Tau particle.

Carmen Belloso Marrec.

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1 Introduction.

The Tau particle, also known as Tau lepton or Tauon, appears to be an elemen-tary particle (or “building block”), which means either it is not made of othersubparticles or the required technology to discover these subparticles is not de-velopped yet. A sketch of principal particles and their clasification is shown infigure (1).

Figure 1: Clasification of main particles.

Whereas leptons are found individually, quarks are always found in packages,building other particles called hadrons. Whether hadrons made by two quarksare called mesons, the other ones, made of three quarks, are called baryons.

All the elementary particles are fermions, which means that th spin is an half-integer. Fermions behaviour is described by Fermi-Dirac statistics (see equation(1)) and fullfils Pauli’s exclusion principle, that states that no more than oneparticle will be at the same state with the same quantum numbers.

ni =1

1 + e("i�µ)kBT

(1)

This is the Fermi-Dirac distribution, where ni is the average number offermions in a monoparticualr state with energy "i.

As baryons are made of three quarks (fermions) they will have half-integerspin and they will be also fermions. However, mesons are made of two quarks so

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they have integer spin, in consequence they are bosons, and the average numberof bosons in a monoparticular state with given energy "i follows the Bose-Eisteinstatistics (equation (2)).

ni =1

1� e("i�µ)kBT

(2)

Every elementary particle has an antiparticle. The particle and its antipar-ticle have the same mass and the opposite charge.

Interactions.

Matter is built with particles that interact between them. In nature we findelectromagnetic, gravitational, strong and weak interactions but in the rangewe work with in particle’s physics, we only find that electromagnetic, strongand weak ones are relevant. Electromagnetic interaction acts between particleswith charge, so that neutral particles do not feel this interaction. For lowenergy ranges the mean part of electromagnetic interaction is the electrostaticone. The interaction element of matrix for nuclear distances ( r ⇠ 1 fm) andunitary charges can be taken as hHemi ' 1MeV. The electrostatic potentialexpresion is

Vee (r) = ↵Z1Z2h̄c

r

where ↵ is the fine structure constant, which value is ↵ = 1137 , Z1 is the charge of

the first interacting particle, Z2 is the charge of the second interacting particleand r is the distance between both particles. Electromagnetic interaction isattractive or repulsive depending on the sign of charges Z1 and Z2.

Strong interaction is felt by hadrons, is the most powerful interaction in thenuclear range. The interaction matrix element value (for r ⇠ 1fm) is hHsi '100MeV and the potential can be modeled by a semi finite squarre well or bythe more accurate model of Yukawa (figure (2)).

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Figure 2: Model of semi finite squarre well (left) and Yukawa’s potential (right).

Weak interaction has the shortest range between all the interactions. thematrix element of interaction can be approximated to hHwi ' 10�4MeV for avolume ⌦ ⇠ 1fm3. Weak interaction is modeled in Fermi’s theory as

Hw = GF �3 (~r) (⌧+ + ⌧�)

2 Leptons.

Leptons are clasified in two types: electron-like leptons (with charge) and neu-tral leptons or neutrinos (without charge). Both types of leptons do not feel thestrong interaction but the weak one, electron-like leptons also undergo electro-magnetic interaction. There are six kind of leptons, known as flavours and theyare subclasified in three generations with increasing masses. In each generationthere are a electron-like lepton and a neutrino. Eventually, each lepton has anantilepton. In figure (3) we see a clasification of leptons.

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Figure 3: Leptons clasification.

Each generation of leptons has asociated a flavor. It is thought that neutri-nos are not completely belonging to a flavor but there are oscillations betweenflavors, so that if we have a bean of electron neutrinos, when we collect thebean after a period of time, we are going to collect also muon neutrinos andtau neutrinos. The change of neutrino states was postulated when a bean ofneutrinos from the sun was collected; although all of them were supposed to beelectron neutrinos, other neutrinos were detected.

Brief chronology.

Electrons are the best known leptons beacuse they are stable leptons whilemuons and tau particles decay and because a high level of energy is requiredto create non electronic leptons, among other reasons. Therefore the electronwas the first discovered lepton by J.J. Thomson in 1897. In 1936 Carl D.Anderson discovered a “meson” that acted like an electron, later, in 1947 thelepton concept was introduced and in 1948 Leon Rosenfeld fixed the Andersonmissunderstandig. Even if the new particle was heavier than the electron itdid not feel the strong interaction and acted like the well known lepton, soRosenfeld concluded that it was the same kind of particle than the electron:the muon is a lepton. In 1930 Wolfgang Pauli was postuled to explain certaincharacteristics of beta decay. It was eventually observed in the Cowan–Reines

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neutrino experiment conducted by Clyde Cowan and Frederick Reines in 1956.In 1962 Leon M. Lenderman discovered the muon neutrino with Melvin Schwartzand Jack Steinberger. The discovery of the tau particle had to wait until 1974,when Martin Lewis Perl achieved to detect some reactions that only could existif a heavier than muon leepton existed.

