# Measuring and calculating free quark masses

Particle data book contains masses of the free quarks. I wonder, how do experimentalists determine the masses of the free quarks even though they are trapped inside hadrons (except perhaps in quark-gluon plasma)? Can quark masses be theoretically calculated and how much do they agree with experiments?

Nobody has seriously calculated theoretically a quark mass from first principles. So there is no issue of agreement with experiment. They are parameters in experimental fits, but sometimes remarkably consistent across a broad range of experiments-- and the QCD/EW calculations using them as inputs. If someone pretends to know their origin, he/she is bluffing.

Constituent quark masses have been fitted to hadron masses using simple potential models in the style of additive nuclear models. They range from 0.34Gev to 177GeV and are not too informative, as they are mostly glue for the light quarks, i.e. they arose out of chiral symmetry breaking---see below. They are not of any use in QCD/EW perturbative calculations, and, culturally, they have a life of their own, of possible assistance to diffractive scattering studies.

The more fundamental current quark masses that are used in the fundamental lagrangian of the SM are extracted from DIS fits (deep inelastic scattering), for the heavy ones; but, mostly for the light ones, they are extracted, sometimes with the aid of lattice theories, out of chiral perturbation theory on the masses of the pseudoscalar mesons, via Dashen's formula of chiral symmetry breaking.

They range from 2MeV to 175GeV. For example, stringing several such formulas together one finds fits such as the popular one, $$\frac{m_u+m_d}{2m_s}=\frac{m_\pi^2}{2m_K^2-m_\pi^2}\approx \frac{1}{25}~.$$

It is possible to calculate the mass of free quarks. The calculation shows values between 2.1 and 3.27 MeV/C2. This gives an average mass of 2.67 MeV/C2 for the up quarks. The down quarks will have roughly double the mass of the up quarks (since this was the base for the calculation). However, using the average weighted mass of the up and down quarks (approx. between 3.15 and 4.9 MeV/C2) is the approach used to first calculate the mass of the proton, and then backward calculate the up quark mass. The calculated proton mass Mp = (7-ln(20))/(3-ln(20)); Neutron-Proton mass difference is 1.33 MeV/C2. The proton mass distribution is as follows:

• due to quarks (11.4%)
• due to gluons (27.2%)
• quark-quark/quark-gluon interaction (22%)
• due to internal momentum and other effects (39.4%)

It was possible to estimate the percentages of visible matter, antimatter, dark energy and dark matter (4.62; 2.04; 64.7 and 28.6 respectively). It was also possible to estimate the mass of the universe (6.7E54 kg); Volume of the universe (6.4E80 m3); density (1.04E-26 kg/m3); radius of the universe (5.4E26 m). However, the timeline ended up at 38E9 yrs (from 2.3E-39 sec) which was a bit confusing although the Gravitational constant was maintained throughout the timelime.

N.B: No reference(s) has been made in support of the above info because it is still work in progress.

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