Key to the Universe
The restrooms of the downtown Dortmund pub Kraftstoff (meaning “fuel”) are wallpapered with a superhero cartoon, in which the protagonist announces stone-faced: “I’m looking for a very rare key, made out of the finest crystal and hidden in a deep vault.” This picture is an ideal metaphor for neutrino physics in the new millennium. Neutrinos are indeed sought in the deep vaults of underground labs, and they indeed could serve as keys for GUT theories—or even more exotic theories—to explain the physics of elementary particles. The link between neutrino masses and the deepest mysteries of the particle world is the mechanism of neutrino mass generation: the answer to why the neutrino mass is so special. The discovery of neutrino mass in the 1990s provided the theorists with two rows to hoe. First: How can neutrino masses be implemented in the Standard Model? Second: Why are neutrinos so much lighter than the other elementary particles such as quarks or the electron and its heavier siblings, muon and tau? And how can neutrinos be described successfully in a unified theory together with the charged leptons and quarks if they are at least a million times lighter?
To clarify these questions, particle theorists have proposed several models of neutrino mass generation. The most popular explanation is known as the seesaw mechanism and uses a logic that appears rather strange at first glance: The observable, left-handed neutrino is so light because its right-handed partner is so heavy. The idea behind this is that the left-handed neutrino, in order to generate a mass, has to fluctuate temporarily into the heavy right-handed state. Since the probability of this quantum fluctuation, which relies on the energy version of the uncertainty principle (see Chapter 4), is small when the energy or mass that has to be “borrowed” from the vacuum is large, the process is extremely unlikely and the resulting mass is small. As a metaphor one could imagine a mountain being so high that most mountaineers are discouraged from trying to climb it and an ascent is reported only rarely.
Why is this explanation so popular among physicists? One reason is that it allows one to connect the neutrino with fundamental puzzles of particle physics such as the realization of a unified GUT theory or the question of why the universe contains almost exclusively matter, and not matter and antimatter in equal parts. Beginning in the year 2000, a downright industry of theoretical research groups sprang up whose members studied the interrelations among GUT physics, neutrino masses, and observables such as lepton-flavor-violating decay rates. Toilers in this industry included J. Alberto Casas and Alejandro Ibarra in Madrid, Sergey Petcov and Werner Rodejohann (at that time in Trieste), and Frank Deppisch, Andreas Redelbach, Reinhold Rückl, and me (at that time all in Würzburg).
The other reason is that the seesaw mechanism arises quite naturally as soon as one tries to endow the Standard Model with neutrino masses. Recall that the neutrino is special among the elementary particles in two important respects:
• Neutrinos are the only electrically neutral particles among the elementary fermions, or matter particles.
• Neutrinos are far lighter than the other matter particles.
The seesaw mechanism (as well as most other mechanisms proposed for neutrino mass generation) postulates a relation between these two special properties: It assumes that the neutrino is so light because it is neutral.
Let’s remind ourselves of Majorana’s last work, which he wrote shortly before he disappeared from the ferry to Palermo: Since the neutrino doesn’t carry any charge, it is possible that it is its own antiparticle. But things are not that easy. The left-handed neutrino that we know from the Standard Model and that can be produced and annihilated in weak-interaction processes doesn’t carry any electrical charge, but it carries the generalized charge of the weak interactions, isospin. We remember how the masses of the electrically charged leptons and quarks are generated: A mass corresponds to a transition from a left-handed into a right-handed state (or the other way around). For quarks or charged leptons, this transition is possible only because the particles are coupled to the Higgs, which absorbs or delivers the difference of the weak charges of the left-handed particle and its weakly uncharged right-handed partner. This is the reason why masses can’t become much larger than the vacuum energy of the Higgs field. If one wanted to generate a mass that transforms left-handed neutrinos into right-handed antineutrinos, including the two Standard Model states that are observable in experiments, both of these states would have to shed isospin charge. To make this possible one would need a novel Higgs field that could absorb the isospin excess, a so-called Higgs triplet. This possibility is now known as seesaw-II.
