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

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

Compare 3 things Data A new formula MINOS far 1.374  0.004 + 0.012 – 0.010 MINOS near 1.288  0.004  0.025 Other previous mostly near 1.25-1.28 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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