Neutrino oscillations Oleg Lychkovskiy ITEP 2008 Plan n

Neutrino oscillations Oleg Lychkovskiy ITEP 2008

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

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

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

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

Two-flavor oscillations, wave packet formalism

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:

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

Three-flavor mixing Unknown: absolute values of masses, θ 13 , δ, α 1 , sign of Δm 232 , octet of θ 23

Three-flavor mixing sin 2 13 3 | m 232 | (Mass)2 2 1 or } m 2 21 | m 232 | 3 sin 2 13 inverted hierarchy normal hierarchy e 2 1

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

Three-flavor oscillations: νμ νl’ L Δm 221 /4 E<< π, sin 2 13 neglected Assume Then, neglecting Relevant for the majority of accelerator experiments and for atmospheric neutrinos and one obtains Example: K 2 K (E=1 Ge. V, L=250 km)

Three-flavor oscillations: νe , sin 2 13 neglected Assume the detector registers only electron neutrinos Neglecting |Ue 3|2 = |s 13|2 < 0. 05 , one obtains The same result one can get in a more illuminating way

Three-flavor oscillations: νe , sin 2 13 neglected Two-flavor mixing effectively! = 12 , m 2= m 221 Relevant for Kam. LAND

Three-flavor oscillations: νe , small baselines, 13 in play If one does not neglect s 132 , oscillations with small amplitude ~ s 132 and small period Losc = 4 E/Δm 231 are superimposed on the Δm 21– If in related additionoscillations. one comes to http: //dayawane. ihep. ac. cn/docs/experiment. html Example: Double Chooz (E=4 Me. V, L=1 km Relevant for

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

Matter (MSW) effect for the details see lecture notes by Y. Nir, ar. Xiv: 0708. 1872

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

Relevance of matter effect Earth: ρ =(1 -10) g/cm 3 Key parameter: V = (0. 4 -4) 10 -13 e. V Reactors: E ~ few Me. V Δm 212 /2 E ~ (1 -10)10 -11 e. V Δm 312 /2 E ~ (3 -30)10 -10 e. V Matter effect is irrelevant Supernova core: ρ ~ 1012 g/cm 3 Sun core: E ~10 Me. V r~ 100 g/cm 3 V ~ 0. 1 e. V V ~0. 5 · 10 -11 e. V 2 /2 E ~0. 5 · 10 -11 e. V Δ m 21 E ~ (0. 5 -20) Me. V Δm 312 /2 E ~ 10 -10 e. V Overwhelming Δm 212 /2 E ~(0. 2 -8)10 -11 e. V relevant matter effect! Accelerators, atmospheric neutrinos: E ~ few Ge. V Δm 212 /2 E ~ (0. 1 -1)10 -13 e. V Δm 312 /2 E ~ (0. 6 -24) 10 -10 e. V 2 -12 Δm 31 /2 E ~ (0. 3 -3)10 e. V irrelevant Matter effect may be relevant

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

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).

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

SOURSE ν/ν, flavor relevant energy MSW what was (can be) extracted Sun νe 0. 5 -19 Me. V of major importance θ 12 , m 221 irrelevant m 221, θ 12 θ 13 relevant θ 23 , m 232 octant of θ 23 Reactors νe 1 -6 Me. V Cosmic rays νμ, 0. 1 Ge. V minor fraction (atmospheric of other 10 Te. V flavor s ν’s) νμ, Accelerators minor fraction of other flavors Supernova all species 0. 5 -50 Ge. V relevant of major 1 -40 Me. V importance m 232, θ 23 θ 13 , δ hierarchy, octant hierarchy, θ 13

Solar neutrinos

Neutrino oscillations in the matter of the Sun We are interested in νe oscillations and we neglect θ 13 Effectively two-flavor case with 1 -2 mixing: θ =θ 12 , m 2= m 221 ne=ne(r), r is the distance from the center of the Sun adiabaticity condition holds: , m=m(r), θ= θ(r)

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

Neutrino oscillations in the matter of the Sun Probability weakly depends on m 221 , but, nevertheless, is sensitive to its sign!

