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

LANSCE.

- 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.

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