1. Studying Very Light Gravitino at ILC Collaborators: T. Moroi (Tokyo) [for basic idea: arXiv:1104.3624] & K. Fujii (KEK), T. Moroi (Tokyo), T. Suehara (ICEPP) [for realistic evaluations.] Shigeki Matsumoto (IPMU) Q. Is it possible to study the property of the very light gravitino ( ～ O(10) eV) at the ILC? A. Yes it is by observing the distribution of the impact parameter, which is obtained by the decay products of the stau NLSP!

2. The Gravitino LSP Very Light Gravitino, whose mass is O(1)-O(10) eV, is quite attractive from the viewpoint of Cosmology! Gravitino = Super partner of Graviton! Its spin is 3/2! Gravitino Mass = /M pl /3 1/2, & = SUSY breaking scale! Its interactions are suppressed by 1/ ～ 1/(M pl m 3/2 ) T. Moroi, hep-ph/9503210 1/6 10 –8 10 –9 10 –10 10 –11 10 –12 10 –13 10 –7 Structure Formation of Universe LEP, SN cooling Vacuum Stability

3. What happens at the ILC? We focus on the case that the NLSP is Stau! 2/6 Next Lightest Supersymmetric Particle (NLSP) is living long! How long?   ～ 100 x M pl 2 x m 3/2 2 /m NLSP 5 ～ O(10 –13 ) sec.  c  ～ 100  m !!! (Decay length is not long!) Prod. Decay! 1st layer NLSP 16mm e + e –  Stau pair

4. Impact Parameter  3/6 Gravitino Stau  Impact parameter  is one of convenient quantities to measure the lifetime of the NLSP in such a circumstance. Signal & Background processes [Signal] e + e –  +  – [  -BG] e + e – e + e –  e + e –  +  – Hadronic decay (p ±, K ±, etc.) ~ ~ (+ ISR) Impact parameter 

5. Kinematical Cuts 4/6 100% efficiency for tagging and no contamination assumed. ① To reduce  -BG. Tagging forward e ± will also be useful. (E vis = Total energy of charged particles.) ② (  = Scattering angle of the  -jet.) , W, and Z in BG are likely to be produced with high rapidity. ③ (  = Azimuthal angle of the  -jet.) (L-lim.) Two  s in [  -BG] are almost back-to-back even w/ ISR. (U-lim.) To reduce  leptons from the Z boson decay. ④ ( is the momentum of isolated  (> 30 GeV)) Two  s and isolated  in [  -BG] should be on one plane. ⑤ Stau Mass = 120 GeV Luminosity = 100 fb -1 CM Energy = 500 GeV

6. Results 5/6 BG Stau Mass = 120 GeV CME = 500 GeV Stau Mass = 120 GeV CME = 500 GeV Lum = 100 fb -1 Bin size = 20  m (0mm <  < 2mm) & &

7. Summary & Discussions 6/6 Stau Mass = 120 GeV CME = 500 GeV Lum = 100 fb -1 It is possible to study the light gravitino with the mass of O(10) eV at the ILC. When the lifetime is longer than ～ 10 -14 sec, the lifetime can measured accurately. Information of the lifetime translated to the scale of the SUSY breaking. 1.How can be large the efficiency of the t-tagging? 2.Polarization of the incident e ± can reduce the BG? 3.Is there the effect of the magnetic field to detect the signal? 4.Changing the CME increases the significance to detect the signal? 5.3-prong decay of  can be used to detect the decay point?  Go to a full simulation with realistic detector setup.