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RS model with a small curvature and inclined air showers

RS model with a small curvature and inclined air showers. Alexandre Kisselev (IHEP, Russia). XXth Rencontres de Blois “Challenges in Particle Astrophysics” Chateau de Blois, France, 18th-23rd May 200 8. SUMMARY. Randall- Sundrum model with the small curvature

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RS model with a small curvature and inclined air showers

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  1. RS model with a small curvature and inclined air showers AlexandreKisselev (IHEP, Russia) XXth Rencontres de Blois “Challenges in Particle Astrophysics” Chateau de Blois, France, 18th-23rd May 2008

  2. SUMMARY • Randall-Sundrum model with the small curvature • Trans-Planckian scattering of SM fields on the brane • Cosmic neutrino-nucleon interactions at ultra-high energies • Conclusions

  3. WarpedExtra Dimension with the Small Curvature Background (AdS5 ) metric (Randall & Sundrum, 1999) - Minkowski tensor - radius of ED Hierarchy relation - Planck mass - gravity scale in 5 dimensions

  4. Gravity lives in the bulk Gravity Planck brane TeV brane SM SM fields are confined to the TeV brane

  5. Gravitational 5-dimensional field (M, N = 0, 1…4) Kaluza-Klein (KK ) gravitons Radion (scalar) field - graviton masses

  6. Interaction Lagrangian on the TeV brane physical scale Large curvature option series of massive resonances

  7. Small curvature option (Giudice et al., 2004, Kisselev & Petrov, 2005) narrow low-mass resonances with the small mass splitting Formal relation to gravity in flat space-time with one compact ED is the radius of ED

  8. Lower bounds on gravity scale M5 (LEP) (DELPHI Coll., 2006) (Tevatron) (Kisselev, 2008) LHC search limit: (for L = 30 fb-1)

  9. Trans-Planckian Scattering on the Brane (Kisselev & Petrov, 2005) eikonal approximation Kinematical region t - 4-momentum transfer Born amplitude is the sum of the reggeized gravitons in t-channel Gravi-Reggeons: - string tension

  10. Gravitational amplitude i … + + j sum of gravi-reggeons i,j - SM fields (q, g, l, n...) (for all SM fields)

  11. Neutrino-nucleon Interactions at Ultra-high Energies n n i i i i p p

  12. Differential cross section - inelasticity Amplitude Eikonal

  13. Skewed (t-dependent) parton distribution - standard distributions parameters of the hard Pomeron is used (Petrov & Prokudin, 2002)

  14. Number of neutrino induced air showers - shower energy - shower energy Effective aperture for neutrinos flux attenuation detector efficiency Neutrino bound (Pierre Auger Coll., 2007)

  15. (detector efficiency for Auger) (for hadronic showers) (for electromagnetic showers) (Anchordoqui et al., JCAP,2005)

  16. Inclined neutrino induced air showers (Berezinsky, Zatsepin & Smirnov, 1969/1975) Expected rate at the Auger Observatory (in yr-1) Flavor ratio on Earth: 1:1:1 SM: 0.08 events per year (W-B)

  17. CONCLUSIONS • In the RS model with the small curvature KK graviton contributions could be comparable or even larger than SM contributions • Trans-Planckian gravity induced scattering of brane fields is given by the infinite sum of t-channel reggeized gravitons (gravi-reggeons) • Gravity effects from ED are large enough to be measured in ultra-high-energy neutrino-nucleon inclined events at the Pierre Auger Observatory

  18. Back Up Slides

  19. RS model with the small curvature is not similar to a model with one large ED of the size For instance, can be realized only for d- is the number of ED’s solar distance • strongly limited by • astrophysical bounds

  20. Background RS metric (Randall & Sundrum, 1999) Four-dimensional gravitational action of gravitational field in the RS model: (Boos et al., 2002) Expression is not covariant: indices are raised with the Minkowski tensor while the metric is

  21. Change of variables:

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