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Tau Physics: An Introduction

Barry C. Barish

California Institute of Technology Pasadena, CA 91125, U.S.A.

The properties of the neutrino are discussed and the recent result reporting direct detection for the first time is presented. The status of the experimental results relating to the of the nt, both from missing energy in tau decays and from experiments are reviewed. Finally, I give a perspective on future directions in studies of the physics of tau .

1. INTRODUCTION might play an important role in the interpretation of the observations of high energy cosmic rays The was inferred as the third above the Greisen, Kuzmin, Zatsepin (GKZ) neutrino (ne, nm and nt) at the time the tau bound indicating new physics. was discovered and determined to be a lepton. Finally long baseline neutrino experiments

Since that time, direct studies of the nt have will be able to study the role of the tau neutrino proven elusive, however, due to the fact that the in the atmospheric neutrino oscillations with tau is so heavy and difficult to abundantly precision, with the possibility of an even more produce. Finally, the fact that the tau is very powerful experimental probe in the future if a short lived makes the creation of an intense neutrino factory is built, offering perhaps even ‘beam’ of tau neutrinos not so simple. the possibility of observing CP violation in the Much is known about the properties of the neutrino sector. tau neutrino despite the fact that direct detection has only been reported this past summer. In fact, 2. THE NUMBER OF NEUTRINOS that detection is clearly one of the more important results experimental results reported in The evidence that there are three families of high energy physics this year. I review that and is strong. Of course we are evidence in this presentation and a more left with the puzzle why there are the three complete talk will be given later in this families, as well as the problem of determining workshop. the large mass splittings between the families.

It is interesting that the nt was the last of The evidence for the number of standard the leptons and quarks in the three families to be neutrinos comes from two sources: big bang observed in the laboratory, even after the top nucleosynthesis, and the accurate determination , which took a huge effort at to that comes from the partial widths in Z-decay pin down and measure the mass. The fact that measured at LEP. the n is the last to be detected is an indication t 2.1. of the experimental challenge that was involved The earlies indications that there are a finite in making the direct detection of n interactions. t and small number of families in nature came The main interest in the nt has focused on from big bang nucleosynthesis. the issue of neutrino mass and oscillations. The primordial abundances determined for Direct mass measurements have yielded limits 3 4 7 on the neutrino mass, while the indications are D, He, He and Li are affected by the number very strong that atmospheric neutrino of neutrinos produced in the big bang. The observations indicated oscillations between the predictions and understanding of these neutrino and the tau neutrino with a mass abudndances[1] is a major triumph of the standard big bang model of the early . difference of Dm2 ~ 10-3 eV2. This, of course, The abundances of these light elements range implies that the nt has finite mass, but over nine orders of magnitude! The first undoubtedly much smaller than the limits set in 4 the direct mass measurements. constraint on these abundances is on Y, the He Future developments in tau neutrino fraction. From number of when physics look quite promising. Experiments nucleosynthesis began, we know that Y is observing supernovae could lead to quite bounded, Y < 0.25. accurate mass determinations, tau neutrinos Nn = 2.984 ±0.008 This impressive measurement gives strong credence to the view that there are three families of leptons and quarks

3. TAU NEUTRINO EXISTENCE

The existence of the tau neutrino has relied on the indirect (though very strong) evidence until this past summer. The initial evidence was presented by Feldman et al [6] in 1981 from tau decay data. The DONUT experiment [7] at Fermilab has now reported the first direct

observations of detected nt interactions. They observe the tau and its decays from nt charged current interactions The general principal of the DONUT experiment is to produce a strong source of tau neutrinos by interactions of the 800 GeV beam with a beam dump. The proton interactions produce a large number of Ds, having a very short lifetime and subsequently Figure 1. The abundances of light elements in yielding nt’s in the final state. This scheme to nucleosynthesis, which vary by a factor of 109 produce the intense beam of tau neutrinos is are shown. The parameter h is the to shown in figure 2. The data run reported used an ratio x1010, which is not well determined. integrated total number of on target of 3.6 1017 , and the data was taken from April to The observed value of Y (figure 1) is September 1997.

