right symmetric model and prospects for unification including gravity, through division algebras. We investigate the possibility of obtaining three generations of fermions and charge/mass ratios through the exceptional Jordan algebra J3(O) and the exceptional groups F4 and E6. I. INTRODUCTION The quaternions were initially introduced by Hamilton to explain rotations in three dimensions, and they form a non-commutative division algebra. To begin with, the use of quaternions and arXiv:2108.01858v1 [hep-ph] 4 Aug 2021 octonions (the next division algebra in the series) was very limited in physics partly because of their complicated multiplication rules and also because vector algebra was able to explain rotations in three-space, as an alternative to quaternions. In [1], Gunaydin and Gursey proposed the use of octonions to understand quarks.