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Neutrino oscillations Oleg Lychkovskiy ITEP2008

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Plan Lecture I Lecture I Introduction Introduction Two-flavor oscillations Two-flavor oscillations Three- flavor oscillations Three- flavor oscillations Matter effect Matter effect Lecture II Lecture II Overview of experiments and observations.

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Introduction: acquaintance with neutrinos SM interactions: Low energy (E<<100 GeV) interactions: β – decay: (Z, A) (Z+1,A) + e - + v e v e – capture: v e + p n + e + π – decay: Deep inelastic scattering: … and so on Typical energies: MeV-PeV >> m: always ultrarelativistic!

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Two-flavor oscillations Key feature: flavor eigenstates, in which neutrinos are created and detected, do not coincide with mass eigenstates! m 1 and m 2 - masses of v 1 and v 2

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Two-flavor oscillations, wave packet formalism (at given t only x=Vt ± a/2 are relevant)

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Two-flavor oscillations, wave packet formalism

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Two-flavor oscillations, plane wave formalism Final oscillation probability does not depend on the specific form of the wave packet F(x)! Thus we may put F(x)=1, x=L and drop the integration over x! We get the same final result with less calculations:

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Three-flavor mixing 3 angles: θ 12, θ 13, θ 23 3 angles: θ 12, θ 13, θ 23 ν e, ν μ, ν τ - flavor eigenstates ν 1, ν 2, ν 3 - mass eigenstates with masses m 1, m 2, m 3 2 CP-violating Majorana phases: α 1, α 2 2 CP-violating Majorana phases: α 1, α 2 (physical only if are Majorana fermions) (physical only if ν’s are Majorana fermions) 1 CP-violating Dirac phase: δ 1 CP-violating Dirac phase: δ

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Three-flavor mixing Unknown: absolute values of masses, θ 13, δ, α 1, α 1, sign of Δm 2 32, octet of θ 23

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Three-flavor mixing e normal hierarchy inverted hierarchy m 2 32 (Mass) 2 m 2 21 } m 2 32 m 2 21 } or sin 2 13

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Three-flavor oscillations In particular, one can see that Majorana phases do not enter the oscillation probability

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Three-flavor oscillations: ν μ ν l’ L Δm 2 21 /4E<< π, sin 2 13 neglected Assume Then, neglecting and one obtains Relevant for the majority of accelerator experiments and for atmospheric neutrinos Example: K2K (E=1GeV, L=250km)

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Three-flavor oscillations: ν e ν e, sin 2 13 neglected Assume the detector registers only electron neutrinos Neglecting |U e3 | 2 = |s 13 | 2 < 0.05, one obtains The same result one can get in a more illuminating way

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Three-flavor oscillations: ν e ν e, sin 2 13 neglected Two-flavor mixing effectively! = 12 m 2 m 2 21 Relevant for KamLAND

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Three-flavor oscillations: ν e ν e, small baselines, 13 in play If one does not neglect s 13 2, oscillations with small amplitude ~ s 13 2 and small period L osc = 4E/Δm 2 31 are superimposed on the Δm 21 – related oscillations. If in addition one comes to Relevant for Double Chooz, Daya Bay Example: Double Chooz (E=4 MeV, L=1 km)

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Matter (MSW) effect in neutrino oscillations ν e -e interaction (through W-boson exchange): averaging of this Lagrangian over the matter electrons gives an effective matter potential: ν l -e interaction through Z-boson exchange does not depend on flavor and thus does not influence oscillations ν l -e interaction through Z-boson exchange does not depend on flavor and thus does not influence oscillations

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Matter (MSW) effect for the details see lecture notes by Y.Nir, arXiv:

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Neutrinos in matter, two-flavor case, n e =const Resonance: Overwhelming matter effect: Oscillations with the maximal amplitude! No oscillations!

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Relevance of matter effect Supernova core: ρ ~ g/cm 3 E ~10 MeV V ~ 0.1 eV Δm 21 2 /2E · eV Δm 21 2 /2E ~0.5 · eV Δm 31 2 /2E eV Δm 31 2 /2E ~ eVOverwhelming matter effect! Key parameter: Sun core: ~ 100 g/cm 3 · V ~0.5 · eV E ~ (0.5-20) MeV Δm 21 2 /2E eV Δm 21 2 /2E ~(0.2-8) eVrelevant Δm 31 2 /2E eV Δm 31 2 /2E ~ (0.6-24) eVirrelevant Earth: Earth: ρ =(1-10) g/cm 3 V = (0.4-4) eV Reactors: E ~ few MeV Δm 21 2 /2E eV Δm 21 2 /2E ~ (1-10) eV Δm 31 2 /2E (3-30) eV Δm 31 2 /2E ~ (3-30) eV Matter effect is irrelevant Accelerators, atmospheric neutrinos: Accelerators, atmospheric neutrinos: E ~ few GeV Δm 21 2 /2E eV Δm 21 2 /2E ~ (0.1-1) eV Δm 31 2 /2E (0.3-3) eV Δm 31 2 /2E ~ (0.3-3) eV Matter effect may be relevant

