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Mass of the Neutrino Indian Journal of Pure & Applied Physics Vol. 48, October 2010, pp. 691-696 Review Article Mass of the neutrino S Sahoo Department of Physics, National Institute of Technology, Durgapur 713 209, West Bengal E-mail: [email protected] Received 11 January 2010; revised 12 May 2010; accepted 2 July 2010 In the standard model (SM) of particle physics, neutrinos are massless and neutral spin ½ particles. But from recent experiments, it is found that neutrinos undergo flavour oscillations, violating lepton flavour conservation which implies that neutrinos have non-zero mass. The absolute scale of neutrino masses is very important for understanding the evolution and the structure formation of the Universe as well as for nuclear and particle physics beyond the present standard model. In this review article, first we have tried to put some logical arguments to support that neutrinos have mass. Then various ways of determining the neutrino masses are briefly discussed and their sensitivities are compared. Neutrino mass is a window for new physics beyond the SM. Keywords: Neutrino, Special theory of relativity, Neutrinoless double beta decay, Dirac equation 1 Introduction behaviour of the neutrinos. However, these neutrinos The existence of the neutrino was postulated by themselves are also not free from puzzles. There are Wolfgang Pauli 1 in 1930, in order to explain the three puzzles associated with neutrinos, namely solar continuous beta spectrum as well as the spin-statistic neutrino puzzle, atmospheric neutrino puzzle and relation in the beta ( β) decay. Neutrinos were finally, LSND anomaly. However, these above 2-4 introduced as chargeless and massless particles to neutrino puzzles are solved by assuming that explain something that was missing during beta “neutrinos have mass” and that neutrino mass decay. At first the existence of only one type of eigenstates and weak eigenstates differ, hence, the neutrino was predicted in β-decay. Pauli’s hypothesis neutrinos oscillate. The phenomenon of neutrino was verified around 1953 when the electron-type oscillation was pointed out by Pontecorvo 8. That is neutrino (actually the anti-neutrino νe ) produced in a nothing but a quantum mechanical phenomenon in reactor was observed directly by its rescattering by which one type of neutrino flavour can later be Reines and Cowen 5. The second neutrino species measured to have another kind. During 1995, a group (flavour), muon-neutrino ( νµ), associated with µ in its of researchers in Los Alamos National Laboratory interactions, was detected by its rescattering to first found evidence from accelerator collisions that − + neutrinos can ‘oscillate’ or transmute from one kind produce a muon via νµn →µ pp( ν µ →µ n ) by (flavour) to another. But the rationale for why such an Danby et al. 6 at Brookhaven in 1962. The third oscillation or change implies that neutrinos have neutrino species, tau-neutrino ( ), was observed in 9-11 ντ mass, has not yet been provided satisfactorily . The 2000 by the DONUT experiment at Fermilab by existence of non-zero neutrino mass was firmly observing the τ leptons produced via established by the Super-Kamiokande Collaboration 12 − + 7 ντn →τ pp( ν τ →τ n ) in a nuclear experiment . in 1998, and intensively studied subsequently. These According to the Big Bang model, the Universe discoveries represent the first deviations from the SM began 13.7 billion years ago as a tiny region of pure of particle physics that postulated massless neutrinos energy that expanded and cooled to create the cosmos and conservation of the individual as well as of the we see today. The Big Bang implies: (i) Equal amount total lepton numbers. Several attempts have been of matter and antimatter must have created, and (ii) taken to understand the mechanism behind neutrino they should have annihilated with each other. But in masses and lepton mixing. Current neutrino our present Universe, we observe more matter than experiments measure mass squared differences ∆m2. antimatter ( Baryon Asymmetry ). Now, it is believed But the absolute mass of neutrino is not determined so that the answer to this puzzle could come from the far. In this review article, first we have tried to put 692 INDIAN J PURE & APPL PHYS, VOL 48, OCTOBER 2010 some logical arguments to support that neutrinos have Now we can put our logical arguments to support mass. Then various ways of determining the mass of neutrinos have mass. If neutrino is massless, it moves neutrinos are briefly reviewed and their sensitivities at ‘ c’ with γ = ∞, hence, it must be timeless i.e. are compared. ∆tm = ∞. Consequently, a massless neutrino is changeless. So it cannot spontaneously transform to 2 Arguments for the Existence of Neutrino Mass other form. And it certainly cannot oscillate. But it is It is about 11 years since the discovery of the observed that neutrinos undergo flavour oscillation; existence of neutrino mass. Here, we have put two which imply neutrino must have mass. The flavour different arguments to bring us to this same oscillation does not occur if the neutrinos have zero conclusion i.e. neutrinos must have mass. These are: mass. (i) Relativistic explanation, and (ii) Neutrino’s weak interaction. 