[Big Science, quantum foundations]

While already following this Big Science project [1], with construction underway (for the next 3 years), I felt that a specific post was appropriate. The Deep Underground Neutrino Experiment (DUNE) is a massive worldwide collaboration between countries, organizations, and over a 1000 scientists. All hail neutrinos! [2]

I spent some time yesterday pondering neutrino oscillation. Measuring how these particles change their identities is one of DUNE’s research objectives. Recently I viewed some YouTube videos (noted below) by Fermilab‘s Don Lincoln on this topic – helping to clarify how neutrino mass and flavor are sort of superpositions – a mixed vs. pure state.

DUNE construction

• Symmetry Magazine > “DUNE moves to the next stage with a blast” by Lauren Biron and Leah Hesla (June 24, 2020) – Construction workers have carried out the first underground blasting for the Long-Baseline Neutrino Facility, which will provide the space, infrastructure and particle beam for the international Deep Underground Neutrino Experiment.

On June 23, construction company Kiewit Alberici Joint Venture set off explosives 3650 feet beneath the surface in Lead, South Dakota, to begin creating space for the international Deep Underground Neutrino Experiment, hosted by the Department of Energy’s Fermilab.

The blast is the start of underground excavation activity for the experiment, known as DUNE, and the infrastructure that powers and houses it, called the Long-Baseline Neutrino Facility, or LBNF.

DUNE Experiment

Wiki:

The Deep Underground Neutrino Experiment (DUNE) is a neutrino experiment under construction, with a near detector at Fermilab and a far detector at the Sanford Underground Research Facility that will observe neutrinos produced at Fermilab. It will fire an intense beam of trillions of neutrinos from a production facility at Fermilab (in Illinois) over a distance of 1,300 kilometers (810 mi) to an instrumented 70-kiloton volume of liquid argon located deep underground at the Sanford Lab in South Dakota. The neutrinos will travel in a straight line through the Earth, reaching about 30 kilometers (19 mi) underground near the mid-point; the far detector itself will be 1.5 kilometers (4,850 ft) under the surface). About 870,000 tons of rock will be excavated to create the caverns for the far detectors. More than 1,000 collaborators work on the project.

Fermilab:

The Deep Underground Neutrino Experiment is an international flagship experiment to unlock the mysteries of neutrinos. DUNE will be installed in the Long-Baseline Neutrino Facility, under construction in the United States. DUNE scientists will paint a clearer picture of the universe and how it works.

The U.S. Department of Energy’s Fermilab is the host laboratory for DUNE, in partnership with funding agencies and more than 1,000 scientists from all over the globe. They contribute expertise and components, which provide economic benefits to each of the partner institutions and countries. DUNE consists of massive neutrino detectors, at Fermilab in Illinois and Sanford Underground Research Facility in South Dakota. LBNF produces the world’s most intense neutrino beam and provides the infrastructure. The PIP-II particle accelerator at Fermilab powers the neutrino beam.

The neutrino mix

• YouTube > Fermilab > Don lincoln > “Subatomic Stories #10: Understand neutrino oscillations like the pros” (June 11, 2020).

• Episode #11 (June 17, 2020) is on the Heisenberg uncertainty principle [3], but the Q&A part has some questions about neutrinos. [4]

• YouTube > Fermilab > Don lincoln > “Subatomic Stories #12: What scientists know about neutrino masses” (June 24, 2020).

Neutrino mysteries

This Fermilab page lists some of the essential questions about the neutrino:

• How much does a neutrino weigh?
• Which neutrino is the lightest?
• How many flavors of neutrinos are there?
• Are neutrinos their own antiparticles?
• Are all neutrinos left-handed?
• Do neutrinos violate the symmetries of physics?
• Where do the most energetic neutrinos come from?

