The masses of the quarks are input parameters for QCD and the Standard Model (SM). There is no theory that enables one to calculate the quark masses from first principles. Solitary quarks have never been found, which precludes measuring the quark masses directly. The values quoted in the literature are model dependent results extracted from selected hadron-spectroscopy data. The favored method for the three light quarks is based on an expansion of the masses of light baryons and mesons, particularly the Goldstone bosons, in powers of the quark masses. The uncertainty in using this procedure may be evaluated using chiral perturbation theory. The Particle Data Group quotes 50% uncertainty in the masses of the three light quarks.
There is special interest in the mass difference between the up, down and strange quarks because they are accessible to direct measurement. The up-down quark mass difference can be obtained from suitable SU(2)-breaking measurements such as charge-symmetry and G-parity violations. The strange-down quark-mass difference is measured from SU(3)-breaking.
The quark-mass project is a program to determine the masses of the
three light quarks to an accuracy that benefits the input parameters to QCD
and the SM, namely 10%. In the first phase the project is focused on
measuring accurate values of SU(2)- and SU(3)-breaking. This is accomplished
in two ways. First, by
making new determinations of isospin multiplet and SU(3) multiplet mass
splittings of a wide variety of nucleon, delta, lambda and sigman resonances of
all spins and both parities of the SU(3) octets, decuplets and singlets. This
allows the systematic study of the dependence of the quark mass differences on
the flavors of the spectator quarks and on the quark configurations. The
second way consists of measuring 
,
and
mixing in
a variety of different nuclear environments. Finally, the theoretical side is
supported by new data for applying chiral perturbation theory. For this
purpose the major eta decays are very useful: this is the subject of
another project.
This first phase is carried out using the 672-element SLAC Crystal
Ball as a multiphoton detector. This enables us to measure simultaneously all
neutral final states of the various baryon resonances produced by
and
induced reactions on protons
leading to 
,
,
,
,
,
etc.
In the second phase we plan to add a charged-particle tracker to the Crystal Ball. The third phase calls for the installation of an insert in the CB consisting of a small split superconducting solenoid magnet. This affords the measurement of the momenta of the charged particles enabling us to investigate the properties of many baryon and meson resonances.
We are also planning to measure
,
and
mixing in selected production
reactions.
It is important to realize that the determination of the masses of the light quarks to a good precision requires a comprehensive program of hadron spectroscopy. There is no single crucial experiment. What is required is a well chosen collection of important measurements. Finally, the determination of the quark masses necessarily requires substantial theoretical input.
References
1. B. Nefkens, G. Miller and I. Slaus, Comments on Nucl. Part.
Physics 
,
221(1992).
2. G. Miller, B. Nefkens and I. Slaus Physics Reports 
,
1 (1990).
3. AGS Proposal 913, M. Sadler, B. Tippens and H. Spinka, Spokesmen.
4. AGS Proposal 914, B. Nefkens, A. Efendiev and S. Kruglov, Spokesmen
5. B. Nefkens in Proc. Baryons 95, editor B. Gibson, Santa Fe, NM, Oct. 1995. Also Report UCLA-10-P25-247
