The observation of hadron jets from electron-positron collisions (LEP) is explained (e.g. Wilczek, The Lightness of Being, p 55) as follows- e,p collide and produce a virtual photon. the photon goes into a quark, antiquark pair, and one jet of hadrons comes out of the quark, and an opposing jet comes out of the anti-quark.

Question: How can a quark with fractional electric charge produce a jet of particles that all have integral electric charge? What happens to electric charge conservation in the process?


2 Answers 2


We agree that the pair has integral charge (zero in fact), right?

So now we need a model of hadronization (the process in which the quarks generate hadrons). You've probably got some picture of the quarks flying apart and then separately undergoing a process to produce a bunch of stuff.

Unfortunately that picture isn't really correct.

The principle of "confinement" is that colored objects (i.e. quarks) can not exist in isolation, so you should think of the pair of quarks being connected by a region of high strong-nuclear force potential (often called a "flux tube"). The nature of the strong force is that it get stronger as the separation between colored objects increases; so as the quarks pull further and further apart the the total energy in the flux tube grows at the pair separates until production occurs.

So you go from

$q$ -- $\bar{q}$


$q$ ----------- $\bar{q}$


$q$ ---- $x$ $\bar{x}$ ------- $\bar{q}$


$q$ ----- $x$ -- $\bar{x}$ ---- $\bar{q}$

and these may keep on separating from there (energy permitting, of course).

Depending on the nature of $x$ and $\bar{x}$ this could be the end of it, you get two mesons and you're done. But that is unlikely: more often one or both pairs are not color neutral or not bound so they pull apart some more and the new flux tubes also break.

For concreteness pretend that

  1. $q$ is red-up
  2. $x$ is antired-antidown
  3. the kinematics are such that $q$ and $x$ can end up bound, but $\bar{x}$ and $\bar{q}$ won't

this meas the next step might loop like

$u\bar{d}$ ------- $d$ ------- $\bar{y}$ -- $y$ ----- $\bar{u}$

and when the first pair binds

$\pi^+$ ------- $d$ ------- $\bar{y}$ -- $y$ ----- $\bar{u}$

But since we started neutral and each breaking produces a particle--anti-particle (which is neutral in total) the total will end up neutral. And it is confinement that insures that each particle is either a baryon or a meson (because those are the only color neutral bound states known (people are still hoping to see more complex states)).

So the picture that you should have is of extra pairs being formed in the middle until we run out of energy or everything has combined by lucky chance.


I would like to supplement dmckee's answer for completeness, since the "middle" comment might be misinterpreted, it is middle in energy.

One might think that the hadrons are formed centrally or distributed spherically in space, which is not the case. Experimentally the so called leading particle effect dominates the data, and before the advent of QCD gave the parton model proposed by Feynman. The leading partons fragmented into jets defining the direction of the quarks. This leading effect was laboriously reproduced by QCD, laboriously because calculations in QCD are not simple.

This search gives experimental data from the decay of Z into two quarks that shows both the effect and that the jets from the quarks are different depending on the quark type.

Gluon jets were established at PETRA, again collimated hadrons about the jet, and their difference with quark jets studied by DELPHI and OPAL extensively. In fig 2 you can see that the three parton jets, two quarks and the gluon, are separated cleanly.

  • $\begingroup$ Good point. The picture I give above is strictly qualitative. $\endgroup$ Jan 1, 2012 at 14:55
  • $\begingroup$ One should also give references to some late 1970s papers by Feynman and collaborators, which I believe were some of the first quantitative models of jet formation. I don't know the history very well on this, but it seems to be some strangely neglected Feynman (at least in theory-land). $\endgroup$
    – Ron Maimon
    Jan 1, 2012 at 17:47
  • $\begingroup$ @RonMaimon are you talking of the Feynman and Field model? Here is a summary phys.ufl.edu/~rfield/cdf/FeynmanFest.pdf with a list of references. It is a phenomenological model, which Feynman favored before QCD came into age as a bona fide gauge theory. In this model, gluon jets could not exist, and PETRA results and high pt tails in neutrino scatterings showed that indeed they do exist, so the model faded out. $\endgroup$
    – anna v
    Jan 1, 2012 at 18:18

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