Branching ratios and spectral functions of tau decays: Final ALEPH measurements and physics implications

decay branching fractions. Extensive systematic studies are performed, in order to match the large statistics of the data sample corresponding to over 300 000 measured and identified

\tau

decays. Branching fractions are obtained for the two leptonic channels and eleven hadronic channels defined by their respective numbers of charged particles and

\pi^0

's. Using previously published ALEPH results on final states with charged and neutral kaons, corrections are applied to the hadronic channels to derive branching ratios for exclusive final states without kaons. Thus the analyses of the full LEP-1 ALEPH data are combined to yield a complete description of

\tau

decays, encompassing 22 non-strange and 11 strange hadronic modes. Some physics implications of the results are given, in particular related to universality in the leptonic charged weak current, isospin invariance in

a_1

decays, and the separation of vector and axial-vector components of the total hadronic rate. Finally, spectral functions are determined for the dominant hadronic modes and updates are given for several analyses. These include: tests of isospin invariance between the weak charged and electromagnetic hadronic currents, fits of the

\rho

resonance lineshape, and a QCD analysis of the nonstrange hadronic decays using spectral moments, yielding the value

\alpha_s(m^2_\tau) = 0.340 \pm 0.005_{\rm exp} \pm 0.014_{\rm th}

. The evolution to the

Z

mass scale yields

\alpha_s(M_Z^2) = 0.1209 \pm 0.0018

. This value agrees well with the direct determination from the

Z

width and provides the most accurate test to date of asymptotic freedom in the QCD gauge theory.

Note:

139 pages, 75 figures, submitted to Physics Reports

13.35.Dx
13.66.Jn
12.38.Qk
13.66.Bc
14.60.Fg
review
electron positron: colliding beams
electron positron: annihilation
Z0: electroproduction
tau: pair production

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