Relative enhancement of low-mass vector-boson exchange in higher waves matrix elements: parity non-conservation in hydrogen

Models of unification predict additional $Z'$ boson, which contributes to parity non-conservation (PNC) in atoms. If $Z'$ boson is light, ratio of $Z'$ boson contribution to the Standard Model $Z$ boson contribution to atomic PNC increases with decreasing nuclear charge $Z$ faster than $1/Z^2$. This motivated our previous study of PNC in hydrogen and deuterium proportional to the weak interaction matrix elements $<s|W|p>$. An enormous additional relative enhancement appears in the matrix elements between higher waves, such as $<p_{1/2,3/2} | W | d_{3/2,5/2}>$, since $p_{3/2}$ and $d_{3/2,5/2}$ wave functions vanish at $r \to 0$, suppressing matrix elements of the contact $Z$ boson mediated contact electron-nucleus interaction. Measurements of $<p_{1/2,3/2} | W | d_{3/2,5/2}>$ will simplify disentanglement of the $Z'$ contribution from the Standard Model background.