Atomic Parity Violation

The electroweak theory

In the Standard Model of particle physics, the electroweak theory is the unified description of electromagnetism (quantum electrodynamics) and the weak interaction. The theory claims that all electromagnetic and weak phenoma are manifestations of one universal electroweak interaction mediated by four massless spin-1 bosons, two charged (W^±) and two neutral ones (Z⁰ and the photon). After the spontaneous breaking of the electroweak symmetry by the vacuum, three of the four bosons acquire mass. The weak interaction is mediated by the three massive gauge bosons, namely the charged W^± (80.4 GeV/c²) bosons and the neutral Z⁰ (91.2 GeV/c²). Due to these large masses, the range of the weak interaction is extremely short, ~10^-3 femtometer, as opposed to the range of the electromagnetic interaction, which is infinite.

The Weinberg angle

A fundamental parameter of the electroweak theory is the γ-Z0 mixing angle, θw, the so-called electroweak mixing angle or Weinberg angle. This mixing angle connects the two independent coupling constants of the electroweak theory: the electric charge, e, and the weak coupling constant, gw, by the relationship sin²θw = e²/g²w. At high energies (100 GeV) the electron’s weak charge (which is closely related to the mixing angle) has been accurately measured at high energy facilities at Stanford and CERN. The electroweak theory is a quantum field theory, however, which means that the coupling “constants” are not constant, but instead depend on the energy scale at which they are probed. This effect is due to the polarization of the vacuum by particle-antiparticle pairs and causes the mixing angle to vary slightly as a function of the four-momentum scale Q, or sin²θw(Q) = e²(Q)/g²w(Q). This “running” of the Weinberg angle is a poorly tested prediction of the electroweak theory.

The running of the electroweak mixing angle

Fig. 1 shows a plot of the (square of the) Weinberg angle as a function of the momentum scale, as predicted by electroweak theory (blue line).

As the figure shows, the mixing angle slowly decreases (by some 3 %) in going from low energies to about 100 GeV. This is due to vacuum polarization by the formation of quark-antiquark pairs. These form a “screen” which effectively reduces the weak charge of the interacting particles and results in a decrease of gw. The Feynman diagram of the screening of the weak charge is shown in Fig. 2 in the left picture. At higher energies, W^± pairs start to dominate the vacuum polarization leading to an anti-screening of the interacting particles. This results in an increase of the weak charge gw and, consequently, an increase of the mixing angle. The corresponing Feynman diagram is shown in Fig. 2 in the right picture.  

Experimental verification of the running

The running of the weak angle is so far not a well-tested prediction of the quantum structure of the electroweak theory. As Fig. 1 shows, at high Q, near the mass of the Z⁰ boson, the weak angle has accurately been measured by SLAC's SLD experiment and the LEP experiments at CERN (indicated by Z-pole in the figure). A very recent parity-violating electron-electron scattering experiment by the SLAC E158 collaboration (Qw(e) in the figure) has resulted in a value for the mixing angle at intermediate Q that is in reasonable agreement with the electroweak theory. However, a recent neutrino scattering experiment by the NuTeV collaboration (ν-DIS in the figure) at comparable Q disagrees with the prediction of the electroweak theory. At Jefferson laboratory, the planned Qweak experiment (Q _^w (p) in the figure) aims to determine the mixing angle by measuring parity violation in electron-proton scattering.

At very low energies, the benchmark is set at present by the high-precision measurement performed by the Boulder group of Weiman and collaborators in an atomic beam experiment. In this experiment the weak charge of cesium was measured to a precision of about 0.4%. The value for the mixing angle extracted from this experimental value is also plotted in Fig. 1. It is not precise enough to confirm the predicted running of sin2θw. In fact, it is also still consistent, within about two standard deviations, with the mixing angle not running at all. An independent measurement of the mixing angle at this low energy could confirm the running of the mixing angle over some five orders of magnitude. It is this independent measurement we hope to contribute by measuring parity non-conservation in a single trapped radium ion.

Atomic parity violation

Atomic parity violation is caused by the exchange of Z⁰ bosons between the electrons and the quarks in the nucleus. This process interferes with the “normal” Coulomb interaction between the electrons and the quarks. Tree-level diagrams of both processes are shown in Fig. 3.

The exchange of a Z⁰ boson is a parity violating effect and it causes the atomic states to acquire a small admixture of opposite-parity states. The effect is dominated by the admixture of P states into S states, S ® S + εP. In this case a parity-forbidden electric quadropole E2 S ® D transition is joined by an E1 parity non-conserving transition. The parity mixing effect is tiny, but it has been shown (Bouchiat & Bouchiat, 1974) that it scales faster than Z3, so the effect will be larger for heavier atoms. Cesium...

APV in one single trapped barium ion

The idea of measuring APV in one single trapped ion or atom was originally proposed by Fortson in 1993 (barium ion page). The group of Fortson in Seattle has chosen to use barium for the APV experiment, we plan to use radium. Radium has several advantages compared to barium. The Z3 law tells us that the expected PNC effect will be twenty times larger in radium, and the lasers needed for the experiment are for radium at much friendlier wavelengths than for barium. Since radium is iso-electric to barium, we have the added advantage that a proof of principle of some of the crucial ideas of the experiment have been given by the Seattle group. The idea of the experiment, as outlined by Fortson, is described below.

PNC induced light shifts

Figure 4 shows the relevant energy levels in spectrum of the radium ion.

The exchange of Z⁰ bosons between the electrons and the quarks of the nulceus cause a small admixture of P_1/2 states into the ground 6S_1/2 state.