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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 19th 2020

a bare sub-section with a list of references – to be !included into relevant entries – mainly at confinement and at mass gap problem (where this list already used to live)

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJun 17th 2020

• Craig D. Roberts, Sebastian M. Schmidt, Reflections upon the Emergence of Hadronic Mass (arXiv:2006.08782)

together with the following quotes from it:

More than 98% of visible mass is contained within nuclei. In first approximation, their atomic weights are simply the sum of the masses of all the neutrons and protons (nucleons) they contain. Each nucleon has a mass $m_N \sim 1$ GeV, i.e. approximately 2000-times the electron mass. The Higgs boson produces the latter, but what produces the masses of the neutron and proton? This is the question posed above, which is pivotal to the development of modern physics: how can science explain the emergence of hadronic mass (EHM)?

$[\cdots]$

Modern science is thus encumbered with the fundamental problem of gluon and quark confinement; and confinement is crucial because it ensures absolute stability of the proton. $[\cdots]$ Without confinement,our Universe cannot exist.

As the 21st Century began, the Clay Mathematics Institute established seven Millennium Prize Problems [ 11 ]. Each represents one of the toughest challenges in mathematics. The set contains the problem of confinement; and presenting a sound solution will win its discoverer \$ 1,000,000. Even with such motivation, today, almost fifty years after the discovery of quarks [12–14], no rigorous solution has been found. Confinement and EHM are inextricably linked. Consequently, as science plans for the next thirty years, solving the problem of EHM has become a grand challenge.

$[\cdots]$

In trying to match QCD with Nature, one confronts the many complexities of strong, nonlinear dynamics in relativistic quantum field theory, e.g. the loss of particle number conservation, the frame and scale dependence of the explanations and interpretations of observable processes, and the evolving character of the relevant degrees-of-freedom. Electroweak theory and phenomena are essentially perturbative; hence, possess little of this complexity. Science has never before encountered an interaction such as that at work in QCD. Understanding this interaction, explaining everything of which it is capable, can potentially change the way we look at the Universe.

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeJun 17th 2020

And a solution to the Millennium Prize problem

may be of limited value (p. 3)

So their strategy is rather

the view that a single renormalisation group invariant (RGI) mass-scale, $m_0$, emerges from strong interactions within the Standard Model and all mass-dimensioned quantities derive their existence and values from $m_0$.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJun 17th 2020

Not sure what they mean here. The mass gap problem asks for a proof of the emergence of the positive mass of the the bound states of Yang-Mills theory. That’s exactly what they highlight as the problem they are looking at.

Probably they saw some comments in the Jaffe/Witten problem description as following a different strategy than what they are after. But the mass gap Millennium Problem does not prescribe the strategy of the proof, it is quite vague on what math to use. Clearly, part of the problem is to find the framework in which it can be mathematically answered.

But I am impressed that they, being pheneomenologists, make this connection to the mathematical mass gap problem at all. It’s the first time since I started writing about it here that I see other authors follow this.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTime7 days ago