Takaaki Kajita (ICRR, U.of Tokyo) Production of atmospheric neutrinos Some early history (Discovery of atmospheric neutrinos, Atmospheric neutrino anomaly) Discovery of neutrino oscillations Studies of atmospheric neutrino oscillations Sub-dominant oscillations –present and future- III International Pontecorvo Neutrino Physics School Alushta, Ukraine, Sep. 2007

Introduction We know that neutrinos have mass: e      23 =45±8  12 =34±3  13 < 11 Small  13 and  m 12 2 <<  m 23 2  OK to interpret the present data with 2 flavor oscillation framework: P(    )=1-sin 2 2  ij ・ sin 2 (1.27  m ij 2 ・ L/E) Atmospheric LBL Solar KamLAND Future experiments

Event statistics in atmospheric neutrino experiments TK and Y.Totsuka, RMP73, 85 (2001) Sorry: MINOS not included yet. More than 20,000 now.

Super-Kamiokande: history and plan accident SK full reconstruc tion SK-ISK-IISK-III today The following discussion: based on the SK-I+II (or SK-I) data

(  m 2, sin 2 2  )

SK-I+II atmospheric neutrino data CC e CC  SK-I: hep-ex/ SK-II 800 days Osc. No osc. SK-I: 92 kton ・ yr SK-II: 49 kton ・ yr Total: 141 kton ・ yr

Estimating the oscillation parameters Down- going Up- going Transition point (as a function of energy)   m 2 Confirmation of non-oscillated flux Accurate measurement possible due to small syst. in up/down (2% or less)

    2-flavor oscillation analysis (SK-I + SK-II combined analysis)     2-flavor oscillation analysis (SK-I + SK-II combined analysis) FC 1ring e-like FC multi-r e-like FC 1ring -like FC multi-r -like PC stop PC thru UP stop P lep Sub-GeV Multi-GeV CC e CC  38 event type and momentum bins x 10 zenith bins  380 bins 38 event type and momentum bins x 10 zenith bins  380 bins Various detector related systematic errors are different between SK-I and SK-II.  SK-I and SK-II data bins are not combined. Various detector related systematic errors are different between SK-I and SK-II.  SK-I and SK-II data bins are not combined. 380 bins for SK-I bins for SK-II  760 bins in total UP through non-showering UP through showering Each box has 10 zenith-angle bins

Poisson with systematic errors N obs : observed number of events N exp : expectation from MC  i : systematic error term  i : sigma of systematic error Definition of  2 Number of data bins Number of syst error terms  2 minimization at each parameter point (  m 2, sin 2 2 , …). Method (  2 version): G.L.Fogli et al., PRD 66, (2002).

70 systematic error terms ● (Free parameter) flux absolute normalization ● Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu < 5GeV ) ● Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu > 5GeV ) ● Flux; anti-nu_e / nu_e ratio ( E_nu < 10GeV ) ● Flux; anti-nu_e / nu_e ratio ( E_nu > 10GeV ) ● Flux; anti-nu_mu / nu_mu ratio ( E_nu < 10GeV ) ● Flux; anti-nu_mu / nu_mu ratio ( E_nu > 10GeV ) ● Flux; up/down ratio ● Flux; horizontal/vertical ratio ● Flux; K/pi ratio ● Flux; flight length of neutrinos ● Flux; spectral index of primary cosmic ray above 100GeV ● Flux; sample-by-sample relative normalization ( FC Multi-GeV ) ● Flux; sample-by-sample relative normalization ( PC + Up-stop mu ) ● Solar activity during SK1 ● Solar activity during SK-II ● M A in QE and single-  ● QE models (Fermi-gas vs. Oset's) ● QE cross-section ● Single-meson cross-section ● DIS models (GRV vs. Bodek's model) ● DIS cross-section ● Coherent-  cross-section ● NC/CC ratio ● nuclear effect in 16 O ● pion spectrum ● CC   cross-section ● Reduction for FC ● Reduction for PC ● Reduction for upward-going muon ● FC/PC separation ● Hadron simulation (contamination of NC in 1-ring  -like) ● Non- BG ( flasher for e-like ) ● Non- BG ( cosmic ray muon for mu-like ) ● Upward stopping/through-going mu separation ● Ring separation ● Particle identification for 1-ring samples ● Particle identification for multi-ring samples ● Energy calibration ● Energy cut for upward stopping muon ● Up/down symmetry of energy calibration ● BG subtraction of up through  ● BG subtraction of up stop  ● Non- e contamination for multi-GeV 1-ring electron ● Non- e contamination for multi-GeV multi-ring electron ● Normalization of multi-GeV multi-ring electron ● PC stop/through separation Flux (16) interaction (12) Detector, reduction and reconstruction (21×2) (SK-I+SK-II, independent) Detector, reduction and reconstruction (21×2) (SK-I+SK-II, independent)

    2 flavor analysis     2 flavor analysis Best Fit:m 2 = 2.5 x eV 2 sin 2 2 = 1.00  2 = / 755 dof (18%) 1.9 x eV 2 < m 2 < 3.1 x eV 2 sin 2 2 > 0.93at 90% CL 1.9 x eV 2 < m 2 < 3.1 x eV 2 sin 2 2 > 0.93at 90% CL 1489 days (SK-1)+ 800 days (SK-II) Preliminary  2 distributions

Allowed Parameter Space from atmospheric and Accelerator Long Baseline experiments Accuracy:  m 2 : Atm  LBL, sin 2 2  : still atm.

