Two weeks ago, a team of particle physicists unveiled the most precise measurement yet of a neutrino, scaling down the maximum possible mass of these elusive - almost massless specks of matter that permeate our universe. The result, published in the journal Science, does not define the exact mass of a neutrino, just its upper limit, given as:
resulting in an upper limit of mν <
0.45 eV at 90% confidence level.
But this finding helps bring physicists closer to figuring out just what is wrong with the so-called Standard Model, their best — albeit incomplete — theory of the laws that rule the subatomic realm. One way physicists know it is not quite accurate is that it suggests that the neutrino should not have any mass at all.
At grander scales, learning more about neutrinos may help cosmologists fill in their ever hazy picture of the universe, including how galaxies originally clustered together and what influences the expansion of the cosmos since the Big Bang.
Neutrinos occur in abundance across the cosmos, created virtually anytime atomic nuclei fuse or fission. But they carry no electric charge and are notoriously difficult to detect. Neutrinos also come in three types, which physicists describe as flavors.
Let's review again the basis for these neutrino flavor states. If there are three such states: electron, muon and tau, then there must be three different corresponding neutrino masses which we can call: m1, m2 and m3. Further, the three "flavors" are really different superpositions of the 3 basic neutrino mass states. Moreover, and to make it more complex, we know that quantum interference between mass states means a neutrino originating in one "flavor" can transmogrify to another over its transit.
Because of the oscillations and quantum interference we need to reckon in a "misalignment" between flavor and the basic neutrino masses. This is done by reference to three independent "mixing angles": Θ 12 , Θ 23 and Θ 13. To a good approximation, oscillation in any one regime is characterized by just one Θ ij and a corresponding mass difference, defined:
D m ij2 = [m j2 - m i2]
Unlike the latest research published in Science, this earlier edition was confined only to mass differences ( D m) not to neutrino mass itself or even upper limits.
As an example, the probability that a muon neutrino of energy E acquires a different flavor after traversing distance L is:
P = sin2 Θ 23 sin2 (l23)
where l23 is the energy -dependent oscillation length, given by:
4ħ E c / (D m 322)
How well do we know the parameters? Atmospheric neutrino observations yield:
Θ 23 » 45 degrees, while D m 322 = 0.0024 eV2.
Meanwhile, solar neutrino data yield » 33 degrees for Θ12 and D m 212 = 0.00008 eV2. (Note: ħ is the Planck constant of action divided by 2 π) If then:
D m 312 = [D m 212 + D m 322 ] = 0.00008 eV2 + 0.0024 eV2
We know, D m 312 = 0.00248 eV2
Oddly, neutrinos can morph from one flavor to another as they move through space and time, a discovery recognized by the Nobel Prize in Physics in 2015. The underlying mechanism that makes these transformations possible, physicists realized, meant that neutrinos must have some mass. Neutrinos are mind boggingly light, and physicists don’t know why.
Uncovering the exact values of the mass of neutrinos could lead to “some kind of portal” to new physics, said Alexey Lokhov, a scientist at the Karlsruhe Institute of Technology in Germany. According to Lokhov, quoted in a NYT piece, referring to his team’s measurement:
Lokhov and his colleagues used the Karlsruhe Tritium Neutrino, or KATRIN, experiment to narrow down the mass of a neutrino. At one end of the 230-foot-long apparatus was a source of tritium, a heavier version of hydrogen with two neutrons in its nucleus. Because tritium is unstable, it decays into helium: One neutron converts into a proton, which spits out an electron in the process. It also spits out an antineutrino, the antimatter twin of a neutrino. The two should have identical mass.
The mass of the original tritium is split among the products of the decay: the helium, electron and antineutrino. Neither neutrinos nor antineutrinos can be directly detected, but a sensor at the other end of the experiment recorded 36 million electrons, over 259 days, shed by the decaying tritium. By measuring the energy of the electron’s motion, they could indirectly deduce the maximum mass possible for the antineutrino. They found that value to be no more than 0.45 electronvolts, in the units of mass used by particle physicists, a million times lighter than an electron.
Note that the upper bound on the mass: mν < 0.45 eV
was measured for only one flavor of neutrino. But Wilkerson said that nailing down the mass of one makes it possible to calculate the rest. The latest measurement pushes the possible mass of the neutrino lower than the previous limit set in 2022 by the KATRIN collaboration, of no more than 0.8 electron volts. It is also nearly twice as precise.
Elise Novitski, a physicist at the University of Washington who was not involved in the work, commended the KATRIN team’s careful effort. In the words of Novitski:
“It’s really just a tour de force. I have full confidence in their result.”.
Other experiments will also contribute to a better understanding of the neutrino’s mass, including Project 8 in Seattle and the Deep Underground Neutrino Experiment, spread across two physics facilities in the Midwest. The good new is the KATRIN team is currently working on an even tighter boundary on the neutrino mass from 1,000 days of data, which it expects to collect by the end of the year. That will give the physicists even more electrons to measure, leading to a more precise measurement.
Astronomers studying the structure of the cosmos at large, thought to be influenced by the vast collection of neutrinos flooding the universe, have their own measurement of the particles’ maximum mass. But according to Prof. Wilkerson, the boundaries set by astronomers staring out into the void don’t match up with what particle physicists calculate in the lab, as they scrutinize the subatomic world. Is there a neutrino mass shrinkage? According to Wilkerson:
“There’s something really interesting going on. And the likely solution to that is going to be physics beyond the Standard Model.
The neutrino’s mass is a particularly elusive quarry because it stubbornly refuses to abide by the tenets of the Standard Model of particle physics. Famously, almost all of this theory’s predictions have been experimentally confirmed, yet some of its forecasts for the neutrino have notoriously fallen flat. The model predicts that neutrinos should be completely massless. This was ultimately refuted by a Nobel-winning experiment that showed neutrinos not only have mass but also, for whatever reason, change mass by oscillating between three different neutrino varieties, or “flavors.”
Elaborating a bit: this so-called 'Standard Model' is
generally defined as the symmetry:
SU(3) x SU(2) X U(1)
where each of the above denotes a specific matrix, or more exactly
a group. See, e.g.
http://brane-space.blogspot.com/2010/04/looking-at-groups.html
In the case of SU(2) we describe it as the "special unitary group"
which has the form:
S =
(a.........-b*)
(b..........a*)
where a*, b* are complex conjugates and we have (aa* + b*b) = 1. Thus the
elements of SU(2) are the unitary 2 x 2 matrices with DET (determinant) = 1.
These groups thus define the behavior of a specific class of subatomic
particles. Spontaneous symmetry breaking would therefore resolve this
combination into constituent parts, e.g.: SU(3) associated with the 'color
force' of quarks:
SU(2) x U(1)
associated with the electro-weak force.
One possible symmetry breaking (quark -boson format) is:
SU(3) x SU(2) X U(1) -> SU(3) + SU(2) x U(1)
which would occur at a particular ambient temperature (T_qb) for the universe
at some epoch (E_qb) in the past. In the foregoing, the synthesis of SU(2) and
U(1) into the locally gauge invariant electro-weak theory requires a
mechanism which confers mass to three vector bosons while
leaving the photon massless. This 'mass-giving' mechanism is called the
Higgs Field or Higgs mechanism, and it demands the existence of one or
more massive, spin-0 bosons otherwise called Higgs bosons. See e.g.
The final resolution of the neutrino’s mass may well have to await the construction of a giant neutrino detector in the Antarctic. Below, how its size compares with the Eifel Tower - set in the lower right:
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