Yang-Mills mass gap problems

In classical physics, the equations that describe gauge fields predict that the waves (like those mediating forces) travel at the speed of light and are massless. However, observations show that the corresponding quantum particles—such as the glueballs of quantum chromodynamics (QCD)—have positive, non-zero mass.

According to the Standard Model, a gluon is a standard boson; it must be massless, because if it had mass, it would break the standard symmetry of the QCD model.

But if gluons had no mass, it would be impossible to explain the color confinement properties within hardrons.

In book "The Universe is a unified object", author Ngo Quang Ha thoroughly addressed this issue. The author provided a formula for the mass of gluons without breaking the standard symmetry.

The book (in English) is available on Amazon: https://www.amazon.com/dp/B0HCGYPFK1