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9. Atmospheric neutrinos and Neutrino oscillations (Cap book) Corso “Astrofisica delle particelle” Prof. Maurizio Spurio Università di Bologna a.a. 2014/15

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Outlook Some history Neutrino Oscillations How do we search for neutrino oscillations Atmospheric neutrinos 10 years of Super-Kamiokande Upgoing muons and MACRO Interpretation in terms on neutrino oscillations – Appendix: The Cherenkov light

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Once upon a time… At the beginning of the ’80s, some theories (GUT) predicted the proton decay with measurable livetime The proton was thought to decay in (for instance) p e + 0 e Detector size: 10 3 m 3, and mass 1kt (=10 31 p) The main background for the detection of proton decay were atmospheric neutrinos interacting inside the experiment Proton decay e Neutrino Interaction Water Cerenkov Experiments (IMB, Kamiokande) Tracking calorimeters (NUSEX, Frejus, KGF) Result: NO p decay ! But some anomalies on the neutrino measurement!

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Neutrino Oscillations | e , | , | = Weak Interactions (WI) eigenstats 1 , | , | = Mass (Hamiltonian) eigenstats Idea of neutrinos being massive was first suggested by B. Pontecorvo Prediction came from proposal of neutrino oscillations Neutrinos propagate as a superposition of mass eigenstates Neutrinos are created or annihilated as W.I. eigenstates

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Weak eigenstates ( e, , ) are expressed as a combinations of the mass eigenstates ( 1, 2, 3 ). These propagate with different frequencies due to their different masses, and different phases develop with distance travelled. Let us assume two neutrino flavors only. The time propagation : (t) = ( 1 , 2 ) M = (2x2 matrix) (eq.2) (eq.1)

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eq.1 becames, using eq.2) whose solution is : with During propagation, the phase difference is: (eq.4) (eq.6) (eq.5) Time propagation

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| e = cos 1 + sin 2 | = -sin 1 + cos 2 = mixing angle (eq.3) Time evolution of the “physical” neutrino states: Let us assume two neutrino flavors only (i.e. the electon and the muon neutrinos). They are linear superposition of the n1,n2 eigenstaten: (eq.7) Using eq. 5 in eq. 3, we get:

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At t=0, eq. 7 becomes: By inversion of eq. 8: (eq.8) For the experimental point of view (accelerators, reactors), a pure muon (or electron) state a t=0 can be prepared. For a pure beam, eq. 9: (eq.9) (eq.10)

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The time evolution of the state of eq. 8 : By definition, the probability that the state at a given time is a is: (eq. 12) Using eq. 11, the probability: i.e. using trigonometry rules: (eq.11) (eq. 13) (eq. 14)

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Finally, using eq.5: With the following substitutions in eq.15: - the neutrino path length L=ct (in Km) - the mass difference m 2 = m 2 2 – m 1 2 (in eV 2 ) - the neutrino Energy E (in GeV) To see “oscillations” pattern: (eq. 15) (eq. 16)

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How do we search for neutrino oscillations?

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..with atmospheric neutrinos m 2, sin 2 2 from Nature; E = experimental parameter (energy distribution of neutrino giving a particular configuration of events) L = experimental parameter (neutrino path length from production to interaction)

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Appearance/Disappearance

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Atmospheric neutrinos

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The recipes for the evaluation of the atmospheric neutrino flux-

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E -3 spectrum GZK cut < E< eV galactic ? E < eV Galactic E eV Extra-Galactic? Unexpected? < E< eV i) The primary spectrum

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ii)- CR-air cross section pp Cross section versus center of mass energy. Average number of charged hadrons produced in pp (and pp) collisions versus center of mass energy It needs a model of nucleus-nucleus interactions

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iii) Model of the atmosphere ATMOSPHERIC NEUTRINO PRODUCTION: high precision 3D calculations, refined geomagnetic cut-off treatment (also geomagnetic field in atmosphere) elevation models of the Earth different atmospheric profiles geometry of detector effects

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Output: the neutrino ( e, ) flux See for instance the FLUKA MC: utrino.html

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iv) The Detector response Fully Contained Partially Contained Energy spectrum of for each event category Through going Stopping Energy spectrum (from Monte Carlo) of atmospheric neutrinos seen with different event topologies (SuperKamiokande) up-stop up-thru

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Rough estimate: how many ‘Contained events’ in 1 kton detector 1. Flux: ~ 1 cm -2 s Cross section 1GeV): ~ cm 2 3. Targets M= ( nucleons/kton ) 4. Time t= s/y N int = (cm -2 s -1 ) x (cm 2 )x M (nuc/kton) x t (s/y) ~ ~ 100 interactions/ (kton y) e

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15 years of Super-Kamiokande Start data taking K2K started data taking was stopped for detector upgrade Accident partial reconstruction data taking was resumed data taking stopped for full reconstruction data taking was resumed 2001 Evidence of solar oscillation (SNO+SK) 1998 Evidence of atmospheric oscillation (SK) 2005 Confirm oscillation by accelerator (K2K) SK-I SK-II SK-III SK-IV 2009 data taking