Leptonic number.

There is a number that characterizes the nature od the leptons, that is theleptonic number. There are three types of leptonic numbers: the electronic, themuonic and the tauonic one. Their values are recovered in the table (2)

Le Le Le

e�, ⌫e 1 0 0e+, ⌫̄e -1 0 0µ�, ⌫µ 0 1 0µ+, ⌫̄µ 0 -1 0⌧�, ⌫⌧ 0 0 1⌧+, ⌫̄⌧ 0 0 -1

Table 1: Leptonic numbers.

For no leptonic particles the leptonic number is 0. There is no evidence ovleptonic number violation, but if the neutrinos mass is different from zero thisviolation could be produced.

3 Tau discovery.

In 1975 Martin Lewis Perl discovered the tau particle with a group of re-searchers from the Stanford Accelerator Center and from the Lawrence BerkeleyLaboratory. The initial purpose of the research included the measurement ofhadrons form factors throught the electron-positron annihilation into hadrons-antihadrons pairs. The title of the experiment was “An Experimental Survey of

Positron- Electron Annihilation into Multiparticle Final States in The Center of

Mass Energy Range 2GeV to 5GeV ”. The last purpose of this experiment (heavylepton searches) was considered as “a joke” by most of the physicist. HoweverMartin Perl was finding a heavier lepton than muon because in reactions likethe following one an amount of energy is lost

e+ + e� ! e± + µ⌥

For a first analysis the Stanford Positron Electron Asymmetric Rings (SPEAR)was used, it was taking a large amount of data from the spring of 1973 throughthe spring of 1974 and allowed a maximum beam energy of about 4.8 GeV in

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the center of mass. All the 4.8 Gev generated data gave the the table shown infigure (4), where one of the most interesting data has been highlined.

Figure 4: Events obteined in the experiment.

A problem was that twenty-four events with an electron and a muon but nophotons could not be explained by conventional backgrounds. The detector usedwas called “Mark I” and it was a general purpose detector and it was not goodenough to detect muons properly and there were not money to buy a bettermuon identification system.

The first explanation was given by Perl: procces which could give a muon, anelectron and no other observed particles could occur through hadron misidenti-fication, and it was very probable in the Mark I detector.

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Figure 5: The general purpose detector Mark I in 1974.

The main way of estimating possible backgrounds was to overestimate thebackground by assuming that there were not anomalous sources of leptons , andto use the number of identified electrons an muons in the data as a mesure ofthe misidentification probability. After doing some estimations, Perl came tothe conclusion that the average misidentification to electrons and muons was18% and 20% respectively. In conclusion, the expectred background was 4.7events or 7 events as maximum. The probability of these numbers fluctuatingto 24 is less than one in a million. There was no way in which the events couldbe explained by backgrounds. There were two possible sources of these events,either a boson decaying by a two - body decay

e+ + e� ! B+ +MB�

B+ ! e+ + ⌫ B� ! µ� + ⌫̄

or a lepton decaying by a three-body decay

e+ + e� ! L+ + L�

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L+ ! e+ + ⌫ + ⌫̄ L� ! µ� + ⌫̄ + ⌫

Perl studied the momentum distribution of the 48 leptons from the 24 eventsat 4.8 GeV, as we see in figure (6) the correct hypothesis can not be told.

Figure 6: Momentum spectrum of leptons from the original 24 eµ events from4.8 GeV data. The solid and dashed curves represent the expectation of a 1.9GeV/c2 lepton and a 2.0 GeV/c2 meson respectively.

Some events that appeared to come from the production of a new parti-cle in the mass range 1.6 to 2.0 GeV/c2 were found, but it was impossible todeterminate whether the particle was a lepton or a boson.

Supposing a systematic mistake in the misidentifications was not made, aquestion had to be answered: what was the nature of the particles that wasproduced? As possible sources of the events ended releasing a muon, in orderto understand the procces, an improval of the muon detector was required. Anadditional absorbed was placed on the top of the detector, called “the muontower” as it is shown in figure (7).

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Figure 7: The detector MArk I after the addition of the muon tower.

As an iron detector (was would be used normally) was too expensive andit would mean a lot of time, barium-loaded concrete pads were used, that hadhalf the density of iron. There were some eµ events in which muon penetratedat least half of the muon tower even a few of them penetrated all the trheeabsorbers (see figure(8)).

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Figure 8: An eµevent in which the muon penetrates both layers of the muontower.

