The K- p --> pi0pi0sigma0 reaction is studied within a chiral unitary model. The distribution of pi0sigma0 states forming the lambda(1405) shows, in agreement with a recent experiment, a peak at 1420 MeV and a relatively narrow width of gamma = 38 MeV. The mechanism for the reaction is largely dominated by the emission of a pi0 prior to the K- p interaction leading to the lambda(1405). This ensures the coupling of the lambda(1405) to the K- p channel, thus maximizing the contribution of the second state found in chiral unitary theories, which is narrow and of higher energy than the nominal lambda(1405). This is unlike the pi- p --> K0pisigma reaction, which gives more weight to the pole at lower energy and with a larger width. The data of these two experiments, together with the present theoretical analysis, provide firm evidence of the two-pole structure of the lambda(1405).
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