MTV-G experiment : probing a non-standard strong gravitational field at nuclear scale using geodetic precession

The MTV-G project has started in 2011 to explore a strong gravitational field around nuclei utilizing an experimental technique developed to search time reversal symmetry violation in nuclear beta decay experiment at a radioactive beam facility. A large electron spin-precession due to a possible strong gravitational field, which has been predicted by a large extra dimension model, is investigated in an electron-nuclear scattering experiment at TRIUMF. The experimental design, which use a spin polarized electron source and a Mott-spin analyzer, the commissioning experiment, the preliminary results, together with an introduction to the next generation device, are described in this article.


Introduction
Gravitational phenomena have been completely ignored in particle and nuclear physics since the Newtonian gravity is about 10 −38 weaker than the other three gauge interactions. However, if we seriously think about the possibility of a strong gravitational field predicted by the so called large extra dimension model which is known as the ADD (N. Arkani-Hamed, S. Dimopoulos, G. Dvali) model [1], a small correction in nuclear phenomena coming from the enforced gravitational field should be carefully investigated. In fact, gravity is the most mysterious interaction among the four fundamental interactions. Its extreme weakness prevents particle theorists from building unified theories. Recently, a possible existence of a very strong gravitational field at a microscopic scale was discussed based on the large extra dimension model. According to the ADD model, the gravitational inverse square law can be modified due to the existence of additional spatial dimensions. In order to naturally resolve the hierarchy problem unifying the Planck energy at around 1 TeV in the higher dimensional world, at least two extra dimensions with sizes of the order a millimeter are required. In this case, however, no precision test of the inverse square law has been performed. Two possible ways to test the large extra dimension scenario have been proposed. One way is to perform a direct laboratory test of the gravitational law below the millimeter scale, using a torsion balance pendulum or a similar Cavendish-type device [2]. Another way is based on a high energy collider experiment trying to search for quantum gravity related phenomena such as mono jet events and micro black hole creation [1,3].
In the present study, we aim to investigate a possible strong gravitational field around nuclei as a new approach to search for the large extra dimension. If there are two large extra dimensions of the order of 0.1mm, we should expect to see a 10 22 times stronger gravitational field comparing to the original Newtonian prediction. It can be shown that in a 4 + n dimensional model the gravitational potential is: If we assume that the size of the extra dimension is λ = 0.1 mm and the number of extra dimensions are n = 2, 3, and 4, then the gravitational potential strength is modified as: 10 10 +15 +12 Figure 1. A summary of the experimental search for the Yukawa term. The experimentally excluded region is illustrated as a shaded area. The region which the present study aims to explore is indicated at around 100 fm. Figure 1 shows a summary of experimental tests of the Newtonian inverse square law at various length scales λ [4]. The vertical axis is the coupling constant α of an additional Yukawa term defined in a modified gravitational potential with a Yukawa term as: The shaded area of this figure indicates the experimentally excluded region in the α−λ parameter space. It can be noticed that very little is known below the atomic scale. The length scale where α(λ) > 1 indicates that even the existence of the Newtonian gravity has not been get confirmed in the current experimental precision. If we assume that the inverse square law is tested with 100% relative precision above 0.1 mm, i.e. α < 1 at λ > 0.1 mm, the gravity for the n = 2, 3, 4 cases can respectively be 10 22 , 10 33 , 10 44 times greater than the original Newtonian predictions.
In the present study, we are aiming to test the inverse square law at a precision of α ∼ 10 37 at around 100 fm scale.

