Conclusions and Recommendations for Second Week of Parity Workshop

The second week of the International Workshop on Parity Violation in
Atomic, Nuclear, and Hadronic Systems focussed on Nuclear and Hadronic
Systems. However, it is to be noted that hadronic parity violation
(due to W- and Z-boson exchanges between the quarks) also plays a role in
electron-nucleus parity violation as embedded in the axial form factor
corrections. The recommendations that follow below with regards to
future experimental and theoretical efforts are the result of lengthy
discussions and present consensus expressions.

 *  There exist at present an inconsistency between the value of the weak
    pion-nucleon coupling constant f^{1}_\pi as deduced from the circular
    polarization of the 1.081 MeV gamma-rays from the decay of the
    well-known parity mixed doublet in ^{18}F (for which the nuclear
    structure is adequately known) and as deduced from the anapole moment
    of ^{133}Cs. One notes that there are several experiments which have
    measured the circular polarization of the 1.081 MeV gamma-rays from
    ^{18}F, giving results in mutual agreement:

    Recommendation - Proceed vigorously with the measurement of the
    **************   gamma-ray asymmetry in \vec n + p \rightarrow d +
                      \gamma, an experiment presently being mounted at

                   - Proceed rapidly with the measurement of
                     \vec \gamma + d \rightarrow n + p at 5 to 6 MeV above
                     threshold. Also consider seriously the possibility of
                     a measurement closer to threshold which is sensitive
                     to the weak rho- and omega-meson-nucleon coupling
                     constants. Initial measurements are presently ongoing
                     with the CEBAF injector at Jefferson Laboratory.

 *  The TRIUMF proton-proton parity violation experiment has obtained a
    result for the longitudinal analyzing power A_z, at an incident energy
    (221 MeV) where only the weak rho-nucleon coupling constant plays a
    role. Together with the low energy proton-proton results for A_z from
    SIN (now Paul Scherrer Institute) and the University of Bonn,
    constraints can now be imposed on both the weak rho-nucleon and
    omega-nucleon coupling constants. However, the 221 MeV result, being
    close to the zero-crossing of A_z, has presently a larger fractional
    error than the low energy results:

    Recommendation - Proceed vigorously to improve both the statistical
    **************   and systematic errors of the 221 MeV TRIUMF
                     experiment in order to arrive at a fractional error
                     comparable to that of the low energy results. The
                     221 MeV experiment MUST be completed with a most
                     significant determination of the weak rho-nucleon
                     coupling constant.

                   - Give serious consideration to a further 450 MeV
                     experiment to establish the energy dependence and
                     to determine the possible role of intermediate \Delta
                     Isobar contributions to the conventional one-boson
                     exchange model for the weak hadronic interaction.

 *  The 5.1 GeV proton-nucleus (water target) parity violation experiment
    performed with the ZGS of Argonne National Laboratory stands with a
    result more than ten times larger than what is expected applying
    simple scaling arguments. The result is left unexplained both
    experimentally and theoretically:

    Recommendation - Perform a proton-proton parity violation experiment
    **************   measuring A_z as close as possible to 5.1 GeV.

 *  A combination of the parity violating neutron spin rotation in ^{4}He
    and the parity violating longitudinal analyzing power in proton-^{4}He
    elastic scattering provides another determination of the weak
    pion-nucleon coupling constant f^{1}_\pi:

    Recommendation - Complete the parity violating neutron spin rotation
    **************   measurement on ^{4}He, currently in progress at NIST,
                     as expediently as possible.

                   - Give serious consideration to mounting a parity
                     violating neutron spin rotation measurement on
                     hydrogen as it provides a more direct determination
                     of f^{1}_\pi.

 *  There are various unresolved questions regarding the semi-leptonic
    and non-leptonic weak decays of the hyperons, e.g., the \Lambda.
    A new approach is to measure the cross section and longitudinal
    analyzing power for the reaction \vec p n \rightarrow p \Lambda.
    Due to the smallness of the cross section (~ 10^{-13} times the
    elastic scattering cross section) ingenious and novel experimental
    techniques are required:

    Recommendation - Strong encouragement is given to proceed with the
    **************   current efforts at RCNP of Osaka University to
                     measure \vec n p \rightarrow p \Lambda.

 *  There are still experimental questions regarding the anapole moments
    of ^{133}Cs and ^{205}Tl. Clearly experimental verification by
    another independent measurement is very essential, in particular as
    it relates to f^{1}_\pi:

    Recommendation - Further measurements of the anapole moments are
    **************   essential for the progress of this subfield.

 *  Theoretical considerations regarding all of the above mentioned
    experimental efforts were discussed at great length. It was noted
    that in the low energy region, up to the present, most successful
    has been the meson exchange model theoretical description of nuclear
    parity violation of Desplanques, Donoghue, and Holstein (DDH), based
    on their paper of some twenty years ago. Clearly, with the new
    generation of precision parity violation experiments one expects
    a great deal more in terms of theoretical efforts:

    Recommendation - Refine and update the calculations of parity
    **************   violating observables in both the meson exchange
                     model and the chiral perturbation theory approach.
                     The meson exchange model calculations allow a more
                     direct comparison with experimental observables involving
                     more than 2 or 3 nucleons or at high momentum transfers,
                     while the chiral perturbation theory approach may
                     allow more QCD insight to be obtained.

                   - Recast the DDH language for measuring the short range
                     weak meson-nucleon coupling constants in terms of
                     measuring effective short range parity violating N-N
                     interactions. This is necessary because of important
                     ambiguities and inconsistencies in the treatment of
                     the strong interaction. For instance the rho-meson,
                     exchanged in one-boson exchange models of the N-N
                     interaction, represents multiple meson exchanges as
                     an effective single boson.

                   - Apply the understanding of hadronic parity violation
                     to the calculation of electroweak radiative
                     corrections. These radiative corrections are embedded
                     in the axial form factor contributions to electron-
                     proton and deuteron parity violating asymmetries,
                     e.g., in the SAMPLE and G0 experiments.

                   - Perform lattice calculations of f^{1}_\pi or related
                     quantities including chiral extrapolations.
                     Study the neutral and charged current contributions
                     to f^{1}_\pi.

                   - Perform self consistent calculations that include
                     \Delta Isobar contributions to interpret proton-
                     proton parity violation measurements above the
                     threshold for pion production.

                   - Study a possible density dependence of the parity
                     violating interactions and the resulting weak meson
                     exchange currents. What about parity violating
                     three-body forces.

                   - Once the current controversy regarding f^{1}_\pi has
                     been resolved perform improved calculations of the
                     ^{133}Cs and other anapole moments.