Go to previous page Go up Go to next page

5.4 Spin polarized torsion balances

Clock comparison experiments constrain the ~bJ parameter for protons and neutrons. Spin polarized torsion balances are able to place comparable limits on the electron sector of the mSME [56]. The best limits on ~bi (where i is the spatial direction, including that parallel to the earth’s rotation axis) for the electron come from two balances, one in Washington [170141] and one in Taiwan [148Jump To The Next Citation Point]. We detail the Washington experiment for pedagogical purposes - the two approaches are similar. In the Washington experiment two different types of magnets (SmCo and Alnico) are arranged in an octagonal shape. Four SmCo magnets are on one side of the octagon and four Alnico magnets are on the other. The magnetization of both types of magnets is set to be equal and in the angular direction around the octagon. This minimizes any magnetic interactions. However, with equal magnetization the net electron spin of the SmCo and Alnico magnets differs as the SmCo magnets have a large contribution to their overall magnetization from orbital angular momentum of Sm ions. Therefore the octagonal pattern of magnets has an overall spin polarization in the octagon’s plane.

A stack of four of these octagons are suspended from a torsion fiber in a vacuum chamber. The magnets give an estimated net spin polarization ---> s equivalent to approximately 1023 aligned electron spins. The whole apparatus is then mounted on a turntable. As the turntable rotates a bound on Lorentz violation is obtained in the following manner. Lorentz violation in the mSME gives rise to an interaction potential for non-relativistic electrons of the form ~ i V = bis, where i stands for direction and i s is the electron magnetic moment. As the turntable rotates, since ~b points in some fixed direction in space, the interaction produces a torque on the torsion balance. The magnet apparatus therefore twists on the torsion fiber by an amount given by

Q = VH sin(f0 - wt)/k, (66)
where VH is the horizontal component of V, w is the frequency of rotation, f0 is an initial phase due to orientation, and k is the torsion constant. Since k and w are known, a measurement of Q will give the magnitude of VH. Since i s is also known, VH gives a limit on the size of ~ bi. The absence of any extra twist limits all components of |~b| for the electron to be less than 10 -28 GeV. The Taiwan experiment uses a different material (Dy Fe 6 23[148]. The bounds from this experiment are of order - 29 10 GeV for the components of ~ bi perpendicular to the spin axis and -28 10 GeV for the parallel component.

To conclude this section, we note that the torsion balance experiments are actually sensitive enough to also constrain the dimension 5 operators in Equation (40View Equation). Assuming that all lower dimension operators are absent, the constraint on the dimension five operators is |jR - jL| < 4 [230Jump To The Next Citation Point].

  Go to previous page Go up Go to next page