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Measurement of contained events and SuperKamiokande (Japan) 1000 m Deep Underground ton of Ultra-Pure Water PMTs Working since 1996

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As a charged particle travels, it disrupts the local electromagnetic field (EM) in a medium. Electrons in the atoms of the medium will be displaced and polarized by the passing EM field of a charged particle. Photons are emitted as an insulator's electrons restore themselves to equilibrium after the disruption has passed. In a conductor, the EM disruption can be restored without emitting a photon. In normal circumstances, these photons destructively interfere with each other and no radiation is detected. However, when the disruption travels faster than light is propagating through the medium, the photons constructively interfere and intensify the observed Cerenkov radiation. Cherenkov Radiation

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Effetto Cerenkov Per una trattazione classica dell’effetto Cerenkov: Jackson : Classical Electrodynamics, cap 13 e par e 13.5 La radiazione Cerenkov e’ emessa ogniqualvolta una particella carica attraversa un mezzo (dielettrico) con velocita’ c=v>c/n, dove v e’ la velocita’ della particella e n l’indice di rifrazione del mezzo. Intuitivamente: la particella incidente polarizza il dielettrico gli atomi diventano dei dipoli. Se >1/n momento di dipolo elettrico emissione di radiazione. <1/n 1/n

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L’ angolo di emissione c puo’ essere interpretato qualitativamente come un’onda d’urto come succede per una barca od un aereo supersonico. Esiste una velocità di soglia s = 1/n c ~ 0 Esiste un angolo massimo max = arcos(1/n) La cos( ) =1/ n e’ valida solo per un radiatore infinito, e’ comunque una buona approssimazione ogniqualvolta il radiatore e’ lungo L>> essendo la lunghezza d’onda della luce emessa

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Numero di fotoni emessi per unità di percorso e intervallo di lunghezza d’onda. Osserviamo che decresce al crescere della Il numero di fotoni emessi per unita’ di percorso non dipende dalla frequenza

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L’ energia persa per radiazione Cerenkov cresce con . Comunque anche con 1 e’ molto piccola. Molto piu’ piccola di quella persa per eccitazione/ionizzazione (Bethe Block), al massimo 1%.

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1)Esiste una soglia per emissione di luce Cerenkov 2)La luce e’ emessa ad un angolo particolare Facile utilizzare l’effetto Cerenkov per identificare le particelle. Con 1) posso sfruttare la soglia Cerenkov a soglia. Con 2) misurare l’angolo DISC, RICH etc. La luce emessa e rivelabile e’ poca. Consideriamo un radiatore spesso 1 cm un angolo c = 30 o ed un E = 1 eV ed una particella di carica 1. Considerando inoltre che l’efficienza quantica di un fotomoltiplicatore e’ ~20% N pe =18 fluttuazioni alla Poisson

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Cherenkov Radiation One of the PMTs of SK

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How to tell a from a e : Pattern recognition

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e

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e or Fully Contained (FC) No hit in Outer Detector One cluster in Outer Detector Partially Contained (PC) Reduction Automatic ring fitter Particle ID Energy reconstruction Fiducial volume (>2m from wall, 22 ktons) E vis > 30 MeV (FC), > 3000 p.e. (~350 MeV) (PC) Fully Contained 8.2 events/day E vis <1.33 GeV : Sub-GeV E vis >1.33 GeV : Multi-GeV Partially Contained 0.58 events/day Contained event in SuperKamiokande

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Contained events. The up/down symmetry in SK and e ratio. Up/Down asymmetry interpreted as neutrino oscillations Expectations: events inside the detector. For E > a few GeV, Upward / downward = 1 E =0.5GeV E =3 GeVE =20 GeV

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Zenith angle distribution SK:1289 days (79.3 kty) /e DATA /e MC = Data Electron neutrinos = DATA and MC (almost) OK! Muon neutrinos = Large deficit of DATA w.r.t. MC ! Zenith angle distributions for e-like and µ-like contained atmospheric neutrino events in SK. The lines show the best fits with (red) and without (blue) oscillations; the best-fit is m 2 = 2.0 × 10 −3 eV 2 and sin 2 2θ = 1.00.

