Hier wird Wissen Wirklichkeit 1 Gravitational Radiation From Ultra High Energy Cosmic Rays In Models With Large Extra Dimensions Benjamin Koch ITP&FIGSS/University of Frankfurt

Hier wird Wissen Wirklichkeit 2 Outline The ADD model High energetic cosmic rays Gravitational radiation from elastic scattering Energy loss of high energetic cosmic rays Summary

Hier wird Wissen Wirklichkeit 3 Motivation: Why is?

Hier wird Wissen Wirklichkeit 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...

Hier wird Wissen Wirklichkeit 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);

Hier wird Wissen Wirklichkeit 6 Matching Newtons law: : : Newton with LXDs: Newton as we know him: Matching:

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

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

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

Hier wird Wissen Wirklichkeit 10 Einsteins equations Notation:M,N..: 1..(4+d),..: 1..4 (M)=(t,x,y) MN =diag(1,-1,-1,-1,-1...) with

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

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

Hier wird Wissen Wirklichkeit 13 Gravitational wave in d-dimensions III - solve equation of motion with Greens function*: *

Hier wird Wissen Wirklichkeit 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,

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

Hier wird Wissen Wirklichkeit 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:

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

Hier wird Wissen Wirklichkeit 18 Integrated energy loss (problems) description via Mandelstam variables only valid for =k 0 <<P 0 problems from collinear infinities: regularized either by proton mass m p or by gravitational radiation pointing into extra dimensions k d therefore extra dimensional case simpler than 3 dimensional

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

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

Hier wird Wissen Wirklichkeit 21 Differential energy loss of a propagating proton

Hier wird Wissen Wirklichkeit 22 Differential energy loss of a propagating proton

Hier wird Wissen Wirklichkeit 23 Relative energy loss Add energy loss to air shower simulation code SENECA*: *

Hier wird Wissen Wirklichkeit 24 Reconstructed flux

Hier wird Wissen Wirklichkeit 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

Hier wird Wissen Wirklichkeit 26 Outlook

Hier wird Wissen Wirklichkeit 27 Backups:

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

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

Hier wird Wissen Wirklichkeit 30 Loss for compactification (example d=6): - For compacification 1/(x ) can not simply be dropped:

Hier wird Wissen Wirklichkeit 31 Matching from einstein Hilbert: