## Thursday, May 31, 2018 ... //

### MiniBooNE confirms LSND's anomaly calling for new neutrino species

For decades, it's been almost clear that the neutrinos aren't quite massless. They have a tiny mass. Since the late 1990s, the measurement of the neutrino masses became the task for actual real-world experiments.

These masses are most obviously seen through neutrino oscillations. One type of a neutrino automatically turns into another, and then back – the probabilities of being one or the other oscillate like a sine function between two values. There have been various experimental surprises that made it clear that the oscillations existed, indeed. The solar neutrino problem was seen – the Sun only creates electron neutrinos and their number should be clear from the known reactions and the outgoing energy. But on Earth, we saw significantly fewer (by 30-50 percent) electron neutrinos than expected.

The explanation that was ultimately adopted says that these electron neutrinos from the Sun change – oscillate – into other neutrinos. It was assumed that they were muon and tau neutrinos. Similar experiments on Earth have provided us with growing evidence that there's an additional channel of oscillations involved to explain why some neutrinos disappear while going through our blue, not green planet.

Neutrinos are electrically neutral partners of charged leptons (electron, muon, tau) – and this pairing is analogous to the pairing of up-type and down-type quarks. So the masses may also be rather analogous. Throughout the years, it was becoming natural for everyone to believe that just like the quarks are mixed thanks to the CKM matrix, the neutrinos are mixed according to the PMNS matrix.

So the three-dimensional space of electron+muon+tau neutrinos has three mass eigenstates – there are three corresponding mass eigenvalues. And one must remember the unitary transformation that gets us from the mass eigenstates to the $SU(2)_{\rm weak}$ partners of the charged lepton (electron+muon+tau) mass eigenstates.

Neutrino phenomena that are measurable are compatible with the existence of the Majorana neutrinos – in which the helicity is correlated with the particle's being a neutrino or an antineutrino. Whether the neutrinos are Majorana or Dirac particles remained an open question – the Dirac neutrinos would mean that there exists a neutrinoless double beta decay – which would display the Majorana-style violation of the lepton number by $\Delta L = \pm 2$.

The helicity is conserved – basically because the angular momentum is conserved – so even with the Majorana type, you can't easily turn a particle into an antiparticle. But such a transformation is possible at low speeds or for virtual neutrinos etc. if they're of the Majorana type.

On top of the Majorana-vs-Dirac dilemma which remains mostly open, there have been some question which of the "two detached basins" in the parameter space are realized – the masses of the "increasingly heavy" charged leptons' neutrino partners (or the masses of the neutrino mass eigenstates that are closest to these three) may be increasing or decreasing – it's the normal vs inverted hierarchy. Some recent experiments have claimed that this question has been settled.

OK, so to describe the neutrino masses and mixing, you should need three mass eigenvalues (only the differences of squared masses are easily measurable by oscillations, the single overall shift of the masses towards higher values is hard to observe); and four angles needed to describe the unitary $SU(3)$ matrix turning the neutrino mass eigenstates to the $SU(2)$ partners of the charged leptons' mass eigenstates.

These four angles may be imagined as three Euler angles needed to produce an $SO(3)$ matrix, a rotation in three dimensions that many of us have encountered in their real lives, plus one CP-violating phase $\delta_{CP}$ that remembers how much the unitary matrix is complex (non-real). You may also figure out that there are four phases in the unitary matrix by seeing that a general $U(3)$ matrix has 9 degrees of freedom. But 5 of them can be set to $1$ – a preferred number on the unit circle – by choosing the phases of the 3+3 eigenstates of the neutrinos and the charged leptons. If you ask how it's possible that $3+3=5$, it's an extremely good question of yours. The deficit of one appears because if you change all the six phases by the same amount, the $U(3)$ matrix doesn't change at all, so there are only 5-dimensional, and not 6-dimensional, orbits inside the $U(3)$.

OK, 3 mass eigenvalues plus 4 angles give you 7 parameters. Almost all neutrino experiments were compatible with this 7-parameter model of the neutrino sector. Among the three Euler angles, the last one was observed just a decade ago (or it has already been a decade – it depends whether you want to complain about the speed of time).

But there was one exceptional experiment that didn't agree with this 7-parameter model, the LSND experiment. Take 167 tons of mineral oil, add some 6.4 kilograms of an organic scintillating material, 1220 photomultiplier tube, drive the stuff to Los Alamos, and tell them to do some interesting experiment with this stuff. What you get is LSND.

The experiment was running between 1993 and 1998 and its results disagreed with the simple 7-parameter model above. The electron-to-muon neutrino oscillations should have been enough but they weren't quite enough – the deviation was 3.8 sigma. It wasn't too much but it was strong enough.

Most deviations below 4 sigma usually go away – they're either statistical flukes that sometimes have to occur, or they're results of mistakes (usually described euphemistically as unaccounted for systematic errors). Almost everyone assumed that the LSND anomaly was either a statistical fluke, or the physicists in LSND were on LSD which could also explain the name of the experiment. ;-)

So a new experiment was paid for, MiniBooNE, which was collecting data between 2002 and 2012. Instead of Los Alamos, it was moved to the Fermilab, and the physicists in the collaboration were only allowed to take marijuana, no LSD. 167 tons of mineral oil was replaced by 800 tons of mineral oil, 1220 photomultiplier tubes were upgraded to 1280 photomultiplier tubes (almost the same), and the 6 kilos of the scintillating organic junk was replaced by some beam from the Fermilab dirty gadgets.