There is in fact a simpler possibility for generating neutrino masses—adding a right-handed neutrino to the Standard Model particle roster. In order to endow neutrinos with masses, they must be able to transmute into right-handed particles. It therefore seems natural to assume that in analogy to the mass generation of charged leptons and quarks, a right-handed neutrino exists, and that the left-handed neutrino can be transformed into it via interaction with the Higgs field. This right-handed particle can now really be a Majorana particle, meaning its own antiparticle, since it carries neither electric charge nor color charge nor isospin: It is totally neutral, or sterile. This right-handed particle can thus possess a mass that transforms the right-handed neutrino into a left-handed antineutrino. Both are equally sterile, meaning no charges obtained from the Higgs field are necessary to make this metamorphosis possible. The resulting mass can then be much larger than the vacuum energy of the Higgs field, which is not needed at all. It typically is as large as the energy where a more extensive symmetry, such as a GUT symmetry, shows up. Such a symmetry may create novel forces—such as leptoquark forces under which the right-handed neutrino now is charged eventually—thus setting the cutoff for the right-handed neutrinos just as the Higgs does for the normal masses of charged leptons and quarks. Such an extremely heavy right-handed neutrino (or left-handed antineutrino, that is) can only be produced from an extremely short-lived quantum fluctuation, and it immediately decays back into a right-handed antineutrino with another coupling to the Higgs field (see Fig. 11.1).
The logic following from this chain of arguments seems rather compelling, and the consequences are breathtaking:
• The known left-handed neutrinos are so light because they acquire their masses from a short-lived quantum fluctuation into an extremely heavy right-handed neutrino.
• Neutrinos may carry information about the physics at the GUT or even at the much higher-energy string scale, which could be approached directly only with accelerators having a circumference of a trillion kilometers or more.
• A possible answer to the question Why is there something rather than nothing? or Why does the universe contain matter, and not matter and antimatter in equal amounts that would annihilate in a gigantic explosion?
• By taking a detour through heavy right-handed neutrinos, left-handed neutrinos can turn themselves into right-handed antineutrinos. This metamorphosis can then cause neutrinoless double beta decay.
Figure 11.1. Mechanisms of neutrino mass generation, from top to bottom: (1) Simple seesaw, meaning fluctuation into a heavy right-handed neutrino. (2) Seesaw II: radiation of a quantum fluctuation of a heavy Higgs triplet. (3) Coupling with a majoron field. (4) Fluctuation into a SUSY particle, the squark, and a quark.
The credit for the discovery of the seesaw mechanism is often given to Murray Gell-Mann (father of quarks), Pierre Ramond (father of superstrings), and Richard Slansky (who worked in group theory); and independently to Tsutomu Yanagida, who later also invented leptogenesis, a mechanism for generating the matter excess in the universe by neutrino decays. When, in 2004, a workshop celebrating the twenty-fifth anniversary of the seesaw mechanism was held at the Institut Henri Poincaré in Paris, however, almost every second person in the audience seemed to have a claim for the discovery of the mechanism, among them Sheldon Glashow (Boston University), father of the Standard Model and the first GUT theory; Rabi Mohapatra (Maryland); Goran Senjanovic (ICTP Trieste), who also introduced the seesaw-II mechanism; and Jose Valle (Valencia) and his PhD advisor Joel Schechter (Syracuse University), who in 1980 had developed a very general representation of neutrino mass generation. As it turned out, though, the very first who had speculated about the seesaw mechanism—in fact even two years earlier than the title of the workshop suggested—was the GUT developer Peter Minkowski of Bern University in Switzerland. Minkowski, however, being too relaxed to seriously fight for credit, didn’t participate in the 2004 meeting in Paris, and had almost forgotten his discovery, or at least forgotten in which of his papers he had published it.1
In any case, the Standard Model has to be extended in order to explain neutrinos’ masses—leading to the wonderful consequence that neutrino physics allows one to obtain information about GUTs or other theories of unification that are realized at energy scales inaccessible to accelerator experiments. As popular as the seesaw mechanism is, there naturally are alternatives (Fig. 11.1). The inverse (a.k.a double) seesaw, which was proposed in 1986 by Rabi Mohapatra and Jose Valle, utilizes a ladder of two neutrino particles without isospin into which the original neutrino oscillates, one after the other. The fact that the two sterile neutrinos can share the suppression between themselves allows, among other things, for a significantly lower mass scale of the right-handed neutrinos, perhaps at the TeV scale, which could be probed at the LHC.
