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Gravitational Radiation From Ultra High Energy Cosmic Rays In Models With Large Extra Dimensions

Gravitational Radiation From Ultra High Energy Cosmic Rays In Models With Large Extra Dimensions. Benjamin Koch ITP&FIGSS/University of Frankfurt. Outline. The ADD model High energetic cosmic rays Gravitational radiation from elastic scattering

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Gravitational Radiation From Ultra High Energy Cosmic Rays In Models With Large Extra Dimensions

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  1. Gravitational Radiation FromUltra High Energy Cosmic RaysIn Models With Large Extra Dimensions • Benjamin Koch ITP&FIGSS/University of Frankfurt

  2. Outline • The ADD model • High energetic cosmic rays • Gravitational radiation from elastic scattering • Energy loss of high energetic cosmic rays • Summary

  3. Motivation: Why is?

  4. Models with LXDs Main motivation hierarchy problem: Why is gravitation so weak? String theory suggests XDs but it is hard to make predictions • Effective theories with LXDs: • Arkani-Hamed, Dimopoulos & Dvali (ADD) • Randall & Sundrum (RS) • Universal Extra Dimensions (UXD) • Warped and more ...

  5. The ADD model • 3+d space like dimensions • d dimensions on d-torus with radii R • only gravity propagates in all dimensions (bulk) • all other in 4-dim. space time (brane) N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Lett. B 429, 263 (1998);

  6. : : Matching Newtons law: Newton with LXDs: Matching: Newton as we know him:

  7. Possible observables: - microscopic black holes - graviton production- modified cross sections missing ET More than 1 XD Newton checked to m range Strongest constraints on R for all d Observables of LXDs MeV region supernova and neutron star cooling 400 TeV ultra high energetic cosmic rays CM Energy 14 TeV Large Hadron Collider LHC Measuring Newtons law TeV region todays colliders

  8. - What would be the influence of graviton emission on this spectrum? - Could graviton emission help to explain one of these questions? High energetic cosmic rays Fluxes of cosmic rays: incoming particle # versus energy Lots of open questions: - origin - shape (knee, ankle) - highest energies GZK cutoff

  9. Idea: graviton that escapes into XDs is not in the simulation code -> reconstruction modified -> shape of spectrum might change Energy reconstruction in cosmic rays - Not observed directly: detector array measures secondary particles and rays that reach ground. Comparison to numerical simulation  energy reconstruction Need cross section for gravitational radiation

  10. Einsteins equations Notation: M,N..: 1..(4+d) ,..: 1..4 (M)=(t,x,y) MN=diag(1,-1,-1,-1,-1...) with

  11. Gravitational wave in d-dimensions I - Ansatz: - Into Einstein equations gives: with: still complicated but...

  12. Gravitational wave in d-dimensions II - equation of motion: - use gauge invariance & choose coordinate system: (harmonic gauge) - obtain simplified equation of motion:

  13. Gravitational wave in d-dimensions III - solve equation of motion with Greens function*: *

  14. Gravitational wave in d-dimensions IV - expand solution into spherical harmonics: for distances much greater than extension of the source (x>>y) only keep monopole term: with the following abreviations: , and

  15. Energy of a gravitational wave - Polarization gives energy momentum tensor of the gravitational wave: -Use this to derive formula for energy radiation

  16. Energy of a gravitational wave: - bring d to the left side and plug in everything we have result for 3+d dimensions obtained by: for d=0 first derived by Weinberg:

  17. Integrated energy loss integrate over d-sphere and 3-sphere separately use Mandelstam variables for 2 to 2 processes:

  18. Integrated energy loss (problems) description via Mandelstam variables only valid for =k0<<P0 problems from collinear infinities: regularized either by proton mass mp or by gravitational radiation pointing into extra dimensions kd therefore extra dimensional case simpler than 3 dimensional

  19. Integrated energy loss found solutions for t0 , t=s/2 and t =s. Solution for small momentum transfer t0 is:

  20. * Integrated energy loss to obtain energy loss for a given physical process need differential cross section of this process * physical boundary condition:

  21. Differential energy loss of a propagating proton

  22. Differential energy loss of a propagating proton

  23. Relative energy loss Add energy loss to air shower simulation code SENECA*: *

  24. Reconstructed flux

  25. Summary - In our optimistic scenario the flux reconstruction of high energetic cosmic rays will be significantly modified in if large extra dimensions exist. - Still this modification can not be used as explanation for: -knee -new cut of before GZK -disagreement between experiments thanks to Hajo Drescher, Marcus Bleicher, Stefan Hofmann

  26. Outlook

  27. Backups:

  28. Boundary conditions Energy momentum tensor of standard model particles: Periodicity: gives for d=1: General KK gravitons look like massive:

  29. The Lagrangian Notation: M,N..: 1..(4+d) ,..: 1..4 (M)=(t,x,y) Metric: Lagrangian: G. F. Giudice, R. Rattazzi and J. D. Wells, Nucl.\ Phys.\ B 544 (1999)

  30. Loss for compactification (example d=6): - For compacification 1/(x) can not simply be dropped:

  31. Matching from einstein Hilbert:

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