How have they guessed that the weak interaction distinguish left and right?

How the understanding of asymmetry of the weak interaction was coming

Following pions, in 1947 positively charged kaons were discovered, which decay into either two or three pions. These decays are relatively slow as occur due to the weak interaction. The state with two pions is symmetric w.r.t the mirror reflection of space while that with three pions is anti-symmetric. The conservation of the left-right (mirror) symmetry in particle decays seemed natural back then since this has been tested for both the electromagnetic and strong interaction, and therefore Pauli is credited with words: God could not be lefty in the weak sense … . So initially it was assumed there are two different particles behind those two decays. However, the fact of the amazing similarity of characteristics of these two particles made Lee and Yang in 1956 to advance the assumption of violation of the left-right symmetry in the weak interaction, which was proved almost simultaneously in two specially designed experiments. Technically, these experiments had been possible for many years prior to the event, but the experimenters were not taken for them as theorists were convincing them that there is no need to do so.

Violating the left-right symmetry in the weak interaction

The discovery of the left-right symmetry violation was one of those that are counter-intuitive.

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