Atmospheric neutrinos n from decay of p K

Atmospheric neutrinos • n from decay of p, K and m produced by interactions of cosmic rays in the atmosphere • Up-down symmetric except for geomagnetic effects • Useful beam for neutrino oscillations? References: • TKG & M. Honda, Ann. Revs. Nucl. Part. Sci. 52 (2002) • TKG, Proc. Neutrino 2002 Tom Gaisser October 29, 2002 Oxford From D. Ayres, A. K. Mann et al. , PR D 84 (1984) 902 & Snowmass, 1982

Historical context p Particle physics with cosmic rays: pre-1960 • Discovery of positron, muon, pion and kaon • Hadronic scaling (Heitler & Janossy, 1949) -- Fsecondary(E) = Zps Fp(E) • Study of elementary particles by the photographic method Powell, Fowler & Perkins, 1959 m Stability of matter: search for proton decay, 1980’s • • IMB & Kamioka -- water Cherenkov detectors KGF, NUSEX, Frejus, Soudan -- iron tracking calorimeters Principal background is interactions of atmospheric neutrinos Need to calculate flux of atmospheric neutrinos e nm Two methods: p ne • From muons to parent pions infer neutrinos (Zatsepin & Kuz’min; Perkins) • From primaries to p, K and m to neutrinos (Cowsik, TKG & Stanev…) • Giles Barr 1986/87 Tom Gaisser October 29, 2002 Oxford nm

p Historical context (cont’d) Atmospheric neutrino anomaly - 1986, 1988 … • IMB too few m decays (from interactions of nm) 1986 • Kamioka m-like / e-like ratio too small. • Neutrino oscillations first explicitly suggested in 1988 Kamioka paper Discovery of neutrino oscillations • • • p m e Super-K: “Evidence for neutrino oscillations” at Neutriino 98 Subsequent increasingly detailed analyses from Super-K 1998… Confirming evidence from MACRO and Soudan SNO results on oscillations of solar neutrinos nm Analyses based on ratios comparing to 1 D calculations Need for precise, complete, accurate, 3 D calculations • • ne Q ~ PT / E is large for sub-Ge. V neutrinos Bending of muons in geomagnetic field important for n from m decay Complicated angular/energy dependence of primaries (AMS measurement) Use improved primary spectrum and hadroproduction information Tom Gaisser October 29, 2002 Oxford nm

Outline of talk • Overview of calculations • En < 10 Ge. V (contained) – Sources of uncertainty • Primary spectrum • Hadronic interactions – Comparison of calculations – Geomagnetic effects – 3 D calculations • High energy (nm m & ne) – Importance of kaons – Calibration of n - telescopes – Prompt background • Summary Distribution of En for 4 classes of events determines how oscillation effects appear P(nm-->nm) = 1 - sin 22 q sin 2[1. 27 dm 2(e. V 2) Lkm / EGe. V ] for two-flavor mixing in vacuum Tom Gaisser October 29, 2002 Oxford

Overview of the calculation Tom Gaisser October 29, 2002 Oxford

Primary spectrum • Largest source of overall uncertainty – 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): Protons Helium • +/-15%, E < 100 Ge. V • +/- 30%, E ~ Te. V Tom Gaisser October 29, 2002 Oxford

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 Tom Gaisser October 29, 2002 Oxford

Hadronic interactions • n-yields depend most on treatment of p production • Compare 3 calculations: – Bartol (Target) – Honda et al. (1995: Fritiof; present: Dpmjet 3) – Battistoni et al. (Fluka) • Uncertainties from interactions ~ +/-15% Tom Gaisser October 29, 2002 Oxford

Comparison (using same flux) Kamioka • New calculations lower than old, e. g. : nm – Target-2. 1/ -1 – Dpmjet 3 / HKKM – 3 new calculations agree at Kamioka but not for Soudan/SNO ne • Larger uncertainty at high geomagnetic l nm ne – Interactions < 10 Ge. V are important Tom Gaisser October 29, 2002 Soudan/SNO Oxford

New hadro-production data • Diagram: – Lego plot shows phase space weighting for sub. Ge. V events – Bars show existing data • New sources of data – HARP – NA 49 (P 322) – E 907 Tom Gaisser October 29, 2002 Oxford HARP P 322

Geomagnetic cutoffs & E-W effect as a consistency check • Picture shows: – 20 Ge. V protons in geomagnetic equatorial plane – arrive from West and from near the vertical – but not from East N • Comparison to data: – provides consistency test of data & analysis Tom Gaisser October 29, 2002 Oxford From cover of “Cosmic Rays” by A. M. Hillas (1972)

Response functions, sub-Ge. V n • Eprimary ~ 10 -20 x En • Up/down ratio opposite at Kamioka vs Soudan/SNO Tom Gaisser October 29, 2002 Oxford

Measurement of East-West effect with atmospheric neutrinos--an important confirmation of analysis & interpretation of Super-K data as neutrino oscillations Cutoffs at Super-K N E S n flux, 0. 4 < En < 3 Ge. V -0. 5 < cos(q) < 0. 5 measured by Super-K and compared to 3 calculations W Honda Bartol Lipari 3 D Tom Gaisser October 29, 2002 Oxford