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Remarks upon the previous lecture Misprint: tree-flavor three-flavor Misprint: tree-flavor three-flavor MSW effect = Mikheyev-Smirnov-Wolfenstein effect MSW effect = Mikheyev-Smirnov-Wolfenstein effect “octant”=… = 1/4 of the coordinate plane “octant”=… = 1/4 of the coordinate plane

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Lecture II. Neutrino oscillations. Overview of experiments and observations. Based on the review by O.Lychkovskiy, A.Mamonov, L.Okun, M.Rotaev, to be published in UFN (УФН).

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Three-flavor mixing 3 angles: θ 12, θ 13, θ 23 3 angles: θ 12, θ 13, θ 23 ν e, ν μ, ν τ - flavor eigenstates ν 1, ν 2, ν 3 - mass eigenstates with masses m 1, m 2, m 3 2 CP-violating Majorana phases: α 1, α 2 2 CP-violating Majorana phases: α 1, α 2 (physical only if are Majorana fermions) (physical only if ν’s are Majorana fermions) 1 CP-violating Dirac phase: δ 1 CP-violating Dirac phase: δ

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SOURSE ν/ν, flavor relevant energy MSW what was (can be) extracted Sunνeνe MeV of major importance θ 12 θ 12 m 2 21 Reactorsνeνe 1-6 MeV irrelevant, θ 12 m 2 21, θ 12 θ 13 Cosmic rays (atmospheric ) ν’s) ν μ, ν μ, minor fraction of other flavor s 0.1 GeV - 10 TeV relevant θ 23 θ 23 m 2 32 octant of θ 23 Accelerators ν μ, ν μ, minor fraction of other flavors GeV relevant, θ 23 m 2 32, θ 23 θ 13, θ 13, δ hierarchy, octant Supernova all species 1-40 MeV of major importance hierarchy, θ 13

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Solar neutrinos

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Neutrino oscillations in the matter of the Sun θ 13 We are interested in ν e ν e oscillations and we neglect θ 13 n e =n e (r), r is the distance from the center of the Sun Effectively two-flavor case with 1-2 mixing: θθ 12 θ =θ 12, m 2 = m 2 21 θ= θ(r), m=m(r), θ= θ(r) adiabaticity condition holds:

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Neutrino oscillations in the matter of the Sun At the Earth (r=R) where averaging over the production point r 0 is performed

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Neutrino oscillations in the matter of the Sun Probability weakly depends on m 2 21, but, nevertheless, is sensitive to its sign!

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Radiochemical experiments Homestake: ν e + 37 Cl 37 Ar + e - 37 Ar 37 Cl + e + + ν e E th =0.86 MeV t 1/2 =35 days Result: ~ 4 times less neutrinos, than predicted by the SSM SAGE, GALLEX/GNO: ν e + 71 Ga 71 Ge + e - 71 Ge 71 Ga+ e + + ν e 71 Ge 71 Ga + e + + ν e E th =0.23 MeV t 1/2 =11.4 days Result: ~ 2 times less neutrinos, than predicted by the SSM

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Cherenkov detector experiments Kamiokande ((1-3) kt of H 2 O) and Super-Kamiokande (50 kt of H 2 O): ν l + e ν l + e SNO: (1 kt of D 2 O): ν e + d p + p + e ν l + d p + n + ν l ν l + e ν l + e E th >5 MeV The total flux was measured, and it coincided with the SSM prediction! SSM verified the ν e deficite is due to oscillations! SSM verified the ν e deficite is due to oscillations!

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Borexino Main goal: mono-energetic (E= 862 кэВ) 7 Be neutrinos Scintillation detector: low threshold (E th = 0.5 MeV), but no direction measured !!!First real-time low-energy solar neutrinos: 47 ± 7 stat ± 12 syst 7 Be ν / (day · 100 t) (arXiv: )

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Reactor Reactor experiments ν e : -decays in nuclear reactors: produced in β-decays in nuclear reactors: (A,Z) (A,Z+1) + e - + (A,Z) (A,Z+1) + e - + ν e n + e + detected through ν e + p n + e + scintillation detectors used scintillation detectors used antineutrino energy: few MeV antineutrino energy: few MeV Long-baseline, L=O(100) km: KamLAND Short-baseline, L=O(1) km: Chooz, Double Chooz, Daya Bay oscillations

