Why there is no nuclear dependence in dimuon production

Comparison of dimuon production in medium mass nuclei with that in the deuteron shows no effect of the nuclear environment for values of 0.1 < x < 0.3, just the region in which the pion excess model has produced an enhancement. In the lowest-order approximation there is no meson excess, which can be understood by the common scaling of all masses and cutoffs m_N^* m_N = m_σ^* m_σ = m_ω^* m_ω = Λ^* Λ, etc. In the next order, correction must be made for the fact that the pion mass m_π does not scale in-medium. This is small. A second correction, pion rescattering by nucleonic excitations, is also small because of the local field correction g'₀(q). The g'₀(q) is only ~ 0.525 for q = 0, but its growth with q provides an effectively large g'_o, and this cancels the attraction in the pionic rescattering channel. Thus the pionic enhancement in the small-x region is suppressed. Inclusion of isobar excitation in the rescattering provides a small enhancement, and the coupling of the ρ-meson between nucleon and isobar can be chosen within the range of preferred values so that there is no net effect of the nuclear environment in the small-x region considered.