1. Event Rates vs Cross Sections
Neutrino Telescopes
August 29, 2006
Shahid Hussain
University of Delaware

2. Look at the upward case in more detail ….
down neutrinos
 = 0
 = 90
upward neutrinos
Mantle (2900km,4.5-10g/cm^3)
Outer core (2270, )
1220, 13.5
Look at the upward case in more detail ….

3. Horizontal surface-detector
EVent rates
A simple model:
Earth A’ A d
Horizontal surface-detector
Volume-detector

4. Solve (analytically): volume-detector with d=0:
surface-detector:

5. How does the simple model compare with
a detailed simulation? Let's do a detailed
numerical simulation using ICECUBE as
an example....

6. SIMULATION
Neutrino propagation through the Earth: Solve the coupled Boltzmann equations for three neutrino flavors and the tau lepton, keeping the following details:
Calculate neutrino-nucleon, deeply inelastic, cross sections (differential and total).
Include regeneration/down scattering terms.
3. Use variable density model of the Earth.
4. Include tau decays and tau energy losses.
5. Volume detector at depth d=0, 1.9km.
Finally, as an example, calculate shower, muon, and tau event rates, as a function of the neutrino nucleon cross sections, for ICECUBE using WB flux model.

7. We simulate three possibilities for cross-section scaling: CASE I:
Target nucleon xP
q(G) k
shower k’
neutrino
Graviton exchange
We simulate three possibilities for
cross-section scaling:
CASE I:
CASE II:
CASE III:
Target nucleon xP k
neutrino
shower
Black hole formation

9. Horizontal surface-detector
Earth A’ A
d=2km
Horizontal surface-detector
Volume-detector
Importance of depth
For a detector at a finite depth d, at large
cross-sections ( ) and energies
( ) even for the horizontal
direction:

12. SUMMARY
For a given neutrino telescope, the scaling of event rates with neutrino-nucleon cross-sections depends on the event type, neutrino energy, and cross-section model.
Details are important:
1. Detector depth: Above a 100PeV, even a 2km detector depth may cause a significant loss in event rates at cross-sections larger than the SM value.
2. Cross-section inelasticity: Significant differences in event rates for cross-section models with different inelasticities.

13. For energies around 1-10 PeV, within a decade of change in cross-section :
Downward rates:
showers ~ ; leptons ~
Upward rates:
showers ~ ;
leptons ~ ( , )
surface
volume

14. As an example, for the model 6. 10^-8 (GeV. cm^2
As an example, for the model 6*10^-8 (GeV.cm^2.s)^-1 (E(GeV))^-2, simulation for ICECUBE gives (upward rates/yr) in the SM:
For the bin PeV:
showers=0.7; muons=0.8; taus =0.2, 0.1
Rates integrated above a PeV:
showers=2.4; muons=2.2; taus =0.9, 0.3