Radiochemical experiments Homestake: SAGE, GALLEX/GNO: νe + 37 Cl 37 Ar + e- νe + 71 Ga 71 Ge + e- 37 Cl + e+ + νe 71 Ga + e+ + νe 37 Ar 71 Ge Eth=0. 86 Me. V Eth=0. 23 Me. V t 1/2=35 days t 1/2=11. 4 days Result: ~ 4 times less neutrinos, than predicted by the SSM Result: ~ 2 times less neutrinos, than predicted by the SSM

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

Borexino Main goal: mono-energetic (E= 862 кэ. В) 7 Be neutrinos Scintillation detector: low threshold (Eth= 0. 5 Me. V), but no direction measured !!!First real-time low-energy solar neutrinos: 47 ± 7 stat ± 12 syst 7 Be ν / (day · 100 t) (ar. Xiv: 0708. 2251)

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

Kam. LAND • Sources of : 55 Japanese reactors • Baselines: L=(140 - 210) km • energies: 1. 7 Me. V < E < 9. 3 Me. V • Probability of survival: Status: running Sensitive to Δm 221 and θ 12

Kam. LAND ar. Xiv: 0801. 4589 v 2 !!!The latest result: Also 70± 27 geo-neutrinos registered!

Chooz • Source: Chooz nuclear station • Baseline: L=1. 05 km • energies: 3 Me. V < E < 9 Me. V • Probability of survival: Status: finished The final result: sin 22θ 13 < 0. 2 90%CL

Future experiments: Double Chooz and Bay Goal: Daya measuring θ 13 Daya Bay near Double detectors Chooz will be built sin 22θ 13 < 0. 01 sin 22θ 13 < 0. 03 Double Chooz sensitivity evolution the initial spectrum will be measured, by 2013 ar. Xiv: hep-ex/0701020 v 3 not bycalculated 2012

Double Chooz and Daya Bay sensitivities

Atmospheric neutrinos • Source: cosmic rays, interacting with the atmosphere. Major fraction: Minor fraction: Negligible fraction: • Detection reactions: deep inelastic scattering νμ + N μ + hadrons • Experiments: Kamiokande, IMB, Super-Kamiokande, Amanda, Baikal, MACRO, Soudan, Ice. Cube, … • “Baselines”: L=(0 - 13000) km • Energies: 0. 1 Ge. V < E < 10 Te. V

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

Atmospheric neutrino fluxes

SK atmospheric neutrino results sin 22θ 23 > 0. 92 1. 5 · 10 -3 < m 232 < 3. 4 · 10 -3 e. V 2 90% CL Evidence for appearance! Phys. Rev. Lett. 97: 171801, 2006, hep-ex/0607059 Prospects for resolving hierarchy ambiguity ar. Xiv: 0707. 1218 Phys. Rev. D 71 (2005) 112005, ar. Xiv: hep-ex/0501064 v 2

Accelerator neutrino experiments • νμ and νμ are produced decays in meson oscillations • energies: few Ge. V μ hundreds of kilometers • baselines: Main goals: appearance observations: search for e or τ measuring 13 precise measurement of m 223 , 23 mass hierarchy CP

Accelerator neutrino experiments К 2 К MINOS OPERA Mini. Boo. NE Т 2 К NOVA LSND e m 232, sin 22 23 sterile 13 For К 2 К, MINOS (? ) and OPERA (? ) L Δm 221 /4 E<< π, 13=0 approximation is valid T 2 К, NOv. A and, probably, OPERA and MINOS, will go beyond this approximation! CP(? )

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

First LBL experiment К 2 К disappearance 1999 -2005 e L/E 200 L=250 km <E > 1. 3 Ge. V Predictions of flux and interactions at Far Detector by Far/Near ratio 98. 2% 1. 3% Signal of oscillation at K 2 K Reduction of events Distortion of energy spectrum ~1 event/2 days at SK

K 2 K final result - # Events + PRD 74: 072003, 2006 - Shape distortion Expected: 158. 1 + 9. 2 – 8. 6 Observed: 112 Expected shape (no oscillation) Best fit Null oscillation probability (shape + # events) = 0. 0015% (4. 3 ) Best fit values sin 22 = 1. 00 m 2 [e. V 2] = (2. 80 0. 36) 10 -3 Kolmogorov-Smirnov test Best fit probability = 37%

MINOS Precise study of “atmospheric” neutrino oscillations, using the NUMI beam and two detectors Far Det: 5400 tons 735 km Near Det: 980 tons Beam: Nu. MI beam, 120 Ge. V 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)

