Non-linear sigma model solutions for the disoriented chiral condensate at O(p4)

Boost-invariant (1+1) dimensional solutions for the Disoriented Chiral Condensate (DCC) are obtained numerically, in the context of the SU(2)L ⊗ SU(2)R non-linear sigma model at O(p4) in the momentum expansion. We ignore the mass terms in the Lagrangian, as we are mainly interested in the behavior of the solutions for small values of proper time τ. The solutions obtained at O(p4) are matched to those of O(p2) at a late proper time τ ⪢ 1mπ, where mπ = 140 MeV is the mass of the pion. We find that at O(p4) the solutions for the DCC do not have singular behavior at early proper times τ ⪡ 1mπ. The solutions indicate that for τ ≲ (0.5–0.8) fm the O(p4) corrections become important. We take the sizes of the field derivatives to be indicators of the validity of the momentum expansion. Thus, we deduce that the O(p4) solutions can be used to represent the qualitative behavior of the DCC down to proper times of about 0.2 fm. Since below ∼ 0.2 fm the formalism is not reliable, we conclude that the inclusion of higher order terms beyond O(p4) is not needed to extend the validity of the solutions to earlier proper times.