Working to all orders in dimensionally regularized QCD with massless quarks, we study the radiation of a photon whose energy is much lower than that of external partons. The conventional soft photon theorem receives corrections at leading power in the photon energy, associated with soft virtual loops of massless fermions. These additive corrections give an overall factor times the nonradiative amplitude that is infrared finite and real to all orders in ${\alpha }_s$. Based on recent calculations of the three-loop soft gluon current, we identify the lowest-order three-loop correction.

• Received 8 December 2023
• Revised 29 January 2024
• Accepted 1 February 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.091902

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Published by the American Physical Society