  We develop a model that describes the gamma p -> K^+ pi Sigma reaction in the
Lambda(1405) region. The model consists of gauge invariant photo-production
mechanisms, and the chiral unitary model that gives the rescattering amplitudes
where Lambda(1405) is contained. The model also contains phenomenological
parameters, associated with short-range dynamics, to be used in fitting data.
We successfully fit recent CLAS data for the pi-Sigma invariant mass
distributions (line-shape) in the gamma p -> K^+ pi Sigma reaction for all the
charge states. We find that the higher mass pole for Lambda(1405) of the chiral
unitary model plays an important role in the reaction. We also find the
non-resonant background contribution is not negligible, and its sizable effect
shifts the Lambda(1405) peak position by several MeV. 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).
