Threshold pion production in proton-proton collisions at NNLO in chiral EFT

Abstract

The reaction N N → N N π offers a good testing ground for chiral effective field theory at intermediate energies. It challenges our understanding of the first inelastic channel in nucleon-nucleon scattering and of the charge-symmetry breaking pattern in hadronic reactions. In our previous studies, we presented a complete calculation of the pion-production operator for s-wave pions upto-and-including next-to-next-to-leading order (NNLO) in the formulation of chiral effective field theory, which includes pions, nucleons and ∆(1232) degrees of freedom. In this paper we calculate the near threshold cross section for the pp → dπ + reaction by performing the convolution of the obtained operators with nuclear wave functions based on modern phenomenological and chiral potentials. The available chiral N N wave functions are constructed with a cutoff comparable with the momentum transfer scale inherent in pion production reactions. Hence, a significant portion of the dynamical intermediate-range physics is thereby cut off by them. On the other hand, the NNLO amplitudes evaluated with phenomenological wave functions appear to be largely independent of the N N model used and give corrections to the dominant leading order contributions as expected from dimensional analysis. The result gives support to the counting scheme used to classify the pion production operators, which is a precondition for a reliable investigation of the chirally suppressed neutral pion production. The explicit inclusion of the ∆(1232) is found to be important but smaller than expected due to cancellations.

Neutron properties from light nuclei

“…[51], we have analyzed in detail the convergence of the MCS for the reaction pp → dπ + . At threshold, only S-wave pion production has to be considered, and the only contribution to the amplitude emerges from the initial pp 3 P 1 partial wave.…”

Importance of d-wave contributions in the charge symmetry breaking reaction $dd \to {}^4\text{He}π^0$

“…[9]. The formalism has recently been pushed to next-to-next-to-leading order for s-waves [10,11]. The contribution of p-waves has been investigated in Ref.…”