Scientists are making steady progress in quantifying the properties of the neutrinos. There are seven experiments probing the neutrino oscillation parameters, another seeking to directly measure the absolute value of the lightest neutrino mass, and multiple astronomy collaborations using indirect means to measure neutrino properties including those like IceCube that measure income neutrinos from space directly. As a result of these experiments we are steadily closing the gap of what we know.

The prospects look very good for a precisely known full set of Standard Model neutrino parameters over the next ten to fifteen years, with significant improvements even in the next five years.

In absolute terms, the neutrino masses are already the most precisely known Standard Model parameters and three of the four mixing parameters are also known with decent precision. But, the relative precision with which we know these parameters it the lowest in the Standard Model although this state of affairs may not last too long.

A new new Snowmass 2021 paper has a nice six color chart showing how much progress has been made since 1998 and 2002 when the fact that neutrinos have mass was first discovered.

What we know and don't know is recapped in the executive summary from the Snowmass 2021 paper, the balance of which reviews the various experimental efforts that are underway to answer those questions.

The discovery of neutrino oscillations in 1998 and 2002 added at least seven new parameters to our model of particle physics, and oscillation experiments can probe six of them.

To date, three of those parameters are fairly well measured: the reactor mixing angle θ(13), the solar mixing angle θ(12), and the solar mass splitting ∆m^2(21), although there is only one good measurement of the last parameter. Of the remaining three oscillation parameters, we have some information on two of them: we know the absolute value of the atmospheric mass splitting ∆m^2(31) fairly well, but we do not know its sign, and we know that the atmospheric mixing angle θ(23) is close to maximal ∼ 45º, but we do not know how close, nor on which side of maximal it is. Finally, the sixth parameter is the complex phase δ related to charge-parity (CP) violation, which is largely unconstrained.

Determining these remaining three unknowns, the sign of ∆m^2(31), the octant of θ(23), and the value of the complex phase δ, is of the utmost priority for particle physics. In addition to the absolute neutrino mass scale which can be probed with cosmological data sets, they represent the only known unknown parameters in our picture of particle physics.

It is our job as physicists to determine the parameters of our model. The values of these parameters have important implications in many other areas of particle physics and cosmology, as well as providing insights into the flavor puzzle. To measure these parameters, a mature experimental program is underway with some experiments running now and others under construction. In the current generation we have NOvA, T2K, and Super-Kamiokande (SK) which each have some sensitivity to the three remaining unknowns, but are unlikely to get to the required statistical thresholds. Next generation experiments, notably DUNE and Hyper-Kamiokande (HK) are expected to get to the desired thresholds to answer all three oscillation unknowns. Additional important oscillation results will come from JUNO, IceCube, and KM3NeT. This broad experimental program reflects the fact that there are many inter-connected parameters in the three-flavor oscillation picture that need to be simultaneously disentangled and independently confirmed to ensure that we truly understand these parameters.

To achieve these ambitious goals, DUNE and HK will need to become the most sophisticated neutrino experiments constructed to date. Each requires extremely powerful neutrino beams, as many measurements are statistics limited. Each will require a very sophisticated near detector facility to measure that beam, as well as to constrain neutrino interactions and detector modeling uncertainties, which are notoriously difficult in the energy ranges needed for oscillations. To augment the near detectors, additional measurements and theory work are crucial to understand the interactions properly, see NF06. Finally, large highly sophisticated far detectors are required to be able to reconstruct the events in a large enough volume to accumulate enough statistics. DUNE will use liquid argon time projection chamber (LArTPC) technology most recently demonstrated with MicroBooNE. LArTPCs provide unparalleled event reconstruction capabilities and can be scaled to large enough size to accumulate the necessary statistics. HK will expand upon the success of SK’s large water Cherenkov tank and build a new larger tank using improved photosensor technology.

It is fully expected that with the combination of experiments described above, a clear picture of three-flavor neutrino oscillations should emerge, or, if there is new physics in neutrino oscillations (see NF02 and NF03), that should fall into stark contrast in coming years. . . .

The body text continues to make some useful observations:

The Jarlskog invariant, which usefully quantifies the “amount” of CP violation, for the quark matrix is J(CKM) = +3 × 10^−4 J(max) while for leptons it could be much larger, |J(PMNS)| < 0.34 J(max) where J(max) ≡ 1/(6√3) ≈ 0.096. Understanding this mystery of CP violation is a top priority in particle physics. . . .

There are various other means of probing the six oscillation parameters. In particular, measurements of the absolute mass scale can provide information about the mass ordering in some cases.

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Kinematic end-pointexperiments such as KATRIN, ECHo, HOLMES, and Project-8 are sensitive to the sum of for all i of |Uei|^2*m(i)^2 which is greater than or equal to 10 meV in the NO and greater than or equal to 50 meV in the IO, although these experiments may not have sensitivity to the mass ordering before oscillation experiments do.•

Cosmologicalmeasurements of the cosmic microwave background temperature and polarization information, baryon acoustic oscillations, and local distance ladder measurements lead to an estimate that the sum of for all i of m(i) < 90 meV at 90% CL which mildly disfavors the inverted ordering over the normal ordering since the sum of for all i of m(i) greater than or equal to 60 meV in the NO and greater than or equal to 110 meV in the IO; although these results depend on one’s choice of prior of the absolute neutrino mass scale. Significant improvements are expected to reach the σ(the sum of for all m(ν)) ∼ 0.04 eV level with upcoming data from DESI and VRO, see the CF7 report, which should be sufficient to test the results of local oscillation data in the early universe at high significance, depending on the true values.• If lepton number is violated via an effective operator related to neutrino mass, then we expect neutrino-less double beta decay to occur proportional to m(ββ) = |the sum of for all i of U(ei)^2*m(i)| which could be as low as zero in the NO but is expected to be > 1 meV in the IO, thus a detection below 1 meV would imply the mass ordering is normal. The latest data from KamLAND-Zen disfavors some fraction of the inverted hierarchy for favorable nuclear matrix element calculations which are fairly uncertain.

• Finally, a measurement of the cosmic neutrino background is sensitive, in principle, to a combination of the absolute mass scale, whether neutrinos are Majorana or Dirac, and the mass ordering.

Among these non-oscillation measurements, only the cosmological sum of the neutrino masses is likely to be sensitive to the atmospheric mass ordering within the next decade.

Consensus is starting to build around (1) a normal mass ordering, (2) a second quadrant (i.e. greater than 45º) value for θ(23), (3) a near minimal value of the lowest absolute neutrino mass, and (4) a complex phase δ for neutrino oscillation CP violation that is non-zero and is close to, but not exactly, maximal.

Neutrinoless double beta decay also remains elusive, if it exists at all. It is undoubtedly already constrained to be very rare, at a minimum and the constraints will continue to grow more strict in the coming years (unless it is finally discovered).

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