What Determines the Range of the Strong Interaction?

[kashiark]

the strong interaction's range is 10^-15m, but because gluons are massless shouldn't it be infinite? is it something to do w/ confinement?

 

[humanino]

Yes, it has very much to do with that. There are several ways to interpret the fact that gluons are confined. Most people will say that a glue string will develop if any parton (quark or gluon) tries to escape a hadron. This is not wrong, but it's not clear whether it's relevant for light partons confined in light hadrons, which is what is relevant for our protons and neutrons. In another language, gluons and quarks, although massless when "naked" (or when you look at them with an infinitely magnifying glass, or at infinitely high energy), do acquire a (possibly) large mass at long (of the order of the size you quote) distances (or at low energy). This technical language would be referred to as Dyson-Schwinger equation, where one attempts to calculate non-perturbatively a relativistic propagator for the partons inside hadronic bound states. One thing which is clear and model independent is that the vacuum outside hadrons is different from what partons feel inside hadrons.

You may also think of which interaction you are interested in. At the range you quote, strong interaction are better described not in terms of gluon exchange, but in terms of meson exchange, which have the right mass compared to the range.

 

[kashiark]

oooh ok so let me make sure i have this straight: inside hadrons there is gluon exchange but at ranges farther away than that mesons are exchanged? and by mesons do you mean like "glueballs" or like pions? btw tyvm!

 

[humanino]

In the quantum field theory description of elementary particles, we are used to "effective interaction". It's deeply related to the renormalization procedure. Any physical phenomenon must be described using the right variables, or degrees of freedom. The relevant degrees of freedom depend on the scale. At short distances, the fundamental degrees of freedom, quarks and gluons, are revealed, and it is appropriate to use them in our language, we understand what happens most easily by thinking in terms of them. However at long distances, it is not practical to describe strong interaction using its fundamental degrees of freedom. Exactly because of confinement, meson exchange is better suited.

Note that I never referred to glueballs. There are kinematical regimes in which hadron interactions are well described in terms of gluon ladder exchanges, also called Pomerons, or Reggeons, but that even does not qualify as "glueballs".

 

[kashiark]

ah ok tyvm!

 

[Bob S]

An interesting effect relating to the range of the strong interaction is comparing pionic and muonic atoms, where the negative pion or muon gets into atomic orbits around the nuclus. The pionic or muonic atoms emit x-rays during the atomic cascades, and their energies have been measured to high precision (about 2 parts per million), and compared to theory to derive mass measurements. The negative pion has to be in highly circular (l = n-1) orbits (e.g., 4F-3D transitions in titanium) to keep it away from the nucleus, because the lifetime of the pion in nuclear matter is very short, but it is probing the extent of the range of the strong interaction.

 

[granpa]

and protonium atoms too