From: "Hitoshi Murayama" To: "Teruki Kamon" Cc: "Hitoshi Murayama" Subject: references Date: Monday, June 30, 2008 9:20 AM Teruki, It was nice to see you in Seoul. I was very impressed by the prospect of looking for "delayed photons" by a picosend time scale. The motivation to look for ultralight gravitino from cosmology is originally discussed in Cosmological constraints on the light stable gravitino. T. Moroi, H. Murayama, Masahiro Yamaguchi (Tohoku U.) . TU-424, Jan 1993. 14pp. Published in Phys.Lett.B303:289-294,1993. It shows tight upper limits on the reheating temperature for gravitino mass above keV, with little constraint below keV. More recent cosmological data using Lyman alpha further strengthens the limit to 16 eV, Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman-alpha forest. Matteo Viel (Cambridge U., Inst. of Astron.) , Julien Lesgourgues (Annecy, LAPTH & INFN, Padua) , Martin G. Haehnelt (Cambridge U., Inst. of Astron.) , Sabino Matarrese (Padua U. & INFN, Padua) , Antonio Riotto (INFN, Padua) . DFPD-05-08, LAPTH-1086-05, Jan 2005. 10pp. Published in Phys.Rev.D71:063534,2005. e-Print: astro-ph/0501562 But many people feel Lyman alpha analysis at this moment is not reliable enough. I would say the limit is around 100 eV. The wide range of models that allow for such ultralight gravitino was proposed in Simple Scheme for Gauge Mediation. Hitoshi Murayama, Yasunori Nomura (LBL, Berkeley & UC, Berkeley) . UCB- PTH-07-03, LBNL-62350, Jan 2007. 13pp. Published in Phys.Rev.D75:095011,2007. e-Print: hep-ph/0701231 and its cosmological metastability confirmed by Stability of Metastable Vacua in Gauge Mediated SUSY Breaking Models with Ultra Light Gravitino. Junji Hisano, Minoru Nagai, Masato Senami, Shohei Sugiyama (Tokyo U., ICRR) . Aug 2007. 11pp. Published in Phys.Lett.B659:361-366,2008. e-Print: arXiv:0708.3340 [hep-ph] The lifetime of neutralino into gravitino+photon was discussed (despite the lack of models) a while back in Experimental signatures of low-energy gauge mediated supersymmetry breaking. Savas Dimopoulos (Stanford U., Phys. Dept. & CERN) , Michael Dine (UC, Santa Cruz) , Stuart Raby (Ohio State U.) , Scott D. Thomas (SLAC) . SLAC-PUB-7104, SCIPP-96-08, Jan 1996. 10pp. Published in Phys.Rev.Lett.76:3494-3497,1996. e-Print: hep-ph/9601367 For the nominal choice of parameters in Eq. (3.4), you find 0.4 picosecond lifetime. Note, however, the strong dependence on the neutralino mass and gravitino mass (through Eq. (3.1)). I hope this helps. Hitoshi Murayama Director, Institute for the Physics and Mathematics of the Universe, University of Tokyo 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8568, Japan Tel: +81-4-7136-5952 FAX: +81-4-7136-4941 director@ipmu.jp MacAdams Professor of Physics, University of California, Berkeley, CA 94720 Tel: +1-510-642-1019 FAX: +1-510-643-8497 hitoshi@berkeley.edu Faculty Senior Staff, Lawrence Berkeley National Laboratory, MS 50A-5104, Berkeley, CA 94720 Tel: +1-510-486-6659 FAX: +1-510-486-6808 murayama@lbl.gov