In his videos (noted above), Don Lincoln presents some tables about neutrino flavors (electron, muon, and tau) and masses (ν1, ν2, and ν3). There’s no one-to-one correspondence: “… mass and flavor neutrinos do not overlap perfectly.” This Fermilab page summarizes two mass scenarios:

ν1 ~< ν2 < ν3

ν3 < ν1 ~< ν2

Scientists can check whether neutrinos come in the normal or inverted mass ordering with experiments that look at how neutrinos change over long distances. If things are “normal,” certain neutrino oscillations (changes between flavors) should happen at a higher rate than in the inverted world.

The best measurement of that mass difference comes from looking at the energies of neutrinos that come from reactors, usually carrying energies of a few million electronvolts, that are about 200 kilometers away from their source.

Scientists have been able to pin down the large mass difference very well, too. The best measurement of that mass difference comes from looking at the energies of neutrinos that come from accelerator sources. Those neutrinos have on the order of a billion or a few billion electronvolts, and the detectors are typically located 300 to 800 kilometers away from the source.

Each neutrino of a specific flavor is actually a combination of neutrinos of different masses. As a result, each neutrino of a specific mass has a certain chance [probability] of interacting as a particular flavor. For example, ν1 is very likely to interact as an electron neutrino.

Neutrino oscillations are characterized by “mixing parameters,” which dictate how the mass states add up to form the particular flavor states. (Mixing parameters also look at the differences between the squares of the three mass states.)

The probability that the neutrino flavor at the point of interaction is different from the flavor at the point of creation depends on the speeds at which the three mass neutrinos move. This fact tells scientists both that neutrinos have mass and that those masses are different, because if neutrinos were massless, they would all travel at the speed of light.

In the simplest explanation for neutrino flavor change, the three neutrino flavors are quantum mechanical combinations of three neutrino mass states. This means that neutrinos travel as a combination of the three mass states rather than as a single, static flavor.

… we still don’t know the absolute mass of the neutrino. What we do know is that the three known types of neutrinos have different masses and that the sum of all three of those types is still less than one millionth the mass of an electron.

Neutrinos are the lightest of the massive fundamental particles in the Standard Model. We know that neutrinos have mass because we have observed them change from one flavor into another, a process that can happen only if the neutrinos have mass. Interestingly, that process also requires the different flavors to have different masses. But unfortunately, the flavor change process depends only on the masses of the different flavors being different; it cannot tell us anything about the actual mass of the neutrino.

The charged leptons and quarks acquire their masses through interactions with the Higgs boson, but that isn’t necessarily the case for neutrinos. It also isn’t ruled out completely. One theory predicts that the neutrino has a very heavy partner that exists for a very brief time, and that heavy partner interacts with the Higgs boson to produce the light neutrinos we observe. Through the Higgs mechanism, then, the light neutrino mass would be in a “seesaw” relationship with the heavy partner mass – as the mass of the partner goes up, the mass of the light neutrino goes down. But this seesaw relationship has not yet been experimentally verified.

This University of California @ Irvine page notes that:

The probability of a neutrino changing type is related to the distance travelled by the neutrino from its point of production to its point of detection. As a general rule, neutrinos travelling greater distances will exhibit greater depletion from oscillation. Moreover, the oscillation probability varies smoothly over increasing distance.

Neutrino oscillation – analogies?

So, I do not recall seeing any particlular analogies for modeling neutrino oscillation. For mere mortals. Hopefully in lectures somewhere. Currently my best idea was to review visualizations for coupled ocillators, e.g., two coupled pendulums. And then consider a neutrino as sort of a coupled Majorana (particle-antiparticle) pair, with masses (ν1, ν2, ν3) as three modes, and “neutrino” oscillation as transitions between (or superpositions of) those modes. The mode with highest interaction corresponds to the highest mass (energy).

The search for sterile neutrinos is an active area of particle physics.

Do neutrinos and antineutrinos differ only in their chirality? Or do exotic right-handed neutrinos and left-handed antineutrinos exist as separate particles from the common left-handed neutrinos and right-handed antineutrinos?