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KamLAND Sources of : 55 Japanese reactors Sources of : 55 Japanese reactors Baselines: L=( ) km Baselines: L=( ) km energies: 1.7 MeV < E < 9.3 MeV energies: 1.7 MeV < E < 9.3 MeV Probability of survival: Probability of survival: Sensitive to Δm 2 21 and θ 12 Status: running

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KamLAND !!!The latest result: Also 70 ± 27 geo-neutrinos registered! arXiv: v2 arXiv: v2

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Chooz Source: Chooz nuclear station Source: Chooz nuclear station Baseline: L=1.05 km Baseline: L=1.05 km energies: 3 MeV < E < 9 MeV energies: 3 MeV < E < 9 MeV Probability of survival: Probability of survival: The final result: sin 2 2θ 13 < %CL Status: finished

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Future experiments: Double Chooz and Daya Bay Goal: measuring θ 13 Daya Bay sin 2 2θ 13 < 0.01 by 2013 Double Chooz sin 2 2θ 13 < 0.03 by 2012 Double Chooz sensitivity evolution arXiv:hep-ex/ v3 near detectors will be built near detectors will be built the initial spectrum will be measured, not calculated the initial spectrum will be measured, not calculated

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Double Chooz and Daya Bay sensitivities

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Atmospheric neutrinos Source: cosmic rays, interacting with the atmosphere. Source: cosmic rays, interacting with the atmosphere. Major fraction: Major fraction: Minor fraction: Minor fraction: Negligible fraction: Negligible fraction: Detection reactions: deep inelastic scattering Detection reactions: deep inelastic scattering ν μ + N μ + hadrons Experiments: Experiments: Kamiokande, IMB, Super-Kamiokande, Amanda, Baikal, MACRO, Kamiokande, IMB, Super-Kamiokande, Amanda, Baikal, MACRO, Soudan, IceCube, … Soudan, IceCube, … “Baselines”: L=( ) km “Baselines”: L=( ) km Energies: 0.1 GeV < E < 10 TeV Energies: 0.1 GeV < E < 10 TeV

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Atmospheric neutrinos Original flux and energy spectrum are poorly known large theoretical flux uncertainties MSW-effect and 3-flavor oscillations in play, extended source no simple precise expressions! Approximate expressions:

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Atmospheric neutrino fluxes

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SK atmospheric neutrino results Phys.Rev. D71 (2005) , arXiv:hep-ex/ v2 arXiv:hep-ex/ v2 sin 2 2θ 23 > < < eV · < m 2 32 < 3.4 · eV 2 90% CL 90% CL Evidence for appearance! Phys.Rev.Lett.97:171801,2006, hep-ex/ Prospects for resolving hierarchy ambiguity arXiv:

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Accelerator neutrino experiments ν μ and ν μ are produced in meson decays energies: few GeV energies: few GeV baselines: hundreds of kilometers baselines: hundreds of kilometers μ oscillations Main goals: appearance observations: search for e or τ measuring 13 precise measurement of m 2 23, 23 mass hierarchy CP

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Accelerator neutrino experiments К2К MINOS OPERA MiniBooNE Т2К NOVA LSND e m 23 2, sin 2 2 23 sterile 13 CP (?) For К2К, MINOS (?) and OPERA (?) L Δm 2 21 /4E<< π, 13 =0 approximation is valid T2К, NOvA and, probably, OPERA and MINOS, will go beyond this approximation!

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Next several slides are from the talk by Yury Kudenko at NPD RAS Session ITEP, 30 November 2007 Accelerator neutrino experiments

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L/E 200 L=250 km 1.3 GeV 98.2% e 1.3% First LBL experiment К2К ~1 event/2 days at SK Predictions of flux and interactions at Far Detector by Far/Near ratio Signal of oscillation at K2K Reduction of events Distortion of energy spectrum disappearance

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Expected: – 8.6 Observed: # Events Expected shape (no oscillation) Best fit Best fit values sin 2 2 = 1.00 m 2 [eV 2 ] = (2.80 0.36) Kolmogorov-Smirnov test Best fit probability = 37% Null oscillation probability (shape + # events) = % (4.3 ) K2K final result - Shape distortion PRD74:072003,2006 +

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Near Det: 980 tons Far Det: 5400 tons 735 km Beam: NuMI beam, 120 GeV Protons - beam Detectors: ND, FD Far Det: 5.4 kton magnetized Fe/Sci Tracker/Calorimeter at Soudan, MN (L=735 km) Near Det: 980 ton version of FD, at FNAL (L 1 km) Precise study of “atmospheric” neutrino oscillations, using the NUMI beam and two detectors MINOS

