# Nonconservation of axial charge

1. May 29, 2010

### TriTertButoxy

It has been known that in addition to the electron mass, quantum effects anomalously break conservation of axial charge: $\partial_\mu J^\mu_A = 2im\bar\psi\gamma_5\psi-\frac{g^2}{16\pi^2}\epsilon^{\mu\nu\rho\sigma}F_{\mu\nu}F_{\rho\sigma}$.

Does anyone know if any experimenter has set up parallel E- and B- fields and observed this anomalous effect? If not, is it possible to observe?

2. May 30, 2010

### ansgar

the pi0 decay for instance..

3. May 30, 2010

### tom.stoer

The eta-prime mass.

Usually the eta and the eta prime (together with the pions etc.) would both be Goldstone bosons for the whole chiral symmetry goup which is spontanenously broken in QCD. But as the axial symmetry is broken by an anomaly there is no Goldstone boson for this symmetry. Therefore the eta-prime mass is much higher as all other masses in this multiplet and especially as the eta mass: pion to eta masses from 135 MeV to 548 MeV; eta-prime has 959 MeV)

4. May 30, 2010

### TriTertButoxy

Yes, I know about the anomaly mediated decay of the pion. I was asking if anybody had set up the necessary external (electric and magnetic) fields to directly observe the non-conservation of axial charge for the electron.

5. May 30, 2010

### tom.stoer

This is not so easy. The non-conservation is a purely quantum mechanical effect. w/o quantum corrections the axial charge is conserved, so there are no "classical" experiments which would demonstrate its non-conservation.

6. May 30, 2010

### TriTertButoxy

But, people have set up experiments to detect quantum mechanical interference patterns -- their equipment only needs to be sensitive enough. Isn't it, in principle, possible to set up an experiment that is sensitive to the quantum mechanical anomalous effect? I'm just wondering if anyone has tried this, or even contemplated this.

7. May 30, 2010

### tom.stoer

Isn't an isolated pion that creates (due to quantum fluctuations) its own decay mode photons w/o any additional experimental setup simple enough?

What does the anomaly say? It says that the current is not conserved, i.e.

$$\partial_\mu j^\mu_a = g^2C\,{}^\ast \! F_{\mu\nu}\,F^{\mu\nu}$$

Is you idea to set up an experiment with a certain electromagnetic field and measure the decay of the axial charge? I am not sure if this will work w/o taking quantum fluctuations into account. But if you need quantum fluctuations, then the pion in vacuum is certainly better as there is no need for external fields at all.

Last edited: May 30, 2010
8. Jun 1, 2010

### TriTertButoxy

Yes, it is enough to use the decay of the pion as confirmation for the anomalous non-conservation of the axial charge.

But my question is more academic: I want to see the anomalous effect in pure QED, involving the electronic axial current. (This is kind of like the academic question of electron-loop mediated photon-photon scattering, which induces non-linear terms in Maxwell's equations.) Is it possible to set up an experiment that can count the axial charge of a system of electrons, and see that it is anomalously non-conserved in the presence of parallel E and B fields?