A symmetry of nature:

Parity is a fundamental symmetry in physics. Mathematically it is defined as the reflection against the origin of the coordinates system. Physically this is equivalent to take the mirror image of a process and rotate it by 180 degrees. But since rotation invariance is a direct consequence of angular momentum conservation the parity symmetry simply compares a process with its image in a mirror.

Weak interaction but strong personality:

A new probe:

The aim of our experiments is not to study the structure of the weak interaction itself. Indeed it has been already extensively constrained by measurements at high energy colliders like CERN and SLD. Thanks to the work of the two last decades one has now a precise theoretical description of the weak processes included in the so-called Standard Model of the elementary particles and their interactions. In our measurements, the weak current is considered as an input, a clean probe which gives us new insights on the complex hadronic matter. This approach is complementary to the previous studies with the electromagnetic probe. The different nature of the interaction provides us with a set of new observables we couldn't have reached otherwise.
The SPhN participates in a program of Parity Violation experiments at JLab. The experimental method is to elastically scatter an electron beam on a hadronic target (proton or nuclei). Electron and hadrons both feel the weak interaction and can exchange a Z0 boson during the elastic process. This boson is the messenger of the weak neutral interation and have a mass of ~91.2 GeV. Extracting its contribution in the scattering gives us the new information we are seeking.

Parity violating asymmetries:

There physics appears one more time as a science of compromises: you never get extra informations for free. Actually this time the problem is obvious, the weak interaction is ... weak. Electrons will mainly interact with matter via the electromagnetic force which overwhelm the Z0 signal. The probability of each interaction to occur has the following features:


At Q²=1 GeV², the ratio of the weak/electromagnetic amplitudes is 10E-5 only. How can we enhance the weak contribution? If the transfert Q² comes close to M_Z² the propagator of the Z-boson becomes huge. Actually this is exactly what high energy colliders do. They fix the energy in the center of mass at the Z-pole to study the weak interaction. Unfortunately in our case we want to keep the transfert well below this region because we are interested in the non-perturbative structure of hadrons, where QCD looses its predective power ... and where the Z-contribution is definitively smaller than the electromagnetic one.
Neutrino beams could do it, they are pure weak probes. But it would take decades to accumulate the statistic...
Then you think that Parity Violation could be part of the trick, and you are right. If we can measure two mirror-image scattering processes in the same experimental conditions, the difference between the two counting rates will isolate the weak contribution. In practice we'll measure the ratio of the difference over the sum which cancels out all the errors of normalization and allow accurate measurement of small quantities. This ratio is called a parity violating asymmetry. Since the difference is proportionnal to the weak transition and the sum is dominated by the electromagnetic part, our asymmetry is basically the ratio of the two probabilities illustrated above. In the kinematical domain of our experiments (Q²< 1GeV²) it varies between 0.5 and 15 parts per million (ppm). This is a small quantity but directly proportional to the Z0 signal and measurable with a good precision thanks to the absence of normalization errors.
To get a mirror-image of a scattering process we note that Parity operation reverses the sign of vectors like position and momentum but lets axials vectors like spin (product of two vectors) unchanged. Hence buildind a Parity symmetric scattering process would require to flip all the particles directions but not the spin. Experimentally we choose a more convenient and equivalent method which consist in keeping everything unchanged but flipping the spin. The picture is the following:



we send a polarized electron beam on an unpolarized hadronic target. Processes with the electron spin parallel (Right state) or anti-parallel (Left state) to the beam direction are related by Parity operation. The P.V. asymmetry then simply becomes the asymmetry in the Left/Right counting rates.

New observables:

Coming soon ...