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Register a new userThe possible $Sigma^0$-$Lambda$ mixing in QCD sum rules
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Shi-Lin Zhu
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We calculate the on-shell $Sigma^0$-$Lambda$ mixing parameter $theta$ with the method of QCD sum rule. Our result is $theta (m^2_{Sigma^0}) =(-)(0.5pm 0.1)$MeV. The electromagnetic interaction is not included.
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The $Sigma$--$Lambda$ mixing angle is calculated in framework of the QCD sum rules. We find that our prediction for the mixing angle is $(1.00pm 0.15)^0$ which is in good agreement with the quark model prediction, and approximately two times larger than the recent lattice QCD calculations.
The method of QCD sum rules in the presence of external elctromagnetic fields is used to calculate the $Omega$ magnetic moment $mu_{Omega^-}$ and $Sigma^0$-$Lambda$ transition magnetic moment $mu_{Sigma^0Lambda}$, with the susceptibilities obtained previously from the study of octet baryon magnetic moments. The results $mu_{Omega^-}=-1.92mu_N$ and $mu_{Sigma^0Lambda}=1.5mu_N$ are in good agreement with the recent experimental data.
We evaluate the pion-nucleon and the pion-Delta sigma terms by employing the method of quantum chromodynamics (QCD) sum rules. The obtained value of the pion-nucleon sigma term is compatible with the larger values already anticipated by the recent calculations. It is also found that the pion-Delta sigma term is as large as the pion-nucleon sigma term.
We calculate the isoscalar axial-vector coupling constants of the Lambda hyperon using the method of QCD sum rules. A determination of these coupling constants reveals the individual contributions of the u, d and the s quarks to the spin content of Lambda. Our results for the light-quark contributions are in agreement with those from experiment assuming flavor SU(3). We also find that the flavor-SU(3)-breaking effects are small and the contributions from the u and the d quarks to the Lambda polarization are negatively polarized as in the flavor-SU(3) limit.
We analyze the mixing between $Sigma^0$ and $Lambda^0$ based on the baryon masses. We distinguish the contributions from QCD and QED in the baryon mass splittings. We find that the mixing angle between $Sigma^0$ and $Lambda^0$ is $(2.07pm 0.03)times 10^{-2} $, which leads to the decay branching fraction and up-down asymmetry of $Lambda_c^+ to Sigma^0 e^+ u_e$ to be ${cal B}(Lambda_c^+ to Sigma^0 e^+ u_e)=(1.5pm 0.2)times 10^{-5}$ and $alpha(Lambda_c^+ to Sigma^0 e^+ u_e)=-0.86pm 0.04$, respectively. Moreover, we obtain that $Delta {cal B}equiv {cal B}(Lambda_c^+to Sigma^0 pi^+) - {cal B}(Lambda_c^+to Sigma^+pi^0)=(3.8pm 0.5)times 10^{-4}$ and $Delta alpha equivalpha(Lambda_c^+to Sigma^0 pi^+) -alpha(Lambda_c^+to Sigma^+pi^0)=(-1.6pm 0.7)times10^{-2}$, which should vanish without the mixing.
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