[Physics] Physical Interpretation of Forward-Backward Asymmetry

particle-physics

Like my topic, I'd like to know why we need to analyze the forward-backward asymmetry:
$$A_{FB}=\frac{\int_0^1dz\frac{d\sigma}{dz}-\int_{-1}^0dz\frac{d\sigma}{dz}}{\int_{-1}^1dz\frac{d\sigma}{dz}}$$
in particle physics. What physical concept does it relates to?

The equation you present is perhaps not the most intuitive, but it falls under the more general "forward-backward" ratio or asymmetry equation, which looks something like

$$\mathcal{A}=\dfrac{F-B}{F+B},$$

where $F$ and $B$ are quantities evaluated in the defined "forward" and "backward" regions respectively. The idea being that any deviation of $\mathcal{A}$ from 0 would indicate such an "asymmetry", whatever that is.

Since you ask in the context of particle physics, let's try to connect it to a practical example.

In the 1990's, people were colliding electrons and positrons and looking at the various outcomes (final states), particularly at pairs of muons and anti-muons

$$e^++e^-\to\mu^++\mu^-.$$

Now, this process could be mediated by a photon and would have a cross-section $\sigma_\gamma\propto (1+\cos^2\theta)$. However, as it was historically realized, it can also be mediated through a $Z^0$ boson, which leads to a much more complicated $\sigma_Z$, such that the final observable cross-section actually results from the interference of these two possible processes.

Instead of being an even function of the scattering angle $\theta$, the cross-section $\sigma_\mathrm{tot}$ now favours "one side" rather than the other; defining "forward" and "backward" regions appropriately, and counting the number of final states $F$ and $B$ produced in those, you end up with a non-zero asymmetry $\mathcal{A}$, which can in turn tell you a lot about the various parameters that go in your cross-section and the exact nature of electroweak interactions etc.

To make the idea more visual, the following plot is from the JADE experiment. The solid line is $\sigma_\gamma$, while the dashed line (which seems like a much better fit to data) includes the $Z$ interference.