FUNDAMENTAL INTERACTIONS

There are some simple rules for understanding what the various fundamental forces of nature do to fundamental particles like quarks and leptons.

• Electromagnetic interactions do not change anything carrying a label. The particles emit and absorb photons, but are not changed intrinsically by those processes. Favors are not changed... down quarks do not become up quarks. Colors are not changed... red quarks do not become green quarks. Of course charge is conserved, and all other additive quantum numbers do not change.

• Strong interactions change color, but not flavor, and of course do not affect charge. That is, a down red quark can emit a red-antiblue gluon and become a blue down quark. But emitting a gluon cannot change flavor, cannot change a down quark to an up quark, for instance. Thus if the only interactions that occur in a process are strong interactions, the identities (flavors) of all the quarks involved do not change... if you started with an up, a down, a strange, an antiup and an antistrange quark, you still have all those quarks at the end of the process.

• The weak interaction always changes flavor, and never changes color. That is, the weak interaction can change a red down quark to a red up quark.   The weak interaction is also infamous for changing the parity of a system; in fact it violates parity conservation to the maximum possible amount, whereas strong and electromagnetic processes tend to conserve parity quite well. The clearest way to understand what is going on is to draw a Feynman diagram. One of the conventions of Feynman diagrams is that antiparticles are usually drawn as if they are propagating backward in time!  Not everybody does this.


A Feynman diagram for the weak decay of a neutron into a proton. A down quark in the neutron changes into an up quark by emitting a W− boson, which in turn creates a particle-antiparticle lepton pair... an ordinary electron, and an anti-electron neutrino.

A Feynman diagram describing the strong interaction between a proton and a negative pi meson... when the systems merge momentarily gluon exchange (indicated by the springs) pushes an up quark inside the proton into the pion, and pushes a down quark inside the pion into the baryon.  The result is that the negative pion becomes a  neutral pion, and the proton becomes a neutron.  Notice in the final state we still have precisely the same quarks, u, d, u, d and anti u, that we had in the initial state.

A Feynman diagram for one electron scattering from another electromagnetically, via exchange of a photon.


A combination of weak and strong processes in the decay of a K-plus meson into two pi-plus mesons and a pi-minus meson.  The weak process converts an antistrange quark into an antiup and creates an up and an antidown, while the strong process creates a down and antidown pair.
Collision of an electron and a positron creates a virtual photon which in turn creates a b and an anti-b quark.  Ignore at least one of the arrows and all the colors.

Feynman diagram of one of many processes that can create a Higgs boson, a famous boson that is the only known example of a fundamental particle with spin zero.  Annihilation of a down and antidown quark pair produces a Z boson which decays to a Higgs and another Z boson.  The Z boson creates a tauon-antitauon pair, while the Higgs creates a top-antitop quark pair, and the tops decay by the weak interaction into bottoms, antibottoms, leptons and antileptons!

Let's make sure we understand pair creation and annihilation. Quick review! When a fermion  collides with its antiparticle, the two can convert into two photons, or any two other paired neutral particles, for example a muon and its antiparticle, or any other pair of total charge zero that satisfies all the conservation laws.  And any boson can create an appropriate particle-antiparticle pair, but if the boson is charged, the particle and antiparticle must be of different varieties, to conserve charge.


When Dirac made quantum physics relativistic in 1928, he found antiparticle solutions for each fermion he applied the equation to. Every fundamental particle has an antiparticle, although in cases where the particle has no additive quantum numbers, it is its own antiparticle. [The photon is an example of this.] A composite particle like the proton has an antiparticle, because, for example the proton contains valence quarks, and so the antiproton can contain the same valence antiquarks.


Dirac (1902 – 1984)
Feynman (1918 – 1988)


So what does the interaction potential between quarks, or a quark and an antiquark, actually look like? This question can be answered two ways, first by looking at the excited states of a meson that is made of a very heavy quark and antiquark, such as charm-anticharm, bottom-antibottom or top-antitop. These systems are actually nonrelativistic, you can solve the Schrödinger equation to fit the energy levels. The result is that the potential looks like a Coulomb potential at short distances, but increases in proportion to r for larger distances. Thus the systems have only bound states, and no quark or antiquark can ever be removed from a hadron.  This result can be verified by directly calculating the states and potential energy of a quark-antiquark system using the so-called lattice gauge theory.  The agreement between these two approaches is remarkably good.


Baryons and mesons are complex systems and since the binding energies are infinite, each system has an infinite number of exited states. For historical reasons, the excited states sometimes have labels as if they were different particles, but the standard spectroscopic notation is still used to identify the various excitations of what is actually the same system.



When the dust settles, the only known truly stable fermion particles are the proton and electron. All other baryons, leptons and mesons decay into states of less energy; the time the decay takes depends on the interaction involved... short for the strong process, intermediate for the electromagnetic process, and long for the weak process, relatively speaking.  Wait, what about neutrinos?  They have mass too small to measure and it would seem they have nothing of lower energy to decay into, so should be stable.  But there is a trick, as always for neutrinos.  The flavor eigenstates are NOT stable, they steadily oscillate into one another with no damping.  However, the individual particles themselves are stable, and as a result neutrino telescopes offer us one of the most fascinating windows onto the near and the distant universe.  How about bosons?  The photon is clearly stable... with zero mass there is nothing it can decay into, so a free photon can propagate and live forever, unless absorbed by matter.  Since the matter density of the universe is low, photons can easily reach us across nearly 13.8 billion years of the universe's history.  The only other source of information about things taking place vast distances away is the radiation component of the gravitational field. In recent decades, gravitational radiation has been an increasingly important source of astrophysical information. By the way, do you know what a Cosmic Ray is?



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