Lawrence Berkeley National Laboratory

The study of lepton flavor universality violation (LFUV) in semitauonic b-hadron decays has become increasingly important in light of long-standing anomalies in their measured branching fractions, and the large datasets anticipated from the LHC experiments and Belle II. In this review, a comprehensive survey of the experimental environments and methodologies for semitauonic LFUV measurements at the B factories and LHCb is undertaken, along with an overview of the theoretical foundations and predictions for a wide range of semileptonic decay observables. The future prospects of controlling systematic uncertainties down to the percent level, matching the precision of standard model (SM) predictions, are examined. Furthermore, new perspectives and caveats on combinations of the LFUV data are discussed and the world averages for the R(D(∗)) ratios are revisited. Here it is demonstrated that different treatments for the correlations of uncertainties from D∗∗ excited states can vary the current 3σ tension with the SM within a 1σ range. Prior experimental overestimates of D∗∗τν contributions may further exacerbate this. The precision of future measurements is also estimated; their power to exploit full differential information, and solutions to the inherent difficulties in self-consistent new physics interpretations of LFUV observables, are explored.