1. NuMI MINOS Seasonal Variations in the MINOS Far Detector Eric W. Grashorn University of Minnesota Thursday, 5 July, 2007

2. 05/07/07Eric W. Grashorn NuMI MINOS Page 2/15 Far Detector 2341 ft (2100 m.w.e.) Scintillator and steel tracking calorimeter 486 octagonal planes 2 “Supermodules” 5.4 Kton 1.5 T magnet

3. 05/07/07Eric W. Grashorn NuMI MINOS Page 3/15 Seasonal Variation Underground experiments (Barrett, MACRO, AMANDA) reported positive correlation between muon intensity and atmospheric temperature Correlation motivated by upper atmosphere density –Higher temp = lower density Primary interactions take place higher in the atmosphere at higher temperatures Thus, mesons are more likely to decay than interact

4. 05/07/07Eric W. Grashorn NuMI MINOS Page 4/15 Temperature Coefficient Determine   experimentally (for pion only hypothesis): Effective Temperature (T eff ) treats the atmosphere as isothermal –Weighted average of uniform atmospheric levels

5. 05/07/07Eric W. Grashorn NuMI MINOS Page 5/15 Muon Data Selection Data from 08/03-08/06 –1096 days of detector running (968 live-days) –40.38 million CR events Cuts: –Pre-analysis: DeMux FOM failures, “Bad run”, multiple muon, coil status –Data Quality cuts: Length <2, N planes <20, Fiducial cut, “fit quality” cut 24.6 Million events survived, 60.9% of the data

6. 05/07/07Eric W. Grashorn NuMI MINOS Page 6/15 Cosmic Ray Events Time between consecutive events, log y –   /ndof = 90.9/105 – Slope = 0.287 Hz Rate per day:

7. 05/07/07Eric W. Grashorn NuMI MINOS Page 7/15 Temperature Data Selection IGRA (Integrated Global Radiosonode Archive) data taken from International Falls, MN (150 Km NW of Soudan) Cuts: –Two balloon flights, 1100 and 2300 (C.S.T.) –Column height > 60 g/cm 2 –128 days excluded Error on T eff data was calculated by subtracting the rms from the mean.

8. 05/07/07Eric W. Grashorn NuMI MINOS Page 8/15 T eff Distribution over the three year period: 221.0 K

9. 05/07/07Eric W. Grashorn NuMI MINOS Page 9/15 Deviation from Mean (%): Left:  R  (top)  T eff (bottom) over three years Right:  R  (  T eff ) over the same three year period –Fit a straight line (error bars in both dimensions) –   /ndof = 1420/953

10. 05/07/07Eric W. Grashorn NuMI MINOS Page 10/15 Correlation The temperature coefficient (  T ) is the slope of the linear fit of  R  (  T eff ). The MINOS result (pion only hypothesis):  T = 0.87 ± 0.03 Correlation for these two distributions: 0.79

11. 05/07/07Eric W. Grashorn NuMI MINOS Page 11/15 Theoretical  T Calculate with a simple Monte Carlo: – Choose a random E , cos(  from the differential intensity spectrum, find random , assume flat overburden to find X. – Use E , cos(  in  T calculation if E  > E th. – Calculate  T (from Barrett) with 10,000 such successful muons at slant depths up to 4000 mwe.

12. 05/07/07Eric W. Grashorn NuMI MINOS Page 12/15 Theoretical  T Data: Barrett 1, 2 (Barrett, 1952), AMANDA (Bouchta et al, 1999), all other points from Ambrosio et al, 1997. Curve is calculated  T (depth)

13. 05/07/07Eric W. Grashorn NuMI MINOS Page 13/15 Charge Separated Charge separated seasonal fluctuations as % diff from the mean;   in circles (top),   in triangles (bottom). Reverse field Used qp/  qp > 2.2 11.86 Million events survive: – 6.74 million   – 5.12 million   Livetime: –774 days forward –192 days reverse

14. 05/07/07Eric W. Grashorn NuMI MINOS Page 14/15 Charge Separated Charge separated  R  (  T eff ) Correlation coefficient: –   : 0.54;   : 0.47.  T : –   : 0.84 +/- 0.05 –   : 0.84 +/- 0.06

15. 05/07/07Eric W. Grashorn NuMI MINOS Page 15/15 Conclusions Temp Coefficient,  T, in MINOS: 0.87 +/- 0.03 This precise measurement of a small signal ( +/- 4% fluctuations), shows MINOS’ sensitivity Result is slightly below expectation Charge Separated: –  T for   : 0.84 +/- 0.05;  T for   : 0.84 +/- 0.06 –Within error, these are identical; there is nothing new here (as expected).

16. 05/07/07Eric W. Grashorn NuMI MINOS Page 16/15 Backup Slides

17. 05/07/07Eric W. Grashorn NuMI MINOS Page 17/15 Temperature Coefficient Correlation between I  and T given by Barrett as: Rewriting I  for a particle counter: So, to determine   experimentally:

18. 05/07/07Eric W. Grashorn NuMI MINOS Page 18/15 Effective Temperature In order to evaluate the integral, we use the “effective temperature” approximation of Barrett: where    g/cm 2,    g/cm 2

19. 05/07/07Eric W. Grashorn NuMI MINOS Page 19/15 Effective Temperature We now have: Which gives: *Note that T eff is for pion induced muons only

20. 05/07/07Eric W. Grashorn NuMI MINOS Page 20/15 Pre-analysis: DeMux FOM failures, “Bad run”, multiple muon, coil status Data Quality cuts: Length >2, N planes > 20, Fiducial cut, “fit quality” cut 24.6 Million events survived the cuts, 53.4% of the data Cuts

21. 05/07/07Eric W. Grashorn NuMI MINOS Page 21/15 Cuts Table of events that survive each cut: Total Tracks46.13 x 10 6 Cut Fraction Remaining Pre-Selection 1. Demux FOM failure0.883 2. Good Run List0.865 3. Multi-muon0.838 4. Coil Status0.829 Analysis Cuts 1. Length > 2 m0.760 2. Number of Planes > 200.560 3. Fiducial0.549 4. Fit Quality0.534

22. 05/07/07Eric W. Grashorn NuMI MINOS Page 22/15 Theoretical  T For differential intensity distributions of the form: With    GeV,  k = 860 GeV Barrett gives: With E th the threshold muon energy required to survive to slant depth X (mwe), given by E th  = 0.5(TeV)(e 0.4X -1)

23. 05/07/07Eric W. Grashorn NuMI MINOS Page 23/15 Conclusions: Binned by day, there seems to be a correlation between R  & T eff for charge-separated events as well  T for   : 0.84 +/- 0.05;  T for   : 0.84 +/- 0.06 Within the error for each measurement, these are identical, so the charge separated sample doesn’t tell us anything new (this is good)