We present new Herschel PACS observations of 32 T Tauri stars in the young ($sim$3 Myr) $sigma$ Ori cluster. Most of our objects are K & M stars with large excesses at 24 $mu$m. We used irradiated accretion disk models of DAlessio et al. (2006) to compare their spectral energy distributions with our observational data. We arrive at the following six conclusions. (i) The observed disks are consistent with irradiated accretion disks systems. (ii) Most of our objects (60%) can be explained by significant dust depletion from the upper disk layers. (iii) Similarly, 61% of our objects can be modeled with large disk sizes ($rm R_{rm d} geq$ 100 AU). (iv) The masses of our disks range between 0.03 to 39 $rm M_{Jup}$, where 35% of our objects have disk masses lower than 1 Jupiter. Although these are lower limits, high mass ($>$ 0.05 M$_{odot}$) disks, which are present e.g, in Taurus, are missing. (v) By assuming a uniform distribution of objects around the brightest stars at the center of the cluster, we found that 80% of our disks are exposed to external FUV radiation of $300 leq G_{0} leq 1000$, which can be strong enough to photoevaporate the outer edges of the closer disks. (vi) Within 0.6 pc from $sigma$ Ori we found forbidden emission lines of [NII] in the spectrum of one of our large disk (SO662), but no emission in any of our small ones. This suggests that this object may be an example of a photoevaporating disk.
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