Yobserved = 0.238±0.002±0.005 The presence of additional neutrinos would at the time of nucleosynthesis increases the energy density of the Universe and hence the expansion rate, leading to larger Y. The relation below gives the magnitude of the effect due to an additional neutrino,

DYBBN= 0.012-0.014 DNn 1.7 < Nn < 4.3The most precise measurements of the number of light neutrinos come from Z e+ + e- partial width measurements at LEP. The invisible partial width, Ginv, is determined by subtracting the measured visible partial widths (Z decays to quarks and charged leptons) from the Z width. The invisible width is assumed to be due to NnIn the , (Gn /Gl)SM = 1.991 ± 0.001,where using the ratio reduces the model dependence. Using this prediction and comparing with the accurate LEP measurements, Figure 2. The DONUT tau neutrino beam is the value [5] for the number of neutrinos is created using 800 GeV protons incident on a bounded by beam dump as shown.

The total number of nt interactions is estimated to be ~1100 ( nm , ne , nt ) for the entire DONUT data run. They found 203 candidates for nt in a 6 total of 6.6 10 triggers. The reported nt events satisfied the event topology shown in figure 3, where they measure the parent tau and identify a kink . They also search for the topology were the tau is too short lived to emerge from the 1 mm steel absorber, but they have not reported on that topology. In that case, they do not measure the parent tau but identify the candidates by the apparent kink when the track is projected back toward the vertex.

Figure 4. The pT distribution of candidate events, where the events identified as nt events typically have larger pT.

4. TAU NEUTRINO PROPERTIES Figure 3. The event topology signature for observing tau neutrino interactions in the 4.1 of the nt DONUT experiment. The parent tau is The spin of the nt has been established [5] indentified and the kink from the subsequent tau as J = 1/2. The possibility of J = 3/2 has been decay is observed and measured using nuclear ruled out by establishing that the r- is not in a emultions. pure H ± -1 helicity state in the decay - - The final experimental challenge is t ®r + nt. ‘proving’ that the observed events are due to tau neutrino interactions and not background events 4.2 Magnetic Moment of nt satisfying the topological requirements. Detailed We expect mn = 0 for Majorana or chiral tests and modeling has been done to understand massless Dirac neutrinos. If SU(2)xU(1) is the backgrounds, as well as characterizing extended to include massive neutrinos, measured parameters that can at least statistically 2 -19 distinguish tau neutrino events from background. mn = 3eGFmn /(8p 2)= (3.20´10 )mn mB Background events can come from various sources like overlapping events (randomly where mn is in eV and mB = eh/2me Bohr associated tracks) that fake this topology, magnetons. Using the upper bound mt < 18 scattering of a track to look like a kink or MeV, one obtains m < 0.6 10-11 m . This + n B reconstructed charm events D decays without should be compared to the experimental limit of the lepton identified. Fig. 4 illustrates the pT -7 - - mn < 5.4 10 mB from nt + e ® nt + e distribution of both ‘signal’ events and the scattering as measured in BEBC. candidates identified as background events. As a result of a detailed analsysis of the candidate 4.3 Electric Dipole Moment of the n events, their final result is summarized below. t The electric dipole moment of the n has been t established as < 5.2 10-17 e cm from G (Z ®ee) nt events observed 4 at LEP. expected 4.1 ± 1.4 background 0.41± 0.15 neutrino illustrating how the events limit the neutrino mass.

4.4 nt Charge The charge of the nt has been determined to -14 be < 2 10 from the Luminosity of Red Giants [8]

4.5 nt Lifetime The nt lifetime has been determined to be > 2.8 15 10 sec/eV Astrophysics for mn < 50 eV [9]

4.6 Direct Mass Measurement of nt

Direct bounds on the nt mass come from reconstruction of t multi-hadronic decays. The best limits come from the Aleph experiment at LEP studying the reactions [10]:

- - + Figure 5. Two sample events from the reaction t ® 2p + p + nt - ® - + + 0 t 3p 2p + (p ) + nt with the error contours they set a limit of mt < 22.3 MeV from a to be compared with the kinematic limits for total of 2939 events. different neutrino masses.

