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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)
added today’s
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.
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 $m_0$.
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.
added one more item to the list of quotes:
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 publication data for:
added one more item to the list of quotes:
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.
and one more:
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 quote:
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.
added one more quote, from a replacement appearing today:
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 an item from yesterday:
Perhaps the gauge/string duality has provided us with a “physicist’s proof of confinement” in some exotic gauge theories like the one described by the warped deformed conifold. Yet, we still don’t have a quantitative handle on the Asymptotically Free theories in 3+1 dimensions. $[\cdots]$ Don’t take confinement for granted, even in 1+1 dimensions where it seems obvious. Proof of Color Confinement in 2+1 and 3+1 dimensions would be very important.
also the companion talk:
also added this item:
added one more item to this list of references+quotes on the open problem of confinement:
Yakov Shnir, Section 9.1. of: Magnetic Monopoles, Springer 2005 (ISBN:978-3-540-29082-7)
$[$confinement$]$ still remains one of the very few Big Unsolved Problems of the theoretical physics of the XXI-st century. Moreover, this is the “classic question that has resisted solution over the years”, which was included by the Clay Mathematics Institute in the list of seven Millennium Prize Problems $[14]$. The award will amount to USD 1,000,000, thus, it is worth-while to account for more information about the matter.
added one more item to the list, from today’s
on the proton radius problem:
In the beginning God created quarks, And made them interact through the strong forces, And it was dark… And God said, “I do not understand a damn thing”
added to the list a pointer to today’s
with this quote:
in the infrared (IR) limit, QCD enters entirely different, strongly-coupled domain, rendering the Perturbation Theory inapplicable and creating substantial problems for making reliable predictions at intermediate and low momentum transfers, i.e. at large distances. While it is conventionally believed that QCD should remain the correct theory of strong interactions also at large distances, in the so-called confined regime, deriving reliable predictions remains a big theoretical challenge.
$[\cdots]$
The problem of confinement concerns the strongly-coupled sector of QCD composed of interacting colored partons (quarks and gluons). $[\cdots]$ Despite the major efforts of the research community and tremendous progress made over last few decades, it does not appear to be fully and consistently resolved yet.
added one mote item to the list, today’s
with this quote:
QCD and its relatives are special because QCD is the theory of nature. QCD is strongly coupled in the infrared domain where it is impossible to treat it quasi-classically – perturbation theory fails even qualitatively. It does not capture drastic rearrangement of the vacuum structure related to confinement. The Lagrangian is defined at short distances in terms of gluons and quarks, while at large distances we deal with hadrons, e.g. pions, ρ mesons, protons, etc. Certainly, the latter are connected with quarks and gluons in a divine way, but this connection is highly nonlinear and non-local; even now, 50 years later, the full analytic solution of QCD is absent.
Non-perturbative methods were desperately needed.
Finally dug out this gem:
With this quote:
While the LHC is best known for the observation of the first fundamental scalar particle, the Higgs Boson [33, 34], it has also yielded many observations of yet unknown hadrons. Hadrons are composed of quarks and are thus not fundamental particles of the Standard Model. However, their properties follow from yet unsolved mysteries of the strong interaction.
Although the QCD Lagrangian is expected to completely describe the spectrum of hadrons and all of their properties, there is no rigorous first-principle way of expressing this mathematically. The quark confinement conjecture is experimentally well tested, but mathematically still unproven. And it is still unknown which combinations of quarks may or may not form hadrons. Experimental guidance is needed to help improving theoretical models.
Modern alchemy: “properties follow from yet unsolved mysteries” :-)
added pointer to today’s
added another item to the list:
asymptotic freedom implies that the theory is innately nonperturbative at short distances, which in turn means that it is extremely difficult to describe QCD’s dynamics at the $fm$ scale. Indeed, QCD’s colour-charged degrees of freedom, the massless gluons and the light up and down quarks, have never been observed in isolation: they are confined in colour-neutral bound-states, the hadrons, of which the (light) pion and the (heavy) proton are primary examples. It should be noticed that without a mass-scale confinement would not be possible: colour-singlet combinations of quarks would still be there, but the participating particles would need not be close together, since in a scale invariant theory all lengths are equivalent. Accordingly, the question “how does confinement appear in QCD” is inextricably connected to the question “how does mass emerge in strong dynamics”.
added one more item:
At large distances, however, the nonperturbative nature of the strong interactions becomes dominant and a basic understanding of the essential features of hadron physics from first principles QCD has remained an important unsolved problem in the standard model of particle physics. Hadronic characteristics are not explicit properties of the QCD Lagrangian but emergent phenomena, notably, the origin of the hadron mass scale, the mechanism of color confinement, the relation between chiral symmetry breaking and confinement, the massless pion in the chiral limit (the limit of zero quark masses), bound states and the pattern of hadron excitations.
added another item to the list
with this quote:
We have known for over fifty years that protons are made up of quarks and gluons. We have pinned down the masses and couplings of quarks to a startling degree of accuracy. Yet we still don’t know why the proton’s mass is almost exactly a factor of 100 greater than the sum of the masses of its constituent quarks. This mystery persists because quarks and gluons are strongly coupled at low energies: they interact so forcefully and often that our usual calculational tools – based almost entirely on perturbation theory – fail.
added another item to the list:
pp 126: Heuristically, one may speculate that, since the coupling constant of QCD is too large, quarks bind together so that any single quark may not be able to exist alone. However, it has never been proved theoretically. After all, at present we have not understood yet QCD, the theory with a large coupling constant in which quantum theoretical effects (many loops in Feynman graphs as in Fig. 2.18) are essential. This is really a serious problem. Actually, one of big seven mathematical millennium problems proposed by Clay mathematical institute in the United States is concerning this QCD, and one million dollars will be awarded for a solution of the problem related with this.
D-branes give us quite an innovative idea, as an approach to this problem. It is called “holography” which is introduced in this chapter.
added one more item to the list, today’s:
Quantum Chromodynamics (QCD) is notorious for being a quantum field theory that is difficult to solve on large length scales $[\ldots]$ what is missing in current QCD literature is a (potentially approximate) solution to continuum QCD that captures the main qualitative features such as confinement in the IR and asymptotic freedom in the UV $[\ldots]$ if such a solution does exist, it cannot be based on a perturbative weak-coupling expansion, because QCD becomes strongly coupled towards long length scales. So the putative solution must arise from non-perturbative methods.
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