Recursion Relation for BCFW Boundary Terms of NLSM Amplitudes
Abstract
When computing tree-level amplitudes of the nonlinear sigma model (NLSM) via the BCFW on-shell recursion relation, boundary terms are inevitable. Here, the BCFW recursion relation refers to the original prescription with momentum-shifts on two external legs, as opposed to the generalized versions with redefined momentum-shifts. We propose a simple general scheme that determines the boundary terms of NLSM amplitudes recursively from lower-point amplitudes. Hidden zeros and mass dimensions severely constrain boundary terms, allowing us to compute these terms from the $2$-split property of the tree amplitudes. Combined with the existing rules in the literature for obtaining the two currents in the $2$-split from on-shell amplitudes, this scheme enables the recursive construction of boundary terms for higher-point amplitudes from lower-point amplitudes.
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BibTeX
@misc{zhou2026recursion,
title = {{Recursion Relation for BCFW Boundary Terms of NLSM Amplitudes}},
author = {Kang Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09238},
eprint = {2610.09238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09238},
note = {CC0},
}
RIS
TY - UNPB
TI - Recursion Relation for BCFW Boundary Terms of NLSM Amplitudes
AU - Kang Zhou
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.09238
UR - https://arxiv.org/abs/2610.09238
AB - When computing tree-level amplitudes of the nonlinear sigma model (NLSM) via the BCFW on-shell recursion relation, boundary terms are inevitable. Here, the BCFW recursion relation refers to the original prescription with momentum-shifts on two external legs, as opposed to the generalized versions with redefined momentum-shifts. We propose a simple general scheme that determines the boundary terms of NLSM amplitudes recursively from lower-point amplitudes. Hidden zeros and mass dimensions severely constrain boundary terms, allowing us to compute these terms from the $2$-split property of the tree amplitudes. Combined with the existing rules in the literature for obtaining the two currents in the $2$-split from on-shell amplitudes, this scheme enables the recursive construction of boundary terms for higher-point amplitudes from lower-point amplitudes.
ER -