The Strange Behavior of Sound Through Solids [ias.edu]:
Not everything needs to be seen to be believed; certain things are more readily heard, like a train approaching its station. In a recent paper, published in Physical Review Letters [aps.org], researchers have put their ears to the rail, discovering a new property of scattering amplitudes based on their study of sound waves through solid matter.
Be it light or sound, physicists consider the likelihood of particle interactions (yes, sound can behave like a particle [scientificamerican.com]) in terms of probability curves or scattering amplitudes. It is common lore that, when the momentum or energy of one of the scattered particles goes to zero, scattering amplitudes should always scale with integer powers of momentum (i.e., p1, p2, p3, etc.). What the research team found however, was that the amplitude can be proportional to a fractional power (i.e., p1/2, p1/3, p1/4, etc.).
Why does this matter? While quantum field theories, such as the Standard Model, allow researchers to make predictions about particle interactions with extreme accuracy, it is still possible to improve upon current foundations of fundamental physics. When a new behavior is demonstrated—such as fractional-power scaling—scientists are given an opportunity to revisit or revise existing theories.
[...] "The detailed properties of scattering amplitudes have recently been studied with much vigor," stated Esposito. "The goal of this broad program is to classify possible patterns of behavior of scattering amplitudes, to both make some of our computations more efficient, and more ambitiously, to build new foundations of quantum field theory."
[...] "The present work reveals a twist in the story, showing that condensed matter physics displays much richer phenomenology of scattering amplitudes than what was previously seen in fundamental, relativistic physics," added Esposito. "The discovery of fractional-power scaling invites further work on scattering amplitudes of collective oscillations of matter, placing solids in the focus."
Tomáš Brauner, Angelo Esposito, and Riccardo Penco, Fractional Soft Limits of Scattering Amplitudes [open], Phys. Rev. Lett. 128, 231601, 2022. DOI: 10.1103/PhysRevLett.128.231601 [doi.org]