1. 6/26/2006David Gerstle1 Muon Cosmic Ray Flux Study David Gerstle LArTPC – Yale University Undergraduate

2. 6/26/2006David Gerstle2 Contents CAPRICE 94 & 97 data and calculations –Includes comparison of data to other trials and –an attempt at correcting for atmospheric depth differences Muon track length in LAr and calculations related to CAPRICE 94 & 97 data. The above applied to the Soudan, MN atmospheric depth and (sort of) geomagnetic cutoff Conclusions Other plots

3. 6/26/2006David Gerstle3 What are the data? Data are taken from Kremer et al., "Measurements of Ground-Level Muons at Two Geomagnetic Locations," PRL 1999, Vol 83, No. 21, pp. 4241 CAPRICE is a spectrometer including: –A ring imaging Cherenkov (RICH) detector –A time-of-flight system –A superconducting magnet spectrometer –A 7 rad length silicon-tungsten imaging calorimeter. Data were taken twice [“Data” tab of Cosmic Rays.xls; see DocDb]: –CAPRICE94: In 1994 at Lynn Lake, Manitoba, Canada (56.5° N, 101.0° W), 360m altitude, a vertical geomagnetic cutoff of 0.5GeV, and atmospheric depth of 1000 g/cm^2. –CAPRICE97: In 1997 at Fort Summer, New Mexico (34.4 ° N, 104.1° W), 1270m altitude, a cutoff of 4.2GeV, and depth of 886 g/cm^2. The data are given as dN/dp (including uncertainty) as a function of momentum. Data are provided in bins of varying width. A mean momentum for each bin is provided. –mu_+ and mu_- data are provided for each study. –The 97 mu_+ 1.6-2.1 GeV/c point was added by linear interpolation.

4. 6/26/2006David Gerstle4 What did I do with them? I copied them into Excel and then reorganized them so they were graphable [“Multiplied Out”], etc. (no longer w/ scaling factors). Using a rectangular method over each bin I calculated the integral of (dN/dp)*dp [“Integral”], giving us N. –This is the ‘best’ method as data were collected and provided in bins of varying width. I plotted dN/dp as a function of p and N (from the integral) as a function of p on the same plot for each data set AND summed the mu_+/mu_- data for each dataset into one plot.

5. 6/26/2006David Gerstle5 [“95 mu_+”] Integral curve is value from 0 GeV/c to plotted p Blue is differential flux (left logarithmic y-axis) Pink is integral flux from 0 GeV/c to p (right linear y-axis)

6. 6/26/2006David Gerstle6 More mu_+ than mu_- [“94 mu_-”] Blue is differential flux Pink is integral flux from 0 GeV/c to p

7. 6/26/2006David Gerstle7 [“97 mu_+”] Blue is differential flux Pink is integral flux from 0 GeV/c to p These are 97 data…

8. 6/26/2006David Gerstle8 [“97 mu_-”] Blue is differential flux Pink is integral flux from 0 GeV/c to p Again, more mu_+ than mu_-

9. 6/26/2006David Gerstle9 Summing mu_+ and mu_- data, 97 appear higher than 94 [“94&97”]

10. 6/26/2006David Gerstle10 97 data really are higher than 94 outside of uncertainty…why? [“Ratio Graph”]

11. 6/26/2006David Gerstle11 Atmospheric depth effect described for 0.3<p<8 GeV/c by Attenuation Length Λ(g/cm^2)= (269±17)+(180±17)*p [M. Boezio, thesis, KTH]. Data are adjusted by e -(x 97 -x 94 )/Λ The remaining low momentum difference can be accounted for by the geomagnetic cutoff on the incident protons (higher cutoff lowers flux) [“Depth Graph”]

12. 6/26/2006David Gerstle12 Data do match other studies Blue is 94 differential flux Pink is 97 differential flux Yellow is from PDG cosmics plot

