A Nightmare Scenario Physics Agenda

The "nightmare scenario" in high energy physics is one in which no beyond the Standard Model high energy fundamental physics are discovered, at least in a "desert" of energy scales from the TeV energy scale that the can be reached at the Large Hadron Collider (LHC) up to somewhere close to the Grand Unification Theory (GUT) scale of 10^13 TeV.

There is still work to be done for high energy physicists if you assume that this scenario is correct.

Pin down the experimentally measured parameters of the Standard Model

The Standard Model contains 15 particle masses, 4 CKM matrix parameters (in this nine element matrix) which govern the probability of a quark transforming into another quark via a W boson mediated interaction, 4 PMNS matrix parameters (in this nine element matrix) which governs the probability of a neutrino of one flavor oscillating into another flavor of neutrino, and 3 coupling constants for the three Standard Model forces (the strong force, the weak force, and the electromagnetic force). These 26 Standard Model parameters aren't entirely independent of each other due to electroweak unification theory relationships between the W boson mass, Z boson mass, the Higgs boson mass, weak force coupling constant, electromagnetic force coupling constant. So there are really only 24 or 25 independent degrees of freedom in the Standard Model's physical constants. In addition, the speed of light and Planck's constant, both of which are known to parts per billion precision, are experimentally determined values (the speed of light is now defined as an exact value but that defined value started with experimentally determined values), which are necessary to do Standard Model physics calculations.

These parameters are known to varying degrees of precision, with the up quark mass only known to ± 7% relative precision, to the electron mass and electromagnetic coupling constant that are known to exquisite precisions of parts per billion and parts per ten billion respectively. But there is always room for improvement in increasing the precision with which these parameters are known.

The most important to pin down more precisely from the perspective of a high energy physicist are: (1) the top quark mass and Higgs boson mass, which despite their high 0.2% and 0.1% respective relative precisions matter because their large absolute values mean small amounts of imprecision can have great practical impact, (2) the strong force coupling constant which is know to roughly 1% precision and plays a central role in every quantum chromodynamics (QCD), i.e. strong force, calculation, (3) the first generation quark masses, which are known to 5-7% precision which are present in the hadrons most commonly found in Nature, and (4) three of the four CKM matrix parameters which are known to 1-4% precision that are used very regularly and have theoretical importance. The tau lepton's mass is known to a precision of one part per 14,800, which while already considerable, is far less than that of the electron and muon, and is notable as a way to test Koide's rule which predicts it to high precision and has been confirmed so far.

Breakthroughs in the Higgs boson mass measurements precision are likely in the near future. Improvements in the other measurements are likely to be slower and incremental.

Meanwhile, all of the seven neutrino physics parameters need a great amount of improved measurement. The absolute neutrino masses can be estimated only of 16% to 100% of best fit value precision and only by relying on very indirect cosmology estimates, and the  PMNS matrix parameters are known only to about 2-15% precision. Significant progress in these measurements is likely in a time frame of about a decade. Neutrino physicists are also continuing to search for neutrinoless double beta decay which would tell us something critical about the fundamental nature of neutrinos if it was observed. Improvements in these measurements by a factor of ten or so should either prove that it exists and with what frequency, or rule out the most straightforward theoretical ways for it to happen, and some progress is likely over the next decade or so. Knowing the absolute neutrino masses more precisely would allow for more precise predictions about how frequently neutrinoless double beta decay should be if it exists in some fairly simple model of it.

Progress in these measurements is also necessary to confirm that proposed explanations for the relationships between Standard Model physical constants are more than just coincidences facilitated by imprecision measurements.

Progress in neutrino physics measurements, meanwhile, have the potential to clarify possible mechanisms by which neutrino masses arise which the Standard Model with massive oscillating neutrinos only currently describes phenomenologically.

Looking For Predicted But Unobserved Phenomena

There are maybe a dozen or two ground state two valence quark mesons and three valence quark baryons that are predicted to exist, but to be rare and only form in fairly high energy collider environments, that have not yet been observed, although a few new hadrons which are predicted to exist seem to be detected every year. Dozens more, and theoretically infinite, numbers of excited hadrons likewise remain to be seen.

Free glueballs, i.e. hadrons made up of gluons without valence quarks, have not yet been observed, but are predicted to be possible in QCD.

Sphaleron interactions, in which baryon number (B) and lepton number (L) are not separately conserved even though B-L is conserved, are predicted to exist at energies about a hundred times greater than those of the LHC, but have not been observed.

A complete failure to find free glueballs or sphaleron interactions where they are theoretically predicted to be present would seem to require slight tweaks to the Standard Model.

There are observed true tetraquarks, pentaquarks, and maybe even hexaquarks, but far more are theoretically possible. We also have a dim understanding of hadron molecules made up of typical two valence quark mesons and three valence quark baryons bound by electromagnetism and the residual strong force, which can be tricky to distinguish from true tetraquarks, pentaquarks and hexaquarks.

The nice aspect of all of these searches is that theory provides a very focused target with very well defined properties to look for. In each of these cases, we know rather precisely the masses and other properties of the unobserved composite particles and the unobserved interaction, and the circumstances under which we can expect to have a chance of seeing them.

First Principles Calculations

Many quantities that, in principle, can be calculated from theory and the measured Standard Model parameters, are in practice determined by experimental measurements.

This includes all of the hadron properties, such as their masses, mean lifetimes, branching decay fractions, and "parton distribution functions" a.k.a. PDFs.

The residual strong force that binds protons and neutrons in atomic nuclei has been determined to fair precision in a manner informed by the Standard Model, but not worked out from first principles.

In both hadronic physics and atomic physics, it hasn't yet been definitely established theoretically if there are "islands of stability" more massive than the current most heavy observed hadrons and atomic isotopes. In the same vein, we have not calculated theoretically the largest possible number of valence quarks that are possible in a strong force bound hadron.

The internal structure of maybe half a dozen or a dozen even parity scalar bosons and axial vector bosons has not yet been worked out.

If we could use first principles calculations to "reverse engineer" observed data to obtain the physical constants necessary to produce the observed particles, this could really move forward the first set of the agenda to measure fundamental constants, and it could also confirm what we already strongly believe, which is that all of the physics necessary to explain, for example, chemistry scale phenomena from the Standard Model, is already known.

Quantum computing which is just around the corner could make these problems which we have known in theory how to calculated for decades, but which have been mathematically intractable to computer, finally possible to solve.