SU(3) Breaking in Axial Matrix Elements

Contributers: P. Ratcliffe and M. Savage.

To determine the strange quark axial matrix element, $\langle\overline{s}\gamma_\mu\gamma_5 s\rangle$, from deep-inelastic scattering the value of the matrix element of the ``T8'' current, $j_\mu^{A,8} = \overline{q}\gamma_\mu\gamma_5 T^8 q$, between nucleon states is required. This matrix element cannot be measured directly but in the limit of exact flavor SU(3) it can be related to axial matrix elements between baryons in the lowest lying octet of SU(3) (the N, $\Sigma$, $\Lambda$, and $\Xi$). To make a precise determination of $\langle\overline{s}\gamma_\mu\gamma_5 s\rangle$the SU(3) breaking in these matrix elements needs to be understood and quantified. Naive estimates for the size of SU(3) breaking indicate that $\langle\overline{s}\gamma_\mu\gamma_5 s\rangle$is consistent with zero (for example, [16]).

1.

Constituent quark model approach to SU(3) breaking

Since the origin of SU(3) breaking lies in the strange quark mass, the pattern of SU(3) breaking in hyperon decays might be driven by the baryon mass hierarchy [17]. The effects of quark recoil in the decays, accounting for relativistic effects, are linked to the constituent quark masses and hadronic mass splittings. A similar approach uses perturbation theory to tie baryon wave-function renormalization to the mass splittings, parametrizing the effects on the axial form factors. Such models can successfully describe the decays of the baryon octet and result in only minor variations in the F and D structure constants. Such an analysis yields $g_1/f_1 \sim 1.15$ for $\Xi^0\to\Sigma^+e\bar\nu$.

2.

The large-Nc expansion

The large-Nc expansion provides a QCD based framework for a systematic calculation of corrections to both the hyperon and decuplet decays[18]. One of the significant advantages the large-Nc analysis has over other methods is that there is a well defined expansion parameter in the theory, 1/Nc. Where the baryon masses are measured with sufficient precision they obey relations that arise in the large-Nc limit. Precise measurements of other combinations of baryon masses are needed to provide a significant test of the large-Nc expansion[19].

The large-Nc limit links SU(3) breaking in the decuplet and octet baryon decays. Different fits to the measured decay rates yield Vus consistent with that extracted from Kl3 decays, but show an important variation in the values of F and D. The results indicate significant corrections to the vector form factors. This analysis gives $g_1 \sim 1.02-1.07$ for $\Xi^0\to\Sigma^+e\bar\nu$.

3.

The KTeV measurement of $\Xi^0\to\Sigma^+e\bar\nu$ The KTeV experiment is able to cleanly study the decay $\Xi^0\to\Sigma^+e\bar\nu$, and has determined a branching fraction of $(2.49\pm0.19\pm0.25)\times10^{-4}$[20]. The 1999 run will reduce the errors by about a factor two. Angular asymmetries and the muon mode may also become accessible. KTeV will be able to substantially improve the $\Xi^0$ mass measurement, allowing mass relations predicted in the large-Nc expansion to be tested and hadronic models constrained.

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