Abstract
We investigate how non-linear scalar field theories respond to point sources. Taking the symmetron as a specific example of such a theory, we solve the non-linear equation of motion in one spatial dimension for (i) an isolated point source and (ii) two identical point sources with arbitrary separation. We find that the mass of a single point source can be screened by the symmetron field, provided that its mass is above a critical value. We find that two point sources behave as independent, isolated sources when the separation between them is large, but, when their separation is smaller than the symmetron's Compton wavelength, they behave much like a single point source with the same total mass. Finally, we explore closely related behavior in a toy Higgs-Yukawa model, and find indications that the maximum fermion mass that can be generated consistently via a Yukawa coupling to the Higgs in 1+1 dimensions is roughly the mass of the Higgs itself, with potentially intriguing implications for the hierarchy problem.
Highlights
Scalar field theories with nonlinear equations of motion are increasingly common in modern physical models
We have solved for the symmetron field in one spatial dimension around point particles
We have seen that pairs of point particles, when separated by less than a Compton wavelength μ−1, behave as a single point particle with the same total mass, and the field is constant in between
Summary
Scalar field theories with nonlinear equations of motion are increasingly common in modern physical models. We briefly discuss the electrostatic analogy for the symmetron theory [13,14], which has proven to be a powerful tool for understanding symmetron and chameleon dynamics and screening It was recently argued, within the electrostatic approximation, that the symmetron force between a small, unscreened point charge and a large, screened object could become repulsive when the separation between them is sufficiently small [15]. Thanks to their linear matter coupling and unbounded self-interaction potential, do not admit the point-particle screening behavior we found for the symmetron.
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