(9.38) where

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is the momentum carried by u quarks and antiquarks, and similarly for Ed' Equation (9.38) follows from (9.27) and (9.28) after neglecting the strange quarks which carry a small fraction of the nucleon's momentum. From (9.37), we have

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and on solving (9.38), we obtain

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= 0.36,

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= 0.46.

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(9.39)

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Hence, the gluons carry about 50% of the momentum, which was unaccounted for by the charged quarks.

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Partons

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In summary, an analysis of data on deep inelastic scattering of leptons by nucleons reveals the presence of point-like Dirac particles inside hadrons through Bjorken scaling. A study of the quantum numbers of these partons allows us to identify them with the quarks introduced in the study of the hadron spectrum in 2. The momentum distribution of the quarks forces us to the conclusion that a substantial fraction of the proton's momentum is carried by neutral partons, not by quarks. These are the gluons of QCD.

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Quantum Chromodynamics

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10.1 The Dual Role of Gluons

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We have seen in the previous chapter that deep inelastic scattering measurements actually require the existence of electrically neutral as well as charged constituents of the proton. We concluded that the charged partons could be identified with the colored quarks postulated in 2 to explain the observed systematics of the hadron spectrum. It is tempting to identify the neutral partons with gluons. Is this identification justified That is, does experiment actually require the existence of gluons independent of the formal arguments which were the original motivation for postulating their existence Recall that the color charge of quarks was originally introduced to remedy a statistics problem in constructing the ~ ++ wavefunction (see Section 2.11). It is interesting to reflect on the fact that although it is economical to associate the same color charge with the charge of the strong interaction and although it is helpful that such a force, mediated by the exchange of gluons, is asymptotically free (see Sections 1.3 and 7.9) so that we can apply perturbation theory, none of these arguments constitutes direct evidence that quantum chromodynamics (QCD) is the correct physical theory. It is clearly crucial to check that the gluons, introduced in s 1 and 2, can indeed be identified with the neutral partons discovered as "missing momentum" in deep inelastic scattering. Subsequently, we can ask more probing questions and verify that their dynamical properties correspond to those of the carriers of the color force. In order to proceed, it is not necessary at this stage to formally develop QCD as a color gauge theory. It is sufficient to recall the essential properties of the theory. We have already discussed them in s 1 and 2.

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Quarks carry color as well as electric charge; there are three colors, R, G, andB. Color is exchanged by eight bicolored gluons (see Fig. 1.4). Color interactions are assumed to be "a copy of electromagnetic interactions." To be precise, quark-gluon interactions are computed by the rules of QED with the substitution ..r;; -+ at each vertex (see Fig. 1.9) and

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Quantum Chromodynamics

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Fig. 10.1

Pictorial representation of the parton model for ep

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the introduction of a color factor, which may be computed by the methods of Section 2.15. That is, the qqg vertex has the same structure as the eey vertex. The (eight) gluons are massless and have spin l. Gluons themselves carry color charge, and so they can interact with other gluons. That is, there is a ggg as well as a qqg vertex in the theory (see Fig.

lAd).

At short distances, as is sufficiently small so that we can compute color interactions using the perturbative techniques familiar from QED.

The crucial statement that "color interactions are a copy of electromagnetic interactions" will be given a formal meaning in 14, where both QED and QCD are shown to be a consequence of local gauge symmetries. How does the color dynamics of the partons (quarks and gluons) affect our discussion of deep inelastic scattering in the two previous chapters The parton model of 9, symbolically represented by Fig. 10.1, completely ignores the dynamical role of gluons as the carriers of the strong force associated with colored quarks. We have, for instance, neglected the fact that quarks can radiate gluons. We must therefore allow for the possibility that the quark in Fig. 10.1 may radiate a gluon before or after being struck by the virtual photon, y*. These possibilities are shown in Fig. 10.2. Moreover, a gluon constituent in the target can contribute to deep inelastic scattering via y*g -+ qq pair production as shown in Fig. 10.3. In a computational sense, the processes in Figs. 10.2 and 10.3 are O( aa s ) contributions to the cross section, whereas the leading contribution in Fig. 10.1 is O(a).