# Analytic Solutions to Compact Binary Inspirals With Leading Order Spin-Orbit Contribution Using The Dynamical Renormalization Group

## TL;DR

This paper derives exact analytic solutions for the motion and spin precession of spinning compact binaries during inspiral, using the dynamical renormalization group to improve accuracy and computational efficiency over traditional methods.

## Contribution

It introduces a novel application of the dynamical renormalization group to obtain closed-form solutions for binary inspiral dynamics with spin-orbit effects at leading order.

## Key findings

- Resummed solutions outperform adiabatic approximations in accuracy.
- Solutions are computationally faster than numerical integration.
- Applicable to arbitrary mass and spin configurations.

## Abstract

We calculate the real-space trajectory and spin precession of a generic spinning compact binary inspiral at any time instant using the dynamical renormalization group formalism. This method leads to closed-form analytic solutions to the binary motion through treating radiation reaction as perturbations and resumming the secular growth of perturbative terms. We consider the spin-orbit effects at leading order and the 2.5PN radiation reaction without orbit averaging or precession averaging for arbitrary individual masses and spin magnitudes and orientations. The solutions are written in a moving reference frame, with the orbital angular momentum and binary radial directions aligned along two of the axes. The resummed solutions show improved accuracy compared to adiabatic solutions while also being an order of magnitude faster computationally compared to numerical integration methods.