Principles
In order to probe the possible strong gravitational field around nuclei, we performed an electron scattering experiment. Electrons emitted from a beta-unstable radiation source are naturally polarized in their longitudinal direction because of the parity violating nature of the weak interaction. The spin precession effects, due to the gravitational geodetic precession, from the strong gravitational field around nuclei are examined in this experiment. The geodetic precession is a precessing effect of a spinning particle travelling in a warped spacetime produced by a gravitational field, which is predicted by the general relativity theory [5]. The existence of the geodetic precession phenomena has been confirmed in 2011 by the NASA satellite Gravity Probe B as a precession of a gyroscope on an orbit around the Earth [6]. As shown in Figure 2, in our experiment, we regard the nuclei as the Earth, and the polarized electron as the gyroscope on the satellite.
We utilize an experimental device designed for the MTV experiment (Mott polarimetry for T-Violation experiment), which aims to search for a large time reversal symmetry violation in the nuclear beta decay [7], to measure a tiny transverse polarization of electrons using the Mott scattering analyzing power. The MTV experiment is measuring a transverse polarization of the electrons emitted from spin-polarized 8 Li nuclei, which should be negligible in the standard model, in a 0.1% polarization precision. In this Mott-analyzer, the backscattering left-right asymmetry from a Mott scattering at a thin lead foil is used as a measurement of the transverse polarization. Because The present project aims to examine gravitational phenomena utilizing the MTV experimental device, it is called the MTV-G (MTV-Gravity) experiment. As shown in Figure 3, the MTV-G experiment consists of a 90 Sr radiation source, a primary scattering lead foil, and the MTV polarimeter with a secondary scattering foil and an electron tracking chamber. The existence of strong precession effects at the primary scattering foil is examined with the MTV polarimeter by checking the secondary scattering asymmetry.

The experiment and the results
The experiment was performed at TRIUMF in 2011 (Figure 3 and 4) at the MTV experimental beam line with a 37 MBq 90 Sr source for about two weeks during which data were  collected. The relative setting angle θ between the radiation source and the primary scattering foil can be changed in order to see the scattering angular dependence. By changing this scattering angle, we can measure the distance dependence from the nuclei. The secondary scattering leftright asymmetry, defined as Asymmetry = (N lef t − N right )/(N lef t + N right ) , is measured as a function of the primary scattering angle θ. In order to cancel out the detector intrinsic efficiency deference, the source configuration flipping between UP/DOWN position settings was performed.
In  The obtained results are compared with possible Yukawa type interactions. In the Coulomb scattering, the electron spin precession is dominated by the electromagnetic Thomas precession, which exists even in zero magnetic fields. The contribution from the Thomas precession is estimated using a numerical simulation. After subtracting the Thomas precession contributions, the maximum allowed strength α is estimated supposing a classical geodetic precession formula.
We set a possible constraint on the α − λ parameter space using the obtained results, as shown in Figure 6. In Figure 6, the experimental limit at the atomic scale is taken from an analysis of an anti-protonic atom [8]. Thus, the present study sets a new constraint at the shortest scale.

Discussion, Conclusions and Future plans
The present analysis supposes a classical geodetic precession expressed as which describes the trajectory of a spinning particle following a free fall motion in the gravitational field [5]. Here, M is the mass of the nuclei, r is the radius of the electron's orbit, ⃗ v is the electron's velocity. The real situation is not a free fall, but it is dominated by the Coulomb potential. In addition, the phenomena are in a microscopic scale, therefore, it might not be appropriate to apply a classical treatment. Repeating the calculation of the present study by including a quantum gravitational treatment with a Coulomb field should be theoretically interesting and a challenging subject for theorists. The results shown in this paper are based on a first stage experiment with many parameter ambiguities, such as de-polarization factor, precision estimation of electromagnetic Thomas precession etc. We are now going to build a next generation experiment using cylindrical drift chamber (CDC) shown in Figure 7, which may provide better results with increased precision. The radiation source is set at the center of the CDC, together with the primary scattering foil. The secondary Mott analyzing foil is set outside of the CDC, followed by stopping scintillation counters. By measuring the azimuthal angular dependence around the symmetry axis of the CDC setup, experimental reliability is significantly improved from the previous setup with the planer drift chamber shown in Figure 3.
In conclusion, we have performed the first MTV-G experiment aiming to probe a strong gravitational field around nuclei by utilizing geodetic precession in an electron-nuclear scattering phenomenon. As a result, we have succeeded to set a new constraint on the shortest length scale around 100 fm on the α − λ plot. Now, we are going to improve this experiment with the new CDC, and will take special care to reduce the systematic errors. The first test experiment using the CDC was already performed in 2012, and the full-scale data production is scheduled in 2013.