Review
Precision tau physics

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Abstract

Precise measurements of the lepton properties provide stringent tests of the Standard Model and accurate determinations of its parameters. We overview the present status of τ physics, highlighting the most recent developments, and discuss the prospects for future improvements. The leptonic decays of the τ lepton probe the structure of the weak currents and the universality of their couplings to the W boson. The universality of the leptonic Z couplings has also been tested through Z+ decays. The hadronic τ decay modes constitute an ideal tool for studying low-energy effects of the strong interaction in very clean conditions. Accurate determinations of the QCD coupling and the Cabibbo mixing Vus have been obtained with τ data. The large mass of the τ opens the possibility to study many kinematically-allowed exclusive decay modes and extract relevant dynamical information. Violations of flavour and CP conservation laws can also be searched for with τ decays. Related subjects such as μ decays, the electron and muon anomalous magnetic moments, neutrino mixing and B-meson decays into τ leptons are briefly covered. Being one the fermions most strongly coupled to the scalar sector, the τ lepton is playing now a very important role at the LHC as a tool to test the Higgs properties and search for new physics at higher scales.

Introduction

Since its discovery  [1] in 1975 at the SPEAR e+e storage ring, the τ lepton has been a subject of extensive experimental study [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]. The very clean sample of boosted τ+τ events accumulated at the Z peak, together with the large statistics collected in the Υ region, have considerably improved the statistical accuracy of the τ measurements and, more importantly, have brought a new level of systematic understanding, allowing us to make sensible tests of the τ properties. On the theoretical side, a lot of effort has been invested to improve our understanding of the τ dynamics. The basic τ properties were already known, before its actual discovery  [1], thanks to the pioneering paper of Tsai  [21]. The detailed study of higher-order electroweak corrections and QCD contributions has promoted the physics of the τ lepton to the level of precision tests.

The τ lepton is a member of the third fermion generation which decays into particles belonging to the first and second ones. Thus, τ physics could provide some clues to the puzzle of the recurring families of leptons and quarks. In fact, one naively expects the heavier fermions to be more sensitive to whatever dynamics is responsible for the fermion mass generation. The pure leptonic or semileptonic character of τ decays provides a clean laboratory to test the structure of the weak currents and the universality of their couplings to the gauge bosons. Moreover, the τ is the only known lepton massive enough to decay into hadrons; its semileptonic decays are then an ideal tool for studying strong interaction effects in very clean conditions.

All experimental results obtained so far confirm the Standard Model (SM) scenario, in which the τ is a sequential lepton with its own quantum number and associated neutrino. The increased sensitivities of the most recent experiments result in interesting limits on possible new physics contributions to the τ decay amplitudes. In the following, the present knowledge on the τ lepton and the prospects for further improvements are analysed. Rather than giving a detailed review of experimental results, the emphasis is put on the physics which can be investigated with the τ data. Exhaustive information on more experimental aspects can be found in Refs.  [22] and [23].

The leptonic τ decays can be accurately predicted in the SM. The relevant expressions are analysed in Section  2, where they are compared with the most recent measurements of the μ and τ leptonic decay widths, and used to test the universality of the leptonic W couplings in Section  3, which also includes the universality tests performed with π, K and W decays. The Lorentz structure of the leptonic charged-current interactions is further discussed in Section  4. While the high-precision muon data shows nicely that the bulk of the μ decay amplitude is indeed of the predicted VA type, the Lorentz structure of the τ decay is not yet determined by data; nevertheless, useful constraints on hypothetical new-physics contributions have been established. Section  5 describes the leptonic electroweak precision tests performed at the Z peak, confirming the family-universality of the leptonic Z couplings and the existence of (only) three SM neutrino flavours.

