Flavor physics without flavor symmetries

Abstract

We quantitatively analyze a quark-lepton flavor model derived from a six-dimensional supersymmetric theory with SOð10Þ × Uð1Þ gauge symmetry, compactified on an orbifold with magnetic flux. Two bulk 16-plets charged under the Uð1Þ provide the three quark-lepton generations whereas two uncharged 10-plets yield two Higgs doublets. At the orbifold fixed points mass matrices are generated with rank one or two. Moreover, the zero modes mix with heavy vectorlike split multiplets. The model possesses no flavor symmetries. Nevertheless, there exist a number of relations between Yukawa couplings, remnants of the underlying grand unified theory symmetry and the wave function profiles of the zero modes, which lead to a prediction of the light neutrino mass scale, m ν 1 ∼ 10 −3 eV and heavy Majorana neutrino masses in the range from 10 12 to 10 14 GeV. The model successfully includes thermal leptogenesis.

Proton decay in flux compactifications

“…The effective low-energy theory contains two Higgs doublets and possibly light higgsinos, whereas scalar quarks and leptons have GUT scale masses. The theory can account for quark and lepton masses and mixings [27,28], and it can be consistently matched to a supersymmetric theory at the compactification scale, which approximately equals the GUT scale [29][30][31]. Light higgsinos can be made consistent with constraints from direct detection by mixing with an additional singlet [32].…”

“…The considered 6D GUT model has been described in detail in [25,27,28]. The bulk gauge group is SO(10) × U (1) A .…”

“…Furthermore, there are two 16-plets, Ψ and Ψ c , yielding singlets for spontaneous B − L breaking, and eight 10-plets required by 6D anomaly cancellation, which contain two Higgs doublets, H u and H d , and further vector-like split multiplets that acquire GUT scale masses. The vector-like split multiplets are crucial to obtain realistic mass matrices for the light quarks and leptons, as discussed in [27,28]. However, they have no effect on proton decay amplitudes and we can therefore ignore them in the following.…”

“…Since the parities are associated with matrices that do not commute with SO(10), the parities of the different Standard Model fields contained in the 16-plets are in general different. The choice in [28] leads to the decompositions given in Eqs. (6).…”

“…where b is the one-loop coefficient of the β-function. For the gauge group SO (10) with N = 2 supersymmetry, eight 10-plets and six 16-plets, which corresponds to the model in [28], one obtains 1 b = 12. Due to the large number of bulk matter fields one reaches the strong coupling regime, 1/g 2 i ≈ 0, already close to the compactification scale, at Λ/M c 3.7.…”