# Tau (particle)

The tau (τ), also called the tau lepton, tau particle, tauon or tau electron, is an elementary particle similar to the electron, with negative electric charge and a spin of 1/2. Like the electron, the muon, and the three neutrinos, the tau is a lepton, and like all elementary particles with half-integer spin, the tau has a corresponding antiparticle of opposite charge but equal mass and spin. In the tau's case, this is the "antitau" (also called the positive tau). Tau particles are denoted by the symbol
τ
and the antitaus by
τ+
.

Composition Elementary particle Fermionic Lepton Third Gravity, electromagnetic, weak τ− Antitau (τ+) Martin Lewis Perl et al. (1975)[1][2] 1776.86±0.12 MeV/c2[3] (2.903±0.005)×10−13 s[3] −1 e[3] None .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}1/2[3] LH: −1/2, RH: 0 LH: −1, RH: −2

Tau leptons have a lifetime of 2.9×10−13 s and a mass of 1776.86 MeV/c2 (compared to 105.66 MeV/c2 for muons and 0.511 MeV/c2 for electrons). Since their interactions are very similar to those of the electron, a tau can be thought of as a much heavier version of the electron. Because of their greater mass, tau particles do not emit as much bremsstrahlung radiation as electrons; consequently they are potentially much more highly penetrating than electrons.

Because of its short lifetime, the range of the tau is mainly set by its decay length, which is too small for bremsstrahlung to be noticeable. Its penetrating power appears only at ultra-high velocity and energy (above petaelectronvolt energies), when time dilation extends its otherwise very short path-length.[4]

As with the case of the other charged leptons, the tau has an associated tau neutrino, denoted by
ν
τ
.

## History

The search for tau started in 1960 at CERN by the Bologna-CERN-Frascati (BCF) group led by Antonino Zichichi. Zichichi came up with an idea of a new sequential heavy lepton, now called tau, and invented a method of search. He performed the experiment at the ADONE facility in 1969 once its accelerator became operational; however, the accelerator he used did not have enough energy to search for the tau particle.[5][6][7]

The tau was independently anticipated in a 1971 article by Yung-su Tsai.[8] Providing the theory for this discovery, the tau was detected in a series of experiments between 1974 and 1977 by Martin Lewis Perl with his and Tsai's colleagues at the Stanford Linear Accelerator Center (SLAC) and Lawrence Berkeley National Laboratory (LBL) group.[1] Their equipment consisted of SLAC's then-new electron–positron colliding ring, called SPEAR, and the LBL magnetic detector. They could detect and distinguish between leptons, hadrons, and photons. They did not detect the tau directly, but rather discovered anomalous events:

"We have discovered 64 events of the form

e+
+
e

e±
+
μ
+ at least two undetected particles

for which we have no conventional explanation."

The need for at least two undetected particles was shown by the inability to conserve energy and momentum with only one. However, no other muons, electrons, photons, or hadrons were detected. It was proposed that this event was the production and subsequent decay of a new particle pair:

e+
+
e

τ+
+
τ

e±
+
μ
+ 4
ν

This was difficult to verify, because the energy to produce the
τ+

τ
pair is similar to the threshold for D meson production. The mass and spin of the tau was subsequently established by work done at DESY-Hamburg with the Double Arm Spectrometer (DASP), and at SLAC-Stanford with the SPEAR Direct Electron Counter (DELCO),

The symbol τ was derived from the Greek τρίτον (triton, meaning "third" in English), since it was the third charged lepton discovered.[9]

Martin Lewis Perl shared the 1995 Nobel Prize in Physics with Frederick Reines. The latter was awarded his share of the prize for experimental discovery of the neutrino.

## Tau decay

Feynman diagram of the decays of the tau by emission of an off-shell W boson

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.[10][a]

The branching fractions of the dominant hadronic tau decays are:[3]

• 25.49% for decay into a charged pion, a neutral pion, and a tau neutrino;
• 10.82% for decay into a charged pion and a tau neutrino;
• 9.26% for decay into a charged pion, two neutral pions, and a tau neutrino;
• 8.99% for decay into three charged pions (of which two have the same electrical charge) and a tau neutrino;
• 2.74% for decay into three charged pions (of which two have the same electrical charge), a neutral pion, and a tau neutrino;
• 1.04% for decay into three neutral pions, a charged pion, and a tau neutrino.

