Precision
Four of the experimentally measured fundamental constants, all involving neutrino physics, are known to less than 10% precision.
There are another ten that are known to better than 10% precision but less than one percent precision (six mixing angles, two light quark masses, and two related cosmology constants).
Seven more are known to more than one percent precision but less than one part per thousand precision (four quark masses, the Higgs boson mass, one coupling constant, and one mixing angle).
Eleven are known to more than one part per thousand precision, including the speed of light, which is exact by definition and has been measured to a precision of about plus or minus one meter per second.
Theoretically Inferred Properties
Particles With Zero Rest Mass
As a matter of theory, photons, gluons, and the hypothetical graviton have a rest mass of exactly zero, even though they have non-zero mass-energy.
Antiparticles
Antiparticles (which are not shown separately) have the same mass, the same absolute value of total angular moment a.k.a. spin a.k.a J, the opposite electromagnetic and color charge, and the opposite parity, as their ordinary particle counterparts. The W+ boson is the antiparticle of the W- boson and visa versa.
Color Charge
Quarks (top, bottom, charm, strange, down and up) come in three color charges, commonly called red, green and blue, each. Gluons come in eight color charge-anti-color charge combinations. Physicists use the color charges for "accounting purposes" in predicting how quarks and gluons will interact with each other and can infer from number of color charges that exist from their behavior, but physicists can't actually distinguish one quark color or gluon color combination from another.
For example, physicists can't observe where a particular quark has a red or a blue color charge.
Parity and Helicity
All fundamental fermions except neutrinos come in left and right parity versions. In the Standard Model, there are left parity neutrinos and right parity antineutrinos, but not right parity neutrinos and left parity antineutrinos. Bosons have helicity, which is analogous to and in lieu of parity.
Degrees of Freedom
Not all of the experimentally measured fundamental constants are independent of each other. The ratio of the W and Z boson masses are a function of the electroweak coupling constants in the Standard Model. The Fermi constant and Higgs vacuum expectation value shown are function of the W boson mass and electroweak coupling constants. The Hubble constant and the General Relativity cosmological constant lambda are not independent of each other.
Other relationships between the experimentally measured fundamental constants have been proposed as hypotheses, but do not have widespread acceptance.
Energy Scale Related Definitions
All of the fundamental particle masses, the Higgs vacuum expectation value, the three Standard Model coupling constants, and eight mixing angles of the Standard Model have "beta functions" that govern their changing values at different momentum transfer scales (a.k.a. energy scales), because of the "renormalization" concept that is a part of the Standard Model. These beta functions can, in principle at least, be determined exactly from theory. All experiments to date are consistent with them.
The masses shown for the heavier three quarks (top, bottom a.k.a. beauty, and charm, and the three charged lepton masses are "pole masses" (i.e. evaluated at a unique to each fundamental particle energy scale equal to its rest mass at that energy scale). The MS renormalization scheme masses evaluated at 2 GeV shown are used for the lighter three quark masses for which pole masses are ill defined because they are much smaller than the mass of the least massive hadron in which they can be confined. The neutrino masses shown are actually "neutrino mass eigenstates" which don't precisely correspond to the neutrino weak states used in the labels, unless an "on shell" conceptualization of the neutrino masses is used.
The strong force coupling constant shown is evaluated at the Z boson mass momentum transfer scale, as is customary. The other three coupling constants shown are evaluated in the limit of negligible momentum transfer. The Fermi constant is functionally related to the W boson mass the weak force coupling constant (which is itself dimensionless).
Planck's constant, the speed of light, the Hubble constant, and the cosmological constant of general relativity (called lambda) are not defined in a manner that varies with momentum transfer scale, nor are the discrete, theoretically established physical constants such as electromagnetic charge, spin, parity, and color charge.
Mixing Angle Definitions
The parameterizations of the CKM matrix and PMNS matrix shown are standard, and are defined consistently with each other, but these parameterizations are not unique.
