N$^3$LO Quadratic-in-Spin Interactions for Generic Compact Binaries

Understand

We derive the third subleading (N$^3$LO) corrections of the quadratic-in-spin sectors via the EFT of spinning objects in post-Newtonian (PN) gravity.

• These corrections consist of contributions from $4$ sectors for generic compact binaries, that enter at the fifth PN order.
• One of these contributions is due to a new tidal interaction, that is unique to the sectors with spin, and complements the first tidal interaction that also enters at this PN order in the simple point-mass sector.
• The evaluation of Feynman graphs is carried out in a generic dimension via advanced multi-loop methods, and gives rise to dimensional-regularization poles in conjunction with logarithms.