π (s)| 2 the corresponding quantity obtained after accounting for known isospin breaking effects by an isospin rotation from the τ -decay spectra. After correcting the τ data for the missing ρ − γ mixing contribution, besides the other known isospin symmetry violating corrections, the ππ I=1 part of the hadronic vacuum polarization contribution to the muon g − 2 are fully compatible between τ based and e + e − based evaluations. τ data thus confirm result obtained with e + e − data. Our evaluation of the leading order vacuum polarization contribution, based on all e + e − data including more recent BaBar and KLOE data, yields a . For the τ di-pion branching fraction we find B CVC ππ 0 = 25.20 ± 0.0.17 ± 0.28 from e + e − +CVC, while B ππ 0 = 25.34 ± 0.0.06 ± 0.08 is evaluated directly from the τ spectra.

We begin a systematic investigation of the anomalous dimension of subleading power N -jet operators in view of resummation of logarithmically enhanced terms in partonic cross sections beyond leading power. We provide an explicit result at the one-loop order for fermion-number two N -jet operators at the second order in the power expansion parameter of soft-collinear effective theory.

We resum the leading logarithms α n s ln 2n−1 (1 − z), n = 1, 2, . . . near the kinematic threshold z = Q 2 /ŝ → 1 of the Drell-Yan process at next-to-leading power in the expansion in (1 − z). The derivation of this result employs soft-collinear effective theory in position space and the anomalous dimensions of subleading-power soft functions, which are computed. Expansion of the resummed result leads to the leading logarithms at fixed loop order, in agreement with exact results at NLO and NNLO and predictions from the physical evolution kernel at N 3 LO and N 4 LO, and to new results at the five-loop order and beyond.

This report summarises the physics opportunities for the study of Higgs bosons and the dynamics of electroweak symmetry breaking at the 100 TeV pp collider.