Extracting torque from torsion pendulum motion in a short-range test of gravity*

Gravitational effects are well understood from distances ranging from infinity to the millimeter scale.  There are numerous theories that suggest gravity may exhibit new behaviour at sub-millimeter ranges in violation of the Newtonian Inverse Square Law (ISL) or Weak Equivalence Principle.  Our project’s goal is to set limits on the length scale of possible violations by investigating the effects that a large attractor mass has on the motion of a precision torsion pendulum.  The free oscillations of the pendulum are digitally removed using a “notch” style filter, referred to as the torsion filter.  The filter averages two data points separated by half the pendulum free oscillation period and assigns that value as the midpoint.  Following the application of the torsion filter, each data run is subdivided into “cuts” that contain an integer number of  oscillations of the attractor mass.  Each “cut” is then fitted to a polynomial and analyzed via Fourier techniques.  In the final part of the data analysis, the twist angle of the pendulum is converted into a torque by applying various filtering and averaging corrections and accounting for the pendulum’s inertia.  Possible ISL violations could be revealed by comparing the measured torques at harmonics of the attractor modulation frequency to Yukawa, power law, or massive pseudo-scalar predictions.  In this talk I will discuss the progress made in upgrading and implementing these filters into our projects python data analysis program.