From summer of 1975 to winter of 1975, the data set had grown from 86events of which 22 were estimated to be background to 139 events with 34 ofthem backgound in the new detector which had lower misidentification proba-bilities. New momentum spectrums were drawn (figure (9))

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Figure 9: Left: New momentum spectrums given by Mark I detector with themuon tower for three different beans. The solid curve represents the expectationof a 1.8 GeV(c2 lepton, The dashed and dot-dashed curves represent the expec-tations from a 1.8 GeV(c2 boson with spin 0 and spin 1, helicity 0 respectively.Right: On this page of his logbook, Perl plotted the curves you’d expect for athree-body decay and two different kinds of two-body decays.

When Perl looked at where his data points fell, he was convinced that he hadfound what he sought—three-body decay indicating evidence of the tau leptonbecause distributions were correct for a three-body decay but unacceptable forany form of a two-body decay. After concluding there was a three-body de-cay, it was accepted that they had to find two missing particles in each decay.These particles could be photons, neutral kaons or charged particles. Compar-ing these particles with eµ events researchers could determine an upper limiton the number of anomalous eµ events which had missing hadrons or photonswas 39%. The conclusion was that missing particles had to be neutrinos. Thus,each decay had to hace a lepton and two missing neutrinos. The only particlewith this signature was a heavy lepton.

A lead-glass wall was added to the Mark I (see figure (10)) and that provideda better electron identification and it gave experimental confirmation of previousconclusions.

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Figure 10: Mark I with the lead-glass wall added.

The mass of the particle was measured three ways: from a pseudo-transversemomentum, from the acoplanarity angles, and from the inclusive momentumspectrum. The value obtained was 1.9 ± 0.1 GeV. The best thing about thatfact was that they would be consistent only if the hypothesis was right.

Finally the fact that the eµ cross section is proportional to the square ofthe leptonic branching ratio while the inclusive muon cross section in linearlydependent on it was used to mesure the total cross section for the productionof tau particles. The result was a R (the form factor squared) value of 0.9±0.4,that agrees with the notion that tau particle is a point particle

Until 1977 the new particle (now we know it is a heavy lepton) was calledU from unknown particle. In March 1977 Martin Perl introduced the nowadaysname of the particle. They want to give to the particle a Greek name in analogywith the µ, but only � and ⌧ were avalaible. As ⌧ was the first letter of theGreek word for “third”, this symbol was chosen, because it did reference to thethird generation lepton which the tau lepton belongs to.

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4 Tau properties

Tau particle has a greater mass (m(⌧)=1776.86 MeV/c2) than the rest of theleptons but also than some hadrons like pions (m(⇡+)=139.57018 MeV/c2), pro-tons (m(p)=938.272013 MeV/c2), rho meson (m(⇢)=775.45 MeV/c2)... There-fore this particle decays to give other leptons or hadrons.

Most common decay proccesses of ⌧ are:

⌧� ! e� + ⌫̄e + ⌫⌧ (17.4%)

⌧� ! µ� + ⌫̄µ + ⌫⌧ (17.6%)

⌧� ! ⇡� + ⌫⌧ (10.1%)

⌧� ! ⇢� + ⌫⌧ (21.8%)

As we saw previously, the characteristic number of lepton are leptonic num-bers and more especifically, the characteristic numer of tau lepton is tauonicleptonic number Lµ, which value is 1 for tau and tau neutrino, -1 for their an-tiparticles and 0 for the rest of them. Other quantum numbers of tau particleare :

• Charge: q(⌧�)=-1, q(⌧+)=1, q(⌫⌧ )=0, q(⌫̄⌧ )=0.

• Barionic number: B(⌧�)=B(⌧+)=B(⌫⌧ )=B(⌫̄⌧ )=0

• Strangeness: S(⌧�)=S(⌧+)=S(⌫⌧ )=S(⌫̄⌧ )=0

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Figure 11: Topology of e� + e� ! ⌧� + ⌧+ production ⌧ decays to l+⌫l+⌫⌧+hadrons.

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References

[1] Yorikiyo Nagashima. Elemetary Particle Physics. Volume 1: Quantum

Fields Theory and PArticles. Ed. Witey-Vch.

[2] J. Beringer et al. (Particle Data Group). The Review of Particle Physics.pdg.lbl.gov .

[3] Gary J. Feldman. The Discovery of the ⌧ , 1975-1977: A Tale of Three Pa-

pers. Department of Physics Harvard Universiv Cambridge, MA 02138. ATale of Three Papers.

[4] Logbook of the ⌧ lepton. Simmetry: Dimensions Of Particle Physics

[5] Joaquín Gomez Camacho. Física de Partículas en tres créditos.

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