Two-loop gg→ AA amplitudes near threshold and the double parton scattering singularity
Abstract
The two-loop amplitudes for pseudoscalar pair production in gluon fusion, gg→ AA, with each pseudoscalar emitted from its own effective gluon vertex, are known in closed form, but large cancellations near threshold obscure their analytic structure. We expand the IR-finite amplitudes in the pseudoscalar velocity βA through βA6 at fixed scattering angle. All inverse powers of βA and the odd powers through βA5 cancel, and at leading power the angular dependence enters only through ln(2pT/mA). We identify this logarithm with the double parton scattering (DPS) singularity: with the overall constant fixed at threshold, the factorisation formula of Gaunt and Stirling reproduces the velocity dependence of its one-loop coefficient in the forward limit to 3×10−15, and a one-loop gg→ HH analysis confirms the corresponding CP-even weight. At two loops the equal-helicity amplitude grows as ln3pT, with the leading logarithmic ratio of planar 𝒩=4 super Yang-Mills theory, while the opposite helicity amplitude, which has no one-loop DPS logarithm, grows as ln2pT. In the finite virtual correction, relative to the squared tree amplitude, the highest logarithm at order αs2 is −7/64αs2Nc2ln2(2pT/mA). For βA≤0.2 the series reproduce the unexpanded amplitudes with relative errors of at most 6.77×10−5 at the tested points; they provide this two-loop contribution to the hard function for soft-gluon resummation of the pair invariant-mass distribution near mAA=2mA and are released with code for their numerical evaluation.
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BibTeX
@misc{bhattacharya2026twoloop,
title = {{Two-loop $gg\to AA$ amplitudes near threshold and the double parton scattering singularity}},
author = {Arunima Bhattacharya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19024},
eprint = {2610.19024},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19024},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Two-loop gg→ AA amplitudes near threshold and the double parton scattering singularity
AU - Arunima Bhattacharya
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.19024
UR - https://arxiv.org/abs/2610.19024
AB - The two-loop amplitudes for pseudoscalar pair production in gluon fusion, gg→ AA, with each pseudoscalar emitted from its own effective gluon vertex, are known in closed form, but large cancellations near threshold obscure their analytic structure. We expand the IR-finite amplitudes in the pseudoscalar velocity β_A through β_A^6 at fixed scattering angle. All inverse powers of β_A and the odd powers through β_A^5 cancel, and at leading power the angular dependence enters only through ln(2p_T/m_A). We identify this logarithm with the double parton scattering (DPS) singularity: with the overall constant fixed at threshold, the factorisation formula of Gaunt and Stirling reproduces the velocity dependence of its one-loop coefficient in the forward limit to 3×10^−15, and a one-loop gg→ HH analysis confirms the corresponding CP-even weight. At two loops the equal-helicity amplitude grows as ln^3p_T, with the leading logarithmic ratio of planar 𝒩=4 super Yang-Mills theory, while the opposite helicity amplitude, which has no one-loop DPS logarithm, grows as ln^2p_T. In the finite virtual correction, relative to the squared tree amplitude, the highest logarithm at order α_s^2 is −7/64α_s^2N_c^2ln^2(2p_T/m_A). For β_A≤0.2 the series reproduce the unexpanded amplitudes with relative errors of at most 6.77×10^−5 at the tested points; they provide this two-loop contribution to the hard function for soft-gluon resummation of the pair invariant-mass distribution near m_AA=2m_A and are released with code for their numerical evaluation.
ER -