L/E analysis

Motivation: Really oscillation ? Before 2004, what we knew was that neutrinos change flavor if they propagate long enough distances. Other mechanisms were proposed to change the neutrino flavor. For example, they were neutrino decay or neutrino decoherence models.  -like multi-GeV + PC These models explained the atmospheric neutrino data well. decoherence decay oscillation

decoherence decay  Further evidence for oscillations  Strong constraint on oscillation parameters, especially  m 2  Further evidence for oscillations  Strong constraint on oscillation parameters, especially  m 2 Should observe this dip! SK collab. hep-ex/ L/E analysis P  = (cos 2  sin 2  ・ exp(– )) 2 m 22 L E P  = 1 – sin 2 2  ・ (1 – exp(–   )) 2 1 L E

L/E plot in 1998 SK evidence paper… Due to the bad L/E resolution events, the dip was completely washed out. (Or neutrinos decay….) Something must be improved….

Selection criteria Events are not used, if: ★ horizontally going events ★ low energy events Events are not used, if: ★ horizontally going events ★ low energy events Select events with high L/E resolution (  (L/E) < 70%) Select events with high L/E resolution (  (L/E) < 70%) FC single-ring  -like Full oscillation 1/2 oscillation  (L/E)=70% Similar cut for: FC multi-ring  -like, OD stopping PC, and OD through-going PC

L/E distribution MC (no osc.) SK-I+II, FC+PC, prelim.  The oscillation dip is observed. Mostly down-going Mostly up-going Osc. MC (osc.) (Preliminary)

Allowed oscillation parameters from the SK-I+II L/E analysis (preliminary) SK-I+II 2.0 x eV 2 < m 2 < 2.8 x eV 2 sin 2 2 > 0.93at 90% CL 2.0 x eV 2 < m 2 < 2.8 x eV 2 sin 2 2 > 0.93at 90% CL Consistent with the zenith-angle analysis Slightly unphysical region (  2 =0.5)

SK-I+II L/E analysis and non-oscillation models (preliminary) SK-I+II Osc. Decay Decoh. Oscillation gives the best fit to the data. Decay and decoherence models were disfavored by 4.8 and 5.3 , resp. Oscillation gives the best fit to the data. Decay and decoherence models were disfavored by 4.8 and 5.3 , resp. decoherence decay  2 (osc)=83.9/83dof  2 (decay)=107.1/83dof  2 (decoherence)=112.5/83dof

Seach for CC  events

Search for CC  events (SK-I) CC  events    hadrons ● Many hadrons ．．．． (But no big difference with other (NC) events ． ) BAD  - likelihood analysis ● Upward going only GOOD Zenith angle Only ～ 1.0 CC  FC events/kton ・ yr (BG (other events) ～ 130 ev./kton ・ yr) Only ～ 1.0 CC  FC events/kton ・ yr (BG (other events) ～ 130 ev./kton ・ yr) hadrons CC  MC

Selection of  events Pre-cuts: E(visible) >1,33GeV, most-energetic ring = e-like E(visible) Number of ring candidates Max. distance between primary vertex and the decay-electron vertex Sphericity in the lab frame Sphericity in the CM frame  MC Atm. MC data

Likelihood / neural-net distributions Likelihood Neural-net Down-going (no  ) Up-going Zenith-angle

Zenith angle dist. and fit results Likelihood analysis NN analysis cos  zenith , e, & NC background Dat a scaled  MC cos  zenith Number of events 138±48(stat) +15 / -32(syst)134±48(stat) +16 / -27(syst) 78±26(syst)78±27 (syst) Fitted # of  events Expected # of  events Zero tau neutrino interaction is disfavored at 2.4 . Hep-ex/

Constraints on non-standard oscillations

Oscillation to  or sterile ?  -like data show zenith-angle and energy dependent deficit of events, while e-like data show no such effect.   sterile    or x x sterile Propagation Interaction Difference in P(    ) and P(   sterile ) due to matter effect Neutral current interaction Z

Testing    vs.   sterile Up through muons    High E PC events (Evis>5GeV) Multi-ring e-like, with Evis >400MeV Neutral current Matter effect   sterile    sterile  Pure   sterile excluded (PRL85,3999 (2000))

