gravitational radiation from ultra high energy cosmic rays in models with large extra dimensions

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Gravitational Radiation FromUltra 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

• 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);


Matching Newtons law:

:

:

Newton with LXDs:

Newton as we know him: Matching:


Observables of LXDs

Strongest constraintson R for all d

More than 1 XDNewton checked to mrange

400 TeV ultra highenergetic cosmic rays

14 TeV Large Hadron Collider LHC

TeV region todayscolliders

MeV regionsupernova and neutron star cooling

Measuring Newtons law

CM Energy

Possible observables:- microscopic black holes

- graviton production-modified cross sectionsmissing ET


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


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 XDsis not in the simulation code-> reconstruction modified-> shape of spectrum might change

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 III

- solve equation of motion

with Greens function*:

*


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 gravitationalradiation pointing into extra dimensions kd

therefore extra dimensional case simpler than 3 dimensional


Integrated energy lossfound 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 physicalprocess need differential cross sectionof this process

physical boundary condition:

*

*


Differential energy loss of a propagating proton


Relative energy loss

Add energy loss to air shower simulation codeSENECA*:

*


Reconstructed flux


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


Outlook


Backups:


Boundary conditions

Energy momentumtensor of standard modelparticles:

Periodicity:

gives for d=1:

General KK gravitonslook like massive:


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)


Loss for compactification (example d=6):

- For compacification 1/(x) can not simply be dropped:


Matching from einstein Hilbert:

gravitational radiation from ultra high energy cosmic rays in models with large extra dimensions

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