Tau
Composition :
Statistics :
Generation :
Family :
Interaction forces :
Symbol :
Antiparticle :
Mass :
Decays into :
Electric charge :
Color charge
Spin :
Weak isospin :
Weak hypercharge :
Elementary particle
Fermionic
Third
Lepton
weak,
electromagnetic force
gravity
τ
Antimuon (τ or τ⁺ )
1776.86 MeV/c²
can decay into hadron
-1
none
¹/₂
LH : - ¹/₂, RH : 0
LH : -1, RH : -2
_
Definition and characteristics
The tau lepton is one of the six types of leptons in the Standard Model of particle physics, alongside the electron, muon, and their corresponding neutrinos. Leptons are elementary particles, meaning they are not composed of smaller constituents. The tau lepton is denoted by the symbol τ (antiparticle is τ ̅ ). Sometimes the tau lepton is symbolised as τ- and the antiparticle as τ+.
Here are some key features and properties of the tau lepton:
Mass: The tau lepton is heavier than both the electron and the muon. Its mass is approximately 1.777 GeV/c² (giga electronvolts divided by the speed of light squared).
Charge: Like the electron and muon, the tau lepton carries a fundamental electric charge of -1e, where "e" is the elementary charge.
Spin: The tau lepton has a spin of 1/2, which is a characteristic quantum property associated with particles.
Lifetime: The tau lepton has a very short lifetime compared to the electron and muon. It decays through weak interactions, converting into lighter particles. The mean lifetime of the tau is around 2.9 x 10^-13 seconds.
Decay Modes: When a tau lepton decays, it can produce a variety of particles. The most common decay modes involve the emission of neutrinos and charged particles, such as electrons or muons. The specific decay modes depend on the interactions taking place.
Weak Force Interaction: Like all leptons, tau interacts via the weak force, one of the fundamental forces in the Standard Model responsible for processes such as beta decay and neutrino interactions.
Production: Tau leptons are produced in high-energy processes, such as those occurring in particle accelerators or certain types of cosmic ray interactions. They are also produced in high-energy particle collisions, such as those observed at facilities like the Large Hadron Collider (LHC).
Tau Neutrino: For every tau lepton, there is a corresponding tau neutrino (ντ). Neutrinos are neutral, extremely light particles that rarely interact with matter, making their detection challenging.
Combinations with tau
There are no known stable composite particles where the tau lepton is an integral part of the composite structure. The tau lepton itself is considered an elementary particle, meaning it is not composed of smaller constituents.
The tau lepton is predicted to form exotic atoms like other charged subatomic particles. One of such, consists of an antitau and an electron: τ+ e− , called tauonium.
Another one is an onium atom τ+ τ− called ditauonium or true tauonium, which is challenging to detect due to the difficulty to form it from two (opposite-sign) short-lived tau leptons. [1] Its experimental detection would be an interesting test of quantum electrodynamics.
Creation of the tau lepton
Tau leptons can be created in various high-energy processes involving the interaction of particles. Here are some of the main processes that can lead to the creation of tau leptons:
Electron-Positron Annihilation:
When an electron and a positron (its antiparticle) collide, they can annihilate each other, producing energy in the form of photons. These photons, in turn, can create quark-antiquark pairs. These quark-antiquark pairs can further interact to produce tau leptons.
Quark scattering and Higgs Decay:
In the Standard Model, the Higgs boson couples proportionately to mass and will decay into any particle lighter than half of its mass. The probability that the Higgs boson decays into a particle is known as the branching ratio.
If the Higgs boson has a mass less than twice the W boson mass (about 160 GeV), the Higgs boson dominantly decays into bottom quarks and tau leptons. The ratio of widths is approximately Γ(h0→bb¯):Γ(h0→τ+τ−)≃3m2b:m2τ
The factor of 3 arises because there are three different bottom quarks (colloquially called red, green, blue) coming from the fact that the bottom quarks are "colored", that is they are charged under Quantum Chromodynamics. The mass of the bottom quark is approximately 4.5 GeV and the mass of the tau lepton is approximately 1.7 GeV.
From this we find that the ratio of the widths is about 61: 3 or about 20:1.
The branching ratio into taus leptons is then given by Br(h0→τ+τ−)≃Γ(τ+τ−)/(Γ(bb¯)+Γ(τ+τ−)) or about 5%.
Being a little bit more precise, the bottom quark's mass isn't a fixed value, but in fact changes substantially under renormalization group evolution and becomes smaller at high energies. This decreases the width into bottom quarks by about 50%, thereby increasing the probability of decaying into tau leptons. The more correct value is about 8% of light mass Higgs bosons decay into tau leptons.
