Gravitational radiation from ultra high energy cosmic rays in models with large extra dimensions
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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
Gravitational Radiation FromUltra High Energy Cosmic RaysIn Models With Large Extra Dimensions

  • Benjamin Koch ITP&FIGSS/University of Frankfurt


Outline
Outline

  • The ADD model

  • High energetic cosmic rays

  • Gravitational radiation from elastic scattering

  • Energy loss of high energetic cosmic rays

  • Summary


Motivation
Motivation:

Why is?


Models with lxd s
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
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);


Matching newtons law

:

:

Matching Newtons law:

Newton with LXDs:

Matching:

Newton as we know him:


Observables of lxd s

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


High energetic cosmic rays

- 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


Energy reconstruction in cosmic rays

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


Einsteins equations
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
Gravitational wave in d-dimensions I

- Ansatz:

- Into Einstein equations gives:

with:

still complicated but...


Gravitational wave in d dimensions ii
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 iii
Gravitational wave in d-dimensions III

- solve equation of motion

with Greens function*:

*


Gravitational wave in d dimensions iv
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
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 wave1
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
Integrated energy loss

integrate over d-sphere and 3-sphere separately

use Mandelstam variables for 2 to 2 processes:


Integrated energy loss problems
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 loss1
Integrated energy loss

found solutions for t0 , t=s/2 and t =s.

Solution for small momentum transfer t0 is:


Integrated energy loss2

*

Integrated energy loss

to obtain energy loss for a given physical

process need differential cross section

of this process

*

physical boundary condition:




Relative energy loss
Relative energy loss

Add energy

loss to air shower

simulation code

SENECA*:

*



Summary
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
Boundary conditions

Energy momentum

tensor of standard model

particles:

Periodicity:

gives

for d=1:

General KK gravitons

look like massive:


The lagrangian
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)


Loss for compactification example d 6
Loss for compactification (example d=6):

- For compacification 1/(x) can not

simply be dropped:



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