13. 6/26/2006David Gerstle13 What are the track lengths in LAr? From “Atomic Nuclear Properties: Table 289: Muons in liquid argon” [“Track Length”] –Given as a density dependent -dE/dx (MeV cm^2/g) at various energy/momentum values; converted into pure dE/dx. –Integrated (-dx/dE)*dE by a trapezoidal approximation to find the distance traveled between energy points given by the chart. –Summed these to find the integral (-dx/dE)*dE from 0 GeV to a given GeV (which is easily converted to p rather than E). Put these data into the momentum bins of the CAPRICE data. –Interpolated data for CAPRICE momentum bins without Table 289 data by a least-squares quadratic approximation (w/ four points) in relation to Table 289 data already in CAPRICE bins. –Interpolated one point linearly from the Table 289 data. –The curve looks smooth (so I think I interpolated correctly):

14. 6/26/2006David Gerstle14 End plateau accounts for finite detector size Some data are interpolated, and it is good that you cannot tell which [“Length”]

15. 6/26/2006David Gerstle15 Length at each momentum is multiplied by the differential flux; pink is 97, blue is 94. Yellow and Teal are the areas under the blue and pink curves (rectangular over each bin) from zero to p. [“Length and Flux”] Bumps must be results of flux data

16. 6/26/2006David Gerstle16 What is the Bottom Line? By averaging the values from the data sets [“BOTTOM LINE”] : –The choice of 4 sig figs is arbitrary –Total N = 93.77 (m^2 s sr)^-1 –Total N*x(p) = 1267.5 m*(m s sr)^-1 –Average x = 13.54 m*(m^2 s sr)^-1 Photons next…

17. 6/26/2006David Gerstle17 Atmospheric Depth and Geomagnetic Cutoff Corrections Atmospheric depth of Soudan, MN was interpolated by a linear fit of atmospheric depth as a function of altitude between the CAPRICE 94&97 data. Calculations are in “Soudan.xls” Atmospheric Depth was corrected for as outlined in M. Boezio, thesis, KTH –Attenuation Length Λ(g/cm^2)= (269±17)+(180±17)*p –Data are adjusted by e -(x Soudan -x 94 )/Λ and e -(x Soudan -x 97 )/Λ Geomagnetic cutoff corrected for by a simple average between the two sets of corrected CAPRICE data. –The latitude of Soudan (47.8°) is nearly halfway between the CAPRICE latitudes (56.5° and 34.3°). –There is a direct correlation between latitude and geomagnetic cutoff, but I do not know exactly what it is. Read: this is a very crude correction.

18. 6/26/2006David Gerstle18 Blue is 94 to Soudan Pink is 97 to Soudan Yellow is 94 Black is 97 Looks like a good correction; there is some discrepancy below.5 GeV/c, but this is likely because of the different geomagnetic cutoffs of 94&97

19. 6/26/2006David Gerstle19 Looks like a nice curve; probably a good correction. Note that integral flux is from 0 to p and is on the right-hand linear y-axis Blue is differential flux Pink is integral flux

20. 6/26/2006David Gerstle20 Please recall this track length (referred to as x(p)) calculation as I apply it to Soudan…

21. 6/26/2006David Gerstle21 Blue is differential Pink is integral

22. 6/26/2006David Gerstle22 Average is calculated by dividing the integral flux*length (N*x(p)) by the integral flux (N).

23. 6/26/2006David Gerstle23 Soudan (sort of) BOTTOM LINE Integral (dN/dp)*dp = N from 0.2 GeV/c to 120 GeV/c = 86.92 (m^2 s sr)^-1 Integral ((dN*x(p))/dp)*dp = N*x(p) from 0.2 GeV/c to 120 GeV/c = 1218.62 (m s sr)^-1 N*x(p)/N = average x(p) = 14.02 m. It would be good to find out the exact atmospheric depth and geomagnetic cutoff.

24. 6/26/2006David Gerstle24

25. 6/26/2006David Gerstle25 Other plots:

26. 6/26/2006David Gerstle26 [“94”]

27. 6/26/2006David Gerstle27 [“97”]