Sea quarks

The weak interactions change quark and lepton flavors, e.g., a d-quark into -quark or a muon into an electron (this latter, e.g., in the p e Vet /i process). The quark structures of the proton and neutron as well as the properties of nucleons are presented in O Table 2.3. The baryons are built up from three (valence) quarks and massless gluons, but they contain also dynamical (or sea) quarks (quark-antiquark pairs) in a small quantity. The mesons are built up from quark-antiquark pairs and gluons. 

Fig. 3.5 The proton par-ton distribution functions measured at HERA at 2 = lOGeV, for valence quarks and xd, sea quarks xS, and gluons xg. The gluon and sea distributions are scaled down by a factor 20 [23]...

On the theoretical side, an overabundance of mechanisms has been advocated to explain the data and this makes the whole matter somewhat inconclusive. The present prevailing theoretical attitude can be summarized by saying that in the very small x region (x < 0.1) a number of non-perturbative effects (shadowing, sea quarks and gluons) dominate in the intermediate x domain (0.2 nuclear binding and Fermi motion in a nuclear physics approach, and/or, in a parton-QCD approach, to a partial quark deconfinement within the hadronic boundary which affects the basic properties of the hadrons. A nucleon bound in a nucleus appears somewhat larger and somewhat less massive than a free nucleon. 

Prom these we learn principally about the sea quark combination u + d, but once the KM matrix elements are known one can also get information on s x) especially if one studies semi-inclusive charm production (see Section 18.2). 

In this way, we can relate duality to quark-hadron continuity. We considered duality, which is already present at zero chemical potential, between the soliton and the vector mesons a fundamental property of the spectrum of QCD which should persists as we increase the quark chemical potential. Should be noted that differently than in [42] we have not subtracted the energy cost to excite a soliton from the Fermi sea. Since we are already considering the Lagrangian written for the excitations near the Fermi surface we would expect not to consider such a corrections. In any event this is of the order //, [42] and hence negligible with respect to Msoiiton. 

At high density, quarks in dense matter interact weakly with each other and form a Fermi sea, due to asymptotic freedom. When the energy is much less... 

The Fermi sea of up and strange quarks is shown in Fig. 9. Because of the strange quarks mass, they have different Fermi momenta. Note that the Cooperpairing occurs for quarks with same but opposite momenta. Therefore, at least one of the pairing quarks should be excited away from the Fermi surface, costing some energy. Let us suppose that the Cooper-pair gap opens at p p between two Fermi surfaces, psF < p < pf. 

There are two Fermi seas for a given quark number with different volumes due to the exchange splitting in the energy spectrum. The appearance of the rotation symmetry breaking term, oc p U 4 in the energy spectrum (16) implies deformation of the Fermi sea so rotation symmetry is violated in the momentum space as well as the coordinate space, 0(3) —> 0(2). Accordingly the Fermi sea of majority quarks exhibits a prolate shape (F ), while that of minority quarks an oblate shape (F+) as seen Fig. 1 3. ... 

Figure 3. Deformed Fermi seas and the quark pair on each surface. The top figures show those in the absence of A and the middle figures diffusion of the Fermi surfaces in the presence of A . The bottom ones show the quark pairing on the Fermi surfaces.

In this talk we have discussed a magnetic aspect of quark matter based on QCD. First, we have introduced ferromagnetism (FM) in QCD, where the Fock exchange interaction plays an important role. Presence of the axial-vector mean-field (AV) after the Fierz transformation is essential to give rise to FM, in the context of self-consistent framework. As one of the features of the relativistic FM, we have seen that the Fermi sea is deformed in the presence of... 

Extremely stringent lower limits were reported by Rank (29) in 1968. A spectroscopic detection of the Lyman a(2 p - 1 s) emission line of the quarkonium atom (u-quark plus electron) at 2733 A was expected to be able to show less than 3 108 positive quarks, to be compared with 1010 lithium atoms detected by 2 p - 2 s emission at 6708 A. With certain assumptions (the reader is referred to the original article), less than one quark was found per 1018 nucleons in sea water and 1017 nucleons in seaweed, plankton and oysters. Classical oil-drop experiments (with four kinds of oil light mineral, soya-bean, peanut and cod-liver) were interpreted as less than one quark per 1020 nucleons. Whereas a recent value (18) for deep ocean sediments was below 10 21 per nucleon, much more severe limits were reported (30) in 1966 for sea water (quark/nucleon ratio below 3 10-29) and air (below 5 10-27) with certain assumptions about concentration before entrance in the mass spectrometer. At the same time, the ratio was shown to be below 10 17 for a meteorite. Cook etal. (31) attempted to concentrate quarks by ion-exchange columns in aqueous solution, assuming a position of elution between Na+ and Li+. As discussed in the next section, cations with charge + 2/3 may be more similar to Cs+. Anyhow, values below 10 23 for the quark to nucleon ratio were found for several rocks (e.g., volcanic lava) and minerals. It is clear that if such values below a quark per gramme are accurate, we have a very hard time to find the object but it needs a considerably sophisticated technique to be certain that available quarks are not lost before detection. 

Bergstrom, L., Bergstrom, U., 1999. Species diversity and distribution of aquatic macrophytes in the Northern Quark, Baltic Sea. Nordic Journal of Botany, 19, 375-383. 

Of course production of two strange particles can occur through the interaction with one strange quark from the sea via the process... 

Because of the existence of the sea, whose excitation seems to depend upon u, we should not expect the RHS of (16.4.1) to be a constant, nor indeed to be particularly meaningful. On the other hand, if we ask for the net number of say u quarks in the proton we must find 2. Thus... 

Because, by definition, the valence quarks give the proton its correct 517(2) or 517(3) properties, we e jq>ect the sea to be basically neutral, i.e. singlet under these transformations. But the above symmetries are not perfect, and while 517(2) is well respected, in nature 517(3) is broken somewhat. It thus seems reasonable, for the proton, to insist in the simple picture that... 

We would naturally expect the structure of a hadron to be dominated by its valence quarks—u and d for a nucleon. So we might expect the contribution from the sea to be small. But this cannot be true for all x as we saw from the discussion of B x) in Section 16.2. And QCD arguments indicate that the sea should become increasingly important for small x. 

For small x the ratio is close to 1 suggesting little influence of valence quarks at small x and dominance of a symmetric sea contribution in which u + ufud + d. All this is nicely consistent with the conclusions following from the behaviom of B(x) discussed in Section 16.2. 

There are two surprises. Firstly the size of As. Intuitively, since strange quarks are part of the sea in a proton, one might have expected the s, to be more or less unpolarized. The large value of As was unexpected. 

Fig. 17.16 shows quark and antiquark distributions determined in this way from low energy CC data using the approximations U ra u,D rsi d. There is clear confirmation of the increase in the relative importance of the sea at small x. 

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