Finally, we got the new result from MiniBooNE. You've been waiting for this second for a long time, reading all the basic and irrelevant garbage, to get a simple answer to a simple question. Was LSND explained by LSD or is there some deviation? Surely this sentence already has to tell you Yes or No, but it still doesn't. You're running out of patience or exploding by impatience. But here it is:

Observation of a Significant Excess of Electron-Like Events in the MiniBooNE Short-Baseline Neutrino Experiment
The title already makes it clear that MiniBooNE hasn't proven the LSD explanation of LSND. Instead, they see the same kind of an anomaly. Their deviation is 4.8 sigma – close to the 5-sigma threshold for a discovery in the hard sciences – and when they combine their deviation with the similar one from LSND, they get to 6.1 sigma which is safely in the discovery realm. The probability of a false positive – assuming no neglected systematic errors – is about one in one billion.

LSND and MiniBooNE tell us almost the same message – we can consider this anomaly to be one and the same thing. And the message is that the number of neutrino species doesn't seem to be three. The number of neutrino species has been assumed to be three because we know three charged leptons – electron, muon, tau. But CERN accelerators in the 1980s have also measured the number of light enough (sub-Z-mass) neutrino species directly, from the decay rate of the Z-boson, and they got a real number very close to three.

(The number of neutrino species may also be indirectly extracted from the CMB and the Cosmic Neutrino Background so if you mess with the number of species, you may be forced to redo your cosmological fits, too.)

Now, LSND and MiniBooNE measure the "number of neutrino species" in a different way and they seem to want more. They can't be fit by the 7-parameter model of neutrinos of three flavors. The new neutrino species could be added by hand and it's totally plausible that such new particle species exist. Sterile neutrinos (which are called in this way because they don't participate in sex with their $SU(2)$ charged leptonic partners) would seem like another example of "Who ordered that", something that is possible but that didn't seem necessary (for intelligent life etc.), something that just makes our theory uglier.

You could include a sterile neutrino as a dark matter particle but there are some problems with that, too. I don't really say that they're necessarily insurmountable problems but they're serious enough problems that disfavor the most straightforward theory of a sterile neutrino dark matter – that would also explain the LSND/MiniBooNE anomaly.

So it's potentially exciting – a sign of physics beyond the Standard Model. Neutrinos are almost invisible so they're not spectacular. Some new parameter or species in this invisible sector seems to be even less spectacular. Of course most people including myself could prefer a hint of the Beyond the Standard Model physics that would look like fireworks, not some esoteric discrepancy in fingerprints of some ghosts that easily penetrate the Earth. But that's what we're facing.

The dark blue and light blue regions indicate the 90% and 99% LSND confidence level regions in the plane (parameterized by an angle and a mass difference, see the graph for the precise meaning of the axes). The colorful lines indicate the analogous MiniBooNE new results – you clearly see an agreement with LSND. A black disk in the lower right corner – inside the blue area – is their best fit. LSND/MiniBooNE wants $\sin^2 2\theta$ to be as close to one as possible – well, it might prefer a sine that is greater than one if they were allowed to get to these higher values of the sine without LSD. But the other experiments, like KARMEN and OPERA, clearly want a much smaller sine. What these experiments prefer is indicated by the grey (colorless) lines, the full and the dotted one for the two experiments.

On the other hand, LSND/MiniBooNE would love the mass difference to be much smaller than the value from the other experiments. The discrepancy is rather striking.

These experiments measure the number of neutrinos – and their energy distribution. It could be enough data to pick the winning models. Don't forget that there may be lots of uncertainties and ambiguities for quite some time. John von Neumann has calculated that with four parameters, he could fit an elephant, and with a fifth parameter, he could make him wiggle his trunk. For some reasons, however, 7 parameters doesn't seem to be enough to describe even the neutrino experiments only.

Von Neumann could have only gotten something like this with the 4-5 parameters. Fans of precision photography of elephant must be disappointed.

The neutrino sector seems to be an elephant that was thought to wiggle his at least three trunks. But now, it seems that the elephant must have at least four trunks. (The number of trunks is equal to the number of parameters minus 4, I hope that you are still with me.) What are the best ways to draw four or more wiggling trunks of the elephant? Will we know what's the right way to do so? Are they really trunks or wheels? Maybe it's a vehicular elephant. Do these four trunks play any role?

It would be much easier to figure out what a double-tailed lion could be good for. You can turn it into the Czech coat of arms – Luxembourg has this mutated animal as well, and our two nations (that were politically linked in the 14th century) are not the only ones that use this piece of heraldry. (The origin is Czech – others plagiarized it – but the justification isn't quite clear. Czech king Vladislav II got a first lion sign from Friedrich Barbarossa because Czechs were fighting as lions. In 13th century, Přemyslid Ottokar II may have added the second tail just to show he was the second Ottokar. But the reason could have been different.) The purpose of the double-tailed lion is easy. But what about the quadruple-trunked elephant? And doesn't some string theoretical vacuum or grand unified theory or something else give us a natural reason to expect what the new trunks should be like?

Just to sketch something about the answer, the grand unified modelers love to add full representations of the large gauge group – so there are usually many new particle species whose properties are linked. In string theory, on the other hand, vacua often have particle species that are isolated from each other. Some extra sterile neutrinos are rather common in string theory, like other particles – e.g. axions. But as you have heard millions of times, string theory doesn't give us a unique answer about the choice of the new particle species: there are many possibilities.

Stay tuned.