“The fundamental physical basis from which mass emerges is not yet fully understood.”

Another puzzling aspect of the SM Higgs boson concerns the arbitrariness of its couplings to fermions. This is encoded in the SM through a series of Yukawa couplings, one per massive fermion, proportional to the corresponding fermion mass and therefore displaying a huge and unexplained scale hierarchy. … These interactions are not of gauge nature and could be messengers of new physics (NP) that will eventually explain the hierarchy of fermion masses and the flavor dynamics of the SM at a deeper level [36].

The cornerstone of this 2018 CODATA adjustment, as in previous adjustments, is the validity of physical theory as un derstood today.

The EWSB mechanism provides no additional insight on possible underlying reasons for the large variety of mass values of the fermions, often referred to as the flavour hierarchy.

The Higgs boson is the fundamental particle associated with the Higgs field, a field that gives mass to other fundamental particles such as electrons and quarks. … Fundamental particles in our universe acquire mass through their interactions with the Higgs field.

Stars, planets and life could only emerge because particles gained their mass from a fundamental field associated with the Higgs boson. The existence of this mass-giving field was confirmed in 2012, when the Higgs boson particle was discovered at CERN.

More than 99% of the mass of the visible universe is made up of protons and neutrons. Both particles are much heavier than their quark and gluon constituents, and the Standard Model of particle physics should explain this difference.

Even though it is a great achievement to have found the Higgs particle — the missing piece in the Standard Model puzzle — the Standard Model is not the final piece in the cosmic puzzle. One of the reasons for this is that the Standard Model treats certain particles, neutrinos, as being virtually massless, whereas recent studies show that they actually do have mass.

Thus any question about the origin of the masses of fermions reduces to a question about the origin of the interactions of fermions with the Higgs field.

In fact, accurate standard model predictions of both the proton and neutron mass have existed for a decade [4]. … However, physicists would like to understand how the masses emerge from QCD, much the same way they can predict the spectrum of hydrogen from quantum theory.

It is fair to say that we have come a long way exploring the origin of inertia since the nineteenth century, but no one would claim that we fully understand it yet.

There are two mass generating mechanisms in the standard model of particle physics (SM). One is related to the Higgs boson and fairly well understood. The other is embedded in quantum chromodynamics (QCD), the SM’s strong interaction piece; and although responsible for emergence of the roughly 1 GeV mass scale that characterises the proton and hence all observable matter, the source and impacts of this emergent hadronic mass (EHM) remain puzzling.

The Lagrangian that defines QCD, the strong interaction sector of the Standard Model (SM), appears very simple, yet it is responsible for a remarkable array of high-level phenomena with enormous apparent complexity. … This emergence itself is currently beyond a reductionist explanation, unless one is content to find that in the need for ultraviolet renormalisation of four-dimensional quantum field theory.

Understanding how the masses of the known elementary particles are generated has been one of the fundamental endeavours in particle physics for several decades. … Within the current precision, a more complex Higgs sector with additional states, although significantly constrained, is not ruled out. Nor has it been established whether the Higgs boson is an elementary particle or whether it has an internal structure like any other scalar particle observed before it.

It seems we are looking at just the visible tip of an iceberg – hidden below the Standard Model must be a deeper, more fundamental theory that gives reason to what we see on the surface.

By studying the production and decay of the Higgs boson, ATLAS physicists confirmed that the Higgs boson interacts with both bosons and fermions (the latter being particles that make up matter), confirming the prediction by the Standard Model that elementary particles acquire mass via the all-pervasive Higgs field.

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

We now see Newtonian mass as an emergent property. … Most of the mass of standard matter, by far, arises dynamically, from back-reaction of the color gluon fields of quantum chromodynamics (QCD).

These examples are touched upon briefly before going to the most pressing issue of today, which is the origin of elementary particle masses. … The second place where our experimental understanding of the vacuum may be at odds with effective theories is in the generation of elementary particle masses.

In particular, this review is rather a status report than a final answer. … In fact, the ultimate quest of the decades of research presented here is not to change the standard model. Much to the contrary, the goal is to provide a single, consistent description of the standard model, and any theory beyond, as long as it is a quantum gauge field theory.

Our community has been pondering the Higgs’s naturalness problem for decades, and yet many of us suspect that we have not found the right idea yet.

