KMOC Formalism Extends to Soft Radiation, Enabling Analysis Beyond Large-Impact-Parameter Scattering

Classical scattering processes, fundamental to understanding interactions between particles, receive a fresh perspective from research led by Samim Akhtar of the ICTP South American Institute for Fundamental Research, Alok Laddha from the Chennai Mathematical Institute, and Arkajyoti Manna of the Indian Institute of Science, with contributions from Akavoor Manu of the Institute of Mathematical Sciences. This team investigates how a mathematical framework known as KMOC formalism, traditionally applied to large-scale scattering events, can accurately predict the soft radiation emitted during these interactions, even when the impact parameter extends beyond conventional limits. Their work demonstrates that KMOC formalism successfully calculates an inclusive observable linked to this soft radiation, revealing a non-perturbative formula for electromagnetic memory in the classical regime, and importantly, confirms consistency with previous calculations based on saddle point analysis. This achievement expands the applicability of KMOC formalism and provides a powerful new tool for analysing classical scattering and understanding the subtle effects of soft radiation.

Soft Theorems and Classical Scattering Amplitudes

Researchers are exploring the connection between quantum mechanics and classical gravity by investigating soft theorems, which describe the behavior of scattering amplitudes when emitted particles have very low energy. This work aims to derive classical gravitational phenomena, such as persistent signals in gravitational waves, directly from the underlying quantum theory, utilizing the S-matrix and the Kinematic Mean Operator Construction (KMOC) formalism to construct classical solutions from scattering amplitudes. A central focus is understanding how logarithmic terms within the soft expansion accurately predict classical behavior, investigating whether soft theorems universally apply across different theories of quantum gravity and tackling the challenge of calculating the effects of quantum loops on these theorems. This work also explores the relationship between soft theorems and asymptotic symmetries, symmetries that preserve the structure of spacetime at infinity. This research involves sophisticated techniques from quantum field theory and general relativity, including post-Minkowskian expansion, effective field theory, and the concept of null infinity. By studying boundary correlators, scientists aim to connect the S-matrix to measurable quantities, ultimately gaining a deeper understanding of the fundamental nature of gravity and accurately predicting the signals detected by gravitational wave observatories.

Inclusive Amplitudes for Soft Radiative Fields

Scientists have developed a new method for calculating classical scattering processes using the Kosower, Maybee, and O’Connell (KMOC) formalism, analyzing scattering using “inclusive” observables determined solely from on-shell amplitudes. This study extends this formalism to scenarios involving soft radiative fields, specifically calculating electromagnetic memory, a property related to persistent gravitational wave signals. To achieve this, researchers modeled initial particles using coherent states and computed the expectation value of an operator representing energy-momentum, evolving this observable using the S-matrix. The classical limit was reached by recognizing that, in small-deflection scattering, exchange and radiated particle momenta become negligible, defining a measure to accurately account for particle four-momentum.

The study focused on the radiation flux emitted during scattering, defining it as the expectation value of the energy-momentum operator for massless particles, calculating the contribution from any number of radiated particles using a phase space measure. To apply this to realistic scenarios, the team considered the classical scattering of two charged massive scalar particles, modeled using scalar quantum electrodynamics, calculating the radiative flux by taking the expectation value of the photon energy-momentum operator. To isolate the classical contributions, the team examined the behavior of this integral as Planck’s constant approaches zero, finding that the exponential terms become highly oscillatory unless the exchange momenta approach zero while the impact parameter remains fixed. By transitioning to wave number space, the team analyzed the scaling of quantum corrections, confirming their consistency with the classical limit and leveraging factorization properties of the five-point amplitude in the soft limit.

Classical Soft Radiation via Quantum Theorems

Scientists have demonstrated a novel approach to calculating classical soft radiation, specifically electromagnetic memory, using quantum soft theorems and the Kosower, Maybee, and O’Connell (KMOC) formalism. This work establishes a connection between on-shell amplitudes and the computation of inclusive observables, extending beyond the limitations of large impact parameter scattering. The team computed an inclusive observable associated with soft flux, showing that it defines a non-perturbative formula for electromagnetic memory, independent of the details of the hard scattering process. Experiments revealed that the number of photons contributing to the classical limit is not fixed by the order of perturbative expansion, but is instead extremized, mirroring previous findings using multi-soft theorems.

The research focused on a two-particle incoming state, modeled as a coherent state with vanishing impact parameter, demonstrating that soft factorization is sufficient to compute classical electromagnetic memory, independent of knowledge of the hard amplitude. Measurements confirm that this approach successfully calculates electromagnetic memory, aligning with results obtained through saddle point analysis of the classical soft theorem. The team meticulously reviewed the KMOC formalism, emphasizing its application to computing radiative flux using scattering amplitudes, modeling classical particles using coherent states and systematically computing the expectation value of the graviton energy-momentum operator at future null infinity. The analysis shows that the formalism accurately describes classical scattering processes, particularly those involving large impact parameters, and provides a framework for systematically analyzing scattering using on-shell methods.

KMOC Formalism Reveals Classical Memory Formula

This research demonstrates a novel application of the Kosower, Maybee, and O’Connell (KMOC) formalism to the calculation of electromagnetic memory, a persistent change in spacetime caused by gravitational or electromagnetic waves. Scientists successfully computed an inclusive observable related to soft radiation, revealing a non-perturbative formula for electromagnetic memory within the classical limit, extending the applicability of the KMOC paradigm beyond its original scope. The team’s results align with previous calculations employing saddle point analysis of the soft theorem, validating the approach and offering an alternative computational pathway. Importantly, this work highlights the utility of analyzing soft radiation as a means of circumventing the complexities of standard perturbation theory, particularly when considering universal features like electromagnetic memory.