2.2 Neutrino’s weak interaction Now we discuss our second type of argument. 2.1 Relativistic explanation Neutrinos are chargeless and colourless fermions. Let us consider the relationship between (a) mass Neutrinos do not enjoy the electromagnetic and strong and speed and (b) mass and time, as discussed in interactions and respond only to weak interactions. relativistic mechanics. According to special theory of According to Dadhich 14 , whatever interacts with weak relativity, only the massless particles can travel with force must be massive and hence neutrino must have speed ‘c’, where ‘ c’ is the velocity of light in vacuum. non-zero mass, howsoever, small. If the particles have some finite mass, they must travel with a speed less than ‘ c’. 3 Mass of the Neutrino Let us consider a clock is sailing through space at a In this section, various ways of determining the constant speed ν. According to the relativistic mass of neutrinos are briefly discussed and their 13 equation for time dilation : sensitivities are compared. ∆ts 3.1 Beta decay ∆=tm =γ∆ t s , …(1) A nucleus with an over abundance of neutrons can 1v2 / c 2 − transform to a more stable nucleus by emitting an electron and an antineutrino. This kind of process is 1 where γ = known as β-decay and the transformation can be 1− v2 / c 2 denoted by: A Z AZ1+ − Here, ∆ts is known as the “proper time” measured X→ Y + e +ν . …(2) by someone who is stationary with respect to the clock. ∆tm is the time interval measured by someone The mass of the neutrino can be determined from 15 with respect to whom the clock is moving with a the endpoint of the β-spectrum . If mν = 0, then the relative speed v. endpoint of the spectrum is tangential to the abscissa, From Eq. (1), it is clear that for a massless particle whereas if mν ≠ 0, then the endpoint is tangential to (e.g. photon), any finite interval ∆ts will be perceived the ordinate. Thus, the shape of the β-spectrum near to be infinite i.e. ∆tm = infinite. This means someone the endpoint can be used to extract the mass of the at rest on earth watching the photon fly will see its neutrino. In this case, usually the average electron internal clock (clock attach to photon) take infinitely neutrino mass is determined. In this method, the long time between ticks and tocks. He sees ( ∆tm) the ultimate sensitivity appears to be mν ~ 0.2 eV. This photon’s time pass infinitely slow; as if time stops for mass determination is independent of the Majorana or photon when not interacting with matter, photons are Dirac nature of neutrinos 16 . The investigation of the timeless – they can travel for billions of year ( ∆tm = endpoint region of a β decay spectrum is still the most infinite) without the passage of any corresponding sensitive model-independent and direct method to proper time (no change). This would imply that a free determine the neutrino mass 17 . photon cannot undergo spontaneous change. Thus, we Recently, the upper limit on the absolute scale of realise that photons are changeless. We conclude here the electron neutrino mass is obtained from the tritium 18 that photons are changeless as well as timeless. beta decay as m(ve)<2 eV. SAHOO: MASS OF THE NEUTRINO 693 3.2 Neutrinoless double beta decay different neutrons) into two up-quarks and two Double beta decay (ββ )is a nuclear transition electrons, but no neutrinos (dd →uu +e−e−). If 0v ββ (Z, A) (Z+2, A) in which two neutrons bound in a decay is discovered, it would imply that neutrinos are nucleus are simultaneously transformed into two Majarana particles 23 . Current neutrino experiments protons plus two electrons (there may be some light measure mass squared differences ∆m2, but do not particles also). Analogous transition of two protons measure the absolute neutrino masses. Previously, it into two neutrons is also occurred in several nuclei. was believed that the 0v ββ decay can probe absolute 19 There are three main modes of ββ decay : (i) In neutrino mass scale, but now after the discovery of the two-neutrino decay mode (2 v ββ ), there are 2νe large neutrino mixing it is clear that apart from few emitted together with 2e−. The lepton number is particular cases the 0v ββ decay probes some conserved for this mode and this mode of decay is combination of masses and mixing. The 0v ββ decay allowed in the standard model of electroweak does not allow a very precise neutrino mass interaction.
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