COUPLING AND MASS!

In physics, the probability of fundamental processes is determined by what are called coupling constants, numbers that specify the strength with which some additive quantum number couples to a specific fundamental field of nature. For example, the so-called “fine structure constant,” α = e2/ℏc = 1/137 determines the way charge couples to the electromagnetic field, in other words to photons. [In the units physicists use, charge squared has the same units as ℏc, namely MeV-fm.] By analogy, physicists defined a coupling constant for the strong interaction, αs, which describes the coupling of colored quarks to gluons, and for the weak interaction, αw, which describes the coupling of weak charge to the weak bosons.  In the realm of ordinary nuclear physics, αs is just a bit less than 1, and αw is effectively something like 10−6. You might think these numbers are fundamental constants of nature, but the remarkable fact is that they are functions of momentum transfer Q in a given process.  Based on the uncertainty relation ΔrΔQ ≃ ℏ, this means that very high momentum transfer corresponds to very short distances... so that the fundamental forces are found to have a different coupling strength at short distances compared to large distances!


High energy or momentum transfer corresponds to very short interaction distances, while low energy or momentum transfer corresponds to large interaction distances.

The astonishing result is that the strong force (described by the theory called QCD) actually becomes drastically inherently weaker at short distances, so that quarks inside a baryon or meson behave as if they were free particles, being in eigenstates of momentum! On the other hand, the force becomes so drastically stronger at larger distances, that the binding energy of quarks inside a baryon or meson is infinite.   If we look at the electromagnetic force (described by the theory called QED), we find the opposite behavior... the inherent strength of the force becomes much stronger at short distances.  This difference in behavior is related to the peculiarities of color compared to charge, when virtual particles are involved, with clouds of them surrounding the real particles as they interact.  The behavior of the weak force is similar to the behavior of the electromagnetic force... in fact a unified theory of weak and electromagnetic forces is a key part of the Standard Model.  What makes the weak force appear so weak is that its bosons have enormous mass, whereas the bosons of the electromagnetic and strong forces have zero mass.  The combination of QCD with the unified theory of weak and electromagnetic interactions (EWT) resulted in the Standard Model of particles and fields, which since the late 1960s has been the standard theory of particles and fields, and has met every experimental test for the last half century successfully.  Yet it is clearly incomplete, and physicists immediately started thinking of ways to go beyond it.  Almost all of those ways tried to unify the electroweak and strong forces into a single framework, and all those ways have failed completely.

The Electroweak Theory solved a huge problem in theoretical physics. Maxwell's equations exhibit a property called gauge symmetry. It is possible to make fairly arbitrary changes to the fields appearing in the equations, without changing the solutions! This works only if the fields are vector fields, and when these fields are quantized, the bosons of the field must be massless, spin-1 particles. If, and only if, this condition is satisfied, does the theory work and make predictions that agree with experiment. There is therefore no problem with the electromagnetic field (photons are massless), nor is there a problem with the strong interaction (gluons are massless). But catastrophically, the three bosons of the weak interaction have mass, and a huge amount of mass at that, roughly 80 GeV, 80 times the mass of a proton! Thus it initially appeared that no exact theory of the weak force was possible. A solution to the problem was suggested by Peter Higgs and others. If there were in nature a scalar field which existed with non-zero energy even when not excited, the interaction of that field with fundamental point particles could give them a potential energy that served the same function in the equations as mass. To demonstrate that this field existed, physicists had to excite it... to produce a Higgs boson. This was successfully done in 2012. The Higgs field gives mass to all fundamental point particles that have a mass, such as the leptons and the quarks, as well as the bosons of the weak interaction. The mass of ordinary matter is NOT due to the Higgs field, it is due to the masses of protons and neutrons, which in turn are due to the internal kinetic and potential energies of these composite particles.

Peter Higgs died on 4/8/2024



Francois Englert and Peter Higgs, Nobel Prize 2013

More than 10 years after the discovery of the Higgs boson, NO NEW PARTICLES HAVE BEEN FOUND, even though the beam energy and intensity of the LHC has been steadily increased. And no new particles are predicted by the Standard Model, but we know the Standard Model is incomplete... for example, it does not predict the existence of so-called Dark Matter particles, yet it is clear they make up a major component of our universe. It looks as if we have encountered a vast energy desert, where nature refuses to provide us with any hints as to how to improve our description of the fundamental aspects of nature.







ASTROPHYSICS