Visible matter is characterised by a single mass scale; namely, the proton mass. The proton’s existence and structure are supposed to be described by quantum chromodynamics (QCD); yet, absent Higgs boson couplings, chromodynamics is scale-invariant. Thus, if the Standard Model is truly a part of the theory of Nature, then the proton mass is an emergent feature of QCD; and emergent hadron mass (EHM) must provide the basic link between theory and observation.

The mechanism by which the proton mass, one of the most fundamental quantities in our universe, emerges from the dynamics of the strong force is not yet fully understood.

The W and Z particles were discovered in a Nobel prize winning enterprise at CERN in the 1980s, but the mechanism that gives rise to their mass had not yet been understood, and that’s where the Higgs boson comes in. … Is the Higgs boson the only possible answer to the “mass problem”? No, there are other theories that predict the existence of different mechanisms to explain how Nature deals with the mass problem.

Is the Higgs boson the only possible answer to the “mass problem”? No, there are other theories that predict the existence of different mechanisms to explain how Nature deals with the mass problem.

The apparent simplicity of the QCD Lagrangian conceals a wealth of dynamical patterns, giving rise to a vast array of complex "emergent phenomena" [155]. … The generation of a mass scale due to the self-interactions of the gluons represents arguably the most fundamental expression of such an emergence.

With discovery of the Higgs boson, science has located the source for ≲2% of the mass of visible matter. The focus of attention can now shift to the search for the origin of the remaining ≳98%.

The theory of nuclear moments is limited by the incomplete understanding of nuclear structure effects.

A calculation determines four distinct contributions to the proton mass, more than 90% of which arises entirely from the dynamics of quarks and gluons.

Different decompositions (sum rules) for the proton mass have been proposed in the literature. All of them are related to the energy-momentum tensor in quantum chromodynamics.

The conclusion is that measuring the fermion-Higgs couplings at higher levels of precision will significantly improve our understanding of the origin of masses in nature.

Overall, what and wherefrom is mass?

Understanding the proton mass in quantum chromodynamics (QCD) is a very important and current topic in hadronic physics. The decomposition (sum rule) of the proton mass is not unique, and different sum rules, which are related to the QCD energy-momentum tensor, can be found in the literature. We review and compare these sum rules and identify open questions in this field.

The biggest, and oldest222I.I. Rabi’s famous reaction to the discovery of the muon in the 1930s: “Who ordered that?”, unresolved enigma in fundamental particle physics is: Where do the observed masses of elementary particles come from?, the concept of mass is not really understood, and their numerical values remain a mystery.

The biggest, and oldest 1, unresolved enigma in fundamental particle physics is: Where do the observed masses of elementary particles come from?, the concept of mass is not really understood, and their numerical values remain a mystery.

The bad news is that nothing in these ideas explains the origin of the mass of the Higgs particle itself, nor do they greatly elucidate the observed complicated structure of quark and lepton masses and mixings, nor the associated physical phenomena of CP violation, neutrino oscillations, … . … The ugly news is that the origin of most of the mass in the universe, that in dark matter and dark energy, remains deeply mysterious.

What constitutes the final step in this integration process is the construction of what is today referred to as the “Higgs mechanism” in the literature of modern physics.

What we now call the Brout-Englert-Higgs mechanism gives a mass to the W and Z when they interact with an invisible field, now called the “Higgs field”, which pervades the universe.

The discovery of the Higgs boson is a major milestone in our progress toward understanding the natural world.

The oldest enigma in fundamental particle physics is: Where do the observed masses of elementary particles come from?

This contribution sketches forty years of developments in QCD, which suggest a solution to the puzzle, and highlight some of the experiments that can validate the picture. … So, perhaps science has a chance of understanding at least this one piece of the SM? Or, perhaps not.

The new cosmic superconductivity, when implemented in a straightforward, minimal way, suggests the existence of a remarkable new particle, the so-called Higgs particle. The mass of the Higgs particle itself is not explained in the theory, but appears as a free parameter.

A warning note is necessary here. It is usually quoted that the Higgs mechanism Higgs (based upon the ideas of Spontaneous Symmetry Breaking of Nambu Nambu , whom was recently Laureated with the Nobel Prize of Physics 2008), is the origin of the mass in the Universe. This is far from being true.

These lectures review the background to Higgs physics, its current status following the discovery of a/the Higgs boson at the LHC, models of Higgs physics beyond the Standard Model and prospects for Higgs studies in future runs of the LHC and at possible future colliders.