What are the Forces Behind Quark Color?

[xortdsc]

Hi,

the "color" of quarks gives rise to the strong-force. I've read on some page (cannot remember where) that same-color repels and different color attracts. Additionally it was stated that the attractive force between color/anti-color is stronger than color/different color. But no ratios or any details were given. Is there such clear ratio between the two ?

Also if a pair of quark/anti-quark is created will they always be anti-colored (e.g. a green quark and an anti-green anti-quark) ?

 

[nikkkom]

if a pair of quark/anti-quark is created will they always be anti-colored (e.g. a green quark and an anti-green anti-quark)

Yes. Color charge is conserved.

 

[Einj]

the "color" of quarks gives rise to the strong-force. I've read on some page (cannot remember where) that same-color repels and different color attracts. Additionally it was stated that the attractive force between color/anti-color is stronger than color/different color. But no ratios or any details were given. Is there such clear ratio between the two ?

The situation is not that easy. The color charge is not a number as the electric charge. It is, instead, represented by a matrix belonging to the SU(3) group. Consider, for example, two quarks (keep in mind that quarks are not the only particles carrying color, we also have gluons). In group theory language we say that quarks belong to the $3$ representation of SU(3), i.e. their color is represented by the 3x3 Gell-Mann matrices. It turns out that when a quark and an anti-quark (which belongs to the $\bar 3$ representation) interact, this interaction produces two "channels": the singlet, $1$, and the octet, $8$. The singlet is attractive while the octet is repulsive.

However, the situation is complicated. If you want more insight you should look at some QCD book. The most rough way to estimate whether or not the interaction between to colored particles is attractive or not is to use the so-called "one gluon exchange" approximation. I'm sure that you can find enough info on that on Google.

Also if a pair of quark/anti-quark is created will they always be anti-colored (e.g. a green quark and an anti-green anti-quark) ?

It depends on what creates the pair. If the quark/anti-quark pair is created from the vacuum, from photon or from any other colorless source, then the final net color must be zero (by conservation of the color charge), which means that the pair is automatically created in a singlet configuration. However, if the pair is created from a gluon (which belongs to the octet of SU(3)) then it will be created in the octet as well, i.e. in a colorful configuration.

 

[Meir Achuz]

The only color combination for a quark-antiquark state that is seen physically is the color singlet
$$(G-{\overline G}-(R-{\overline R}+(B{\overline B})/\ sqrt{3}$$.
Nothing is known about the dependence on color, because only the one combination is known.

 

[Einj]

Nothing is known about the dependence on color, because only the one combination is known.

The singlet configuration is the so-called "asymptotic state". However this doesn't mean that we can't say anything about the octet configuration. It can appear, for example, in radiative virtual processes. Consider for example the quark/anti-quark loop contribution from the gluon self energy.
You are right when you say that we have never experimentally seen any configuration different from the singlet one, however the fact that QCD works so well in describing the experiment can be considered as a strong indication that quark/anti-quark in the octet representation can actually be produced in non-asymptotic states.