- - + + 0 t ® 3p 2p + (p ) + nt

2 they set a limit of mt < 21.5 MeV/c from 52 events. The combined limit is

2 mt < 18.2 MeV/c

The method is to analyze event topologies having very little Q-value phenomenologically as two body decays

t-(Et,pt) ® h- (Eh,ph) + nt (En,pn)

In the tau rest frame, the hadronic energy is

Eh* = (mt2 + mh2 +mn2) / 2mt Figure 6. The reconstructed events from Aleph In the laboratory frame for the reaction displayed on top of the

kinematical limits for mn = 0 (shaded) and mn = Eh = g (Eh* + b ph* cosJ) 23 MeV (line). interval bounded for different mn The likelihood fit for all the events from the max,min * * Eh = g (Eh ± b ph ) - 0 reaction t ® 5p(p )nt is shown in Fig 7 yielding a 90% confidence limit of ~ 23 MeV. Figure 5 illustrates two sample events superposed on the kinematical limits for different The probability P(nl ® nl’ ) for a neutrino of flavor l to oscillate in vacuum into one of flavor l’ is then just the square of this amplitude. For two neutrino oscillations and in vacuum:

2 2 é 2 Lù P(nl ®nl'¹l ) = sin 2Jsin 1.27dM ëê Eûú

Where dM2 is in eV2, L in km and E in GeV. Figure 8 shows the oscillation phenomena as a function of the parameter L/E. The example chosen is for Dm2 = 3 10-3 eV2, which is the nominal value for the neutrino osciallation solutions to the atmospheric neutrino data described below. Note that the probability is P = ½ for large values of L/E and the most sensitive regime to see the effect of neutrino oscillations is Figure 7. The log likelihood fit for the tau when L/E ~ 1/Dm2. These parameters are neutrino mass using the method and data important in the discussion of atmosheric described above for the Aleph experiment at neutrinos below, and the distance chosen for the - 0 CERN using the reaction t ® 5p(p )nt. next generation long baseline neutrino experiments.

5. NEUTRINO OSCILLATIONS

5.1 Introduction to Neutrino Oscillations Neutrino oscillations were first suggested by B. Pontecorvo in 1957 after the discovery of oscillations in the sector. If neutrinos have mass, then a neutrino of definite flavor, nt, is not necessarily a mass eigenstate. In analogy to the quark sector the nt could be a coherent superposition of mass eigenstates. The fact that a neutrino of definite flavor is a superposition of several mass eigenstates, Figure 8. Neutrino oscillation phenomena for 2 -3 2 whose differing masses Mm cause them to various values of L/E using Dm = 3 10 eV . propagate differently, leads to neutrino oscillations: the transformation in vacuum of a This simple relation should be modified neutrino of one flavor into one of a different when there is a difference in the interactions of flavor as the neutrino moves through empty the two neutrino flavors with . The space. The amplitude for the transformation nl ® neutrino weak potential in matter is: nl’ is given by: ì M 2 L -i m ï * G n ï- 2Y + 4Y forn A(n ®n ) = U e 2 EU F B n e e l l ' lm l'm Vweak = ± ´ í å - 2Y forn m 2 2 ï n m,t ï 0 forn where U is a 3 3 unitary matrix in the î 8 hypothesis of the 3 standard neutrino flavors where the upper sign refers to neutrinos, the (ne, nm, nt). In the hypothesis of a U is a 4 x 4 unitary matrix. lower sign to antineutrinos, GF is the Fermi constant, nB the baryon density, Yn the -3 and Ye the number per baryon (both of nm ® nt indicating a mass difference of ~10 about 1/2 in normal matter). Numerically we eV2 between the tau and muon neutrinos. have 5.2 Atmospheric Neutrinos There are several indications for neutrino G n r oscillations, which are indicated in Fig. 9 [11]. F B -14 = 1.9´10 eV -3 However for the purpose of this presentation, 2 2 gcm which addresses the physics of the tau neutrino, the pertinent data is that on atmospheric The weak potential in matter produces a neutrinos, which provide evidence for finite nt phase shift that could modify the neutrino mass, and a mass difference between the tau oscillation pattern if the oscillating neutrinos neutrino and the of about 10-3 have differ ent interactions with matter. The eV2. Below I review the status of the evidence matter effect could help to discriminate between in atmospheric neutrinos and the implications for different neutrino channels. According to the the tau neutrino. equation above the matter effect in the Earth In the hadronic cascade produced from the could be important for nm®ne and for the nm®ns primary cosmic ray we have the production of oscillations, while for nm®nt oscillations there is neutrinos with the following shower cascade: no matter effect. For some particular values of the oscillation parameters the matter effect could P + Nucleus ® p’s + K’s + enhance the oscillations originating "resonances" p(K) ®m + nm (MSW effect). The internal structure of the m ® e + nm + ne Earth could have an important role in the resonance pattern. However, for maximum From these decay channels one expects at mixing, the only possible effect is the low energies approximately twice as many muon reduction of the amplitude of oscillations. neutrinos as electron neutrinos. Detailed corrections do not change this expectation appreciably. The calculation of the absolute neutrino fluxes is more difficult, with uncertainties due to the complicated shower de- velopment in the atmosphere, uncertainties in the cosmic ray spectrum and to uncertainties in production cross sections. The source of atmospheric neutrinos is from collisions at the top of the atmosphere of primary cosmic rays producing secondary and . These secondary either subsequently interact producing a cascade of more pions and kaons or decay into and neutrinos. The decay products contain a muon neutrino and a muon. Finally, the muons themselves decay and producing both a muon and an . The neutrinos are detected in large underground detectors measuring both the flux and the angular distribution. The difference in path length, L, giving sensitivity to neutrino oscillations is from L = 20 km for downward neutrinos near the zenith to L = 12700 km for Figure 9. Indications for neutrino oscillations those coming directly up through the earth near from solar neutrinos , atmospheric neutrinos and the zenith. Also, those coming up near the from the LSND experiment at Los Alamos. The vertical go through the core of the earth and the atmospheric neutrino favored solution is for the effect can be enhanced by matter oscillations.

