∆d̄(x) and ∆ū(x) in the sea of the nucleon

We present a calculation of the polarized ρ meson cloud in a nucleon using time-ordered perturbation theory in two different variants advocated in the literature. We calculate the induced difference between the distributions ∆d̄(x) and ∆ū(x). We use a recent lattice calculation to motivate an ansatz for the polarized valence quark distribution of the ρ meson. Our calculations show that the two theoretical approaches give vastly different results. We conclude that ∆d̄(x)−∆ū(x) can be of relevant size with important consequences for the combined fits of polarized distribution functions. It is experimentally established beyond doubt that d̄(x) and ū(x) in the nucleon differ substantially [1, 2, 3]. The difference can be described as due to the meson cloud in the nucleon. The relevant process is shown in fig. 1. The nucleon splits up into a meson and a baryon and the meson is hit by the photon in a deep inelastic scattering experiment. The dominant role in the unpolarized case is played by the pion. It is clear that a proton prefers being accompanied by a π instead of an π since in the first case the remaining baryon can be a neutron, but in the second case the remaining baryon with the lowest lying mass is the ∆(1232) resonance. Therefore one can find an enhancement of d̄ quarks over ū quarks in the proton. A large number of papers has been published on this subject, e.g. [4, 5, 6, 7, 8, 9, 10]. Proceeding a step further in this direction one can ask the question whether there is also an asymmetry in the polarized sea, more precisely between the distributions ∆d̄(x) and ∆ū(x). Up to now it is not possible to extract such an asymmetry from experiments but the situation could change in the future. It is clear that the meson cloud model predicts such an asymmetry. The mechanism is the same as in the unpolarized case, ∗email: [email protected] 1