Atmospheric neutrino fluxes Status of the calculations based

Atmospheric neutrino fluxes Status of the calculations based on work with M. Honda May 26, 2002 Thomas K. Gaisser

Outline ¡ ¡ Overview of calculations En < 10 Ge. V (contained) l l l ¡ High energy (nm m & ne) l l l ¡ Geomagnetic effects Response functions Primary spectrum Hadronic interactions Comparison of calculations 3 D effects Importance of kaons Calibration of n - telescopes Prompt background Summary May 26, 2002 Distribution of En for 4 classes of events Thomas K. Gaisser

Overview of the calculation May 26, 2002 Thomas K. Gaisser

Calculations of atmospheric n ¡ 1 dimensional l *Bartol flux: V. Agrawal et al. , ¡ Phys. Rev. D 53 (1996) 1314 l *HKKM: M. Honda et al. : Phys. Rev. D 52 (1995) 4985 l TKG et al. , Hamburg ICRC (2001) p. 1381 l HKKM, Hamburg ICRC (2001) p. 1162 l Fiorentini, Naumov, Villante, Phys. Lett. B 510 (2001) 173 l * Used in analysis of Super-K 3 dimensional l l May 26, 2002 Thomas K. Gaisser G. Battistoni et al. , Astropart. Phys. 12 (2000) 315 -- first 3 D calculation Y. Tserkovnyak et al. , Hamburg ICRC (2001) p. 1196 J. Wentz, Hamburg, p. 1167 (complete but preliminary) Y. Liu et al. , Hamburg, p. 1033 (low result ? ) V. Plyaskin, Phys. Lett. B 516 (2001) 213 (just revised)

Geomagnetic cutoffs & E-W effect as a consistency check ¡ Picture shows: l l l ¡ 20 Ge. V protons in geomagnetic equatorial plane arrive from West and from near the vertical but not from East N Comparison to data: l provides consistency test of data & analysis From cover of “Cosmic Rays” by A. M. Hillas (1972) May 26, 2002 Thomas K. Gaisser

Cutoffs at Super-K N E S n flux, W 0. 4 < En < 3 Ge. V -0. 5 < cos(q) < 0. 5 measured by Super-K and compared to 3 calculations Honda Bartol Lipari 3 D May 26, 2002 Thomas K. Gaisser

Response functions, sub-Ge. V n ¡ ¡ Eprimary ~ ( 10 ) x En Up/down ratio opposite at Kamioka vs Soudan/SNO May 26, 2002 Thomas K. Gaisser

Solar modulation ¡ Neutron monitors l l l well correlated with cosmic-ray flux provide continuous monitor response like sub-Ge. V neutrinos with no cutoff SNO, Soudan: <20% variation Kamioka: <5% (10 %) for downward (upward) May 26, 2002 Thomas K. Gaisser P. Lipari

Primary spectrum ¡ Protons Largest source of overall uncertainty l l Helium May 26, 2002 Thomas K. Gaisser 1995: experiments differ by 50% (see lines) Present: AMS, BESS within 5% for protons discrepancy for He larger, but He only 20% of nucleon flux overall range (neglect highest and lowest): ¡ +/-15%, E < 100 Ge. V ¡ +/- 30%, E ~ Te. V

Hadronic interactions ¡ n-yields depend most on ¡ treatment of p production Compare 3 calculations: l l l ¡ Bartol (Target) Honda et al. (1995: Fritiof; present: Dpmjet 3) Battistoni et al. (Fluka) Uncertainties from interactions ~ +/-15% May 26, 2002 Thomas K. Gaisser

Comparison (using same flux) ¡ nm New calculations lower than old, e. g. : l l l ¡ Kamioka Target-2. 1/ -1 Dpmjet 3 / HKKM 3 new calculations agree at Kamioka but not for Soudan/SNO Larger uncertainty at high geomagnetic l l May 26, 2002 ne Interactions < 10 Ge. V are important Thomas K. Gaisser nm ne Soudan/SNO

Comparison (using same event generator) ¡ Kamioka nm sub Ge. V flux increases slightly using new flux from AMS & BESS ne AMS/BESS nm ne Soudan/SNO May 26, 2002 Thomas K. Gaisser

