Fractional soft limits

Abstract

It is a common lore that the amplitude for a scattering process involving one soft Nambu--Goldstone boson should scale like an integer power of the soft momentum. We revisit this expectation by considering the $2\to 2$ scattering of phonons in solids. We show that, depending on the helicities of the phonons involved in the scattering process, the scattering amplitude may in fact vanish like a fractional power of the soft momentum. This is a peculiarity of the 4-point amplitude, which can be traced back to (1) the (spontaneous or explicit) breaking of Lorentz invariance, and (2) the approximately collinear kinematics arising when one of the phonons becomes soft. Our results extend to the general class of non-relativistic shift-invariant theories of a vector field.

6 pages, 1 figure

References in corpus (10)

• Effective Field Theories from Soft Limits
• A Periodic Table of Effective Field Theories
• The quantum mechanics of perfect fluids
• Geometric Soft Theorems
• From Amplitudes to Contact Cosmological Correlators
• Solid Soft Theorems
• Multi-spin soft bootstrap and scalar-vector Galileon
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Cited by in corpus (3)

• Inflationary Adler Conditions
• Soft Phonon Theorems
• Flavour-kinematics duality for Goldstone modes