## QCD and Hadrons

Although quarks and gluons are among the fundamental building blocks of nature, experiments only directly detect hadrons, particles like the proton or pion. This phenomenology is explained using different descriptions for different situations. The language of quarks and glue uses, at short distances, of partons and, at larger distances, employs effective constituent quarks which have much larger masses than the partons. An alternative ansatz avoids talking about quarks and gluons and this is the dialect of string models and effective hadron fields. For the case of a proton these two possibilities are indicated below:

Note that, as described here, colour charge is only well-defined on gauge invariant objects and so only the picture on the right contains quarks with good colour. A central aim of work in Plymouth is to show how these pictures can emerge from the underlying gauge theory of quarks and gluons, Quantum Chromodynamics.

Much hadronic phenomenology is framed in terms of constituent quarks. These objects can be constructed by dressing valence (partonic-type) quarks with glue. Such effective quarks (or gluons) need to be described in a way that respects the symmetries of QCD and, in particular, they must be gauge invariant. We have shown how to generate such gauge-invariant quarks and gluons in a systematic way which can be extended to an arbitrary order of perturbation theory. We have also demonstrated that, at short distances between the quarks, these variables correspond to the energetically favoured variables. This means that we have described the dominant gluonic configurations in hadrons at small separations between the quarks and that individual constituents are visible.

Why then do we not see quarks and gluons as physical particles? It is widely accepted that such states would correspond to extremely high energies and that, as a consequence, quarks and gluons are confined inside hadrons. The difficulty for physicists is that at large separations we need non-perturbative calculations and these are hard. We have, however, proven that there exists a fundamental non-perturbative obstruction to constructing a gauge invariant quark or gluon, you can read more about this here.

So at short distances quark structures are energetically favoured and at large separations we cannot even talk about quarks. For a meson we therefore have the following picture of coloured quarks at short distances and colourless hadrons at larger scales