Detecting GRB ν’s –an Opportunity For Observing Lorentz Invariance Violation

Uri Jacob and Tsvi PiranThe Hebrew University

Jerusalem, Israel

ν

γ

Several quantum-gravity theories predict the Several quantum-gravity theories predict the break of the Lorentz symmetry when break of the Lorentz symmetry when approaching the Planck mass scaleapproaching the Planck mass scale

Despite the great affection for the Lorentz Despite the great affection for the Lorentz symmetry, it is a viable possibility that this is symmetry, it is a viable possibility that this is only an approximateonly an approximate

28c G 1 22 10 eV/ . .

A possible violationA possible violationof Lorentz invariance?of Lorentz invariance?

symmetry. There may symmetry. There may exist a more exist a more complete accurate complete accurate symmetry of nature symmetry of nature for which the Lorentz for which the Lorentz symmetry emerges as symmetry emerges as a very good a very good approximation for our approximation for our low-energy particle low-energy particle observations.observations.

Further motivation for investigating a possible Further motivation for investigating a possible deformation of the Lorentz symmetry is achieved deformation of the Lorentz symmetry is achieved by considering certain astrophysical observations.by considering certain astrophysical observations.

Observations at Earth of Ultra High Energy Observations at Earth of Ultra High Energy Cosmic Rays and to a lesser extent of multi TeV Cosmic Rays and to a lesser extent of multi TeV photons may present a paradox with standard photons may present a paradox with standard physics.physics.

It has been suggested in several works that a It has been suggested in several works that a violation of Lorentz invariance could explain violation of Lorentz invariance could explain these issues. Remarkably, this is the only these issues. Remarkably, this is the only mechanism found to resolve both apparent mechanism found to resolve both apparent paradoxes.paradoxes.

An incentive:An incentive:Lorentz invariance violation Lorentz invariance violation may resolve experimental may resolve experimental

paradoxesparadoxes

A phenomenological A phenomenological approachapproach

We consider here a simple phenomenological We consider here a simple phenomenological approach for Lorentz invariance deformation approach for Lorentz invariance deformation (LID) that can emerge as the low-energy (LID) that can emerge as the low-energy expansion of some theory which predicts the expansion of some theory which predicts the break of Lorentz symmetry at very high break of Lorentz symmetry at very high energies. With the Planck-scale motivation we energies. With the Planck-scale motivation we write the symmetry breaking energy scale as write the symmetry breaking energy scale as ξξEEplpl..

The leading order approximation for the The leading order approximation for the deformed dispersion relation is expected to deformed dispersion relation is expected to take the form:take the form:

n2 2 2 2 4 2

pl

EE p c m c E E

Validating or Validating or constraining the constraining the

new theoriesnew theories We would like to obtain observational evidence We would like to obtain observational evidence

or limits for the possible deviation from Lorentz or limits for the possible deviation from Lorentz symmetry.symmetry.

Astrophysical measurements allow us a reach Astrophysical measurements allow us a reach of much higher energies than laboratories, and of much higher energies than laboratories, and the cosmological time scales serve as the cosmological time scales serve as amplifiers.amplifiers.

Time-of-flight analyses of observational data Time-of-flight analyses of observational data from from γγ-ray bursts-ray bursts and and other energetic photon other energetic photon sources, searching for sources, searching for energy dependant energy dependant particle speeds that the LID phenomenology particle speeds that the LID phenomenology implies, were conducted by several groups over implies, were conducted by several groups over the last few years.the last few years.

Current statusCurrent status

No LID-induced time delays have yet been No LID-induced time delays have yet been observed.observed.

Hence we have lower bounds on the Hence we have lower bounds on the symmetry breaking scale – for the two symmetry breaking scale – for the two favored scenarios:favored scenarios:

n=1: n=1: ξξ11≳≳0.010.01

n=2: n=2: ξξ22≳≳1010-9-9

Our aim:Our aim:opening a new window opening a new window with highly energetic with highly energetic

GRB GRB νν’s’s The generally accepted GRB models predict the The generally accepted GRB models predict the production of high energy neutrinos alongside the production of high energy neutrinos alongside the γγ--rays.rays.

The intensity and spectrum of these neutrinos are The intensity and spectrum of these neutrinos are somewhat dependant on GRB model parameters, somewhat dependant on GRB model parameters, but at least a few but at least a few GRB GRB νν’s of 100 TeV and above are ’s of 100 TeV and above are expected to be detected per year in a kmexpected to be detected per year in a km33–scale –scale detector (such as is currently being constructed).detector (such as is currently being constructed).