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Zenith Angle Distributions (SK-I + SK-II) – oscillation (best fit) null oscillation - like e- like P<400MeV/c P>400MeV/c P<400MeV/c P>400MeV/c NOTE: All topologies, last results (September 2007) Livetime SK-I 1489d (FCPC) 1646d (Upmu) SK-II 804d (FCPC) 828d(Upmu)

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Atmospheric Neutrino Anomaly Summary results since the mid-1980's: /e Data /e MC R’= Water Cherenkov Calorimetric Double ratio between the number of detected and expected and e

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Upgoing muons and MACRO (Italy) R.I.P December 2000

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The Gran Sasso National Labs

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Up stop In down 1) 2) 3) 4) Neutrino event topologies in MACRO In upUp throughgoing Absorber Streamer Scintillator Liquid scintillator counters, (3 planes) for the measurement of time and dE/dx. Streamer tubes (14 planes), for the measurement of the track position; Detector mass: 5.3 kton Atmospheric muon neutrinos produce upward going muons Downward going muons ~ 10 6 upward going muons Different neutrino topologies

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Energy spectra of events in MACRO ~ 50 GeV throughgoing ~ 5 GeV, Internal Upgoing (IU) ; ~ 4 GeV, internal downgoing (ID) and for upgoing stopping (UGS) ;

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+1 -1 T1T1 T2T2 Streamer tube track Neutrino induced events are upward throughgoing muons, Identified by the time-of-flight method Atmospheric : downgoing from upgoing

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MACRO Results: event deficit and distortion of the angular distribution Observed= 809 events Expected= 1122 events (Bartol) Observed/Expected = 0.721±0.050 (stat+sys) ±0.12 (th) No oscillations ____ Best fit m 2 = 2.2x10 -3 eV 2 sin 2 2 =1.00

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MACRO Partially contained events consistent with up throughgoing muon results Obs. 262 events Exp. 375 events Obs./Exp. = 0.70±0.19 ) Obs. 154 events Exp. 285 events Obs./Exp. = 0.54±0.15 IU ID+UGS MC with oscillations

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underground detector Effects of oscillations on upgoing events Earth If is the zenith angle and D= Earth diameter L=Dcos For throughgoing neutrino-induced muons in MACRO, E = 50 GeV (from MC) cos

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Oscillation Parameters The value of the “oscillation parameters” sin 2 and m 2 correspond to the values which provide the best fit to the data Different experiments different values of sin 2 and m 2 The experimental data have an associated error. All the values of (sin 2 , m 2 ) which are compatible with the experimental data are “allowed”. The “allowed” values span a region in the parameter space of (sin 2 , m 2 ) 1.9 x eV 2 < m 2 < 3.1 x eV 2 sin 2 2 > 0.93(90% CL)

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“Allowed” parameters region 90% C. L. allowed regions for ν → ν oscillations of atmospheric neutrinos for Kamiokande, SuperK, Soudan-2 and MACRO.

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Why not ν μ ν e ? Apollonio et al., CHOOZ Coll., Phys.Lett.B466,415

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disappearance: History Anomaly in R=( /e) observed /( /e) predicted – Kamiokande: PLB 1988, 1992 – Discrepancies in various experiments Kamiokande: Zenith-angle distribution – Kamiokande: PLB 1994 Super-Kamiokande/MACRO: Discovery of oscillation in 1998 – Super-Kamiokande: PRL 1998 – MACRO, PRL 1998 K2K: First accelerator-based long baseline experiment: 1999 – 2004 Confirmed atmospheric neutrino results – Final result 4.3 : PRL 2005, PRD 2006 MINOS: Precision measurement: – First result: PRL2006 Kajita: Neutrino 98

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See for review: The “Neutrino Industry” – Janet Conrad web pages: – Fermilab and KEK “Neutrino Summer School” – Torino web Pages: – Progress in the physics of massive neutrinos, hep- ph/

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Oscillations with neutrino telescopes Oscillations occur for E < 100 GeV Low energy muons dE/dx 2 MeV/cm. Not dependent from E Muon energy estimated from the muon range ANTARES

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How oscillations are seend Distribution of Eν /cosΘ for the selected events of the atmospheric neutrino simulation. Solid lines are without oscillations, the dashed lines include oscillations assuming the best fit values reported in PDG. The red histograms indicate the contribution of the single-line sample, in blue the multi-line events. ANTARES: Range of a 50 GeVmuon= 100 m Distance between storeys = 14.5 m Distance between strings 60 m

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Normalised fit quality of the final multi-line (left) and single-line (right) samples. Data with statistical errors (black) are compared to simulations from atmospheric with oscillations assuming parameters from PDG (red) and without oscillations (green) and atmospheric muons (blue). For a fit quality larger than 1.6 (multi-line) or 1.3 (single-line) the misreconstructed atmospheric muons dominate. The arrows indicate the chosen regions. The role of muon reconstruction

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Results Left: Distribution of E R /cosΘ R for selected events. Black crosses are data, the blue histogram shows simulations of atmospheric without neutrino oscillations (scaled down by a factor 0.86) plus the residual background from atmospheric muons. The red histogram shows the result of the fit assuming oscillations. Right: The fraction of events with respect to the non-oscillation hypothesis.

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Oscillation parameters The best fit point is indicated by the triangle. The solid filled regions show results at 68% C.L. from K2K (green), MINOS (blue) and Super-Kamiokande (magenta) for comparison. 68% and 90% C.L. contours (solid and dashed red lines) of the oscillation parameters as derived from the fit of the of E R /cosΘ R distribution.

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