While the 3x3 matrixes themselves are not unitary, these matrixes and their complex conjugates, are defined so that in the CKM matrix, the PMNS matrix, and the complex conjugates of the CKM matrix and the PMNS matrix respectively, in each column, and in each row, the sum of the absolute values of the square of each of the three matrix entries (which represents the probability of that matrix entry occurring as a fraction of 1) is equal to exactly 1. So, the matrixes are quasi-unitary and can be fully described by four parameters, just as is the case in any true unitary 3x3 matrix.
The PMNS matrix implicitly assumes Dirac neutrinos, and there could be up to two more non-zero CP violation phases in a Majorana variant of the PMNS matrix which has thus far not proven to be necessary to describe the experimental neutrino oscillation data.
Neutrino Mass Uncertainties
The uncertainties in the neutrino masses shown, in addition to being non-gausian (i.e. not having a "normal" bell curve distribution), are correlated with each other because the uncertainties in each absolute neutrino mass is mostly due to the uncertainty in the lightest neutrino mass eigenstate which as a range of 12 meV (at two sigma significance). Addition uncertainty arises from the uncertainty in the two mass differences between the neutrino masses determined from neutrino mixing data. The "normal" mass hierarchy preferred by the data is shown although an "inverse" mass hierarchy is not entirely ruled out at this point.
Stylistic Choices
As much as possible, all values have been displayed at a uniform MeV or MeV^2 scale and with meters rather than multiples of them, for consistency and to show the relative magnitudes of these constants, even though these are not the conventional units used.
Sources
Most of the underlying data is from the Particle Data Group (PDG) website (linked in the sidebar of this blog), which is the leading source of world average values for fundamental physics constants. Four of the quark masses, however, are from the FLAG19 report, another group that compiles world averages for quark masses determined with the same Lattice QCD methods used by PDG, but which is more up to date and is confident enough to make more precise statements about those masses. The charm quark mass is from a 2020 pre-print which has made the most precise determination of that mass to date which was a significant improvement over both the PDG and the not yet updated FLAG19 determinations. The 16 fundamental constants shown with the dimension of mass (MeV/c^2) do not reflect global electroweak fits of these masses or hypotheses such as the original Koide's rule, which provides a much more precise predicted value of the tau lepton that has withstood the test of time, although without a clear theoretical justification.
The tension between different values of the Hubble constant are disputed, and there is a summary of available data in the referenced 2021 pre-print. The average of the values found with two different methodologies is shown, and the difference between the two values was set arbitrarily to the two sigma consistency threshold, on the assumption that the existing tension is due to understated errors in some or all of the measurement and on the assumption that there is just one true value. It is possible, however, that the discrepancy is because the "Hubble constant" is not actually constant, in which case the low z and high z measurements are actually measuring different things.
7 comments:
Would Dark Energy be explained by "redshifting" of gravity waves? (OT I know...)
A systemic error in governing red shift in light and/or gravitational waves to distance/time could look like dark energy. The original version of this hypothesis called "tired light" has been discredited. But possibilities like limited gravitational redshifts due to "near misses" with large masses and photons being absorbed and then reemitted now and then by interstellar dust near their galaxies of origin aren't ruled out.
Confirming the redshift-distance relationship with high precision at high Z is difficult because parallax based measurements (which is the most reliable distance measurement) isn't viable except at very low z (much less than 1). All other tests are quite model dependent.
What I mean is shouldn't the wavelength of gravity waves lengthen due to the metric expansion of space, meaning that gravity's strength would drop off faster than distance-squared at gigaparsec-scale distances?
Not necessarily. And, at gigaparsec-scale distances there's too much noise for it to be a noticeable effect.
Isn't dark energy itself a gigaparsec-scale phenomenon?
Dark energy is a continuous phenomena that spans the history of the universe. But, my physics intuition is that the gravitational wave impact would be a small proportion of the total effect, if any, and that this second or third order effect (maybe none, I haven't really thought it through rigorously) would not be big enough to detect as it is hard to detect the primary dark energy effect period.
Hubble constant uncertainty due to conflicting measurements is about 10%.
Post a Comment