Figure 10. Atmospheric neutrinos produced in the atmosphere from high energy cosmic ray collisions near the top of the atmosphere. The Figure 11. Summary of the experimental results zenith angle both allows sampling different on the ‘internal events’ for atmospheric distances for the neutrino to oscillate and upward neutrinos. The results indicate significantly neutrinos through the core of the earth can fewer muon neutrinos than expectations. This undergo matter oscillations described above. has been interpreted as due to the disappearance of muon neutrinos by the neutrino oscillation There are two basic topologies of neutrino phenomena. induced events in a detector: internally produced events and externally produced events. The Hint 2: The data from internal events from internally produced events have neutrino the Superkamiokande experiment show an interaction vertices inside the detector. There anisotropy up/down and a distortion of the are several hints for neutrino oscillations, which angular distribution of the up-going events. Fig. altogether make a strong case for finite neutrino 12 illustrates the path difference as a function of mass. angle for neutrinos traversing the earth. Hint 1: Internal events, which are typically . less than 1 GeV have been studied in many detectors. Due to the systematic difficulties mentioned above in accurately predicting the flux at these energies, the systematic errors are significantly reduced if the measured ratio of muon to electron neutrino events is measured, and in fact, usually the ratio of the ratios, R = (nm/ne)obs / (nm/ne)pred, observed to predicted are given. The results are shown in Fig 11 and indicate fewer muon neutrinos than predicted from several experiments and, in particular, from the high statistics measurements. An obvious interpretation is that fewer muon neutrinos are observed because of neutrino oscillations causing some of the parent nm to ‘disappear’ because the neutrino has changed identity to another neutrino. As we will see, the most consistent Figure 12. The path diffence as a funciton of interpretation is that the muon neutrino has zenith angle is shown for atmospheric neutrino oscillated into a tau neutrino. events.

Data from Superkamiokande, shown in Fig. observations with solar neutrinos this check has 13 for the angular distrbution of observed not been possible, as only the integrated flux is atmospheric neutrino events shows a defiit near measured above a threshold energy. It is this the zenith, in agreement with the fits shown with evidence that makes the case so strong for neutrino oscillations, while the expectations atmospheric neutrino oscillations, even though without neutrino oscillations (also shown) the phenomena was observed long after hints indicate significantly more events near the existed for solar neutrinos in the observed flux zenith. deficit. The different energy atmospheric neutrinos are selected from the event topologies. As can be seen from Fig. 14, the external events peak near 100 GeV, while the internal events are less than 1 GeV.

