1. Interpretation of the Atmospheric Muon Charge Ratio in MINOS
Phil Schreiner & Maury Goodman
For the MINOS collaboration
July 5, 2007
presenter

2. Introduction & new equation July 5, 2007 m+/m- interpretation
Maury Goodman, ANL
m+/m- interpretation

3. Compare 3 things Data A new formula
MINOS far  – 0.010
MINOS near   0.025
Other previous mostly near
A new formula
Some full simulations (Cort, Honda, Lipari)
One possible conclusion is that the K+/K- ratio in these simulations is too high.
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

4. With some account for energy dependence.
Gaisser’s Equation
Nm = Nm (from p) + Nm(from K)
A new Equation
Nm+ = Nm+ (from p+) + Nm+(from K+)
Nm- = Nm- (from p-) + Nm-(from K-)
And Nm = Nm+ + Nm-
With some account for energy dependence.
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

5. New Equation Gaisser: New: fp fK -fp 0.054(1-fK) July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

6. What’s what fp is related to the m+/m- ratio from p
fK is related to the m+/m- from K
0.054 ( h) is related to K/p ratio
115 GeV(850) is the critical energy above which p (K) interact before they decay
fp, fK & h assumed energy independent (not true, but reasonable if Feynman scaling)
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

7. Parameterization of muon charge ratio
Gaisser sets B=1.1, η=0.054, εp=115 GeV, and εK=850 GeV
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

8. Notice that the ratio depends only on E cos q and not separately on E or q
This has a cause.
This has some implications.
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

9. More Features p+/p-  rp = fp/(1-fp) & K+/K-  rK = fK/(1-fK)
Equation has asymptotic values at low Ecosq & high Ecosq
Both asymptotic values have m’s from both p & K
MINOS is the first high statistics experiment with Ecosq > ep = 115 GeV
h 0.054 rlo =(fp+hfK)/ (1-fp+h(1-fK)) rhi = (epfp+heKfK)/ (ep(1-fp)+heK(1-fK))
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

10. Commments on MINOS data July 5, 2007 m+/m- interpretation
Maury Goodman, ANL
m+/m- interpretation

11. Crude Approximation Our E cos q distribution is a d function
This approximation isn’t used for any data analysis – it is illustrative to see why our E cos q distributions are so narrow.
Zero maximum detectable momentum
Flat surface
Constant density
In the energy loss equation, a is constant
In the energy loss equation, neglect b
E cos (qz) = Emin
The last 4 assumptions imply the energy loss only depends (simply) on zenith angle.
dE/dX = a(E) + b(E)  E
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

12. Minimum Energy to reach MINOS
Depends on zenith angle
surface
Emin
Emin/ (cos qz) qz
MINOS
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

13. Actual ranges of E & Ecosq in MINOS
Far
Near
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

14. July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

15. Data plots In the formula, r only depends on Esurfacecosq !!!
For a long time we concentrate on the dependence of r with Esurface
In the formula, r only depends on Esurfacecosq !!!
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

16. Compare with Simulations July 5, 2007 m+/m- interpretation
Maury Goodman, ANL
m+/m- interpretation

17. Look at Full simulations
We have predictions from
CORT (from V. Naumov)
Lipari
Honda
These all give r vs E in bins of cos(q).
We can ask (independent of all data), do these calculations:
Depend only on E  cos(q)?
Consistent with our formula?
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

18. vs E CORT HONDA Lipari July 5, 2007 m+/m- interpretation
Maury Goodman, ANL
m+/m- interpretation

19. CORT vs E cos(q)
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

20. Honda & Lipari vs Ecosq & fit
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

21. Predictions with Data July 5, 2007 m+/m- interpretation
Maury Goodman, ANL
m+/m- interpretation

22. Fits with data
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

23. Fits & conclusions July 5, 2007 m+/m- interpretation
Maury Goodman, ANL
m+/m- interpretation

24. rK & rp for fits data & simulations
rK=K+/K-
d(rK)
rp =p+/p-
d(rp)
Lipari
2.87
n/a
1.25
CORT
2.39
1.26
Honda
1.63
1.28
Gaisser(91)
3.2
1.4
Agrawal10TeV (96)
2.92
1.35
MINOS PRD
2.03
1.22
MINOS N+F
2.23
0.26
1.232
0.030
MINOS + L3+C + Hebbeker-Timmermans + CosmoALEPH
2.28
0.06
1.224
0.003
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

25. The contributions to the muon flux from p+, p-, K+, K-
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

26. Physics not included in our formula
Variations to Power law
Energy dependence of K/p, p+/p- & K+/K-
Non-isothermal effects (i.e. e(height))
Charm
Variations in chemical composition (n/p)
…but discrepancies (equation & models) not yet understood by us
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation

27. Conclusions
MINOS has the first high stats data with Ecosq >ep & sees a rise in charge ratio
A new formula well describes the data
MINOS data narrow in Ecosq
Some agreement, disagreement with full simulations
Possible guidance to model-builders
Some K+/K- ratios too high
July 5, 2007
Maury Goodman, ANL
m+/m- interpretation