It must be pointed out that the Standard Model of particle physics has a rather baroque structure.
Here is the low-energy SM (all masses in GeV -- protons are 0.9383 GeV, neutrons 0.9396 GeV, 1 atomic mass unit 0.931 GeV). Quantum numbers are (QCD multiplet, electric charge):
- Gauge: gluon (8,0) 0 GeV, photon (1, 0) 0 GeV, W (1,+-1) 80 GeV, Z (1,0) 91 GeV
- Higgs: (1,0) 125 GeV
- Up, charm, top quarks (3, 2/3): 0.0023, 1.275, 173 GeV
- Down, strange, bottom quarks (3, -1/3): 0.0048, 0.95, 4.18 GeV
- Neutrinos (1, 0): around 10^(-11) - 10^(-10) GeV
- Electron, muon, tau (1, -1): 0.000511, 0.106, 1.777 GeV
Here is with unbroken electroweak symmetry. The quantum numbers are now (QCD multiplet, weak-isospin multiplet, weak-hypercharge value). I won't be giving masses here, since only the Higgs particle has an intrinsic mass here, and it's rather odd.
- Gauge: gluon (8,1,0), W (1,3,0), B (1,1,0)
- Higgs (SUSY pair of doublets): Hu (1,2,1/2), Hd (1,2,-1/2)
- Quarks: left-handed up and down together Q (3,2,1/6), right-handed up U (3,1,2/3), right-handed down D (3,1,-1/3)
- Leptons: left-handed neutrino and electron together L (1,2,-1/2), right-handed neutrino (if it exists) N (1,1,0), right-handed electron E (1,1,-1)
I'll summarize some GUT hypotheses:
- SU(5): 1 gauge multiplet, 1 (plain) or 2 (SUSY) Higgs multiplets, 2 (plain) or 3 (with right-handed neutrinos) multiplets per elementary-fermion generation
- SO(10): 1 gauge multiplet, 1 Higgs multiplet, 1 elementary-fermion multiplet per generation
- E6: 1 gauge multiplet, Higgs and EF multiplets in the same kind of multiplet
GUT's require symmetry breaking to get to the Standard Model.
There are some known effects that don't fit into the Standard Model very well.
- Gravity
- Dark matter
- Dark energy
- Cosmic inflation
Turning to Martin Rees's six numbers, ε, the mass fraction of He4's binding energy, is essentially a numerical constant, though it is pushed down a bit by the light quarks' masses. A more serious consequence of a weakened nucleon-nucleon interaction may be deuterium being unstable. That would get in the way of hydrogen burning in the cores of stars. Stronger may make dineutrons and diprotons bound, and that would have consequences of their own.
N, the ratio of two protons' electromagnetic and gravitational interactions, is very large. The quantum-gravity mass scale or Planck mass is about 10^(19) GeV, much larger than Standard-Model masses, but close to GUT masses of around 10^(16) GeV. So why the 10^(14) GUT-to-SM gap?
The next two are about inflation.
The Universe's curvature, Ω, is very close to 1. From inflation, it takes about 60 e-foldings of expansion to produce such flatness. But with only a few more e-foldings, Ω becomes too close to 1 to measure.
The fluctuation amplitude, Q, is around 10^(-5). It is roughly ( (inflation energy scale) / (Planck mass) )^2, giving an inflation energy scale of roughly 10^(16) GeV -- close to expected GUT energies. So we have three effects pointing to GUT energy scales:
- Gauge unification
- Neutrino-mass seesaw model
- Inflation
Turning to Λ, the cosmological constant or dark-energy value, I have seen some speculations as to why it is so prominent at this time. Speculations like "tracking", where the dark-energy density somehow tracks the overall mass/energy density.
Finally, D, the number of space dimensions: 3. There is also one time dimension. Looking at string theory, we find a hint of a solution. Supersymmetric strings or superstrings prefer to live in 10 space-time dimensions, but if six of them are "compactified" into a supersmall ball, that lives four "large" ones, the ones of our Universe. But why six and not some other number?