Abstract
A Monte Carlo simulation is presented of an experiment that could potentially determine whether antihydrogen accelerates vertically up or down as a result of earth's gravity. The experiment would rely on methods developed by existing antihydrogen research collaborations and would employ a Penning trap for the production of antihydrogen within a uniform magnetic field. The axis of symmetry of the cylindrical trap wall would be oriented horizontally, and an axisymmetric aperture (with an inner radius that is smaller than the cylindrical trap wall radius) would be present a short distance away from the antihydrogen production region. Antihydrogen annihilations that occur along the cylindrical trap wall would be detected by the experiment. The distribution of annihilations along the wall would vary near the aperture, because some antihydrogen that would otherwise annihilate at the wall would instead annihilate on the aperture. That is, a shadow region forms behind the aperture, and the distribution of annihilations near the boundary of the shadow region is not azimuthally symmetric when the effect of gravity is significant. The Monte Carlo simulation is used together with analytical modeling to determine conditions under which the annihilation distribution would indicate the direction of the acceleration of antihydrogen due to gravity.
Highlights
No direct measurements have been reported that indicate the direction of free-fall gravitational acceleration of antimatter
Even if all other effects are not negligible, gravity can be the sole cause of an asymmetry in the azimuthal annihilation distribution that occurs at the wall within the shadow region, provided that all other effects that can influence the trajectory of an antiatom are axisymmetric
The vertical and horizontal displacements at the time such a trajectory reaches a location infinitesimally close to the edge of the aperture are y = a and z = aL/R, where a is the inner radius of the aperture, L is the axial distance between the coordinate origin and the far edge of the shadow region, and R is the inner radius of the cylindrical wall
Summary
No direct measurements have been reported that indicate the direction of free-fall gravitational acceleration of antimatter (e.g., antiprotons, positrons, antihydrogen). A gravity experiment using antimatter may be possible by inserting an aperture within a Penning trap that is used to produce antihydrogen. It is assumed here that a detector that can distinguish between antihydrogen annihilations and cosmic rays would be used Such a detector is employed by the ALPHA collaboration.[12] A modification required for an existing experiment would be the axial insertion of a removable aperture. Even if all other effects are not negligible, gravity can be the sole cause of an asymmetry in the azimuthal annihilation distribution that occurs at the wall within the shadow region, provided that all other effects that can influence the trajectory of an antiatom are axisymmetric. Effects that might influence the trajectory of an antiatom in an asymmetric way include electric and magnetic field gradients associated with misaligned electrodes and coils, respectively
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