1. Using GRB Neutrinos to search for Lorentz Invariance Violation
IJC 5/14/08
Erik Strahler

2. Some Quantum Gravitiy theories (i. e
Some Quantum Gravitiy theories (i.e. brane-world) give rise to Lorentz Invariance Violation (LIV).
Happens at some (high) energy Scale EQG
p2c2=E2 becomes p2c2=E2[1+f(E/EQG)]
EQG is expected to be very large (~Epl = 1019 GeV)

3. So, E << EQG and we do a series expansion
n is the order of the expansion. For some models, odd n are disallowed. Only the largest term will be important. So we look at n=1 and n=2 cases.

4. Write down Hamiltonian and set v = dH/dp
Gives LIV term to the velocity, and thus a time delay between particles of differing energies.
See Biesiada and Piorkowska for a nice derivation

5. Current limits from observations of photon arrival times from GRB, AGN, and SNR give
To improve limits, need things far away and with higher Energies.
GRB neutrinos! E~100 TeV, z~.3-6

6. Look for neutrinos from direction of GRB
Cut to neutrino level
Look for neutrinos from direction of GRB
If time delay between neutrino and burst time is less than time you’d expect to see an atmospheric neutrino, you can associate it with the GRB
This is highly energy dependent

9. Limits from photon sources should be factor ~2 better due to them not taking comoving distance into account.
Need a good energy estimator.
Time delay is dependent on your input cosmology

13. Would be interesting to independently calculate these numbers and see what IceCube can do here.
What is the effect of our energy uncertainty on this measurement?
Would need several GRB neutrino detections.
I wonder if anyone is seeing if B gives a better photon limit?