Probing new physics via nuclear spin-dependent parity violation

Layperson’s description

Atoms and molecules are composed of electrons, protons and neutrons. The protons and neutrons are bound together tightly into nuclei by one of Nature’s four fundamental forces, the strong force. The negatively charged electrons are bound to the positively charged nuclei by another fundamental force, the electromagnetic force.  Within both the nuclei and the atoms, the other two fundamental forces—gravity and the weak force—also affect how they are bound. In the language of quantum field theory each fundamental force is related to the exchange of certain patricles.

The effect of gravity within these systems is far too small to detect. The effect of the weak force is, in some cases, large enough to measure. However, because of their tiny effect, certain aspects of the weak force have been poorly measured, to date. The primary goal of this project is to more accurately measure these particular aspects of the weak force.

     Once measured, we will compare our results to the theoretically expected size of these effects. Discrepancies between measured and predicted outcomes could signal the existence of a new, previously undiscovered force.  In addition, we will test whether the weak force we measure is constant over the duration of our experiment, or instead oscillates or drifts over time. Such a time variation could be caused by certain types of a cosmological “background field” that permeates all of space. Fields of this type have been proposed as a possible constituent of “dark matter”, the substance of unknown composition that causes galaxies to be bound together more strongly than if only the gravitational attraction between visible stars were at play.

     The weak force has a critical difference from all other known forces: its strength depends on the handedness of the configuration of particles on which it acts. Put differently, the weak force breaks the symmetry between mirror-image configurations; in the language of quantum physics, this is known as violation of parity symmetry. In our experiment, we use this feature of parity violation to distinguish the tiny effect of the weak force from the much larger effects of electromagnetic and strong forces. In particular, we measure changes in the energy difference between two quantized states in a diatomic molecule, when we put the molecules in configurations of electric and magnetic fields of different handedness. Our experimental approach uses the properties of diatomic molecules, together with a very precisely controlled magnetic field, to greatly amplify the measurable effect of this parity-violating energy change. Compared to prior experiments studying the weak force using atoms instead of molecules, this amplification makes it possible to measure particular aspects of the weak force that were previously difficult to observe.

Zeeman Tuning

     In addition to violating parity, the weak force has another important difference from the other forces: each type of particle has two independent types of “charge” that determines the strength with which the weak force acts on it. One of these weak-force charges, known as the vector weak charge, is exactly analogous to the electromagnetic charge. The other, however has no analogue in the other forces. This unique type of weak-force charge, known as the axial charge, is linked to the angular momentum of each particle—the property known in quantum mechanics as “spin”. 

     Our experiment will specifically measure the product of two weak force charges: the electron’s vector charge and the axial charge of nuclei. This particular combination is predicted to be accidentally small in the Standard Model of particle physics. This small effect has been measured in only one nucleus, in one experiment, to date—and the results of that measurement disagree with theoretical predictions. In addition, the axial charges of protons and neutrons are significantly modified by the presence of the strong force. These modifications are difficult to measure or to predict with very high accuracy. Our experiment will shed important new light on the interplay between weak and strong forces.  

     Our specific initial goal is to measure the axial weak charge of the 137Ba and 135Ba nuclei, in the molecule BaF.  These will be the first measurements of the axial weak charge of nuclei whose spin comes mostly from neutrons.  Once measurements of Ba nuclei are complete, we will apply our method to other nuclei, where the energy shifts are smaller but theoretical predictions for the size of the axial charge are more reliable. This will enhance the possibility to detect the effect of new forces.

More details for physicists

How strongly do electrons interact with the atomic nucleus via the weak force? For electromagnetism the answer is easy: the electron and nuclear charges determine the strength. However, the weak force is more complicated, having two effective types of charge for each particle. The strength of the weak force must be measured in parts.

The parity-violating parts of the weak force in an atom or molecule can be split into two groups: nuclear spin dependent effects (NSD-PV) and nuclear spin independent effects. The spin independent effects are much easier to measure since they grow proportionally with the number of nucleons, while NSD-PV effects arise only from the unpaired spins in a nucleus—of which there is typically only one. Consequently, nuclear spin independent parity violation is stronger and has been measured well while NSD-PV effects are weaker and largely unmeasured.

The two NSD-PV effects that we are principally interested in are Z boson exchange between electrons and nucleons, and the nuclear anapole moment. Z boson exchange is a fundamentally simpler process (it corresponds to a tree level Feynman diagram) and directly addresses the question of how strong the electron-nucleon weak force is. However, the strengths of these two effects are roughly the same order of magnitude and the contribution of the nuclear anapole moment cannot be distinguished from Z boson exchange in a measurement from a single isotope.

Although the nuclear anapole moment complicates the measurement of the strength of the weak force, it is interesting in its own right. Inside the nucleus, the weak force causes the spin of the unpaired nucleon to point in its direction of motion as it orbits the nuclear core. The magnetic moment associated with the nuclear spin is equivalent to a current loop; its orbit around the nuclear core results in an effectively toroidal current. This toroidal current gives rise to an anapole moment, analogous to how a current loop gives rise to a dipole moment. Atomic electrons then interact magnetically with the anapole moment. Measuring nuclear anapole moments will give valuable insight into the strength of the nucleon-nucleon weak force. Furthermore, the magnitude of the nuclear anapole moment is unique to each nucleus, so having a table of these values may be useful in a way analogous to that in which nuclear magnetic moment measurements have been useful to NMR.

Our novel approach to measuring these small effects uses diatomic molecules. The NSD-PV effects cause levels of opposite parity to be mixed, and it is this mixing that we directly measure in order to deduce the NSD-PV strengths. The mixing is very small, but is amplified if the levels are closely spaced in energy. Due to their large moment of inertia, diatomic molecules have rotational levels that are very closely spaced and are thus an ideal system for measuring NSD- PV. The levels are brought even closer together using a magnetic field and associated Zeeman shifts of the levels. Finally, the mixing is amplified through interference with an oscillating electric field, and detected using laser-induced fluorescence from the molecules.

Recently, we assembled a complex “interaction region” which will allow us to apply an electric field and laser beams to the molecules flying through the small confines of our superconducting magnet. We plan to soon make NSD-PV measurements in 138BaF as a test of possible systematic errors in our approach; this system should not exhibit NSD-PV because 138Ba does not have an unpaired nucleon spin. Later, after improvements to our molecular beam flux, we will measure NSD-PV in 137BaF, where the predicted size of the effect is large enough to detect.




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