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Majorana Returns Frank Wilczek in His Short Career, Ettore Majorana Made Several Profound Contributions

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Majorana Returns Frank Wilczek in His Short Career, Ettore Majorana Made Several Profound Contributions perspective Majorana returns Frank Wilczek In his short career, Ettore Majorana made several profound contributions. One of them, his concept of ‘Majorana fermions’ — particles that are their own antiparticle — is finding ever wider relevance in modern physics. nrico Fermi had to cajole his friend Indeed, when, in 1928, Paul Dirac number of electrons minus the number of Ettore Majorana into publishing discovered1 the theoretical framework antielectrons, plus the number of electron Ehis big idea: a modification of the for describing spin-½ particles, it seemed neutrinos minus the number of antielectron Dirac equation that would have profound that complex numbers were unavoidable neutrinos is a constant (call it Le). These ramifications for particle physics. Shortly (Box 2). Dirac’s original equation contained laws lead to many successful selection afterwards, in 1938, Majorana mysteriously both real and imaginary numbers, and rules. For example, the particles (muon disappeared, and for 70 years his modified therefore it can only pertain to complex neutrinos, νμ) emitted in positive pion (π) + + equation remained a rather obscure fields. For Dirac, who was concerned decay, π → μ + νμ, will induce neutron- − footnote in theoretical physics (Box 1). with describing electrons, this feature to-proton conversion νμ + n → μ + p, Now suddenly, it seems, Majorana’s posed no problem, and even came to but not proton-to-neutron conversion + concept is ubiquitous, and his equation seem an advantage because it ‘explained’ νμ + p → μ + n; the particles (muon is central to recent work not only in why positrons, the antiparticles of antineutrinos, ν¯ μ) emitted in the negative − − neutrino physics, supersymmetry and dark electrons, exist. pion decay π → μ + ν¯ μ obey the opposite matter, but also on some exotic states of Enter Ettore Majorana. In his 1937 pattern. Indeed, it was through studies of ordinary matter. paper2, Majorana posed, and answered, the this kind that the existence of different question of whether equations for spin-½ ‘flavours’ of neutrino, corresponding Majorana fermions fields must necessarily, like Dirac’s original to the different types of charged lepton An electrically charged particle is different equation, involve complex numbers. was discovered4. from its antiparticle as it has the opposite Considerations of mathematical elegance Of course, if neutrinos really differ from electric charge, and electric charge is a and symmetry both motivated and guided antineutrinos, then they are not Majorana measurable, stable property. It is possible, his investigation. Majorana discovered fermions. In recent years, however, the however, for an electrically neutral particle that, to the contrary, there is a simple, situation has come to seem less clear-cut, to be its own antiparticle. Photons, which clever modification of Dirac’s equation for it has been discovered that neutrinos have spin 1 in units of the rationalized that involves only real numbers. With oscillate in flavour5. For example, an Planck’s constant ħ, are a familiar case; this discovery, Majorana made the idea electron antineutrino emitted from the Sun neutral pions (spin 0) are a further example, that spin-½ particles could be their own can arrive at Earth as a muon antineutrino and gravitons (spin 2) another. Particles antiparticles theoretically respectable, that or a tau antineutrino. In some sense this that are their own antiparticles must be is, consistent with the general principles is a small effect, but when neutrinos travel created by fields φ that obey φ = φ* — of relativity and quantum theory. In a long way they have time to do rare that is, real fields, because the complex- his honour, we call such hypothetical things. These flavour oscillations show conjugate fields φ* create their antiparticles. particles Majorana fermions. But are there that the separate ‘laws’ of lepton-number The equations for particles with spin 0, physical examples? conservation do not hold: at best, only the spin 1 and spin 2 — the Klein–Gordon, sum Le + Lμ + Lτ can be strictly conserved. Maxwell (electromagnetism) and Are neutrinos Majorana fermions? Thus awakened from our dogmatic Einstein (general relativity) equations, Majorana speculated that his equation slumber, we re-open Majorana’s question: respectively — readily accommodate real might apply to neutrinos. In 1937, could the distinction between neutrino fields, as these equations are formulated neutrinos were themselves hypothetical, and antineutrino, which seems so plainly using real numbers. and their properties unknown. The apparent, be superficial? (Consider the vast On the