ReviewPrecision tau physics
Introduction
Since its discovery [1] in 1975 at the SPEAR storage ring, the 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 events accumulated at the peak, together with the large statistics collected in the region, have considerably improved the statistical accuracy of the measurements and, more importantly, have brought a new level of systematic understanding, allowing us to make sensible tests of the properties. On the theoretical side, a lot of effort has been invested to improve our understanding of the dynamics. The basic 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 lepton to the level of precision tests.
The lepton is a member of the third fermion generation which decays into particles belonging to the first and second ones. Thus, 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 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 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 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 decay amplitudes. In the following, the present knowledge on the 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 data. Exhaustive information on more experimental aspects can be found in Refs. [22] and [23].
The leptonic 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 and leptonic decay widths, and used to test the universality of the leptonic couplings in Section 3, which also includes the universality tests performed with , and 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 decay amplitude is indeed of the predicted type, the Lorentz structure of the 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 peak, confirming the family-universality of the leptonic couplings and the existence of (only) three SM neutrino flavours.
The hadronic decays of the 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 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 lepton. The total hadronic width is currently known with four-loop accuracy, providing a very precise determination of the QCD coupling at the 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 is obtained; the accuracy of this result could be considerably improved in the future with much higher statistics.
Together with hadronic data, the hadronic -decay distributions are needed to determine the SM prediction for the anomalous magnetic moment. Section 9 presents an overview of the , and magnetic, electric and weak dipole moments, which are expected to have a high sensitivity to physics beyond the SM. The lepton constitutes a superb probe to search for new-physics signals. The current status of CP-violating asymmetries in decays is described in Section 10, while Section 11 discusses the production of leptons in decays, which is sensitive to new-physics contributions with couplings proportional to fermion masses. The large 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 decay. The current experimental limits are given in Section 12; they provide stringent constraints on flavour models beyond the SM.
Processes with 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, and , proceed through the -exchange diagrams shown in Fig. 1, with the universal SM strength associated with the charged-current interactions: The momentum transfer carried by the intermediate is very small compared to . 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
Lepton universality
In the SM all lepton doublets have identical couplings to the boson. Comparing the measured decay widths of leptonic or semileptonic decays which only differ in the lepton flavour, one can test experimentally that the interaction is indeed the same, i.e., that . The ratio constrains , while the relation provides information on . The present results are shown in Table 2, together with the constraints obtained from leptonic , and decays.
The
Lorentz structure of the charged current
Let us consider the leptonic decays , where the lepton pair (, ) may be (, ), (, ) or (, ). 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 annihilation proceeds through the electromagnetic and weak neutral-current interactions, shown in Fig. 3: . At high energies, where the contribution is important, the study of the production cross section allows to extract information on the lepton electroweak parameters. The coupling to the fermionic neutral current is given by [108] where and , with the corresponding
Hadronic decays
The 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 probes the matrix element of the left-handed charged current between the vacuum and the final hadronic state , Contrary to the well-known process , which only tests the electromagnetic vector current, the semileptonic
The inclusive hadronic width
The inclusive character of the total hadronic width renders possible [232], [233], [234] an accurate calculation of the ratio [ represents additional photons or lepton pairs] using standard field theoretic methods. The theoretical analysis involves the two-point correlation functions for the vector and axial-vector colour-singlet quark currents (; ): which have
determination
The separate measurement of the and tau decay widths provides a very clean determination of [304]. If quark masses are neglected, the experimental ratio of the two decay widths directly measures . Taking [164] and the HFAG values in Eq. (81), one obtains .
This rather remarkable determination is only slightly shifted by the small -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- charged lepton to the virtual photon involves three different form factors: where is the incoming photon momentum and . The only assumptions are Lorentz invariance and electromagnetic current conservation (required by gauge invariance). Owing to the conservation of the electric charge, . At , 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 and test CP violation in production, but violations of the
Tau production in and decays
Heavy meson decays into final states containing leptons are a good laboratory to look for new physics related to the fermion mass generation. Decays such as , , or 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 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 , 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
Tau Physics at the LHC
The study of processes with 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, leptons provide excellent signatures to probe new physics at high-energy colliders. Moreover, since decays are fully contained within the detector, the distribution of the decay products has precious polarization information.
The signal has been already exploited successfully at the LHC to measure [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 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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