The Physics of Hadronic Tau Decays

TL;DR

Hadronic tau decays provide a uniquely inclusive, high-precision laboratory for testing QCD and the Standard Model. By constructing and analyzing hadronic spectral functions (both nonstrange and strange) and employing both perturbative QCD and the OPE, the paper extracts a precise αs at the tau scale, tests asymptotic freedom, and probes nonperturbative dynamics via V−A sum rules and chiral sum rules. It also leverages τ data to study hadronic vacuum polarization relevant for the muon g−2 and to determine m_s and |V_us|, while comparing τ-based spectral functions with e+e− data through CVC, highlighting tensions and their implications for data interpretation. The work underscores the synergy between experiment and theory in refining fundamental parameters and demonstrates the continuing potential of τ physics to constrain the SM and guide future experimental directions.

Abstract

Hadronic tau decays represent a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables (sum rules) based on the spectral functions of hadronic tau decays can be related to QCD quark-level calculations to determine fundamental quantities like the strong coupling constant, parameters of the chiral Lagrangian, |V_us|, the mass of the strange quark, and to simultaneously test the concept of quark-hadron duality. Using the best available measurements and a revisited analysis of the theoretical framework, the value alpha_s(m_tau) = 0.345 +- 0.004[exp] +- 0.009[theo] is obtained. Taken together with the determination of alpha_s(m_Z) from the global electroweak fit, this result leads to the most accurate test of asymptotic freedom: the value of the logarithmic slope of 1/alpha_s(s) is found to agree with QCD at a precision of 4%. In another approach, the tau spectral functions can be used to determine hadronic quantities that, due to the nonperturbative nature of long-distance QCD, cannot be computed from first principles. An example for this is the contribution from hadronic vacuum polarization to loop-dominated processes like the anomalous magnetic moment of the muon. This article reviews the measurements of nonstrange and strange tau spectral functions and their phenomenological applications.

Figures (32)

• Figure 1: Left: the spectral function (see Section \ref{['sec:tauspecfun']} for the definition) for the decay $\tau^-\xspace \rightarrow\xspace \omega\pi^-\nu_\tau$ vs. the hadronic mass from the CLEO analysis cleo_4pi. The curves are the results of fits to various combinations of $\rho$, $\rho(1450)$, $\rho(1700)$ resonance contributions. Right: the angular distribution in the $\omega\pi$ center-of-mass frame compared to predictions for different ($l$) partial waves. Second-class currents would reveal themselves as $l=0,2$ waves.
• Figure 2: Measurements of the branching fraction for $\tau^-\xspace \rightarrow\xspace e^-\xspace \overline{\nu}\xspace_e\xspace \nu_\tau\xspace$ (left) and $\tau^-\xspace \rightarrow\xspace \mu^-\xspace \overline{\nu}\xspace_\mu\xspace \nu_\tau\xspace$ (right). References for experiments are argus_becleo_bedelphi_beopal_beopal_bmul3_bealeph_taubr. The world averages are indicated by the shaded vertical bands.
• Figure 3: Comparison of results on the main branching fractions for $\tau$ hadronic modes aleph_taubrcleo_becleo_bhpi0cleo_bh2pi0cleo_b3hcleo_b5hopal_bhopal_b5hargus_b5hhrs_b5hbabar_5h. The world averages are indicated by the shaded vertical bands.
• Figure 4: Left hand plots: the inclusive vector (upper) and axial-vector (lower) spectral functions as measured in aleph_taubr. The shaded areas indicate the contributing exclusive $\tau$ decay channels. The curves show the predictions from the parton model (dotted) and from massless perturbative QCD using $\alpha_{ S}\xspace(M_Z^2)=0.120$ (solid). Right hand plots: comparison of the inclusive vector (upper) and axial-vector (lower) spectral functions obtained by ALEPH and OPAL opal_vasf.
• Figure 5: Inclusive vector plus axial-vector (left) and vector minus axial-vector (right) as measured in aleph_taubr (dots with errors bars) and opal_vasf (shaded one standard deviation errors). The lines show the predictions from the parton model (dotted) and from massless perturbative QCD using $\alpha_{ S}\xspace(M_Z^2)=0.120$ (solid). They cancel to all orders in the difference.