Minimal anomaly-free chiral fermion sets and gauge coupling unification

Abstract

We look for minimal chiral sets of fermions beyond the standard model that are anomaly free and, simultaneously, vectorlike particles with respect to colour SU(3) and electromagnetic U(1). We then study whether the addition of such particles to the standard model particle content allows for the unification of gauge couplings at a high energy scale, above $5.0 \times 10^{15}$ GeV so as to be safely consistent with proton decay bounds. The possibility to have unification at the string scale is also considered. Inspired in grand unified theories, we also search for minimal chiral fermion sets that belong to SU(5) multiplets. Restricting to representations up to dimension 50, we show that some of these sets can lead to gauge unification at the GUT and/or string scales.Comment: 13 pages, 5 figures, 8 tables; Comments and references added, final version to appear in Phys. Rev.

Anomaly-free chiral fermion sets and gauge coupling unification

“…In Ref. [6] we extended the study presented here to the case where the chiral fermions were part of SU(5) representations, with dimensions less than 70. It was also studied the gauge and gravitational unification at string scale for both scenarios, fermion with arbitrary quantum numbers and fermions in multiplets of SU(5) representations.…”

“…that we are not interested in (more details see [6]). For three multiplets and limiting the search to d ≡ d 3 (R) ≤ 10 and d 2 (R) ≤ 5 we obtain four different sets of solutions, see Table 1.…”

“…In Ref. [6] it is explained how to compute the one-loop beta coefficients, b i , that are b SM 1 = 41/6, b SM 2 = −19/6 and b SM 3 = −7 for the SM. To study whether the sets in Table 1 lead to unification of the gauge couplings, we performed the so-called B-test.…”

“…In the next two sections we will study [6] which are the minimal sets of chiral fermions, with arbitrary quantum numbers, that are free of anomalies and whether they lead to GCU.…”

More on Fake GUT

“…The cutoff scale Λ cut is a scale larger than the fake GUT scale v 3 and v A corresponding to some heavier particles. An example of such particles is Dirac fermion with (5,3). We may also consider a complex scalar φ 3 in (10, 3) which has a Yukawa coupling L T φ 3 10 and a trilinear coupling φ 3 φ 3 φ 3 (see the App.…”