Does anti-Alice take levo-glucose and dextro-fructose in her anti-tea?
The putative equality of the levo-dextro energy difference our world and the dextro-levo difference in an anti-world would follow from CP-invariance, but CP-invariance is subtly broken by the complex phase of the CKM matrix. The experimental evidence for CP-violation comes from ${{K}^{0}}\And {{B}^{0}}$ decays, but there is as yet no corresponding evidence about CP-violation in leptons. CP-violation is a necessary but probably insufficient condition for inequality, since it is hard to see how this known kind of CP-violation would lead to inequality.
Published articles have calculated tiny levo-dextro differences in ordinary matter from CP-conserving weak neutral current interactions mediated by ${{Z}^{0}}$. They finger electron-neutron interactions as the dominant effect, with the P-violating interaction ${{H}_{PV}}\propto {{(\bar{\psi }{{\gamma }_{0}}\psi )}_{N}}{{(\bar{\psi }{{\gamma }_{5}}{{\gamma }_{0}}\psi )}_{e}}$ yielding terms $\propto {{(\mathbf{p}\cdot \mathbf{s})}_{e}}{{\delta }^{3}}({{\mathbf{x}}_{e}}-{{\mathbf{x}}_{N}})$ for each electron near a nucleus. The $Z$’s vectorial coupling to protons is weaker than its coupling to neutrons, by a factor of $4{{\sin }^{2}}{{\theta }_{W}}-1=-0.11$. One may therefore sum $(N-0.11Z)(\mathbf{p}\cdot \mathbf{s})\rho ({{\mathbf{x}}_{N}})$ over nuclei, where $\rho (\mathbf{x})$ denotes local electron density.
Since $\left\langle ground|{{H}_{PV}}|ground \right\rangle =0$, these P-violating terms have no effect on energy in 1st-order perturbation theory, but they do admix excited states, notably triplet states with parallel spins, which result in bilocal $\mathbf{s{s}'}\And \mathbf{p{p}'}$ correlations.
The articles go on to argue that the P-violating term operates in tandem with a P-conserving spin-orbit term ${{H}_{SO}}\propto (\mathbf{E}\times \mathbf{p})\cdot \mathbf{s}=\mathbf{E}\cdot (\mathbf{p}\times \mathbf{s})$, where $\mathbf{E}$denotes the electric field from another nearby atom. They then calculate energies in the Born-Oppenheimer approximation, which assumes fixed nuclear positions. In an anisotropic environment, particular components of the $\mathbf{s{s}'}\And \mathbf{p{p}'}$ correlations may be dominant. Unless these dominant components are parallel, their cross-product will define a preferred direction for $\mathbf{E}$, hence the chiral preference. The levo-dextro energy difference is 1st-order in ${{H}_{PV}}$ after all.
References:
Bakasov el al: Ab initio calculation of molecular energies including parity violating interactions, J Chem Phys 109 (1998) 7263
Quack & Stohner: How do Parity Violating Weak Nuclear Interactions Influence Rovibrational Frequencies in Chiral Molecules?, Zeitschrift für Physikalische Chemie, 214, 5, 6752703 (2000)