This decay mode can be useful in discovering the Higgs boson at the Large Hadron Collider (LHC). The most promising channel is known as Vector Boson Fusion where two W bosons are radiated off incoming quarks and then fuse to make a Higgs boson which subsequently decays to two taus illustrated below :
Tau Pair Production:
In high-energy environments, it is possible for tau leptons to be produced directly in pairs. This can happen in processes involving the strong force, electromagnetic interactions, or weak interactions, depending on the specific conditions.
W and Z Boson Decays:
The weak force mediates the decay of W and Z bosons, and one of the possible decay channels involves the creation of tau leptons. For example, a W+ boson can decay into a tau neutrino and a tau lepton, or a Z boson can produce a tau-antitau pair.
Top Quark Decays:
The top quark, being the heaviest known quark, can decay into a W boson and a bottom quark. The W boson, in turn, can decay into different particles, including tau leptons.
D-meson decay
The BESIII detector registered the decay of a D+-meson into a tau lepton and a Tau Neutrino.
Antitau decay
See also the chapter of the tau decay where tau leptons can decay into antitau leptons.
Figure 252 - electron-positron annihilation creating a tau lepton
Figure 253 - Higgs boson decay creating a Tau lepton
Figure 254 - Tau pair production
Figure 255 - Top qark decay creating a tau lepton
Figure 256 - D+-meson decay creation tau lepton
Decay of the tau lepton
The decay of a tau lepton involves the weak force, one of the four fundamental forces described by the Standard Model of particle physics. The tau lepton is not a stable particle and undergoes decay into lighter particles. The specific decay process can vary, and it depends on the interaction vertices and the available energy. Generally, the decay of a tau lepton can be categorized into three main channels: leptonic decays, semi-leptonic decays, and hadronic decays.
Leptonic Decays:
Electron Channel
The tau lepton can decay into an electron, an electron antineutrino and a tau neutrino . The interaction involves the exchange of a W⁻ boson.
Muon Channel
Similarly, the tau lepton can decay into a muon, a muon antineutrino and a tau neutrino. This process also involves the exchange of a W⁻ boson.
Tau Neutrino Channel
The tau lepton can decay into a tau neutrino and a pion (π⁻). The pion, being a meson, subsequently decays into a muon and a muon neutrino or an electron and an electron antineutrino.
Semi-Leptonic Decays:
One-Prong Decays
In some cases, the tau lepton can decay into one charged particle (e.g., a pion) and one or more neutral particles (e.g., τ⁻ → π⁻π⁰ν_τ)
Three-Prong Decays
The tau lepton can also decay into three charged particles and neutral particles. (e.g., τ⁻ → π⁻π⁻π⁰ν_τ)
Hadronic Decays:
The tau is the only lepton that can decay into hadrons – the masses of other leptons are too small. Like the leptonic decay modes of the tau, the hadronic decay is through the weak interaction
Multi-Hadron Decays (e.g., τ⁻ → π⁻π⁻π⁺π⁰ν_τ):
In hadronic decays, the tau lepton can produce multiple mesons (pions) along with a tau neutrino.
The specific decay mode and branching ratios are determined by the probabilities associated with different possible final states. The probabilities are influenced by the masses of the particles involved, the available energy, and the coupling constants associated with the weak force.
Figure 257 - Leptonic tau decay via electron channel
Figure 258 - Leptonic tau decay via muon channel
Figure 259 - Leptonic tau decay via neutrino channel
Figure 260 - Hadronic tau decay
Literature
In-Depth Reading
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Decays of the Tau lepton. Patricia R. Burchat. (Stanford Linear Accelerator Center Stanford University Stanford, California 94305) (1986)
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Precision Tau Physics. Antonio Pich (Departament de F´ısica Te`orica, IFIC, Universitat de Val`encia – CSIC Apartat Correus 22085, E-46071 Val`encia, Spain) (2013)
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Physics of Tau Leptons. Simonetta Gentile and Martin Pohl (1995)
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New method for beyond the Standard Model invisible particle searches in tau lepton decays. E. De La Cruz-Burelo , A. De Yta-Hernandez and M. Hernandez-Villanueva. (2020)
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Reconstruction and classification of tau lepton decays with ILD. T. H. Trana, V. Balagura, V. Boudry, J.-C. Brient, H. Videau (2016)
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Reconstruction and identification of τ lepton decays to hadrons and ντ at CMS. (The CMS Collaboration). (2016)
References
[1] d'Enterria, David; Perez-Ramos, Redamy; Shao, Hua-Sheng (2022). "Ditauonium spectroscopy". European Physical Journal C. 82 (10): 923. arXiv:2204.07269. doi:10.1140/epjc/s10052-022-10831-x. S2CID 248218441