Pion production in nucleon-nucleon collisions in chiral effective field theory: next-to-next-to-leading order contributions

Abstract

A complete calculation of the pion-nucleon loops that contribute to the transition operator for $NN\to NN\pi$ up-to-and-including next-to-next-to-leading order (N${}^2$LO) in chiral effective field theory near threshold is presented. The evaluation is based on the so-called momentum counting scheme, which takes into account the relatively large momentum of the initial nucleons inherent in pion-production reactions. We show that the significant cancellations between the loops found at next-to-leading order (NLO) in the earlier studies are also operative at N${}^2$LO. In particular, the $1/m_N$ corrections (with $m_N$ being the nucleon mass) to loop diagrams cancel at N${}^2$LO, as do the contributions of the pion loops involving the low-energy constants $c_i$, i=1...4. In contrast to the NLO calculation however, the cancellation of loops at N${}^2$LO is incomplete, yielding a non-vanishing contribution to the transition amplitude. Together with the one-pion exchange tree-level operators, the loop contributions provide the long-range part of the production operator. Finally, we discuss the phenomenological implications of these findings. In particular, we find that the amplitudes generated by the N${}^2$LO pion loops yield contributions comparable in size with the most important phenomenological heavy-meson exchange amplitudes.

28 pages, 7 figures, 2 tables

References in corpus (6)

• Updated analysis of NN elastic scattering to 3 GeV
• Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• Remarks on N N -> N N pi beyond leading order
• Two-pion-exchange and other higher-order contributions to the $pp\to pp{\pi }^0$ reaction
• Impulse approximation in nuclear pion production reactions: absence of a one-body operator

Cited by in corpus (10)

• Effective Field Theory calculations of $NN\to NN\pi$
• Tensor $O(N)$ model near six dimensions: fixed points and conformal windows from four loops
• Pion production in nucleon-nucleon collisions in chiral effective field theory with Delta(1232)-degrees of freedom
• Differential cross section and analysing power of the pp -> {pp\}_s pi0 reaction at 353 MeV
• Charge Symmetry Breaking in dd->4Heπ0 with WASA-at-COSY
• Threshold pion production in proton-proton collisions at NNLO in chiral EFT
• Two-pion exchange for coupled-channel scattering of two heavy mesons
• Measurement of spin observables in the quasi-free np-> {pp}_s pi- reaction at 353 MeV
• $P$-wave dibaryon resonances in $pp$ elastic scattering and near-threshold pion production
• Pion absorption from the lowest atomic orbital in 2H, 3H and 3He