3 -dimensional effects • Characteristic 3 D feature: – 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 Tom Gaisser October 29, 2002 Oxford n n m m From Battistoni et al. , Astropart. Phys. 12 (2000) 315

3 -D effects at Super-K • 3 D--1 D comparison (pink--blue/green) at Kamioka • Dip near horizon: – due to high local horizontal cutoffs • Size of effect: – p. T(p)/Ep sets scale – ~ 0. 1 Ge. V / En – therefore negligible for En > 1 Ge. V Tom Gaisser October 29, 2002 from M. Honda et al. , Phys. Rev. D 64 (2001) 053001 Oxford

Path-length dependence • Path length shorter near horizon on average in 3 D case Kamioka En = 0. 3 Ge. V En = 1 Ge. V Soudan/SNO – 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 dm 2 L/E …increase dm 2 1%? Tom Gaisser October 29, 2002 Oxford from M. Honda et al. , Phys. Rev. D 64 (2001) 053001

Is the second spectrum important for atmospheric n? – 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) Tom Gaisser Oxford October 29, 2002 10 GV P. Zuccon et al.

Technical aspects of 3 D calculation • Brute force – Generate showers randomly all over globe – e ~ Adetector/Aearth ~ 10 -10 – Use large Aeff • Lipari, Waltham • Neglect bending in geomagnetic field • Battistoni et al. • DST approach: two passes – Giles Barr et al. – Equivalent to brute force but with higher efficiency, e ~ ? Tom Gaisser October 29, 2002 Oxford

Higher energy atmospheric n • Mean En ~ 100 Ge. V for n-induced upward m Tom Gaisser October 29, 2002 Oxford

High energy ( e. g. nm m ) • Importance of kaons vertical 60 degrees – main source of n > 100 Ge. V – p K+ + L important – Charmed analog important for prompt leptons Tom Gaisser October 29, 2002 Oxford

Calibration with atmospheric n • MINOS, etc. • Neutrino telescopes • Example*** of nm / ne – flavor ratio – angular dependence ***Note: this is maximal effect: horizontal = 85 - 90 deg in plots Tom Gaisser October 29, 2002 Oxford

MINOS: m+/m- discrimination 1 < Em < 70 Ge. V Angular distribution of n m Events in 5 yr w / wo osc. a) No Oscillations • Contained + 400 / 260 1 Ge. V • Contained - 620 / 440 contained • External + 160 / 120 • External - 400 / 280 External (x 10 -4) n m TKG & Todor Stanev astr 0 -ph/0210512 10 Ge. V, contained Tom Gaisser October 29, 2002 b) Oscillations: full mixing, d m 2 = 0. 0025 e. V 2 Oxford

sn > sn-, nm m- , nm m+ , so m- / m+ ~ 2 dsn /dy ~ const, but dsn- /dy ~ (1 -y)2, so m- / m+ oscillates vs Em Problems: qnm smears effect; statistics too low in MINOS Em Em En Vertically upward interactions inside detector Tom Gaisser October 29, 2002 Oxford Nine angular bins in n direction

Global view of atmospheric n spectrum Plot shows sum of neutrinos + antineutrinos nm ne Solar n Uncertainty in level of charm a potential problem for finding diffuse neutrinos Prompt m Slope = 2. 7 Slope = 3. 7 Tom Gaisser October 29, 2002 Possible E-2 diffuse astrophysical spectrum (WB bound) Oxford

Uncertainties & absolute normalization • Primary spectrum – +/- 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 • Hadronic interactions – +/- 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, P 322 • Uncertainty in sn Tom Gaisser October 29, 2002 Oxford

Summary (low energy) • Evidence for n oscillation uses ratios: – Contained events • (ne / nm )data / (ne / nm )calculated • upward / downward – Neutrino-induced upward muons • 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 Tom Gaisser October 29, 2002 Oxford

Summary (high energy) • Kaon decays dominate atmospheric nm, ne above 100 Ge. V • Well-understood atmospheric nm, ne useful for calibration • Uncertainty in level of prompt neutrinos (from charm decay) will limit search for diffuse astrophysical neutrinos Tom Gaisser October 29, 2002 Oxford

What next? • Use neutrino fluxes for calibration, etc. – MINOS, SNO, Neutrino telescopes… – Learn about charmed analog of KL production • Finish and use Giles’ 3 D scheme • Incorporate new hadro-production results – HARP below 15 Ge. V – NA 49, E 907 ~ 100 Ge. V Tom Gaisser October 29, 2002 Oxford

Comparison to muons – 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 Data from CAPRICE, 3 D calculation of Engel et al. (2001) Tom Gaisser October 29, 2002 Oxford

Solar modulation • Neutron monitors – 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) Tom Gaisser October 29, 2002 Oxford P. Lipari

Angular distribution of n m 1 Ge. V contained a) No Oscillations b) Oscillations: full mixing d m 2 = 0. 0025 e. V 2 External (x 10 -4) n m 10 Ge. V, contained Tom Gaisser October 29, 2002 Oxford

Tom Gaisser October 29, 2002 Oxford

Soudan 5. 9 k. T yr Electrons Black lines: calculated, no oscillation Blue lines: fitted with oscillations Muons Tom Gaisser October 29, 2002 Oxford M. Goodman, Neutrino 2002