Another idea was proposed in 1980 by Yuichi Chikashige, Rabi Mohapatra, and Roberto Peccei (at that time all in Munich, and now scattered to Tokyo, Maryland, and UCLA): A symmetry forbids the violation of lepton number, and only a spontaneous and small breaking of this symmetry eventually allows for small neutrino masses. The particle that plays the role of the Higgs particle breaking the lepton-number symmetry in such scenarios is called a majoron. It can be emitted in neutrinoless double beta decays. Moreover, in this model, neutrinos are unstable and can decay into majorons, which, by carrying away energy, crucially affect the process of supernova explosions. In my diploma thesis I analyzed double beta decay data to search for majoron-emitting decays. Later, Jose Valle, Ricard Tomas, and I compared the sensitivity of double beta decay and supernova explosions to the size of majoron-neutrino couplings, building on a previous work by Michael Kachelriess.
Finally, neutrinos could acquire their masses from quantum fluctuations into two or more particles, a so-called particle loop. Such models typically assume that the generation of neutrino masses via fluctuation into a single particle is forbidden, while the fluctuation into a pair of particles results in another suppression factor of about one hundred. The first model of this type was proposed by Tony Zee in 1980. Particularly interesting, however, are such models within the context of supersymmetry. In SUSY models, lepton- and baryon-number-violating interactions that violate the so-called R-parity (see Chapter 6) arise naturally. These interactions allow the neutrino to fluctuate into a loop including a SUSY particle and its Standard Model partner, as found out in 1984 by Lawrence Hall and Mahiko Suzuki. Moreover, in such SUSY models neutrinos can acquire their masses also by mixing with zinos, the SUSY partners of the Z bosons, as proposed in 1987 by Arcadi Santamaria and Jose Valle, building on works by Charanjit Singh Aulakh, Rabi Mohapatra, and others. This again leads to a seesaw-like formula. In these models neutrinos do not deliver information about GUT or string theories, but about supersymmetry instead. In particular, the Valencia group around Valle, Santamaria, Martin Hirsch, and Werner Porod—since the 1990s one of the most important centers of neutrino physics worldwide—has studied extensively the relations between R-parity violation and neutrino masses and has found, among other things, interesting signals at colliders such as the LHC. But the violation of R-parity has also been intensely studied by the Bonn group in Germany around Herbi Dreiner and Manuel Drees, and the Kolkata group with Gautam Bhattacharyya and Palash Pal. This argument has also been turned around by Bhattacharyya (who visited our research group in Heidelberg in 1997 and 1999), Klapdor-Kleingrothaus, and me, when we used the smallness of neutrino mass to constrain the possible strength of R-parity-violating interactions. The upper bounds we found in this way improved previous constraints by a factor of a million. Above all it is Jose Valle and Rabi Mohapatra, who deserve credit for carrying out, since the 1990s, the important task of tirelessly reminding the particle-physics community about the crucial role that neutrino physics can play in the quest for new physics beyond the Standard Model. Around the end of the 1990s, these two were joined by Manfred Lindner; out of his group at least seven independent major research groups for neutrino physics have evolved.
Eventually almost all neutrino-mass models can be understood as different realizations of an image shaped by Steven Weinberg in 1979: A neutrino fluctuates—via a twofold interaction with the Higgs condensate—into something heavy and then back into its own antiparticle. The neutrino becomes a Majorana particle. Particle and antiparticle are connected via their mass, and the isospin excess migrates into the Higgs field. The entire process generates a light neutrino mass, suppressed by the unspecified heavy object in the intermediate state.
