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M. Senami et al.
On the other hand, the weak interaction is formulated as SU(2) gauge theory, and W
and Z bosons are mediator of this interaction. These bosons are coupled to ordinary
fermions, such as electrons, only by the V-A coupling, where V and A is the vector and axial-vector currents, respectively. Hence parity is violated maximally in the
weak interaction.
It is known that this parity violation makes the energy difference between enantiomers. This energy difference between them, which is called parity-violating energy
shift, is very small [2]. In spite of the smallness, this energy is studied in many
works by computational methods. The parity-violating energy shift is dominantly
induced by virtual Z boson exchanges between nuclei and electrons. Virtual Z boson
exchanges is quantum effect in relation to uncertainty principle. Since Z boson is
very heavy as 90 GeV∕c 2 , where c is the speed of light, this particle cannot be produced energetically, and, however, uncertainty relation allows this particle to affect in
a very restricted region. Single W boson exchange does not contribute to the parityviolating energy, since if occurs, it is í µí»½ decay. The exchanges between electrons is
known to be subdominant for particularly heavy nuclei [3]. Since nuclei are localized
strongly, the existence of parity-violating energy means the existence of the nonzero
chirality density around nuclei. It is surprising that low energy electrons have polarized chirality, since the electron mass, that is the interaction with Higgs field in the
vacuum, vanishes chirality for free electrons.
The parity-violating energy shift is studied by many researchers as one of solutions for biomolecular homochirality. Due to this energy difference, the amount of
one of enantiomers may be slightly larger than the other through an enhancement
process, such as crystallization. In other viewpoints, some of the authors are interested in the total integrated chirality density of the electron in a molecule, whose
existence has already been reported [4]. If nonzero integrated chirality density of
the electron exists in enantiomers, its interaction rates through weak interaction are
different between enantiomeric pair. This difference of the reaction rate probably
generates the difference of the number density between enantiomers, which is indispensable for the problem of the biomolecular homochirality. Even though this difference is not enough, we are interested in the distribution of the chirality density in a
molecule, since the chirality density is known to be proportional to the zeta potential
[5]. The zeta potential is the potential for the zeta force, which is the counter force to
the spin torque, defined only in quantum field theory [6, 7]. Hence chiral molecules
have nonzero zeta force distribution.
In this work, we study the integrated chirality density of the electron in H 2 X 2
molecules (X = O, S, Se, Te). This structure is one of the simplest chiral molecules
and is chosen in many works [4, 8–10]. The total chirality of the electron of this
structure is reported for H 2 Te 2 in Reference [4]. In this work, the chirality is investigated also for H 2 O 2 , H 2 S 2 , and H 2 Se 2 in relation to the parity-violating energy shift
and the zeta potential.
M. Senami et al.
On the other hand, the weak interaction is formulated as SU(2) gauge theory, and W
and Z bosons are mediator of this interaction. These bosons are coupled to ordinary
fermions, such as electrons, only by the V-A coupling, where V and A is the vector and axial-vector currents, respectively. Hence parity is violated maximally in the
weak interaction.
It is known that this parity violation makes the energy difference between enantiomers. This energy difference between them, which is called parity-violating energy
shift, is very small [2]. In spite of the smallness, this energy is studied in many
works by computational methods. The parity-violating energy shift is dominantly
induced by virtual Z boson exchanges between nuclei and electrons. Virtual Z boson
exchanges is quantum effect in relation to uncertainty principle. Since Z boson is
very heavy as 90 GeV∕c 2 , where c is the speed of light, this particle cannot be produced energetically, and, however, uncertainty relation allows this particle to affect in
a very restricted region. Single W boson exchange does not contribute to the parityviolating energy, since if occurs, it is í µí»½ decay. The exchanges between electrons is
known to be subdominant for particularly heavy nuclei [3]. Since nuclei are localized
strongly, the existence of parity-violating energy means the existence of the nonzero
chirality density around nuclei. It is surprising that low energy electrons have polarized chirality, since the electron mass, that is the interaction with Higgs field in the
vacuum, vanishes chirality for free electrons.
The parity-violating energy shift is studied by many researchers as one of solutions for biomolecular homochirality. Due to this energy difference, the amount of
one of enantiomers may be slightly larger than the other through an enhancement
process, such as crystallization. In other viewpoints, some of the authors are interested in the total integrated chirality density of the electron in a molecule, whose
existence has already been reported [4]. If nonzero integrated chirality density of
the electron exists in enantiomers, its interaction rates through weak interaction are
different between enantiomeric pair. This difference of the reaction rate probably
generates the difference of the number density between enantiomers, which is indispensable for the problem of the biomolecular homochirality. Even though this difference is not enough, we are interested in the distribution of the chirality density in a
molecule, since the chirality density is known to be proportional to the zeta potential
[5]. The zeta potential is the potential for the zeta force, which is the counter force to
the spin torque, defined only in quantum field theory [6, 7]. Hence chiral molecules
have nonzero zeta force distribution.
In this work, we study the integrated chirality density of the electron in H 2 X 2
molecules (X = O, S, Se, Te). This structure is one of the simplest chiral molecules
and is chosen in many works [4, 8–10]. The total chirality of the electron of this
structure is reported for H 2 Te 2 in Reference [4]. In this work, the chirality is investigated also for H 2 O 2 , H 2 S 2 , and H 2 Se 2 in relation to the parity-violating energy shift
and the zeta potential.