New MINOS result 2. 50 POT analyzed ≈ 2 x statistics of 2006 result Improved analysis J. Thomas, talk at Lepton-Photon 2007 # expected (no osc. ) 738 30 # observed 563 Comparison of new and old MINOS results m 223 =(2. 38 +0. 20 -0. 16) x 10 -3 sin 22 23=1. 00 -0. 08

m 223 and 23: SK/K 2 K/MINOS | m 223| | m 213|= (2. 4 0. 2)x 10 -3 e. V 2 23 ~ 45 o

MINOS: projected sensitivity M. Ishitsuka, talk at NNN 07 After 5 years running: expected accuracy of m 232 and sin 22 23 10% chance for first indication of non-zero 13

OPERA direct search P( ) = cos 4 13 sin 2 23 sin 2[1. 27 m 223 L(km)/E(Ge. V) ] High energy, long baseline beam ( E 17 Ge. V kink Target mass 1 mm L ~ 730 km ) ~1300 t E/L ~ 2. 3 10 -2 10 m 223 (atm) pure beam: 2% anti <1% e Pb Emulsion layers after 5 years data taking: ~22000 interactions ~12 reconstructed <1 background event

OPERA: sensitivity M. Spinetti, talk at NNN 07 full mixing, 5 years run 4. 5 x 1019 pot/y New MINOS

Second generation LBL experiments Off Axis Neutrino Beams • Increases flux on oscillation maximum • Reduces high-energy tail and NC backgrounds • Reduces e contamination from K and decay T 2 K NOVA

T 2 K (Tokai to Kamioka) JPARC facility beam off-axis E(Ge. V) Int(1012 ppp) Rate (Hz) Power (MW) JPARC 50 330 0. 29 0. 77 ~1 Ge. V beam ( 100 of K 2 K) on-axis MINOS 120 40 0. 53 0. 41 Opera 400 24 0. 17 0. 5 K 2 K 12 6 0. 45 0. 0052 Statistics at SK OAB 2. 5 deg, 1 yr = 1021 POT, 22. 5 kt ~ 2200 tot ~ 1600 charged current e < 0. 5% at peak

T 2 K off-axis beam Super. K 0 o OA 2° Target. Horns Decay Pipe OA 2. 5° OA 3° 0 deg

Principle Goals of T 2 K - Search for e appearance 13 sensitivity 1 o (90% c. l. ) Background uncertainty CP = 0 CP = /2 CP = - /2 CP = -Measurement m 223 with accuracy of 1% (sin 22 23) 0. 01 ( m 223) < 1 10 -4 e. V 2 10% m 2=2. 5 x 10 -3

T 2 K sensitivity to 13 CHOOZ limit ambiguities: CP - 13 sign m 223 23

NO A P( e) depends on sin 22 13 sign m 223 CP matter effects increase (decrease) oscillations for normal (inverted) hierarchy for Mass hierarchy can be resolved if 13 near to present limit using both anti- beams and sin 22 13 from T 2 K + reactor experiments

13 sensitivities vs time A. Blondel et al. , hep-ph/0606111 Daya Bay goal Short baseline reactor experiments Double-Chooz and Daya Bay 13 ( insensitive to CP)

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

Neutrino production in SN

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

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

Level crossing scheme for SN

Mass hierarchy and θ 13 NH, L IH, L NH and IH, S 0 1 1 1 0 1 NH=Normal Hierarchy, IH=Inverted Hierarchy L=Large θ 13 : θ 13 >0. 03 S=Small θ 13 : θ 13 < 0. 003

Takahashi, Sato, hep-ph/0205070 Future SN neutrino signal in SK R=10 kpc

θ 13 measurment with SN If and the hierarchy is inverted, than θ 13 is measurable! Takahashi, Sato, hep-ph/0205070

Conclusions Present knowledge: central value 2 interval m 212 (10 -5 e. V 2) 7. 6 7. 1 - 8. 3 m 231 (10 -3 e. V 2) 2. 4 2. 0 - 2. 8 sin 2 12 0. 32 0. 26 - 0. 40 sin 2 23 0. 50 0. 34 - 0. 67 sin 2 13 0. 0 <0. 05 5 -year goals: • to increase the sensitivity for m 212 , m 231 , sin 2 12 , sin 2 23 up to (1 -10)% • sin 2 13 sensitivity at the level 0. 003 • mass hierarchy, (? )