3 -dimensional effects ¡ Characteristic 3 D feature: l l ¡ n n excess of n near horizon shown in top, left panel lower panels show directions of m and e cannot see 3 D effect directly; however: Horizontal excess is associated with a change in path-length distribution May 26, 2002 m m From Battistoni et al. , Astropart. Phys. 12 (2000) 315 Thomas K. Gaisser

3 -dimensional effects ¡ ¡ 3 D vs 1 D comparison at Kamioka (3 D: pink; 1 D: blue/green) Dip near horizon: l ¡ due to high local horizontal cutoffs Size of effect: l l l p. T(p)/Ep sets scale ~ 0. 1 Ge. V / En therefore negligible for En > 1 Ge. V from M. Honda et al. , Phys. Rev. D 64 (2001) 053001 May 26, 2002 Thomas K. Gaisser

Path-length dependence ¡ Path length shorter near horizon on average in 3 D case l l l ¡ Kamioka cos(q) > 0 only, phase space favors nearby interaction scattering to large angle 5 -10% (En ~0. 3 -1 Ge. V) Effect not yet included in Super-K analysis May 26, 2002 Thomas K. Gaisser En = 0. 3 Ge. V En = 1 Ge. V Soudan/SNO

Is the second spectrum important for atmospheric n? l l l Cosmic-ray albedo beautifully measured by AMS at 380 km Biggest effect near geomagnetic equator (vertical cutoff ~ 10 GV) Albedo: sub-cutoff protons from grazing interactions of cosmic rays > cutoff (S. B. Treiman, 1953) trapped for several cycles Re-entry rate is low (dashed line) May 26, 2002 Thomas K. Gaisser 10 GV P. Zuccon et al.

Comparison to muons l l l m+, m- vs atmospheric depth newer measurements lower by 10 -15% than earlier comparison not completely internally consistent: ¡ ascent vs float ¡ balloons rise rapidly ¡ fraction detected is small compared to m decayed to n May 26, 2002 Data from CAPRICE, 3 D calculation of Engel et al. (2001) Thomas K. Gaisser

Absolute comparison May 26, 2002 shows new calculation with new flux Thomas K. Gaisser

High energy ( e. g. nm m ) ¡ Importance of kaons l l l vertical 60 degrees main source of n > 100 Ge. V p K+ + L important Charmed analog may be important for prompt leptons May 26, 2002 Thomas K. Gaisser

Calibration with atmospheric n ¡ ¡ ¡ Atmospheric beam well understood Thousands of events in km-scale detector Example*** of nm / ne l l flavor ratio angular dependence ***Note: this is maximal effect: horizontal = 85 - 90 deg in plots May 26, 2002 Thomas K. Gaisser

Global view of atmospheric n spectrum Plot shows sum of neutrinos + antineutrinos nm ne Uncertainty in level of charm a potential problem for finding diffuse neutrinos Solar n Prompt m Slope = 3. 7 May 26, 2002 Thomas K. Gaisser Slope = 2. 7

Uncertainties & absolute normalization ¡ Primary spectrum l l l ¡ Hadronic interactions l l ¡ +/- 10% up to 100 Ge. V (using AMS, BESS only) +/- 20% below 100 Ge. V, +/- 30% ~Te. V (all data) Note lack of measurements in Te. V range +/- 15% below 100 Ge. V 1 D o. k. for comparing calculations and for tracking effects of uncertainties in input Other sources at per cent level ¡ (local terrain, seasonal variations, anisotropy outside heliosphere) New measurements: HARP, E 907 Uncertainty in sn May 26, 2002 Thomas K. Gaisser

Summary (low energy) ¡ Evidence for n oscillation uses ratios: l Contained events ¡ ¡ l Neutrino-induced upward muons ¡ ¡ l ¡ ¡ (ne / nm )data / (ne / nm )calculated upward / downward stopping / through-going vertical / horizontal Broad response functions minimize dependence on slope of primary spectrum Uncertainties tend to cancel in comparison of ratios Observation of geomagnetic effects confirms experiment & interpretation May 26, 2002 Thomas K. Gaisser

Summary (high energy) Kaon decays dominate atmospheric nm, ne above 100 Ge. V ¡ Well-understood atmospheric nm, ne useful for calibration of neutrino telescopes ¡ Uncertainty in level of prompt neutrinos (from charm decay) will limit search for diffuse astrophysical neutrinos ¡ May 26, 2002 Thomas K. Gaisser