Update of the ALEPH non-strange spectral functions from hadronic $\tau$ decays

An update of the ALEPH non-strange spectral functions from hadronic $\tau$ decays is presented. Compared to the 2005 ALEPH publication, the main improvement results from the use of a new method to unfold the measured mass spectra from detector effects. This procedure also corrects a previous problem in the correlations between the unfolded mass bins. Results from QCD studies and for the evaluation of the hadronic vacuum polarisation contribution to the anomalous muon magnetic moment are derived using the new spectral functions. They are found in agreement with published results based on the previous set of spectral functions.