• YouTube > Dan Russell, Penn State University, Graduate Program in Acoustics > “Coupled Pendulum” (Nov 8, 2014).

Another interesting visualization by Dan Russell is a two degree-of-freedom (2-DOF) mass-spring system (two identical masses connected by three identical springs), which exhibits two natural modes and a third coupled interaction.

• Mode 1 = coupling spring static (no cycle of stretching / compression) – like two identical 1-DOF systems in phase (equivalent to one mass with 2 springs but lower frequency by square root of 2). No nodes. Lowest system energy.
• Mode 2 = two masses move in opposite directions; coupling spring cycled in stretching / compression. (One node.) Higher system energy.
• Mode 3 = displaced (perturbed) interaction where one mass is moved from equilibrium position before releasing both; oscillators cycle in trading energy. Highest system energy.

His animation of a 3-DOF mass-spring system has 3 natural modes.

Related posts

Neutrino madness

Blazar neutrinos

The future of (particle) physics?

Online videos > Fermilab > PIP-II: the new heart of Fermilab

Notes

[1] And, keeping things real, massive Big Science projects pose safety and enviromental issues during constrcution and operation, as noted in this article:

Nature > “Italian physicists to stand trial for conditions in underground lab” by Nicola Nosengo (May 16, 2019) – The Gran Sasso National Laboratories have seen no major accidents so far, but prosecutors charge that environmental controls were lax.

[2] And neutrinos play a role in multi-messenger astronomy.

[3] And regarding the uncertainty principle, Lincoln’s explanation corrects what many of us are taught in high school or college about its meaning. All hail the wave function!

Now if you want to have some knowledge of both the position and momentum of the particle, you need to change the wave function from an infinite sine wave to something more localized. To do that, you can simply start adding up the wave functions of particles whose momentum is well known, but for whom the position is not known. You start with a single wave, but then you add a series of waves that have a wavelength that are slightly different than the initial one. The cumulative wave function [Fourier Transform], which is the sum of more and more different wavelengths slowly morphs from being a sine wave to being a wave function that is more localized.

And in order to localize the wave function, you need to add all the wavelengths, which means you have no information about the wavelength and therefore the velocity. Because wavefunctions are built of mixes of wavelengths, the more you focus the position, the broader range of wavelengths is needed. The more you restrict the wavelength, the less information you have about the position. That’s the real reason for the Heisenberg Uncertainty principle.

In the case of virtual [vs. real] particles, the electrons exist for only a very short time. That means that both the energy and momentum could differ from the average and the result is that you could have electrons with a range of masses – even cases where the square of the mass is negative. Virtual particles break a lot of the rules and are super confusing when you first encounter them.

[4] From Q&A of Episode #11 (June 17, 2020) on the Heisenberg uncertainty principle:

• Where do neutrinos get their mass from?

The short answer is that we don’t know. They could get their mass from interactions with the Higgs field, but we aren’t sure about that. Neutrinos are so much less massive than other particles, that it’s possible that they get their mass from another mechanism.

• Can a neutrino could pass through a neutron star?

The answer is basically no, or at least mostly so. The probability that a neutrino will interact depends on energy and the density of the material it is travelling through.

For a high energy neutrino of a hundred billion electron volts of energy, the neutrino will travel less than a tenth of a millimeter before interacting.

For low energy neutrinos, they can penetrate much farther, but we’re still talking a distance of about a meter or so.

Very low energy muon neutrinos don’t have enough energy to make muons, so they bounce around inside the star essentially forever and eventually find their way out.

The neutrino that would penetrate a neutron star most easily would have to an be electron neutrino with a few million electron volts of energy. In principle, they could encounter a proton and make a neutron. The density of protons inside neutron stars is very poorly known, but if you take reasonable numbers, then a very low energy electron neutrino might travel as far as a kilometer before finding a rare proton and turning it into a neutron.