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Using GRB Neutrinos to search for Lorentz Invariance Violation

Using GRB Neutrinos to search for Lorentz Invariance Violation. IJC 5/14/08 Erik Strahler. Some Quantum Gravitiy theories (i.e. brane-world) give rise to Lorentz Invariance Violation (LIV). Happens at some (high) energy Scale E QG p 2 c 2 =E 2 becomes p 2 c 2 =E 2 [1+f(E/E QG )]

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Using GRB Neutrinos to search for Lorentz Invariance Violation

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

  2. Some Quantum Gravitiy theories (i.e. brane-world) give rise to Lorentz Invariance Violation (LIV). • Happens at some (high) energy Scale EQG • p2c2=E2becomes p2c2=E2[1+f(E/EQG)] • EQGis expected to be very large (~Epl = 1019 GeV)

  3. So, E << EQGand 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. 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

  7. 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

  8. 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 080319B gives a better photon limit?

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