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New MINOS result 2.50 POT analyzed ≈ 2x statistics of 2006 result Improved analysis Comparison of new and old MINOS results J.Thomas, talk at Lepton-Photon2007 # expected (no osc.) 738 30 # observed 563 m 2 23 =( ) x sin 2 2 23 =

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m 2 23 and 23 : SK/K2K/MINOS | m 2 23 | | m 2 13 |= (2.4 0.2)x10 -3 eV 2 23 ~ 45 o

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After 5 years running: expected accuracy of m 23 2 and sin 2 2 23 10% chance for first indication of non-zero 13 MINOS: projected sensitivity M.Ishitsuka, talk at NNN07

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OPERA High energy, long baseline beam ( E 17 GeV L ~ 730 km ) direct search pure beam: 2% anti <1% e P( ) = cos 4 13 sin 2 23 sin 2 [1.27 m 2 23 L(km)/E(GeV) ] E/L ~ 2.3 10 m 2 23 (atm) Pb Emulsion layers 1 mm kink after 5 years data taking: ~22000 interactions ~120 interactions ~12 reconstructed <1 background event Target mass ~1300t

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OPERA: sensitivity full mixing, 5 years run 4.5 x10 19 pot/y M.Spinetti, talk at NNN07 New MINOS

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Second generation LBL experiments T2K NOVA Off Axis Neutrino Beams Increases flux on oscillation maximum Reduces high-energy tail and NC backgrounds Reduces e contamination from K and decay

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T2K (Tokai to Kamioka) ~1GeV beam ( 100 of K2K) JPARC facility on-axisoff-axis beam JPARC MINOS Opera K2K E(GeV) Int(10 12 ppp) Rate (Hz) Power (MW) Statistics at SK OAB 2.5 deg, 1 yr = POT, 22.5 kt ~ 2200 tot ~ 1600 charged current e < 0.5% at peak

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OA3° Target Horns Decay Pipe SuperK OA2° OA2.5° T2K off-axis beam 0 deg 0o0o

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Principle Goals of T2K Background uncertainty 10% CP = 0 CP = /2 CP = - /2 CP = - - Search for e appearance 13 sensitivity 1 o (90% c.l.) -Measurement m 2 23 with accuracy of 1% (sin 2 2 23 ) 0.01 ( m 2 23 ) < 1 eV 2 m 2 =2.5x10 -3

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CHOOZ limit T2K sensitivity to 13 ambiguities: CP - 13 sign m 2 23 23

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NO A Mass hierarchy can be resolved if 13 near to present limit using both anti- beams and sin 2 2 13 from T2K + reactor experiments matter effects increase (decrease) oscillations for normal (inverted) hierarchy for P( e ) depends on sin 2 2 13 sign m 2 23 CP

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13 sensitivities vs time A.Blondel et al., hep-ph/ Short baseline reactor experiments Double-Chooz and Daya Bay 13 ( insensitive to CP ) Daya Bay goal

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Summary for accelerator experiments K2K confirmation of atmospheric neutrino oscillations discovered by SK MINOS confirmed the SK и K2K results high precision measurements of oscillation parameters MiniBooNe rules out (98% cl) the LSND result as e oscilations with m 2 ~ 1 eV 2 new anomaly appears run with anti- beam OPERA data taking begun in 2007 T2K-I neutrino beam in 2009 Main goal for next 5 years: 13

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Neutrino production in SN

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Matter effect in Supernova Adiabaticity almost everywhere, resonant layers are possible exeptions Adiabaticity almost everywhere, resonant layers are possible exeptions Three flavors in play, two different resonanses Three flavors in play, two different resonanses H-резонанс: H-резонанс: L-резонанс: L-резонанс:

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Adiabaticity conditions Adiabaticity of H-resonance depends on θ 13 ! L- resonance is always adiabatical! In resonance layer the adiabaticity parameter reads

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Level crossing scheme for SN

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Mass hierarchy and θ 13 NH=Normal Hierarchy, IH=Inverted Hierarchy L=Large θ 13 : θ 13 >0.03 S=Small θ 13 : θ 13 < NH, L IH, L NH and IH, S

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Takahashi, Sato, hep-ph/ R=10 kpc Future SN neutrino signal in SK

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θ 13 measurment with SN If and the hierarchy is inverted, than θ 13 is measurable! Takahashi, Sato, hep-ph/

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Conclusions Present knowledge: central value 2 interval m 2 12 (10 -5 eV 2 ) m 2 31 (10 -3 eV 2 ) sin 2 sin 2 sin 2 < year goals: to increase the sensitivity for m 2 12, m 2 31, sin 2 12, sin 2 23 up to (1-10)% sin 2 13 sensitivity at the level mass hierarchy, (?)

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