An important reason why the simple seesaw remains the most popular mechanism of neutrino mass generation is, besides its naturalness, its cosmological relevance. Tsutomu Yanagida was one of the first to discuss the seesaw mechanism as an explanation for the small neutrino masses. Together with Masataka Fukugita, he then found in 1986 a spectacular application of the seesaw to generate the baryon asymmetry of the universe. Originally it had been assumed that the leptoquark particles that arise in GUT theories and which can cause the conversion and decay of baryons and leptons into each other were responsible for baryogenesis. As it turned out, though, the universe would have had to reheat strongly after inflation in order to reach the necessary temperatures for GUT leptoquarks to be produced. This would, however, also bring about a substantial production of weakly interacting SUSY particles, whose decays would disrupt a successful nucleosynthesis—one of the cornerstones of cosmology.
Another idea goes back to a discovery made by the Dutch Nobel Prize winner Gerard t’Hooft in 1978: Within the Standard Model there are transitions between different vacuum states that correspond to distinct Higgs condensates. These transitions can transmute antileptons into baryons and in this way create a baryon asymmetry as proposed in 1985 by Vadim Kuzmin, Valery Rubakov, and Mikhail Shaposhnikov. The energy necessary for such a transition is known as sphaleron. The hope was that the condensation of the Higgs field at energies of around 1 TeV would proceed so suddenly that an imbalance between baryon production and baryon annihilation would result. As it turned out, though, the mechanism doesn’t work in the Standard Model, where the Higgs condensation process happens slowly, not suddenly.
Baryogenesis with the help of neutrinos, the so-called leptogenesis of Yanagida and Fukugita, combines the idea of particle decay with baryogenesis as a result of sphaleron transitions at low energies. The right-handed neutrinos are identical to their antiparticles. Their mass corresponds to the transmutation of particles into antiparticles. Thus the right-handed neutrinos could indeed be the reason why the universe contains almost no antimatter: In the early universe there may have been particles and antiparticles in equal number. For the right-handed neutrinos, however, there was no way to decide whether they were particles or antiparticles. When the universe cooled down, then, the temperature became insufficient to produce these heavy neutrinos and they decayed a little more often into antileptons than into leptons. Thereafter almost all particles and antiparticles annihilated, with only the tiny excess of antileptons in the decay products of the heavy neutrinos surviving. These were transmuted via sphaleron transitions into baryons, which account for almost all matter in the present universe: We were all neutrinos once.
In this scenario, neutrinos are directly responsible for the existence of matter in the universe. In later work, leptogenesis was worked out in more detail by my Dortmund colleagues Marion Flanz, Emmanuel A. Paschos, and Utpal Sarkar, and also by Wilfried Buchmüller and Michael Plümacher at DESY Hamburg and by Apostolos Pilaftsis (at that time in Munich and today in Manchester). It is now the most popular proposal for the generation of a baryon asymmetry and provides yet one more example of the relevance of neutrinos in cosmology. Moreover, for successful leptogenesis, not even lepton-number violation is necessary. As Evgeny Akhmedov, Valery Rubakov, and Alexei Smirnov, as well as Karin Dick, Manfred Lindner, Michael Ratz, and David Wright found out, a lepton asymmetry in the left-handed sector can be balanced by a corresponding lepton asymmetry in the hidden, noninteracting right-handed sector. In this case the mechanism works even for Dirac neutrinos.
What is probably the most radical proposal for the role of neutrinos was put forward in 1993 by Hitoshi Murayama, Hiroshi Suzuki, Tsutomu Yanagida (at that time all at Tohoku University, Japan), and Jun’ichi Yokoyama (University of Kyoto): The SUSY partner of the neutrino, the sneutrino, they suggested, could be the inflaton. In the decay of the inflaton field, the sneutrino could then directly decay more often into antileptons than leptons, and thus generate a lepton asymmetry, which later would be transformed into baryon asymmetry via sphaleron transitions. An extension of this idea, which allows the neutrino to be incorporated in a better way in GUT theories, has been worked out by Stefan Antusch and collaborators.
According to the ideas outlined in this chapter, the neutrino could be the reason we exist—indeed it may even be the cause of the existence of the entire universe.
Perhaps not quite as important, but similarly mind-boggling, is another speculation about how neutrinos might be related to the universe at large: the possible existence of extra dimensions. That is a topic for the next chapter.