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

TL;DR

This ALEPH study delivers a complete, final analysis of tau decays using the full LEP-1 data set, updating branching fractions for 22 non-strange and 11 strange hadronic modes and providing high-precision hadronic spectral functions. Methodological advances—especially in photon identification, fake-photon corrections, pi0 reconstruction, and data-driven efficiency calibrations—enable rigorous tests of leptonic universality, isospin, and vector/axial-vector separations, with careful cross-checks against kaon and eta/omega channels. The hadronic spectral functions feed a comprehensive QCD analysis, yielding alpha_s(mτ^2)=0.340±0.005_exp±0.014_th and αs(MZ^2)=0.1209±0.0018, offering a stringent test of asymptotic freedom across energy scales. The work also examines CVC via e+e− comparisons, reveals some tensions in certain channels, and underscores the consistency of tau-derived hadronic physics with Standard Model predictions while highlighting areas needing further experimental clarification.

Abstract

The full LEP-1 data set collected with the ALEPH detector at the $Z$ pole during 1991-1995 is analysed in order to measure the $τ$ 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 $τ$ decays. Branching fractions are obtained for the two leptonic channels and eleven hadronic channels defined by their respective numbers of charged particles and $π^0$'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 $τ$ 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 $ρ$ resonance lineshape, and a QCD analysis of the nonstrange hadronic decays using spectral moments, yielding the value $α_s(m^2_τ) = 0.340 \pm 0.005_{\rm exp} \pm 0.014_{\rm th}$. The evolution to the $Z$ mass scale yields $α_s(M_Z^2) = 0.1209 \pm 0.0018$. 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.

Figures (75)

• Figure 1: Determination of the remaining Bhabha contribution in the final $e$-$e$ sample for 1994-1995 data: $\cos\theta^*$ distributions for (a) data, (b) $\tau\tau$ simulation, and (c) Bhabha simulation. The solid line represents a fit of the data with the relative normalization of the $\tau\tau$ and Bhabha contributions left free.
• Figure 2: Determination of the remaining $e^+e^- \rightarrow \mu^+ \mu^-$ contribution in the final $\mu$-$\mu$ sample for 1994-1995 data using the kinematically calculated energy of a hypothetical photon emitted along one of the $e^\pm$ momenta: (a) data, (b) $\tau\tau$ simulation, and (c) $e^+e^- \rightarrow \mu^+ \mu^-$ simulation. The solid line represents a fit of the data with the relative normalization of the $\tau\tau$ and $\mu$-pair contributions left free.
• Figure 3: Determination of the remaining $\gamma^* \gamma^* \rightarrow \mu^+ \mu^-$ contribution in the final $\mu$-$\mu$ sample for 1994-1995 data: acoplanarity angle distributions for (a) data, (b) $\tau\tau$ simulation, and (c) $e^+e^- \rightarrow (e^+e^-) \mu^+ \mu^-$ simulation. The solid line represents a fit of the data with the relative normalization of the $\tau\tau$ and $\gamma\gamma$-induced $\mu$-pair contributions left free.
• Figure 4: Hadron identification efficiency and misidentification probability obtained from the $\tau\tau$ simulation, corrected from data using the control samples, for the 1994-1995 data set.
• Figure 5: Lepton identification efficiencies obtained from the $\tau\tau$ simulation, corrected from data using the control samples, for the 1994-1995 data set.