other hand, the neutron (which experimental study of neutrinos perceptual disconnect between the morning has spin ½), despite being electrically commenced with their discovery3 in 1956, star and the evening star — yet they’re neutral, is not its own antiparticle: several but their observed properties seemed to both Venus.) neutrons can peacefully coexist within disfavour Majorana’s idea. Specifically, there But how can ν = ν¯ be reconciled with an atomic nucleus, but an antineutron seemed to be a strict distinction between those many observations that seemed to rapidly annihilates. Neither, of course, neutrinos and antineutrinos. indicate a distinction? The point is that are the most famous spin-½ particles — The distinction is connected with the the ν particles produced in, for example, electrons and protons, which are electrically law of lepton-number conservation, which π+ → μ+ + ν are in a very different state of charged — their own antiparticles. So it applies for each of the leptons — electron motion from the ν¯ particles produced in is not obvious that we need an equation (e), muon (μ) and tau (τ). For example, π− → μ− + ν¯ . The former are left handed, to describe spin-½ particles that are their for electrons, lepton-number conservation spinning in the sense that the fingers of your own antiparticles. means that, in any reaction, the total left hand point, if your thumb aligns with the 614 NATURE PHYSICS | VOL 5 | SEPTEMBER 2009 | www.nature.com/naturephysics © 2009 Macmillan Publishers Limited. All rights reserved nphys_1380_SEP09.indd 614 24/8/09 11:14:00 perspective velocity, whereas the latter are right handed. equations if we don’t add antineutrinos as have a heavier fermionic (half-integer spin) So, logically, ν and ν¯ and might be the same separate entities to our fundamental theory. partner; and vice versa for each known particle, having different behaviours when it For if neutrinos in the right-handed state fermion. There is suggestive, although is in different states of motion. of motion are not antineutrinos, they must circumstantial, evidence for the existence If you could bring neutrinos and be something else; and that something of these ‘superpartners’. Specifically, if the antineutrinos to rest, and do experiments else must (as it’s escaped detection so far) superpartners exist and are not too heavy, with them, you could test whether they interact with the kinds of matter we know then in their evanescent form, as virtual behave the same way. That is impractical, very feebly indeed. It is hard to fit such particles, they are computed to modify unfortunately: theoretically, the cosmos is oddball entities within the most attractive (partially screen) the basic units of strong, awash with slow neutrinos, but they are too unified theories, which require symmetry weak and electromagnetic charge so as hard to detect. Although such a direct test among their building blocks. to quantitatively account for the different of Majorana’s hypothesis seems out of reach observed charge values — in a unified field for now, several ambitious experiments are Of supersymmetry and dark matter theory where, fundamentally, those values underway to test one of its implications, Neutrinos were Majorana’s own candidates are equal10. In brief, supersymmetry allows namely, that even the last bastion of for Majorana fermions, and although the unification of the fundamental forces. lepton-number conservation, Le + Lμ + Lτ, they look more promising than ever in If supersymmetry is valid, then the can be toppled. Searches for neutrino-less that regard, no longer are they unique. photon has as its superpartner a spin-½ double β decay, such as Ge76 → Se76 + 2e, Other problems at the frontier of particle, the photino. As the photino mirrors are launching a promising fusillade6. In fundamental physics seem to call for more the properties of the photon, it must be this decay, total lepton number changes by Majorana fermions. its own antiparticle. Thus the photino is a two, so its occurrence would disprove the Supersymmetry is a leading proposal Majorana fermion. So, for similar reasons, conservation law definitively. to improve the symmetry and coherence are various other superpartners (such as Meanwhile, the leading ideas on of the equations of physics9. It involves neutral gauginos, as well as Higgsinos). In neutrino masses, rooted in unified field the expansion of spacetime into a new, a word, supersymmetry comes chock-a- theories, predict that neutrinos are quantum dimension. Particles that move block with Majorana fermions. If, as widely Majorana fermions7,8. The detailed logic is in that direction change their mass and anticipated, superpartners are produced — complex, but the basic idea is simple: we spin. If supersymmetry is valid, then every as real, not just virtual, particles — at the get more economical, and much prettier, known bosonic (integer
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