Constants in The Standard Model and In Cosmology
The original standard model of particle physics from the 1970s contained 19 fundamental dimensionless constants describing the masses of the particles and the strengths of the electroweak and strong forces. In the 1990s, neutrinos were discovered to have nonzero mass, and a quantity called the vacuum angle was found to be indistinguishable from zero.
The complete standard model requires 25 fundamental dimensionless constants (Baez, 2002). At present, their numerical values are not understood in terms any widely accepted theory and are determined only from measurement. These 25 constants are:
- the fine structure constant;
- the strong coupling constant;
- fifteen masses of the fundamental particles (relative to the Planck mass), namely:
- six quarks
- six leptons
- the Higgs boson
- the W boson
- the Z boson
- four parameters of the CKM matrix, describing how quarks oscillate between different forms;
- four parameters of the Maki-Nakagawa-Sakata matrix, which does the same thing for neutrinos.
| Dimensionless constants of the Standard Model | ||||
|---|---|---|---|---|
| Symbol | Description | Dimensionless value | Alternative value representation | |
| mu / mP | Up quark mass | 1.4×10−22 – 2.7×10−22 | 1.7 – 3.3 MeV/c2 | |
| md / mP | Down quark mass | 3.4×10−22 – 4.8×10−22 | 4.1 – 5.8 MeV/c2 | |
| mc / mP | Charm quark mass | 1.04×10−19 | 1.27 GeV/c2 | |
| ms / mP | Strange quark mass | 8.27×10−21 | 101 MeV/c2 | |
| mt / mP | Top quark mass | 1.41×10−17 | 172.0 GeV/c2 | |
| mb / mP | Bottom quark mass | 3.43×10−19 | 4.19 GeV/c2 | |
| θ12,CKM | CKM 12-mixing angle | 0.23 | 13.1° | |
| θ23,CKM | CKM 23-mixing angle | 0.042 | 2.4° | |
| θ13,CKM | CKM 13-mixing angle | 0.0035 | 0.2° | |
| δCKM | CKM CP-violating Phase | 0.995 | 57° | |
| me / mP | Electron mass | 4.18546×10−23 | 511 keV/c2 | |
| mνe / mP | Electron neutrino mass | Unknown | ||
| mμ / mP | Muon mass | 8.65418×10-21 | 105.7 MeV/c2 | |
| mνμ / mP | Muon neutrino mass | Unknown | ||
| mτ / mP | Tau mass | 1.45535×10-19 | 1.78 GeV/c2 | |
| mντ / mP | Tau neutrino mass | Unknown | ||
| θ12,PMNS | PMNS 12-mixing angle | 0.5973±0.0175 | 34.22±1° | |
| θ23.PMNS | PMNS 23-mixing angle | 0.785±0.12 | 45±7.1° | |
| θ13,PMNS | PMNS 13-mixing angle | ≈0.077 | ≈4.4° | |
| δPMNS | PMNS CP-violating Phase | Unknown | ||
| α | fine structure constant | 0.00729735 | 1/137.036 | |
| αs | strong coupling constant | ≈1 | ≈1 | |
| mW± / mP | W boson mass | 6.5841±0.0012×10−18 | 80.385±0.015 GeV/c2 | |
| mZ0 / mP | Z boson mass | 7.46888±0.00016×10−18 | 91.1876±0.002 GeV/c2 | |
| mH / mP | Higgs boson mass | ≈1.02×10−17 | ≈125 GeV/c2 (tentative) | |
One constant is required for cosmology:
- the cosmological constant (in terms of Planck units) of Einstein's equations for general relativity.
Thus, currently there are 26 known fundamental dimensionless physical constants. However, this number may not be the final one. For example, if neutrinos turn out to be Majorana fermions, the Maki-Nakagawa-Sakata matrix has two additional parameters. Secondly, if dark matter is discovered, or if the description of dark energy requires more than the cosmological constant, further fundamental constants will be needed.
Read more about this topic: Dimensionless Physical Constant
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