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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 - PowerPoint PPT Presentation
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1 Hier wird Wissen Wirklichkeit
Gravitational Radiation FromUltra High Energy Cosmic Rays
In Models With Large Extra Dimensions
Benjamin Koch ITP&FIGSS/University of Frankfurt
2 Hier wird Wissen Wirklichkeit
Outline
• The ADD model
• High energetic cosmic rays
• Gravitational radiation from elastic scattering
• Energy loss of high energetic cosmic rays
• Summary
3 Hier wird Wissen Wirklichkeit
Motivation:
Why is?
4 Hier wird Wissen Wirklichkeit
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 Hier wird Wissen Wirklichkeit
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 Hier wird Wissen Wirklichkeit
Matching Newtons law:
:
:
Newton with LXDs:
Newton as we know him: Matching:
7 Hier wird Wissen Wirklichkeit
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
8 Hier wird Wissen Wirklichkeit
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
9 Hier wird Wissen Wirklichkeit
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
10 Hier wird Wissen Wirklichkeit
Einsteins equations
Notation: M,N..: 1..(4+d),..: 1..4(M)=(t,x,y)MN=diag(1,-1,-1,-1,-1...)
with
11 Hier wird Wissen Wirklichkeit
Gravitational wave in d-dimensions I
- Ansatz:
- Into Einstein equations gives:
with:
still complicated but...
12 Hier wird Wissen Wirklichkeit
Gravitational wave in d-dimensions II
- equation of motion:
- use gauge invariance & choose coordinate system: (harmonic gauge)
- obtain simplified equation of motion:
13 Hier wird Wissen Wirklichkeit
Gravitational wave in d-dimensions III
- solve equation of motion
with Greens function*:
*
14 Hier wird Wissen Wirklichkeit
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 Hier wird Wissen Wirklichkeit
Energy of a gravitational wave
- Polarization gives energy momentum tensor of the gravitational wave:
-Use this to derive formula for energy radiation
16 Hier wird Wissen Wirklichkeit
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 Hier wird Wissen Wirklichkeit
Integrated energy loss
integrate over d-sphere and 3-sphere separately
use Mandelstam variables for 2 to 2 processes:
18 Hier wird Wissen Wirklichkeit
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
19 Hier wird Wissen Wirklichkeit
Integrated energy lossfound solutions for t0 , t=s/2 and t =s.
Solution for small momentum transfer t0 is:
20 Hier wird Wissen Wirklichkeit
Integrated energy loss
to obtain energy loss for a given physicalprocess need differential cross sectionof this process
physical boundary condition:
*
*
21 Hier wird Wissen Wirklichkeit
Differential energy loss of a propagating proton
22 Hier wird Wissen Wirklichkeit
Differential energy loss of a propagating proton
23 Hier wird Wissen Wirklichkeit
Relative energy loss
Add energy loss to air shower simulation codeSENECA*:
*
24 Hier wird Wissen Wirklichkeit
Reconstructed flux
25 Hier wird Wissen Wirklichkeit
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 Hier wird Wissen Wirklichkeit
Outlook
27 Hier wird Wissen Wirklichkeit
Backups:
28 Hier wird Wissen Wirklichkeit
Boundary conditions
Energy momentumtensor of standard modelparticles:
Periodicity:
gives for d=1:
General KK gravitonslook like massive:
29 Hier wird Wissen Wirklichkeit
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)
30 Hier wird Wissen Wirklichkeit
Loss for compactification (example d=6):
- For compacification 1/(x) can not simply be dropped:
31 Hier wird Wissen Wirklichkeit
Matching from einstein Hilbert: