What is mass of free up and down Quark?

Question

1. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly observed or found in isolation.

2. Color confinement, often simply called confinement, is the physics phenomenon that color charged particles (such as quarks) cannot be isolated singularly, and therefore cannot be directly observed.

3. In theoretical physics, quantum chromodynamics (QCD) is a theory of the strong interaction (color force), a fundamental force describing the interactions between quarks and gluons which make up hadrons (such as the proton, neutron or pion).

4. Yang–Mills theory List of unsolved problems in physics Yang–Mills theory in the non- perturbative regime: The equations of Yang–Mills remain unsolved at energy scales relevant for describing atomic nuclei. How does Yang– Mills theory give rise to the physics of nuclei and nuclear constituents?

When you read about quarks, All folders of Quark model have not been defined. I just want to know what is mass of free Quark? But in my calculations seem free quark have no mass. while Quark become free is like to melt ice.

Answer 1

As you say yourself quarks cannot be free. They can be asymptotically free at very high energies, in a quark gluon plasma for example.

Within their confinement in hadrons two types of masses have been measured, constituent masses :

The quantum chromodynamic binding energy of a valence quark in a hadron is the amount of energy required to make the hadron spontaneously emit a meson containing the valence quark. This is the same as the constituent quark mass. Note that the following values are model dependent:

Up quark = 336 MeV/c^2 Down quark =340 MeV/c^2

There are the bare masses which will appear asymptotically, coming from lattice QCD calculations as fits to the solutions:

Up quark =2.01±0.14 MeV/c^2

down quark = 4.79±0.16 MeV/c^2

The nonperturbative regime of QCD is addressed by lattice calculations, and water in any of its phases is not part of the model.

Answer 2

Confinement precludes free quarks so the question is ambiguous. If you mean invariant mass the answer I think is it depends. It can’t be directly measured. In QCD quark mass as a parameter of the Lagrangian is a re-normalized quantity. The momentum scale and re-normalization scheme scale affect the answer.