We present a framework to compute amplitudes for the gravitational analog of
the Raman process, a quasi-elastic scattering of waves off compact objects, in
worldline effective field theory (EFT). As an example, we calculate third
post-Minkowskian (PM) order ($mathcal{O}(G^3)$), or two-loop, phase shifts for
the scattering of a massless scalar field including all tidal effects and
dissipation. Our calculation unveils two sources of the classical
renormalization-group flow of dynamical Love numbers: a universal running
independent of the nature of the compact object, and a running self-induced by
tides. Restricting to the black hole case, we find that our EFT phase shifts
agree exactly with those from general relativity, provided that the relevant
static Love numbers are set to zero. In addition, we carry out a complete
matching of the leading scalar dynamical Love number required to renormalize a
universal short scale divergence in the S-wave. Our results pave the way for
systematic calculations of gravitational Raman scattering at higher PM orders.
Future Roadmap: Challenges and Opportunities in Gravitational Raman Scattering
In this article, we present a framework for computing amplitudes in the gravitational analog of the Raman process. This process involves the quasi-elastic scattering of waves off compact objects within the context of worldline effective field theory (EFT).
We have provided an example calculation at the third post-Minkowskian (PM) order, or two-loop, phase shifts for the scattering of a massless scalar field. Our calculation includes all tidal effects and dissipation, revealing two sources of classical renormalization-group flow of dynamical Love numbers.
Conclusion 1: Universal Running and Self-Induced Renormalization
We have discovered that there are two distinct sources of renormalization for dynamical Love numbers in gravitational Raman scattering:
- A universal running, which is independent of the nature of the compact object
- A running self-induced by tides
These findings highlight the importance of considering both universal and object-dependent factors when studying gravitational Raman scattering.
Conclusion 2: Agreement with General Relativity
By focusing on black hole cases, we have observed that our EFT phase shifts exactly match those obtained from general relativity. However, this agreement is contingent on setting the relevant static Love numbers to zero. This result further emphasizes that understanding the behavior of Love numbers is crucial for accurate calculations in gravitational Raman scattering.
Conclusion 3: Matching the Leading Scalar Dynamical Love Number
We have successfully carried out a complete matching of the leading scalar dynamical Love number, which is necessary to renormalize a universal short-scale divergence in the S-wave. This achievement opens up opportunities for more systematic calculations of gravitational Raman scattering at higher PM orders.
Future Roadmap
Building on our current findings and conclusions, there are several directions for future research in gravitational Raman scattering:
- Investigating Object-Specific Renormalization: While our present study focused on black hole cases, it would be valuable to analyze gravitational Raman scattering for other types of compact objects, such as neutron stars. Exploring their specific renormalization properties will provide a more comprehensive understanding of the phenomenon.
- Expanding to Higher PM Orders: Our calculation at the third PM order provides an important starting point, but the field would greatly benefit from extending the analysis to higher orders. This will allow us to explore the behavior of gravitational Raman scattering in more detail and derive more accurate predictions for future experiments.
- Considering Tidal Interactions: Tidal effects play a significant role in renormalization-group flow, as we have observed in our calculations. Investigating these effects further and understanding their implications will contribute to refining our understanding of gravitational Raman scattering.
In conclusion, our work has laid the groundwork for future research in the field of gravitational Raman scattering. By expanding our calculations, investigating specific renormalization properties, and considering tidal interactions, we can deepen our knowledge and potentially uncover additional insights into this fascinating phenomenon.