Status of Experimental Searches for Parity Violation in Atoms

Abstract

In this lecture we review the experiments being carried out to observe parity violation in atoms. Since Professor Bouchiat has discussed theoretical aspects of this subject, we shall summarize only briefly the few formulae we need. Parity violation in atoms arises from the weak neutral coupling of atomic electron and nucleus. Since the electronic and hadronic weak neutral currents each possess vector and axial-vector components:

$$\left. \matrix{ {{\rm{J}}_{\rm{e}}} = {{\rm{V}}_{\rm{e}}} + {{\rm{A}}_{\rm{e}}} \hfill \cr {{\rm{J}}_{\rm{N}}} = {{\rm{V}}_{\rm{N}}} + {{\rm{A}}_{\rm{N}}} \hfill \cr} \right\}$$

(1.)

The weak neutral Hamiltonian H’ possesses both scalar and pseudoscalar portions:

$${\rm{H'}} = {{\rm{H}}_{\rm{s}}} + {{\rm{H}}_{\rm{p}}}$$

(2.)

and it is the pseudoscalar portion H_p, of course, that interests us here. Ignoring momentum-transfer dependent terms, it can be written:

$${{\rm{H}}_{\rm{p}}} = {\rm{H}}_{\rm{p}}^{\left( 1 \right)} + {\rm{H}}_{\rm{p}}^{\left( 2 \right)}$$

(3.)

where

$${\rm{H}}_{\rm{p}}^{\left( 1 \right)} = {{\rm{G}} \over {\sqrt 2 }}\sum\limits_{\rm{i}} {{{{\rm{\bar \psi }}}_{\rm{e}}}} {\rm{ }}{{\rm{\gamma }}_{\rm{\lambda }}}{\rm{ }}{{\rm{\gamma }}_{\rm{5}}}{\rm{ }}{{\rm{\psi }}_{\rm{e}}}\left[ {{{\rm{C}}_{1{\rm{p }}}}{{{\rm{\bar \psi }}}_{{\rm{pi}}}}{\rm{ }}{{\rm{\gamma }}^{\rm{\lambda }}}{\rm{ }}{{\rm{\psi }}_{{\rm{pi}}}} + {{\rm{C}}_{1{\rm{n }}}}{{{\rm{\bar \psi }}}_{{\rm{ni}}}}{\rm{ }}{{\rm{\gamma }}^{\rm{\lambda }}}{\rm{ }}{{\rm{\psi }}_{{\rm{ni}}}}} \right]$$

(4.)

$${\rm{H}}_{\rm{p}}^{\left( 2 \right)} = {{\rm{G}} \over {\sqrt 2 }}\sum\limits_{\rm{i}} {{{{\rm{\bar \psi }}}_{\rm{e}}}} {\rm{ }}{{\rm{\gamma }}_{\rm{\lambda }}}{\rm{ }}{{\rm{\psi }}_{\rm{e}}}\left[ {{{\rm{C}}_{2{\rm{p }}}}{{{\rm{\bar \psi }}}_{{\rm{pi}}}}{\rm{ }}{{\rm{\gamma }}^{\rm{\lambda }}}{\rm{ }}{{\rm{\gamma }}_5}{\rm{ }}{{\rm{\psi }}_{{\rm{pi}}}} + {{\rm{C}}_{2{\rm{n }}}}{{{\rm{\bar \psi }}}_{{\rm{ni}}}}{\rm{ }}{{\rm{\gamma }}^{\rm{\lambda }}}{\rm{ }}{{\rm{\gamma }}_5}{\rm{ }}{{\rm{\psi }}_{{\rm{ni}}}}} \right]$$

(5.)

and in each case the sum is taken over all protons (p) and neutrons (n) in the nucleus. The coefficients C_1p, C_1n, C_2p, C_2n are model-dependent and it is the goal of the various experiments to determine them. In the standard (“Weinberg-Salam”) model, one predicts:

$$\left. \matrix{ {{\rm{C}}_{1{\rm{p}}}} = {1 \over 2}\left( {1 - 4{\rm{ si}}{{\rm{n}}^2}{\rm{ \theta }}} \right) \hfill \cr {{\rm{C}}_{1{\rm{n}}}} = - {1 \over 2} \hfill \cr {{\rm{C}}_{2{\rm{p}}}} = {{\rm{g}}_{{\rm{A/2}}}}\left( {1 - 4{\rm{ si}}{{\rm{n}}^2}{\rm{ \theta }}} \right) \hfill \cr {{\rm{C}}_{2{\rm{n}}}} = - {{\rm{g}}_{{\rm{A/2}}}}\left( {1 - 4{\rm{ si}}{{\rm{n}}^2}{\rm{ \theta }}} \right) \hfill \cr} \right\}$$

(5.)

where g_A = 1.25 is the axial vector coupling constant of beta decay, and θ is the Weinberg angle. Diverse results from high energy physics yield sin² θ = 0.23, leading to the predictions:

$$\matrix{ {{{\rm{C}}_{1{\rm{p}}}} = .04;} & {{{\rm{C}}_{1{\rm{n}}}} = - .50;} & {{{\rm{C}}_{2{\rm{p}}}} = .05;} & {{{\rm{C}}_{2{\rm{n}}}} = - .05} \cr } $$

(6.)