Twin Pati-Salam theory of flavour with a TeV scale vector leptoquark

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 $$ {U}_1^{\mu } $$ U 1 μ (3, 1, 2/3) which has been suggested to address the lepton universality anomalies $$ {R}_{K^{\left(\ast \right)}} $$ R K ∗ and $$ {R}_{D^{\left(\ast \right)}} $$ R D ∗ 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 $$ {U}_1^{\mu } $$ U 1 μ (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 $$ {R}_{D^{\left(\ast \right)}} $$ R D ∗ anomaly, given its current value.

Pion electronic decay and lepton universality

In common with a number of simple processes involving elementary particles, charged pion decays are profoundly shaped by applicable Standard Model (SM) symmetries and properties. Given the highly precise SM theoretical description, pion decays are used as selective probes of SM parameters, and of possible SM extensions. The PEN experiment at PSI is studying the \pi^+ \to e^+\nu_e(\gamma)π+→e+νe(γ), or \pi_{e2(\gamma)}πe2(γ) decay. The primary goal is to reach the relative precision of 5 \times 10^{-4}5×10−4 in R_{e/\mu}^\piRe/μπ, the branching ratio for \pi_{e2(\gamma)}πe2(γ) decay. We review the PEN research program, its present status, and prospects.

The $$\uptau $$ challenges at FCC-ee

At FCC-ee, about $$1.7 \times 10^{11}\,\hbox {Z} \rightarrow \uptau ^+\uptau ^-$$ 1.7 × 10 11 Z → τ + τ - events will be produced. This high statistics in the clean $$\hbox {e}^+\hbox {e}^-$$ e + e - environment opens the possibility of much improved determinations of $$\uptau $$ τ -lepton properties and, via the measurement of the $$\uptau $$ τ polarisation, of the neutral-current couplings of electrons and $$\tau $$ τ s. Improved measurements of $$\uptau $$ τ -lepton properties—lifetime, leptonic branching fractions, and mass—allow important tests of lepton universality. The experimental challenge is to match as far as possible statistical uncertainties generally at the $$10^{-5}$$ 10 - 5 level. This applies in particular to the lifetime measurement, which is derived from the 2.2-mm $$\uptau $$ τ average flight distance, and for the branching fraction and polarisation measurements, where the cross-channel contamination is of particular concern. These issues raise strict detector requirements, in particular, on the accuracy of the construction and alignment of the vertex detector and of the precise calorimetric separation and measurement of photons and $$\uppi ^0$$ π 0 s in the collimated $$\uptau $$ τ decay topologies.