added one more quote, from a replacement appearing today:

- Sourav Chatterjee,
*A probabilistic mechanism for quark confinement*(arXiv:2006.16229)

]]>The confinement of quarks is one of the enduring mysteries ofmodern physics. $[\ldots]$ In spite of many decades of research, physically relevant quantum gauge theories have not yet been con-structed in a rigorous mathematical sense. $[$ non-perturbatively, that is $]$ $[\ldots]$ Perhaps the most important example is four-dimensional SU(3)-lattice gauge theory. If one can show that this theory has a mass gap at all values of the coupling strength, that would explain why particles known as glue-balls in the theory of strong interactions have mass. All such questions remain open.

The second big open question is the problem of quark confinement. Quarks are the constituents of various elementary particles, such as protons and neutrons. It is an enduring mystery why quarks are never observed freely in nature. The problem of quark confinement has received enormous attention in the physics literature, but the current consensus seems to be that a satisfactory theoretical explanation does not exist.

added one more quote:

- Guy de Teramond, Stanley Brodsky,
*Longitudinal dynamics and chiral symmetry breaking in holographic light-front QCD*(arXiv:2103.10950)

]]>In spite of the important progress of Euclidean lattice gauge theory, a basic understanding of the mechanism of color confinement and its relation to chiral symmetry breaking in QCD has remained an unsolved problem.

Recent developments based on superconformal quantum mechanics in light-front quantization and its holographic embedding on a higher dimensional gravity theory (gauge/gravity correspondence) have led to new analytic insights into the structure of hadrons and their dynamics.

and one more:

- Koji Hashimoto, Yoshinori Matsuo, Takeshi Morita,
*Nuclear states and spectra in holographic QCD*, JHEP12 (2019) 001 (arXiv:1902.07444)

]]>One of the long-standing problems in QCD is to reproduce profound nuclear physics. The strong coupling nature of QCD prevents us from solving it analytically, and even numerical simulations have a limitation such as the volume of the atomic nucleus versus the lattice size. It is quite important to bridge the particle physics and the nuclear physics, by solving QCD to derive typical fundamental notions of the nuclear physics, such as the magic numbers, the nuclear binding energy and the nuclear shell model. Holographic QCD is an analytic method to approach these problems

added one more item to the list of quotes:

- Koji Hashimoto, Norihiro Iizuka, Piljin Yi,
*A Matrix Model for Baryons and Nuclear Forces*, JHEP 1010:003, 2010 (arXiv:1003.4988)

]]>Nuclear physics is one of the oldest branches of high energy physics, yet remains one of more difficult. Despite the fact that we know the underlying fundamental theory, i.e. QCD, we are still unable to predict, reliably and analytically, behavior of nuclei or even a single proton. The problem is of course that one must understand the strong-coupling regime of QCD, which by and large remains inaccessible except by large-scale lattice simulations. Traditionally, this sets nuclear physics apart from the rest of high energy physics in many aspects. However, recent developments in the so-called gauge/gravity duality began to solve certain strongly coupled field theories,possibly including QCD or its close relatives, allowing the two communities to merge with each other.

added publication data for:

- Craig Roberts, Sebastian M. Schmidt,
*Reflections upon the Emergence of Hadronic Mass*, The European Physical Journal Special Topics volume 229, pages 3319–3340 (2020) (arXiv:2006.08782, doi:10.1140/epjst/e2020-000064-6)

added one more item to the list of quotes:

- Craig Roberts,
*On Mass and Matter*, AAPPS Bulletin volume 31, Article number: 6 (2021) (arXiv:2101.08340, doi:10.1007/s43673-021-00005-4)

]]>The origin of the proton mass, and with it the basic mass-scale for all nuclear physics, is one of the most pro-found puzzles in Nature.

Although QCD is defined by a seemingly simple La-grangian, it specifies a problem that has defied solutionfor more than forty years. The key challenges in modernnuclear and high-energy physics are to reveal the observ-able content of strong QCD and, ultimately, therefromderive the properties of nuclei.

added today’s

- Michael Creutz,
*QCD beyond diagrams*(arXiv:2010.04774)

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.

]]>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 $m_0$.

added today’s

- 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.

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)