The hadronic decays of the τ lepton allow us to investigate the hadronic weak currents and test low-energy aspects of the strong interaction. The exclusive decay modes are discussed in Section  6, which shows that at very low energies the chiral symmetry of QCD determines the coupling of any number of pseudoscalar mesons to the left-handed quark current. The measured hadronic distributions in τ decay provide crucial information on the resonance dynamics, which dominates at higher momentum transfer. Section  7 discusses the short-distance QCD analysis of the inclusive hadronic width of the τ lepton. The total hadronic width is currently known with four-loop accuracy, providing a very precise determination of the QCD coupling at the τ mass scale and, therefore, a very significant test of asymptotic freedom from its comparison with determinations performed at much higher energies. The inclusive hadronic distribution gives, in addition, important information on non-perturbative QCD parameters. The semi-inclusive hadronic decay width into Cabibbo-suppressed modes is analysed in Section  8, where a quite competitive determination of |Vus| is obtained; the accuracy of this result could be considerably improved in the future with much higher statistics.

Together with hadronic e+e data, the hadronic τ-decay distributions are needed to determine the SM prediction for the μ anomalous magnetic moment. Section  9 presents an overview of the e, μ and τ magnetic, electric and weak dipole moments, which are expected to have a high sensitivity to physics beyond the SM. The τ lepton constitutes a superb probe to search for new-physics signals. The current status of CP-violating asymmetries in τ decays is described in Section  10, while Section  11 discusses the production of τ leptons in B decays, which is sensitive to new-physics contributions with couplings proportional to fermion masses. The large τ mass allows one to investigate lepton-flavour and lepton-number violation, through a broad range of kinematically-allowed decay modes, complementing the high-precision searches performed in μ decay. The current experimental limits are given in Section  12; they provide stringent constraints on flavour models beyond the SM.

Processes with τ leptons in the final state are playing now an important role at the LHC, either to characterize the Higgs properties or to search for new particles at higher scales. The current status is briefly described in Section  13, before concluding with a few summarizing comments in Section  14.

Section snippets

Lepton decays

The decays of the charged leptons, μ and τ, proceed through the W-exchange diagrams shown in Fig. 1, with the universal SM strength associated with the charged-current interactions: LCC=g22Wμ{ν̄γμ(1γ5)+ūγμ(1γ5)(Vudd+Vuss)}+h.c. The momentum transfer carried by the intermediate W is very small compared to MW. Therefore, the vector-boson propagator shrinks to a point and can be well approximated through a local four-fermion interaction governed by the Fermi coupling constant GF/2=g2/(8

Lepton universality

In the SM all lepton doublets have identical couplings to the W boson. Comparing the measured decay widths of leptonic or semileptonic decays which only differ in the lepton flavour, one can test experimentally that the W interaction is indeed the same, i.e., that ge=gμ=gτg. The Bμ/Be ratio constrains |gμ/ge|, while the Be/ττ relation provides information on |gτ/gμ|. The present results are shown in Table 2, together with the constraints obtained from leptonic π, K and W decays.

The τ

Lorentz structure of the charged current

Let us consider the leptonic decays ν̄ν, where the lepton pair (, ) may be (μ, e), (τ, e) or (τ, μ). With high statistics, these leptonic decay modes allow us to investigate the Lorentz structure of the decay amplitudes through the analysis of the energy and angular distribution of the final charged lepton, complemented with polarization information whenever available.

The most general, local, derivative-free, lepton-number conserving, four-lepton interaction Hamiltonian, consistent

Neutral-current couplings

In the SM, tau pair production in e+e annihilation proceeds through the electromagnetic and weak neutral-current interactions, shown in Fig. 3: e+eγ,Zτ+τ. At high energies, where the Z contribution is important, the study of the production cross section allows to extract information on the lepton electroweak parameters. The Z coupling to the fermionic neutral current is given by  [108]LNCZ=g2cosθWZμff̄γμ(vfafγ5)f, where vf=T3f(14|Qf|sin2θW) and af=T3f, with T3f=±12 the corresponding

Hadronic decays

The τ is the only known lepton massive enough to decay into hadrons. Its semileptonic decays are ideally suited to investigate the hadronic weak currents and perform low-energy tests of the strong interaction. The decay τντH probes the matrix element of the left-handed charged current between the vacuum and the final hadronic state H, H|(Vudd̄+Vuss̄)γμ(1γ5)u|0. Contrary to the well-known process  e+eγhadrons, which only tests the electromagnetic vector current, the semileptonic τ