In total, the tau lepton will decay hadronically approximately 64.79% of the time.

The branching fractions of the common purely leptonic tau decays are:[3]

• 17.82% for decay into a tau neutrino, electron and electron antineutrino;
• 17.39% for decay into a tau neutrino, muon, and muon antineutrino.

The similarity of values of the two branching fractions is a consequence of lepton universality.

## Exotic atoms

The tau lepton is predicted to form exotic atoms like other charged subatomic particles. One of such, consists of an antitauon and an electron:
τ+

e
.[11]

Another one is an onium atom
τ+

τ
called true tauonium and is difficult to detect due to tau's extremely short lifetime at low (non-relativistic) energies needed to form this atom. Its detection would be an important test of quantum electrodynamics, if possible.[11]

## Footnotes

1. ^ Since the tauonic lepton number is conserved in weak decays, a tau neutrino is always created when a tau decays.[10]

## References

1. ^ a b Perl, M.L.; Abrams, G.; Boyarski, A.; Breidenbach, M.; Briggs, D.; Bulos, F.; Chinowsky, W.; Dakin, J.; Feldman, G. (1975). "Evidence for anomalous lepton production in
e+

e
annihilation". Physical Review Letters. 35 (22): 1489. Bibcode:1975PhRvL..35.1489P. doi:10.1103/PhysRevLett.35.1489.
2. ^ Okun, L.B. (1980). Leptons and Quarks. Translated by Kisin, V.I. North-Holland Publishing. p. 103. ISBN 978-0444869241.
3. Tanabashi, M.; et al. (Particle Data Group) (2018). "Review of Particle Physics". Physical Review D. 98 (3): 030001. Bibcode:2018PhRvD..98c0001T. doi:10.1103/PhysRevD.98.030001.
4. ^ Fargion, D.; de Sanctis Lucentini, P.G.; de Santis, M.; Grossi, M. (2004). "Tau air showers from Earth". The Astrophysical Journal. 613 (2): 1285–1301. arXiv:hep-ph/0305128. Bibcode:2004ApJ...613.1285F. doi:10.1086/423124. S2CID 119379401.
5. ^ Zichichi, A. (1996). "Foundations of sequential heavy lepton searches". In Newman, H.B.; Ypsilantis, T. (eds.). History of Original Ideas and Basic Discoveries in Particle Physics. NATO ASI Series (Series B: Physics). Vol. 352. Boston, MA: Springer. pp. 227–275.
6. ^ 't Hooft, Gerard (1996). In Search of the Ultimate Building Blocks. Cambridge University Press. p. 111.
7. ^ Ricci, R.A.; Barnabei, O.; Monaco, F. Roversi; Maiani, L. (5 June 1998). The Origin of the Third Family: In honour of A. Zichichi on the XXX anniversary of the proposal to search for the third lepton at Adone. World Scientific Series in 20th Century Physics. Vol. 20. Singapore: World Scientific Publishing. ISBN 9810231636. ISBN 978-9810231637
8. ^ Tsai, Yung-Su (1 November 1971). "Decay correlations of heavy leptons in e+ + e+ + ". Physical Review D. 4 (9): 2821. Bibcode:1971PhRvD...4.2821T. doi:10.1103/PhysRevD.4.2821.
9. ^ Perl, M.L. (6–18 March 1977). "Evidence for, and properties of, the new charged heavy lepton" (PDF). In Van, T. Thanh; Orsay, R.M.I.E.M. (eds.). Proceedings of the XII Rencontre de Moriond. XII Rencontre de Moriond. Flaine, France (published April 1977). SLAC-PUB-1923. Retrieved 25 March 2021.`{{cite conference}}`: CS1 maint: url-status (link)
10. ^ a b Riazuddin (2009). "Non-standard interactions" (PDF). NCP 5th Particle Physics Sypnoisis. 1 (1): 1–25.
11. ^ a b d'Enterria, David; Perez-Ramos, Redamy; Shao, Hua-Sheng (2022). "Ditauonium spectroscopy". European Physical Journal C. 82: 923. arXiv:2204.07269. doi:10.1140/epjc/s10052-022-10831-x.