Addendum to “Solar neutrino oscillation parameters after first KamLAND results”

In a previous paper, we presented a three-flavor oscillation analysis of the solar neutrino measurements and of the first data from the KamLAND experiment, in terms of the relevant mass-mixing parameters (δm²,θ₁₂,θ₁₃). The analysis, performed by including the terrestrial neutrino constraints coming from the CHOOZ (reactor), KEK-to-Kamioka (K2K, accelerator), and Super-Kamiokande (SK, atmospheric) experiments, provided a stringent upper limit on θ₁₃, namely, sin²θ₁₃<0.05 at 3σ. We reexamine such an upper bound in light of a recent (although preliminary) reanalysis of atmospheric neutrino data performed by the SK Collaboration, which seems to shift the preferred value of the largest neutrino square mass difference Δm² downwards. By taking the results of the SK official reanalysis at face value, and by repeating the analysis of our previous paper with such new input, we find that the upper bound on θ₁₃ is somewhat relaxed: sin²θ₁₃<0.067 at 3σ. Related phenomenological issues are briefly discussed.