Using chiral perturbation theory to extract the neutron-neutron scattering length from pi- d -> n n gamma

Abstract

The reaction pi- d -> n n gamma is calculated in chiral perturbation theory so as to facilitate an extraction of the neutron-neutron scattering length (a_nn). We include all diagrams up to O(Q^3). This includes loop effects in the elementary pi- p -> gamma n amplitude and two-body diagrams, both of which were ignored in previous calculations. We find that the chiral expansion for the ratio of the quasi-free (QF) to final-state-interaction (FSI) peaks in the final-state neutron spectrum converges well. Our third-order calculation of the full spectrum is already accurate to better than 5%. Extracting a_nn from the shape of the entire pi- d -> n n gamma spectrum using our calculation in its present stage would thus be possible at the +-0.8 fm level. A fit to the FSI peak only would allow an extraction of a_nn with a theoretical uncertainty of +-0.2 fm. The effects that contribute to these error bars are investigated. The uncertainty in the $nn$ rescattering wave function dominates. This suggests that the quoted theoretical error of +-0.3 fm for the most recent pi- d -> n n gamma measurement may be optimistic. The possibility of constraining the nn rescattering wave function used in our calculation more tightly--and thus reducing the error--is briefly discussed.

arXiv comment35 pages, 14 eps figures, references and figure added, discussions of errors extended and clarified, improved conclusions, typos corrected, to be published in PRC

References in corpus (30)

• An accurate nucleon-nucleon potential with charge-independence breaking
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• Construction of high-quality Nucleon-Nucleon potential models
• Chiral Dynamics in Nucleons and Nuclei
• Quantum Monte Carlo Calculations of Light Nuclei
• The two-nucleon system at next-to-next-to-next-to-leading order
• The Two-Nucleon Potential from Chiral Lagrangians
• Nuclear forces from chiral Lagrangians using the method of unitary transformation II: The two-nucleon system
• Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry
• Renormalization of relativistic baryon chiral perturbation theory and power counting
• Towards a Perturbative Theory of Nuclear Forces
• On the pion-nucleon coupling constant
• Chiral two-pion exchange and proton-proton partial-wave analysis
• A New Measurement of the 1S0 Neutron-Neutron Scattering Length using the Neutron-Proton Scattering Length as a Standard
• Are Occupation Numbers Observable?
• Low-energy expansion of the pion-nucleon Lagrangian
• Electromagnetic Corrections to the One-Pion-Exchange Potential
• Neutral pion photoproduction on deuterium in baryon chiral perturbation theory to order q^4
• The S-Wave Pion-Nucleon Scattering Lengths from Pionic Atoms using Effective Field Theory
• Precision calculation of $\gamma d\to {\pi }^{+}nn$ within chiral perturbation theory
• Observation of the Charge Symmetry Breaking d + d -> 4He + pi0 Reaction Near Threshold
• Field Transformations and the Classical Equation of Motion in Chiral Perturbation Theory
• Charge symmetry breaking in n p --> d pi^0
• The role of the nucleon recoil in low--energy meson--nucleus reactions
• Field transformations and simple models illustrating the impossibility of measuring off-shell effects
• Deuteron electromagnetic properties and the viability of effective field theory methods in the two-nucleon system
• Compton Scattering by a Pion and off--Shell Effects
• Nucleon-nucleon bremsstrahlung: An example of the impossibility of measuring off-shell amplitudes
• Neutral Pion Photoproduction on Nuclei in Baryon Chiral Perturbation Theory
• Radiative pion capture by a nucleon

Cited by in corpus (28)

• Modern Theory of Nuclear Forces
• Two-pion exchange electromagnetic current in chiral effective field theory using the method of unitary transformation
• Charge Symmetry Breaking and QCD
• The Virial Equation of State of Low-Density Neutron Matter
• How low-energy weak reactions can constrain three-nucleon forces and the neutron-neutron scattering length
• Proton-proton fusion in pionless effective theory
• Extracting the neutron-neutron scattering length -- recent developments
• Low energy proton-proton scattering in effective field theory
• The long and winding road from chiral effective Lagrangians to nuclear structure
• Dependence of the BCS 1S0 superfluid pairing gap on nuclear interactions
• p-Wave pion production from nucleon-nucleon collisions
• The near threshold N N -> d pi reaction in chiral perturbation theory
• Constraints on a possible dineutron state from pionless EFT
• Effective Field Theory calculations of $NN\to NN\pi$
• Can one extract the pi-neutron scattering length from pi-deuteron scattering?
• Neutron-neutron scattering length from the reaction gamma d --> pi^+ nn employing chiral perturbation theory
• Muon Capture on the Deuteron -- The MuSun Experiment
• Chiral Dynamics in Photo-Pion Physics: Theory, Experiment, and Future Studies at the HI$\gamma$S Facility
• Bridging over p-wave pi-production and weak processes in few-nucleon systems with chiral perturbation theory
• Neutron-neutron scattering length from the ${}^6$He$(p,p\alpha )nn$ reaction
• Chiral O(Q^4) two-body operators for s-wave pion photoproduction on the NN system
• Radiative pion capture in 2H, 3He and 3H
• An update of muon capture on hydrogen
• Few Body Reserch - Summary
• Precision neutron interferometric measurements of the n-p, n-d, and n-3He zero-energy coherent neutron scattering amplitudes
• Search for a bound di-neutron by comparing ${}^3$He(e,e'p)d and ${}^3$H(e,e'p)X measurements
• Unitary Fermi gas in the epsilon expansion
• Non-Strange Meson Production with Hadronic Probes