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

Look at the upward case in more detail …. down neutrinos  = 0  = 90 upward neutrinos Mantle (2900km,4.5-10g/cm^3) Outer core (2270,10-12.8) 1220, 13.5 Look at the upward case in more detail ….

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

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

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

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.

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

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:

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.

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

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 3.16-10PeV: 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