Octet-baryon axial-vector charges and $SU(3)$-breaking effects in the semileptonic hyperon decays

The octet-baryon axial-vector charges and the $g_1/f_1$ ratios measured in the semileptonic hyperon decays are studied up to $\mathcal{O}(p^3)$ using the covariant baryon chiral perturbation theory with explicit decuplet contributions. We clarify the role of different low-energy constants and find a good convergence for the chiral expansion of the axial-vector charges of the baryon octet, $g_1(0)$, with $\mathcal{O}(p^3)$ corrections typically around 20% of the leading ones. This is a consequence of strong cancellations between different next-to-leading-order terms. We show that considering only nonanalytic terms is not enough and that analytic terms appearing at the same chiral order play an important role in this description. The same effects still hold for the chiral extrapolation of the axial-vector charges and result in a rather mild quark-mass dependence. As a result, we report a determination of the leading-order chiral couplings, $D=0.623(61)(17)$ and $F=0.441(47)(2)$, as obtained from a completely consistent chiral analysis up to $\mathcal{O}(p^3)$. Furthermore, we note that the appearance of an unknown low-energy constant precludes the extraction of the proton octet charge from semileptonic decay data alone, which is relevant for an analysis of the composition of the proton spin.

Figure 1

Feynman diagrams contributing up to $\mathcal{O}(p^3)$ to the $g_1^{B^{\prime }B}$ AV form factor. Single solid lines denote octet baryons and double lines decuplet baryons. The dashed lines correspond to mesons and the wiggly line to the external AV field. A number inside the vertex denote its chiral order.

Figure 2

Diagrams contributing to the wave-function renormalization. The notation is the same as in Fig. 1.

Figure 3

Axial-vector charges $g_1^{B{B}^{\prime }}$ and $g_{A,3}^X$ of the SHD and octet baryons compared to our fits including explicit virtual decuplet states. Blue circle markers denote the fitted input data points. The square markers denote our full $\mathrm{B}\chi \mathrm{PT}$ results while the triangle markers show the LO contribution. The shaded area corresponds to the lQCD input from [31] and [32]. In the case of the lQCD data from [32], the data points are listed from left to right with increasing $M_{\pi }$.

Figure 4

Chiral extrapolation of the AV charges $g_{A,3}^X$ of the proton (red), ${\mathrm{\Sigma }}^{+}$ (blue) and ${\mathrm{\Xi }}^0$ (green) as function of $M_{\pi }$. The left figure shows the lowest $M_{\pi }$ data from [31] with $M_K=604\mathrm{MeV}$. The right figure shows the data from [32] along the $SU(3)$ singlet line for $g_{A,3}^{{\mathrm{\Sigma }}^{+}}/g_{A,3}^P$ (blue) and $g_{A,3}^{{\mathrm{\Xi }}^0}/g_{A,3}^P$ (green). We also plot the LO contribution as obtained from the full $p^3$ fit, dashed line, as well as the LO results of Sec. 4a, dotted line.

Figure 5

Chiral convergence of the AV charges. We show the ratio of NLO contributions over the LO one for the $g_{A,3}^X$ of the proton (red), ${\mathrm{\Sigma }}^{+}$ (blue) and ${\mathrm{\Xi }}^0$ (green) as function of $M_{\pi }$.