# chirality oscillations in weak interaction

As far as I have understood, the mass $m$ of a fermion causes a coupling of the both chiralities $\psi_L$ and $\psi_R$. This coupling would induce an oscillation of the chirality within a time scale determined by $\frac 1 m$.

Furthermore, it is known that the weak interaction only couples to the left-handed particles, i.e. only to $\psi_L$.

Combining these two statements, one would have to conclude that the weak interaction of a massive fermion is time dependent, i.e. it is stronger when $\psi_L$ dominates and vanishes completely half an oscillation period later. However, I have never heard about such a strange phenomenon and I conjecture that there's a mistake in my reasoning somewhere.

I'd be grateful if someone could help me find it.

• Suggestion: work out a typical time scale $1/m$ for a particle involved in the weak interaction and compare this to the time resolution of an experiment. – Michael Brown Jul 26 '13 at 10:36
• For example the LHC collides protons in bunches with a spacing of 25 ns according to this LHC data page (not sure how accurate or up to date that is, but I wouldn't expect as much as an order of magnitude difference from that and the actual performance). The triggering system has a latency on the order of microseconds, but I bet the bunch crossing time is a better figure for the time resolution. I'll let an experimentalist say for sure. Either way the time scale is very different than $1/m$. :) – Michael Brown Jul 26 '13 at 10:51
• The time scale for an electron would be of the order of $10^{-20}$ s, obviously much slower than the time resolution of the experiment. But this does not imply that this effect is not observable at all. For example, the cross section of an unpolarized electron beam would be less if this effect really were true. – m4r73n Jul 26 '13 at 12:06
• How so? Chirality suppression is already accounted for in all of the cross sections, decay rates etc. by the $P_L$ projection operators in the interaction. You don't have to artificially reduce the reaction rates over and above that. – Michael Brown Jul 26 '13 at 14:05
• There seems to be a small, zitterbewegung-related chirality leakage effect, cf Bernardini 2006, but it's hard to find contexts where such a chirality violation could amount to much. – Cosmas Zachos Feb 22 '18 at 23:31