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

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

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Gravitational Radiation FromUltra High Energy Cosmic RaysIn 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
- Energy loss of high energetic cosmic rays
- Summary

Motivation:

Why is?

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 ...

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);

- 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 LXDsMeV 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

of graviton emission on this

spectrum?

- Could graviton emission help

to explain one of these questions?

High energetic cosmic raysFluxes of cosmic rays:

incoming particle # versus energy

Lots of open questions:

- origin

- shape (knee, ankle)

- highest energies

GZK cutoff

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

Einsteins equations

Notation: M,N..: 1..(4+d)

,..: 1..4

(M)=(t,x,y)

MN=diag(1,-1,-1,-1,-1...)

with

Gravitational wave in d-dimensions I

- Ansatz:

- Into Einstein equations gives:

with:

still complicated but...

Gravitational wave in d-dimensions II

- equation of motion:

- use gauge invariance & choose coordinate system:

(harmonic gauge)

- obtain simplified equation of motion:

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

Energy of a gravitational wave

- Polarization gives energy momentum tensor of

the gravitational wave:

-Use this to derive formula for energy radiation

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:

Integrated energy loss

integrate over d-sphere and 3-sphere separately

use Mandelstam variables for 2 to 2 processes:

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

Integrated energy loss

found solutions for t0 , t=s/2 and t =s.

Solution for small momentum transfer t0 is:

Integrated energy loss

to obtain energy loss for a given physical

process need differential cross section

of this process

*

physical boundary condition:

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

Boundary conditions

Energy momentum

tensor of standard model

particles:

Periodicity:

gives

for d=1:

General KK gravitons

look like massive:

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)

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