These neutrinos have energies many orders of These neutrinos have energies many orders of magnitude higher than the observed burst photons magnitude higher than the observed burst photons and can open a new window in the examinable LID and can open a new window in the examinable LID parameter space.parameter space.

GRB GRB νν’s LID delay’s LID delay Neutrino masses have a negligible effect on Neutrino masses have a negligible effect on

flight times – we can treat neutrinos as flight times – we can treat neutrinos as massless particles.massless particles.

The delay of a neutrino of observed energy E The delay of a neutrino of observed energy E relative to a low energy photon, both emitted relative to a low energy photon, both emitted at redshift z is given by:at redshift z is given by:

For example, if the LID parameters are n=1, For example, if the LID parameters are n=1, ξξ=1 then a 100 TeV =1 then a 100 TeV νν coming from a z=1 burst coming from a z=1 burst will arrive with a 4048 sec delay (with will arrive with a 4048 sec delay (with standard cosmological parameters).standard cosmological parameters).

nz

n

300 pl

m

1 1 n E dz1 z

H 2 E 1 zt '

''

Identifying GRB Identifying GRB νν’s ’s from noisefrom noise

Supposing a detection of Supposing a detection of νν’s with LID delays, we are ’s with LID delays, we are left with the concern of identifying them as left with the concern of identifying them as originating from GRBs – distinguishing the signal originating from GRBs – distinguishing the signal from noise.from noise.

The most dominant background to the GRB The most dominant background to the GRB νν signal signal consists of muons from atmospheric neutrinos. This consists of muons from atmospheric neutrinos. This noise is decreased greatly by observing only in the noise is decreased greatly by observing only in the relevant energy, time and angular windows.relevant energy, time and angular windows.

The atmospheric The atmospheric νν spectrum is approximately given spectrum is approximately given by:by:

with with ββ=3.7 for E=3.7 for Eνν<100 TeV and <100 TeV and ββ=4 for E=4 for Eνν>100 TeV>100 TeV.. Knowing the cross section for Knowing the cross section for νν interactions in the interactions in the

detector, we calculate the number of background detector, we calculate the number of background events.events.

13atmdN5 10 E 100TeV

dE-1 -2 -1 -1[100TeV] cm sec sr/

wi

noise

ξ=0.1, z=2

ξ=0.1, z=1ξ=1, z=2ξ=1, z=1

ξ=0.1, z=0.1

ξ=1, z=0.1

LID delays for n=1vs.

time period producing 0.0001 noise events

LID delays for n=2vs.

time period producing 0.0001 noise events

noiseξ=10-8, z=2ξ=10-8, z=1

ξ=10-8, z=0.1

ξ=10-7, z=2ξ=10-7, z=1

Bounds on ξ for determiningn=1 LID delays of z=1 GRB ν’s

1000 sec

1 yr

noise

Bounds on ξ for determiningn=2 LID delays of z=1 GRB ν’s

1000 sec

noise1 yr

Lower limits on ξ if LID delay (n=1, z=2)is not larger than 100 seconds

Lower limits on ξ if LID delay (n=2, z=2)is not larger than 100 seconds

1000

0.001

0.1

10

1000010010.010.00011.×10-6

1.×10-5

E (TeV)

ξ

1000

sec

1 yr

noise

LID bounds from various sources for n=1

1000010010.010.00011.×10-6

ξ

1000 sec

1 yr

noise

E (TeV)

1.×10-5

1.×10-11

1.×10-9

1.×10-7

1.×10-13

LID bounds from various sources for n=2

SummarySummary Detecting and identifying high energy Detecting and identifying high energy νν’s’s from from

GRBs is a practical plan for the near future. GRBs is a practical plan for the near future. The arrival time of these The arrival time of these νν’s’s can be compared can be compared to the observed to the observed γγ-rays.-rays.

The highly energetic The highly energetic νν’s’s can provide us insight can provide us insight on a LID parameter space that is hidden from on a LID parameter space that is hidden from other observation methods, probing much other observation methods, probing much higher symmetry breaking scales.higher symmetry breaking scales.

The prospects of determining LID or imposing The prospects of determining LID or imposing very strict constraints on it using GRB very strict constraints on it using GRB νν’s’s appear excellent.appear excellent.