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 N N → N N π 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.2

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

“…[9,10] for pioneering studies along this line and Refs. [11][12][13][14][15] for more recent applications of chiral EFT to the pion-production reaction 1 . As mentioned, the measured near-threshold cross section for the neutral pion production channel is suppressed by almost an order of magnitude compared to charged pion-production channels.…”

“…However, in order to extract reliably CSB observables, it is imperative to have an accurate description of the dominant isospin-symmetric amplitude and to ensure that the expansion of chiral EFT converges. To examine the convergence of chiral EFT, the pp → dπ + channel is a preferable reaction since: (i) unlike pp → ppπ 0 , there is no suppressions of leadingorder (LO) contribution in this charged pion production channel [7,[13][14][15], and (ii) precise experimental data from hadronic atom measurements are available [21,22]. In this work we summarize the various contributions to the pion production operator, which were evaluated up to next-to-next-to-leading order (NNLO) in Refs.…”

“…This suppression is naturally explained in chiral EFT [1,2], where one finds the leading-order amplitude to pp → ppπ 0 to be numerically very small because the dominant isovector Weinberg-Tomozawa operator does not contribute. A quantitative understanding of neutral pion production therefore requires the inclusion of higher-order corrections [9,10,14,15].…”

“…In this work we summarize the various contributions to the pion production operator, which were evaluated up to next-to-next-to-leading order (NNLO) in Refs. [14,15], and calculate the pp → dπ + cross section near threshold in order to test the convergence of chiral expansion of chiral EFT.…”

Measurement of spin observables in the quasifreenp→{pp}sπ−reaction at 353 MeV

“…The large scale, introduced by the initial momentum, has to be considered explicitly [3,4]. Thus, a proper expansion scheme for pion production is now established and a high-precision calculation for the reactions N N → N N π is currently under way [5][6][7][8].…”