Recent CLAS data for the pi Sigma invariant mass distributions (line-shapes) in the gamma p -> K^+ pi Sigma reaction are theoretically investigated. The line-shapes have peaks associated with the Lambda(1405) excitation. Our model consists of gauge invariant photo-production mechanisms, and the chiral unitary model that gives the rescattering amplitudes where Lambda(1405) is contained. It is found that, while the pi Sigma line-shape data in the Lambda(1405) region are successfully reproduced by our model for all the charge states, the production mechanism is not so simple that we need to introduce parameters associated with short-range dynamics to fit the data. Our detailed analysis suggests that the nonresonant background contribution is not negligible, and its sizable effect shifts the Lambda(1405) peak position by several MeV. We also analyze the data using a Breit-Wigner amplitudes instead of those from the chiral unitary model. We find that the fitted Breit-Wigner parameters are closer to the higher pole position for Lambda(1405) of the chiral unitary model. This work sets a starting point for a fuller analysis in which line-shape as well as K^+ angular distribution data are simultaneously analyzed for extracting Lambda(1405) pole(s).
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