Cold neutron-deuteron capture and Wigner-SU(4) symmetry

Journal Article · 22 October 2023 · Physical Review. C

DOI: https://doi.org/10.1103/physrevc.108.044001 · OSTI ID:2229720

Lin, Xincheng  ^[1]; Singh, Hersh  ^[2]; Springer, Roxanne P.  ^[3]; Vanasse, Jared  ^[4]

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1. Duke University, Durham, NC (United States); University of Washington
2. University of Washington, Seattle, WA (United States)
3. Duke University, Durham, NC (United States)
4. Fitchburg State University, MA (United States)

We calculate the cold neutron-deuteron (nd) capture cross section,σ_nd 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 σ_nd = 0.314 ± 0.217 mb, while the experimental result is 0.508(15) mb 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) $$L$$$^{(0)}_{1}$$ of the two-nucleon isovector current appearing at NLO. A fit of $$L$$$^{(0)}_{1}$$ at NLO to the triton magnetic moment yields a NLO prediction of σ_nd = 0.393 ± 0.164 mb, where the error comes from propagating the error from the $$L$$$^{(0)}_{1}$$ fit. At NNLO, we find that a new three-nucleon magnetic moment counterterm is required for renormalization-group invariance of both σnd and the triton magnetic moment. Fitting the NNLO correction to $$L$$$^{(0)}_{1}$$ (denoted $$L$$$^{(1)}_{1}$$) to cold neutron-proton capture (σnp) yields a NNLO prediction of σ_nd = 0.447 ± 0.130 mb, where the error comes from propagating the error from the $$L$$$^{(1)}_{1}$$ fit. We also study different fittings of $$L$$$^{(0)}_{1}$$ and $$L$$$^{(1)}_{1}$$ to σ_np, σ_nd, and/or the triton magnetic moment. For example, fitting $$L$$$^{(0)}_{1}$$ simultaneously to σ_np, σ_nd, and the triton magnetic moment at NLO, and fitting $$L$$$^{(1)}_{1}$$ simultaneously to σ_np and σnd at NNLO, yields σ_nd = 0.480 ± 0.114 mb and 0.511 ± 0.042 mb, respectively, where errors are naively estimated from EFT(π) power counting. Additionally, we discuss how Wigner SU(4) symmetry may alter the naive EFT(π) expansion of σ_nd.

• Research Organization: University of Washington, Seattle, WA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: FG02-00ER41132; FG02-05ER41368; SC0020970
• OSTI ID: 2229720
• Journal Information: Physical Review. C, Journal Name: Physical Review. C Journal Issue: 4 Vol. 108; ISSN 2469-9985
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English