Abstract
We propose a twin Pati-Salam (PS) theory of flavour broken to the G4321 gauge group at high energies, then to the Standard Model at low energies, yielding a TeV scale vector leptoquark {U}_1^{mu } (3, 1, 2/3) which has been suggested to address the lepton universality anomalies {R}_{K^{left(ast right)}} and {R}_{D^{left(ast right)}} in B decays. Quark and lepton masses are mediated by vector-like fermions, with personal Higgs doublets for the second and third families, which may be replaced by a two Higgs doublet model (2HDM). The twin PS theory of flavour successfully accounts for all quark and lepton (including neutrino) masses and mixings, and predicts a dominant coupling of {U}_1^{mu } (3, 1, 2/3) to the third family left-handed doublets. However the predicted mass matrices, assuming natural values of the parameters, are not consistent with the single vector leptoquark solution to the {R}_{D^{left(ast right)}} anomaly, given its current value.
Highlights
The predicted mass matrices, assuming natural values of the parameters, are not consistent with the single vector leptoquark solution to the RD(∗) anomaly, given its current value
We propose a twin Pati-Salam (PS) theory of flavour broken to the G4321 gauge group at high energies, to the Standard Model at low energies, yielding a TeV scale vector leptoquark U1μ(3, 1, 2/3) which has been suggested to address the lepton universality anomalies RK(∗) and RD(∗) in B decays
There are several distinct mass scales in this matrix: the Higgs vacuum expectation value (VEV) H, H, the Yukon VEVs φ, φ and the VL fourth family masses M4ψ, M4ψc. Assuming the latter are heavier than all the VEVs, we may integrate out the fourth family, to generate effective Yukawa couplings of the quarks and leptons which originate from the diagrams in figure 2
Summary
The usual three chiral fermion families originate from the second PS group GI42I2, broken at the high scale, and transform under eq (2.4) as ψ1,2,3(1, 1, 1; 4, 2, 1)(α2,1,1), ψ c 1. There are no standard Higgs fields under GI42I2, no standard Yukawa couplings involving the chiral fermions These will be generated effectively via mixing with vector-like (VL) fermions. Since the VL fermions will mix only with the second and third chiral families, they lead to effective couplings to TeV scale SU(4)I gauge bosons which violate lepton universality. Where i = 2, 3 (i = 1 being forbidden by Z6), x, y are dimensionless coupling constants and M5 are the VL masses These VL fermions do not couple to the TeV scale SU(4)I gauge bosons, they are responsible for effective first family Yukawa couplings. There are no renormalisable couplings involving a mixture of fourth and fifth VL fermions to any Higgs fields
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