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Alexandre Kisselev IHEP ( Protvino , Russia)

Scattering in the RS model with the small curvature. Alexandre Kisselev IHEP ( Protvino , Russia). IXth INTERNATIONAL SCHOOL-SEMINAR “THE ACTUAL PROBLEMS OF MICROWORLD PHYSICS ” Belarus, Gomel, July 2 3 - August 3 , 200 7. SUMMARY. Warped extra dimension (ED)

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Alexandre Kisselev IHEP ( Protvino , Russia)

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  1. Scattering in the RS model with the small curvature AlexandreKisselev IHEP (Protvino, Russia) IXth INTERNATIONAL SCHOOL-SEMINAR “THE ACTUAL PROBLEMS OF MICROWORLD PHYSICS ” Belarus, Gomel, July 23 -August 3, 2007

  2. SUMMARY • Warped extra dimension (ED) with the small curvature • AdS5 metric vs. flat metric with one compact ED • Virtual graviton effects in the Bhabha scattering • Trans-Planckian scattering on the brane • Neutrino-nucleon interactions at ultra-high energies • Conclusions

  3. WarpedExtra Dimension Scenario with the Small Curvature Background (AdS5 ) metric - Minkowski tensor is the 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 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, 2005/6) 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. AdS5 Metric vs. Flat Metric with One Compact ED RS model with the small curvature is not equivalent to a model with one large ED of the size For instance, can be realized only for is the number of ED’s solar distance - strongly limited by astrophysical bounds

  9. Hierarchy relation in d flat ED’s (D=4+d) Limiting case of a similar relation for the warped metric

  10. Virtual s-channel KK Gravitons Scattering of SM fields mediated by graviton exchange For instance Energy region:

  11. Matrix element of the process: Tensor part of the graviton propagator where Energy-momentum tensor Zero width continuous mass distribution approximation (Giudice et al., 2005)

  12. Widths of the KK gravitons: S(s) can be calculated analytically by using (Kisselev, 2006) where

  13. Some consequences: with In trans-Planckian energy region zero width result is reproduced namely, at

  14. Is the mass splitting small enough for mass distribution to be continuous? relevant 0r, equivalently, ADD model:

  15. Search for one ED (DELPHI) (Klein, ICHEP 2006) Photon energy spectrum in single photon events: Main background: (reduced gravity scale)

  16. (gravity+ SM )/SM ratio in two schemes (A.K. vs. zero width approximation) (Kisselev, 2007)

  17. The same as on previous slide but collision energy and gravity scale are larger

  18. The same as on previous slide except for the curvature

  19. The same energy as on previous slide but the gravity scale and curvature are different

  20. The same as on previous slide but the curvature is slightly different

  21. Trans-Planckian Scattering on the Brane (Kisselev & Petrov, 2005/6) Kinematical region eikonal approximation is 4-momentum transfer Born amplitude is the sum of the reggeized gravitons in t-channel Gravi-Reggeons: - string tension

  22. Gravitational amplitude i … + + + j Gravi-Reggeon i,j - SM fields (q, g, l, n…) (for all SM fields)

  23. Imaginary part of the eikonal One has to calculate the sum with At  << M5 , we obtain - gravitational radius

  24. Fields are weakly coupled to gravity: for small The summation of t-channel reggeized gravitons eikonal with no explicit dependence on the brane scale and curvature Radion production is strongly suppressed

  25. Neutrino-nucleon Interactions at Ultra-high Energies i i i i p p

  26. Gravitational amplitude Skewed (t-dependent) parton distribution • standard distribution • of parton i parameters of the hard Pomeron is used (Petrov & Prokudin, 2002)

  27. Differential cross section - neutrino energy fraction deposited to the proton

  28. Inelastic neutrino-proton cross sections dotted curve: SM (cc) cross section

  29. Detectionof quasi-horizontal showers by theAuger Observatory (Berezinsky, Zatsepin, Smirnov, 1969/75)

  30. Expected rate for quasi-horizontal air showers at the Auger Observatory ( Zenith angle > 70º ) Waxman-Bahcall neutrino flux 4.9 per year 1.6 per year 0.22 per year SM: (Anchordoqui et al., 2005)

  31. CONCLUSIONS • In the RS model with the small curvature virtual graviton contributions to the Bhabha scatteringat the LCcould be significantly larger than SM ones • Trans-Planckian gravity induced scattering of thebrane fields is given by an infinite sum of t-channel reggeized gravitons (gravi-Reggeons) • Gravity effects from extra dimension are large enough to be measured in ultra-high-energy neutrino-nucleon events by the Auger detectors

  32. р. Сож

  33. Back Up Slides

  34. 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: the indices are raised with the Minkowski tensor wheares the metric is

  35. Hierarchy relation: Hierarchy problem remains unsolved ! Change of variables:

  36. Neutrino-proton interaction vs. black hole production solid curves: dashed curves:

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