Update on Muon Flux Underground Using Geant4 Simulation Martina Hurwitz University of Chicago Braidwood meeting, 5/14/05

Reminder of goals of exercise Neutrons from cosmic ray muons may contribute significantly to backgrounds at Braidwood First step in being able to simulate neutrons is knowing spectrum of muons underground Not much information on spectrum of muons at Braidwood’s depth available Use best knowledge of muon flux at sea level and Geant4 simulation of muon interactions in rock to find flux underground Exercise has provided some useful results to the collaboration

Reminder: Sea level muon flux Standard Gaisser parameterization doesn’t fit data very well for ~100 GeV muons, particularly at high zenith angles. We use fits to measurements for muons at cosθ = 1.0 and at cosθ = 0.26 with linear interpolation in cosθ in between. Note: At low energies flux of vertical muons roughly equal to flux of muons at high zenith angles. At high energies flux of vertical muons lower than flux of muons at high zenith angles

Reminder: Comparison of G4 flux to MUSIC, data Vertical muons Red points: Geant4 sim Green points: MUSIC sim Used Gaisser spectrum for purpose of comparison Unfilled markers: data Verification that Geant4 giving reasonable results

Limitations of Geant4 program implemented last year Overburden Simplified material description: Z = 11, A = 22 Uniform density (2.5 g/cm3) throughout overburden Generator Muons at sea level were generated up to a 2.5 TeV cutoff energy While fixing this, found bigger problem in setting energy of muons: generator was sampling from vertical muon energy distribution instead of distribution integrated over all zenith angles Depth of detector At time we were still thinking anywhere between 300 and 500 mwe; files of underground muons at 500 mwe

Overburden Read out energies, angles, and position of muons Detailed table of layers of rock, their chemical compositions and densities at end of talk Composition of rock: mostly CaCO3 and SiO2 with some MgCO3; Z/A roughly the same as before. Density effect: stopping power decreased for high-energy muons; average density of overburden has increased roughly 2%

Generator Flux distribution depends on both energy and zenith angle, so program first chooses energy, then angle. Energy sampling: Uses probability distribution function to choose energy (fill array with energies, associated probabilities) Before: filled this array with probabilities based on vertical muon flux at each energy Now: fill this array with probabilities based on muon flux at each energy integrated over all zenith angles This will tend to increase the flux of high-energy muons relative to flux of low-energy muons because flux of high-energy muons is higher at high zenith angles. Increase maximum energy of muons at sea level: No significant effect on flux, since these muons very rare Significantly changes average energy of muons underground

Depth of detector Was 500 m.w.e. Now: 600 ft = 182.9 m Middle of deepest layer of limestone, above layer of sandstone Using densities of layers in overburden, 182.9 m = 463.8 m.w.e.

Effect of changes in MC simulation on fluxes, Eave Depth (mwe) Changes Flux (/m2/sec) ( ± statistical errors) Eave underground (GeV) 500.0 Last year’s estimate 0.145 91.2 463.8 Detector placed at design depth 0.181 ± 0.004 85.9 Modified generator: fixed problem with energy spectrum sampling; high-energy cutoff for generation increased from 2.5 TeV to 100 TeV 0.200 ± 0.004 107.6 Incorporated data from boreholes about density and material composition of overburden 0.213 ± 0.004 110.1

Flux as function of Vertex Energy

Flux as function of energy at detector

Radial distance from vertex to detector Sea level detector Muon R

Angular distribution of muons at detector

Conclusions Have updated G4 simulation of muon flux with details of Braidwood geometry Uncovered major mistake in generator, fixed it Improved generator to simulate high-energy muons Produced new file (same structure) with ~100,000 events

Exact overburden Material Chemical composition Density (g/cm3) Depth of top of layer (m) Soil SiO2 1.60 0.0 Mudstone 2.46 11.3 2.52 27.1 Limestone CaCO3 2.61 42.7 2.63 61.0 2.60 63.1 Dolomitic Limestone 0.63* CaCO3 + 0.37*MgCO3 2.58 82.6 2.62 98.8 2.71 116.4 135.0 142.3 157.6 2.66 168.9