Figure 14. The distribution of energies of detected neutrinos from different event topologies, covering a wide range of energies and allowing important consistency checks for neutrino oscillations.

The high energy data is from upward throughgoing muons resulting from neutrino Figure 13. Angular distributions for both electon interactions in the rock below the detector and and muon neutrinos from the Superkamiokande sending muons up through the detector. The experiment are shown. A deficit near the zenith largest event sample of this type comes from the is noted for muon neutrinos. The best fit MACRO detector at the Gran Sasso. MACRO including neutrino osciallations goes through the has observed: data, while the fit without neutrino oscillations predicts more events near the zenith. Number of observed events 642 Backgrounds 35 Hint 3. The observed anomalies have been Total events 607 found in a consistent way for all energies. Predictions (no oscillations) 825 Atmospheric neutrinos are detected over a very wide range of energies, from sub-GeV neutrinos For these high energy events only muon to neutrinos at energies of 100 GeV or higher. type events are observed, so it is not possible to Since neutrino oscillations are a function of L/E, reduce systematics by making a ratio to electron the consistency over energy showing the type events. The predictions have errors which observed effect is a function of the parameter have been estimated at 17%, making the deficit L/E is a very important check. For the about a 2s effect. The ratio of observed data to results, but the atmospheric data disfavors that the predictions is: solution from the horizontal vs vertical events. So, the favored solution involves oscillation R = 0.84 ± 0.031(stat) ± 0.033(sys) ± 0.12(flux) from muon neutrino to tau neutrino and providing experimental evidence that the tau Where the systematic error is from the neutrino mass is finite. experiment and the flux error from the predictions of the atmospheric neutrino flux. Again, it is possible to also measure the angular distribution and that distribution for MACRO is shown in Fig. 15. Note that the fit to the neutrino oscillation hypothesis not only explains the deficit discussed above, but also explains the observed distortion in the angular distribution showing a deficit near the zenith.

Figure 16. A summary of the two neutrino hypothesis results from the various atmospheric neutrino experiments is shown. The fits are all Figure 15. The angular distribution for high basically consistent with neutrino oscillations of 2 -3 2 energy atmospheric neutrino data from MACRO. nm « nt and having Dm = 3 10 eV . The data indicates a deficit, as predicted by neutrino oscillations which is evident primarily 6. FUTURE PERSPECTIVES near the zenith. 6.1 Supernovae The fits to neutrino oscillations from the What can be learned about the nt from the different experiments, different topologies, next supernovae? If another supernovae occurs different energies, etc are summarized in Fig 16. within our galaxy, potentially it could yield the The effect is seen by many different experiments best direct mass sensitivity for the tau neutrino. in different modes. The data is consistent for Detection of the next supernovae will yield internal contained events, partially contained direct eV scale measurements of m(nm) and m(nt) events, stopping upward events and for from the Supernovae neutrinos [12]. Early black throughgoing upward events. All are consistent hole formation in the collapse will truncate with nm « nt oscillations with maximal mixing neutrino production giving a sharp cutoff, which 2 -3 2 and with Dm = 3 10 eV . allows sensitivity to m(ne) ~1.8 eV for SN at 10 These results are all determined for the two kpc in the Superkamiokande detector. neutrino mixing case. The analysis is somewhat There is a concept for a future supernovae more complicated for three neutrino mixing and detector, OMNIS, that can be used to illustrate space does not permit a discussion here, but the how well the mass of the tau neutrino could be present evidence for neutrino oscillations from addressed from a supernovae. Using the same solar neutrinos, atmospheric neutrinos and principle of sensing the sharpness of timing LSND are not consistent. An additional sterile cutoff, an analysis illustrated in Fig. 17 shows neutrino has been suggested to reconcile all these that from a supernovae at the center of the galaxy one could determine the mass of the tau neutrino over the coming few years and possibly a joint with a sensitivity of 6.2 MeV, which is NASA – ESA science mission in about a decade. significantly better than the limits set at LEP.

Figure 17. The cutoff due to early black hole formation in supernovae can potentially be used to determine the mass of the tau neutrino with sensitivity of about 6.2 MeV.

