Abstract
The standard model does not provide an explanation of the observed alignment of quark flavors i.e. why are the up and down quarks approximately aligned in their weak interactions according to their masses? We suggest a resolution of this puzzle using a combination of left-right and Peccei-Quinn (PQ) symmetry. The quark mixings in this model vanish at the tree level and arise out of one loop radiative corrections which explain their smallness. The lepton mixings, on the other hand, appear at the tree level and are therefore larger. We show that all fermion masses and mixings can be fitted with a reasonable choice of parameters. The neutrino mass fit using seesaw mechanism requires the right-handed ${W}_{R}$ mass bigger than 18 TeV. Due to the presence of PQ symmetry, this model clearly provides a solution to the strong $CP$ problem.
Highlights
The standard model (SM), in spite of its spectacular successes, leaves many questions unresolved such as the gauge hierarchy problem, the strong CP problem, neutrino masses, and dark matter
One rarely discussed puzzle is: why are the up and down quark flavors approximately aligned in their weak interactions according to their masses, i.e., the top quark is aligned with the bottom quark and for other generations? Note that the flavor is defined by the WÆ interaction prior to symmetry breaking and the masses and mixings of fermions are determined by the Yukawa couplings
The difference in our case is that color triplets always connect up quarks to down quarks, which is similar to the up-down connecting sextet field analyzed in [11]
Summary
The standard model (SM), in spite of its spectacular successes, leaves many questions unresolved such as the gauge hierarchy problem, the strong CP problem, neutrino masses, and dark matter. It is not a priori guaranteed that the quarks that appear in the gauge interaction will remain dominantly coupled to each other after symmetry breaking. We will call this the “flavor alignment” puzzle. We propose an alternative solution based on a combination of Uð1ÞPQ symmetry [4] and the left-right symmetry [5] which resolves this puzzle for all the three generations, while simultaneously solving the strong CP, neutrino mass and dark matter problems. Getting quark mixings out of one loop effects requires additional colored scalars in the model [6] with masses in the 10 TeV range. In the Appendix, we explain in detail how the various stages of the symmetry breaking emerge
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