Abstract:
We calculate the cold neutron-deuteron (nd) capture cross section,σnd to next-to-next-to leading order (NNLO) using the model-independent approach of pionless effective-field theory [EFT(π)]. At leading order we find σnd=0.314±0.217 mb, while the experimental result is 0.508(15) mb [Phys. Rev. C 25, 2810 (1982)10.1103/PhysRevC.25.2810] for a laboratory neutron velocity of 2200 m/s. At next-to-leading-order (NLO), we show that σnd is sensitive to the low-energy constant (LEC) L1(0) of the two-nucleon isovector current appearing at NLO. A fit of L1(0) at NLO to the triton magnetic moment yields a NLO prediction of σnd=0.393±0.164 mb, where the error comes from propagating the error from the L1(0) fit. At NNLO, we find that a new three-nucleon magnetic moment counterterm is required for renormalization-group invariance of both σnd and the triton magnetic moment. Fitting the NNLO correction to L1(0) (denoted L1(1)) to cold neutron-proton capture (σnp) yields a NNLO prediction of σnd=0.447±0.130 mb, where the error comes from propagating the error from the L1(1) fit. We also study different fittings of L1(0) and L1(1) to σnp, σnd, and/or the triton magnetic moment. For example, fitting L1(0) simultaneously to σnp, σnd, and the triton magnetic moment at NLO, and fitting L1(1) simultaneously to σnp and σnd at NNLO, yields σnd=0.480±0.114 mb and 0.511±0.042 mb, respectively, where errors are naively estimated from EFT(π) power counting. In addition, we discuss how Wigner SU(4) symmetry may alter the naive EFT(π) expansion of σnd.
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