Common Origin of (–), (–), and Strong CP Conservation

The multiplicative conservation of both lepton and baryon numbers, i.e. (−)L and (−)3B , is connected to an axionic solution of the strong CP problem in a supersymmetric, unifiable model of quark and lepton interactions. New particles are predicted at the TeV scale, with verifiable consequences at the Large Hadron Collider. Experimentally, there is no evidence against the conservation of additive lepton (L) and baryon (B) numbers. Nevertheless, the prevailing theoretical thinking is that neutrino masses are Majorana and only (−) is conserved. This implies the occurrence of neutrinoless double beta decay [1] which is being pursued actively but yet to be confirmed. Recently it has been pointed out [2] that the parallel situation of (−) conservation is also possible, with the consequence of an absolutely stable proton but allowing deuteron decay and neutronantineutron oscillations. In the following these multiplicative conservation laws are connected to an axionic solution of the strong CP problem in a supersymmetric, unifiable model of quark and lepton interactions. Heavy quarks of charge ∓1/3 with B = ∓2/3 at the TeV scale are predicted. The idea of (−) conservation is well-known. The neutrino ν (L = 1) is paired with a singlet neutral fermion N c (L = −1) through the standard Higgs doublet (φ, φ). In the presence of electroweak SU(2)L × U(1)Y symmetry breaking, 〈φ 〉 = v implies a Dirac mass mD linking ν with N . However, N c is a gauge singlet and as such, it is allowed a large Majorana mass mN , thereby breaking L to (−) L and resulting in a small seesaw Majorana mass for ν, i.e. mν = m 2 D/mN . Similarly, the idea of (−) conservation requires a singlet neutral fermion Σ, carrying B = 1 in the effective interaction uid c jd c kΣ. To implement this in a renormalizable theory, the simplest way is to introduce singlet scalar quark fields h̃, h̃ with charges ∓1/3 and B = ∓2/3, so that the interactions udh̃ and h̃dΣ are allowed. Alternatively, h̃, h̃ may be assigned charges ±2/3, in which case ddh̃ and h̃uΣ are allowed. The large Majorana mass mΣ breaks B to (−) 3B under which the usual quarks are odd and the exotic scalar quarks h̃, h̃ are even. The decay of the lightest N c in the early Universe generates a lepton asymmetry, whereas