The inclusive τ hadronic width

The inclusive character of the total τ hadronic width renders possible  [232], [233], [234] an accurate calculation of the ratio [(γ) represents additional photons or lepton pairs] RτΓ[τντhadrons(γ)]Γ[τντeν̄e(γ)], using standard field theoretic methods. The theoretical analysis involves the two-point correlation functions for the vector Vijμ=ψ̄jγμψi and axial-vector Aijμ=ψ̄jγμγ5ψi colour-singlet quark currents (i,j=u,d,s; J=V,A): Πij,Jμν(q)id4xeiqx0|T(Jijμ(x)Jijν(0))|0, which have

Vus determination

The separate measurement of the |ΔS|=1 and |ΔS|=0 tau decay widths provides a very clean determination of Vus   [304]. If quark masses are neglected, the experimental ratio of the two decay widths directly measures |Vus/Vud|2. Taking Vud=0.97425±0.00022   [164] and the HFAG values in Eq. (81), one obtains |Vus|SU(3)=0.210±0.002.

This rather remarkable determination is only slightly shifted by the small SU(3)-breaking contributions induced by the strange quark mass. These effects can be

Electromagnetic and weak dipole moments

A general description of the electromagnetic coupling of an on-shell spin-12 charged lepton to the virtual photon involves three different form factors: M̄γ=eQεμ(q)ū(p)[F1(q2)γμ+iF2(q2)2mσμνqν+F3(q2)2mσμνγ5qν]u(p), where qμ=(pp)μ is the incoming photon momentum and Q=1. The only assumptions are Lorentz invariance and electromagnetic current conservation (required by gauge invariance). Owing to the conservation of the electric charge, F1(0)=1. At q2=0, the other two form factors

CP violation

In the three-generation SM, the violation of the CP symmetry originates from the single phase naturally occurring in the quark mixing matrix  [433]. Therefore, CP violation is predicted to be absent in the lepton sector (for massless neutrinos). However, the fundamental origin of the Kobayashi–Maskawa phase is still unknown. Obviously, CP violation could well be a sensitive probe for new physics.

The electroweak dipole moments dτγ and dτW test CP violation in τ production, but violations of the

Tau production in B and D decays

Heavy meson decays into final states containing τ leptons are a good laboratory to look for new physics related to the fermion mass generation. Decays such as Bτν̄τ, BD()τν̄τ, Bcτν̄τ or Dsτν̄τ involve the heaviest elementary fermions that can be directly produced at flavour factories, providing important information about the underlying dynamics mediating these processes.

An excess of events in two bcτν̄τ transitions has been reported by BaBar  [450]. Including the previous Belle

Lepton-flavour violation

We have clear experimental evidence that neutrinos are massive particles and there is mixing in the lepton sector. The solar, atmospheric, accelerator and reactor neutrino data lead to a consistent pattern of oscillation parameters  [23]. The main recent advance is the establishment of a sizeable non-zero value of θ13, both in accelerator (Minos  [475], T2K  [476]) and reactor experiments (Daya Bay  [477], Double-Chooz  [478], Reno  [479]), with a statistical significance which reaches the 10σ

Tau Physics at the LHC

The study of processes with τ leptons in the final state is an important part of the LHC program. Owing to their high momenta, tightly collimated decay products and low multiplicity, τ leptons provide excellent signatures to probe new physics at high-energy colliders. Moreover, since τ decays are fully contained within the detector, the distribution of the τ decay products has precious polarization information.

The τ signal has been already exploited successfully at the LHC to measure W   [565],

Outlook

The flavour structure of the SM is one of the main pending questions in our understanding of weak interactions. Although we do not know the reason of the observed family replication, we have learned experimentally that the number of SM fermion generations is just three (and no more). Therefore, we must study as precisely as possible the few existing flavours to get some hints on the dynamics responsible for their observed structure.

The τ turns out to be an ideal laboratory to test the SM. It is

Acknowledgements

I would like to thank Martin Jung, Jorge Portolés and Pablo Roig for useful comments which helped to improve the manuscript. This work has been supported in part by the Spanish Government and EU funds for regional development [grants FPA2011-23778 and CSD2007-00042 (Consolider Project CPAN)], and the Generalitat Valenciana [PrometeoII/2013/007].

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