On the role of true and false chirality in producing parity-violating energy differences

In this work, we tackle the problem of showing which type of influences can lift the degeneracy between truly and falsely chiral systems, showing that only when both systems and influences are both truly (falsely) chiral, a parity violating energy difference between left-handed (L) and right-handed (R) systems can be produced. In particular, after considering the enantiomers of a chiral molecule as paradigmatic truly chiral systems, we rigorously show, under a quantum field theoretical approach, that only a truly chiral influence such as the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>Z</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> -mediated electroweak interaction can lift the degeneracy between enantiomers. Indeed, we explicitly show that a falsely chiral influence, such as an axion-mediated interaction in chiral molecules, cannot lift the aforementioned degeneracy. These results extend Barron’s seminal ideas (L. D. Barron, True and false chirality and parity violation, Chem. Phys. Lett. 123 , 423 (1986). (doi: 10.1016/0009-2614(86)80035-5 )) to a quantum-field-theory- (QFT)-based approach.