6.2 Ultra High Energy Cosmic Rays Figure 18. The OWL Airwatch concept is There has been much interest generated shown to mount fluorescence detectors in space recently by the report of observations in several 20 (looking down) to obtain very large acceptance detectors of cosmic rays beyone 10 eV. These in order to study the highest energy cosmic rays. events are above the GZK cutoff where the cosmic rays are absorbed on the way to the earth. Spectra of very high energy neutrinos for One conjecture to avoid this limit is that there are some possible sources that could be detected in super high energy neutrinos incident on the earth Auger or OWL Airwatch is shown in Fig. 19. and several possible mechanisms for production These possible sources could yield neutrinos that have been conjectured. are experimentally accessible in the next The follow up for these observations is the generation of cosmic ray experiments. Auger experiment in Argentina, which is a very large shower array in conjunction with fluorescence detectors. This experiment should be able to confirm with good statistics the events beyond the GZK cutoff. In the longer term, it may be possible to do the measurements with much larger acceptance from space. The idea is to put fluourescence detectors, much like in the the Utah High Res detector into space as shown in Fig 18. The detectors are mounted in spacecraft about 1000 km above the earth’s surface and having a field of view looking down on the earth of 1200 and with two detectors can obtain good spatial resolution. There may be some background Figure 19. Some conjectured sources of ultra issues with lights from the earth and a test high energy neutrinos are shown. It has been mission will be required before a science mission conjectured that neutrinos are the origin of the 20 is scheduled. The plan is to do a test mission events observed beyond 10 eV in cosmic rays.

Possible sources of ultra high energy Fermilab to Soudan Mine), and Opera/Icanoe neutrinos are from interactions of ultrahigh (Europe: CERN to Gran Sasso). energy cosmic ray with 3K cosmic background The first two of the these experiments radiation, neutrinos from AGNs, GRBs, etc, and (K2K and MINOS) are primarily dissappearance Z-bursts – relic neutrinos from big bang experiments, detecting that the muon neutrino cosmology flux has been reduced in transit to the detector, It has been noted that the tau neutrino and the third, ICANOE is able to do an actual content of these ultra high energy neutrinos appearance expeiment, detecting the appearance could be very high [14]. This is due to the short of a tau neutrino interaction from a beam that lived products of the nt giving extra neutrinos began as muon neutrinos. increasing the yield. The nt can be identified by Finally, the ultimate long baseline the characteristic double shower events from experiment might be possible from the first stage charged currect interaction + tau decay into of the proposed muon collider. The muon and nt second shower has typically storage rings can create extremely intense twice as much energy as first “double bang”. The neutrino beams, also providing the possibility of selecting muon neutrinos or anti-neutrinos. The actual flux of nm and nt are approximately equal at these energies. neutrino intensity is very intense allowing long baselines that are optimized for oscillation 6.3 Long Baseline Neutrino Experiments studies. This could be the first truly ‘international’ machine having the neutrino factory on one continent and the detector on another. It will be possible to make precision measurements of the oscillation parameters as illustrated in Fig. 21 having a baseline of 7400 km (for example Fermilab to Gran Sasso). It should also be pointed out that it may even be possible with such a machine to measure CP violation in the neutrino sector!

Figure 21. Precision measurements of neutrino oscillation parameters would be possile from a Fig 20. The sensitivity of the long baseline neutrino factory built as the first stage of a muon neutrino experiments in the region of sensitivity collider. observed for the atmospheric neutrino events. 7. CONCLUSIONS The natural follow up of the atmospheric neutrino experiments detected in deep The physics of the tau neutrino [14] is underground cosmic ray experiments are long becoming an experimentally accessible subject. baseline experiments. The idea is to control the The first evidence for direct observations of the incident beam energy and direction from an tau neutrino by the DONUT experiment is an accelerator and to set L/E in the region of interest important milestone. The determined properties for atmospheric neutrinos. Three long baseline of the tau neutrino are consistent with those of experiments are being build: K2K (Japan: KEK the other neutrinos - ne, nm, nt. Finally, neutrino to Superkamiokande); MINOS (U.S.A.: oscillations opens up a variety of new future possibilities for nt in cosmology, astrophysics and future accelerators

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