Neutrinos and Their Charged Cousins: Are They Secret Sharers?

"Neutrinos they are very small. They have no charge and have no mass and do not interact at all." So wrote the renowned author John Updike, erring twice in one couplet. Indeed, neutrinos are the most storied of particles. Think of Pauli's famous letter proposing them as a "desperate remedy" for the apparent failure of energy conservation in beta decay. He waited 25 years for his neutrinos to be observed. Think of Ray Davis' good news and bad: that he had succeeded in detecting solar neutrinos, but that they were too few. And only once did I witness a standing ovation at a physics conference -at Neutrino-98 in Takayama, Japan, where scientists at Super-Kamiokande announced the observation of atmospheric neutrino oscillations, an effect I had anticipated almost two decades earlier. 1 A few years later scientists at SNO, the Sudbury Neutrino Observatory in Canada, announced their triumphant resolution of Ray's decades-old solar neutrino problem. More front-page neutrino stories are sure to follow! Neutrinos, once ghostlike and elusive, are now mundane. They are seen and studied from many sources: reactors, accelerators, radioactive decays, Earth's interior, cosmic-ray interactions in the stratosphere and from two stars: the sun and supernova 1987a. What we've learned about them is succinctly described by three left-handed neutrino states and a relatively small number of adjustable parameters, but many vexing questions remain: Is the neutrino mass spectrum normal or inverted? Are the masses lepton-number violating, i.e., Majorana; or lepton-number conserving, i.e., Dirac; or are they a bit of both, thereby putting light singlet states, so-called sterile neutrinos, into play? Will astrophysical observations or the Katrin experiment or searches for neutrinoless double beta decay, determine the neutrino mass scale? Is there observable CP violation in the neutrino sector? Will future data belie our simple model? Let me put aside these questions and begin my tale with a brief historical digression. Recall the five eras of lepton hadron symmetry:

(1 × 1) 2 During the 1920s atoms and their nuclei seemed to be made up from just two elementary constituents: protons and electronsone hadron and one lepton, although neither word had yet been coined. (1 × 2) 2 The discovery of neutrons and the invention of neutrinos led to the second era: one doublet of nucleons and one of leptons.

(1 × 3) 2 The detection of strange particles and muons in cosmic rays led Bob Marshak to propose the Kiev symmetry in 1959. The fundamental Sakata triplet of hadrons (p, n, Λ) was likened to the lepton triplet (ν, e, µ). This era was short lived. Sakata’s triplet was replaced by three quarks, but the discovery of a second neutrino in 1963 undid Marshak’s symmetry.

(2 × 2) 2 Soon after Gell-Mann and Zweig devised quarks, James Bjorken and I proposed the existence of yet one more. Our reasoning was purely aesthetic: with charm, two quark doublets would accompany the two lepton doublets, thus restoring lepton-hadron symmetry. Six years passed before John Iliopoulos, Luciano Maiani and I offered substantive and convincing arguments for the existence of charm, another four before the experimental discovery of charmonium.

(3 × 2) 2 Mere months after the discovery of the J/Ψ, groups led by Marty Perl and Leon Lederman spotted half the members of a third family of fundamental fermions. Top quarks and tau neutrinos would show up decades later. In the current and longest-lived era of leptonhadron symmetry, there are three doublets of quarks and and three of leptons.

Fermion masses and mixings were much simpler in the two-doublet era than now. Back then, with only two families and no evidence for neutrino masses, the ‘flavor problem’ involved only seven parameters: four quark masses, two charged lepton masses and Cabibbo’s angle. But when 2×2 matrices became 3×3, things got complicated. Quark masses and mixings involve six masses and four Cabibbo-Kobayashi-Maskawa (CKM) parameters. Meanwhile, observations of solar and atmospheric oscillations showed that neutrinos have small but consequential masses. Thus the lepton sector involves ten analogous quantities: six lepton masses and four Pontecorvo-Maki-Nakagawa-Sakata (PMNS) parameters, as well as two infuriatingly inaccessible Majorana phases.* All twenty of the flavor parameters are either measured or constrained. And yet, frustratingly, no significant relationship among them strikes the eye nor has any been deduced from a plausible theoretical framework.

The CKM matrix has little in common with its leptonic analog. All three quark mixing angles are small: Cabibbo’s is about 13 • , the others much smaller. Contrariwise, atmospheric neutrino oscillations seem nearly maximal and the solar oscillation angle is large as well. But could there be some common attribute hiding amongst the masses of quarks and leptons, if not amongst their mixings?

The three charged leptons are widely disparate in mass. So are

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