How much of a nucleon's mass is due to Higgs field sourced quark mass?
Background
To the nearest 0.1 MeV, the mass of the proton is 938.3 MeV (the experimentally measured value is 938.272 089 43 (29) MeV) and the mass of the neutron is 939.6 MeV (the experimentally measured value is 939.565 421 94 (48) MeV).
A proton has two valence up quarks and one valence down quark. A neutron has one valence up quark and two valence down quarks.
According to the Particle Data Group (relying on state of the art averages of Lattice QCD calculations that extra this from measurable masses of particles made up of quarks bound by gluons which are called hadrons) concludes that the average of the up quark mass and the down quark mass is measured to be 3.49 ± 0.4 MeV, the up quark mass is 2.16 ± 0.4 MeV, and the down quark mass is 4.70 ± 0.4 MeV.
What would the masses of the proton and the neutron be, hypothetically, if the up quark and down quark has zero mass?
A new paper calculates that the proton mass would be 882.4 ± 2.5 MeV (about 94% of its measured value), while the mass of the neutron would be 883.7 MeV ± 2.5 MeV (about 94.1% of its measured value). Thus, this would reduce the total nucleon mass by 55.9 MeV ± 2.5 MeV, and ignoring the effect of the difference between the up quark and down quark masses (which has a roughly 3.5 MeV effect in the average massless quark estimate, according to the body text of the paper).
These masses can be conceptualized as the combined pure gluon and electroweak field source mass of a proton or neutron in a minimum energy ground state.
Naively, one would think that the reduction from the measured value would be smaller, because the sum of three times the average of the up and down quark mass is about 10.5 MeV, and this figure is often cited on popular science discussions of the proton and neutron mass.
But, massive quarks indirectly impact the strength of the gluon field between the three valence quarks of a nucleon, and this indirect effect has a magnitude of roughly 45.4 MeV.
Why does this matter?
Prior to this paper, there was a large gap between the values produced by different kinds of calculations of this amount, which the new paper reconciles.
Also, this is not entirely a hypothetical question, because it is part of, for example, how one calculates the mass of protons and neutrons at higher energy scales, and how one can reverse engineer the quark masses of the proton and neutron masses.
At higher momentum transfer scales (a.k.a. energy scales) the Higgs field is weaker and the quark masses get smaller, and eventually, extrapolated to high enough energy scales, the Higgs field goes to zero and the quarks really are massless.
The strong force coupling constant also runs with energy scale, however, and also gets weaker at higher energies, although not at the same rate at the quark masses.
There is also a modest electroweak contribution to the proton and neutron masses and the electromagnetic force (which predominates over the weak force component) gets stronger at higher energy scales, modestly mitigating the declining quark masses and strong force field strength.
So, in order to be able to make a Standard Model calculation of the expected mass of protons and neutrons at high energies, you need to be able to break these distinct sources of the proton and neutron masses into their respective components, because the different components run with energy scale in different ways.
Charge parity violation and the quark masses
Another new paper argues that because the Standard Model has CP-violation, the masses of the up quarks must be related to the masses of the down quarks, giving rise to five independent degrees of freedom for quark masses rather than six.
A physically viable ansatz for quark mass matrices must satisfy certain constraints, like the constraint imposed by CP-violation. In this article we study a concrete example, by looking at some generic matrices with a nearly democratic texture, and the implications of the constraints imposed by CP-violation, specifically the Jarlskog invariant. This constraint reduces the number of parameters from six to five, implying that the six mass eigenvalues of the up-quarks and the down-quarks are interdependent, which in our approach is explicitly demonstrated.
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