In light of new data we present an updated phenomenological analysis of the simplified $$U_1$$ U 1 -leptoquark model addressing charged-current B-meson anomalies. The analysis shows a good compatibility of low-energy data (dominated by the lepton flavor universality ratios $$R_D$$ R D and $$R_{D^*}$$ R D ∗ ) with the high-energy constraints posed by $$pp\rightarrow \tau {\bar{\tau }}$$ p p → τ τ ¯ Drell-Yan data. We also show that present data are well compatible with a framework where the leptoquark couples with similar strength to both left- and right-handed third-generation fermions, a scenario that is well-motivated from a model building perspective. We find that the high-energy implications of this setup will be probed at the 95% confidence level in the high-luminosity phase of the LHC.

We present a family-non-universal extension of the Standard Model where the first two families feature both quark-lepton and electroweak-flavour unification, via the SU(4) Sp(4)L Sp(4)R gauge group, whereas quark-lepton unification for the third family is realised à la Pati-Salam. Via staggered symmetry breaking steps, this construction offers a natural explanation for the observed hierarchical pattern of fermion masses and mixings, while providing a natural suppression for flavour-changing processes involving the first two generations. The last-but-one step in the symmetry-breaking chain is a non-universal 4321 model, characterised by a vector leptoquark naturally coupled mainly to the third generation. The stability of the Higgs sector points to a 4321 → SM symmetry-breaking scale around the TeV, with interesting phenomenological consequences in B physics and collider processes that differ from those of other known 4321 completions.

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Fierz transformations for four-fermion operators are generalized to the one-loop level. A general renormalization scheme is used to compute QCD and QED corrections to the tree-level relations, which result from Fierz-evanescent operators. The results can be used to perform general one-loop basis transformations involving four-fermi and evanescent operators. We illustrate the usefulness of our results by discussing two examples from a matching calculation and a one-loop basis change.