Limit on oscillations to sterile   (sin  ・ sterile +cos  ・  ) If pure   , sin 2  =0 If pure   sterile, sin 2  =1 SK collab. draft in preparation Consistent with pure    SK-1 data

Mass Varying Neutrinos (MaVaN)? Neutrino dark energy scenario Relic neutrinos with their masses varied by ambient neutrino density (A.Nelson et al. 2004) Possibly their masses also varied by matter density or electron density beyond the MSW effect  m 2 →  m 2 ×(  e /  0 ) n (  0 =1.0mol/cm 3 ) mass varying with electron density 2 flavor Zenith angle analysis (assuming sin 2 2  =1.0) SK-I dataset Check the MaVaN model in atmospheric data

Neutrino flight length About 350m above see level Super-K detector: 1000m underground below the top of Mt. Ikenoyama Down-going neutrinos fly in the air except for the last 1 to (a few) km.

Excluding a pure MaVaN scenario n vs  m 2 for MaVaN model  2 -  2 min  m 2 =1.95x10 -3 )  2 -  2 min n Tested MaVaN scenario is strongly disfavored  m 2 n Best fit :  m 2 =1.95×10 -3 eV 2 n=-0.03  2 =172.2/178 dof Standard oscillation  m 2 →  m 2 ×(  e /  0 ) n

 survival probability for oscillation + decoherence Constraining decoherence parameter Pure decoherence is excluded at about 5 . It might be possible that oscillation and decoherence co-exists. Constraining the decoherence parameter with SK L/E analysis

 2 min = 83.8/81 d.o.f (  0,  m 2,sin 2 2  )= (0 GeV,2.4x10 -3 eV 2,1.0)  0 <1.4x GeV (90%C.L.)  0 (× GeV) New constraint on decoherence parameter SK collab. Draft in preparation SK-I+II More than factor 10 improvement over the previous upper limit (2× GeV) (Lisi et al, PRL 85, 1166 (2000) More than factor 10 improvement over the previous upper limit (2× GeV) (Lisi et al, PRL 85, 1166 (2000)

UNO MEMPHYS Hyper-K INO Super-K

Present: Study of dominant oscillation channels Future: Study of sub-dominant oscillations e     Solar, KamLAND Solar, KamLAND Atmospheric Long baseline Atmospheric Long baseline  12,  m 12 2 Known: Unknown:   13 Sign of  m 23 2 or (CP) If  23 ≠  /4, is it >  /4 or <  /4 ?  23, |  m 23 2 |  Future atmospheric exp’s Present and future osc. experiments

 13

Search for non-zero  13 in atmospheric neutrino experiments (  m 12 2 =0 and vacuum oscillation assumed) Since e is involved, the matter effect must be taken into account. Earth model Simulation Core Mantle

Search for non-zero  13 in atmospheric neutrino experiments Electron appearance in the multi-GeV upward going events. s 2 13=0.05 s 2 13=0.00 null oscillation Monte Carlo, SK 20yrs Electron appearance 1+multi-ring, e-like, GeV cos  E (GeV) cos  Matter effect (  m 12 2 =0 and vacuum oscillation assumed) Assuming 3 is the heaviest:

SK-I multi-GeV e-like data Multi-GeV, single-ring e-like Multi-GeV, multi-ring e-like (special) No evidence for excess of upward-going e-like events  No evidence for non-zero  13

 13 analysis from Super-K-I Normal Inverted Hep-ex/

 2 distributions SK-1 If the shape of  2 continues to be like this, (factor ～ 2) more data might constrain the interesting  13 region at 90%CL. CHOOZ limit

Future sensitivity to non-zero  13 s 2 2  12 =0.825 s 2  23 =0.40 ~ 0.60 s 2  13 =0.00~0.04  cp=45 o  m 2 12 =8.3e-5  m 2 23 =+2.5e-3 Positive signal for nonzero  13 can be seen if  13 is near the CHOOZ limit and sin 2  23 > yrs SK (450kton ・ yr) 33 3  for 80yrs SK ~4yrs HK (1.8Mton ・ yr) sin 2  23 = Approximate CHOOZ limit But probably after T2K/Nova…

Search for non-zero  13 with  disappearance in atmospheric exp. But I was unable to fine the sensitivity plots for magnetized iron detectors. Sorry… INO/2006/01 Project report

Sign of  m 2

 If  m 23 2 is positive, resonance for   If  m 23 2 is negative, resonance for anti-  If  m 23 2 is positive, resonance for   If  m 23 2 is negative, resonance for anti- Very important to measure the charge of leptons  Magnetized detector Very important to measure the charge of leptons  Magnetized detector (With resolution)  13 Blue = normal Red = inverted INO/2006/01 Project report  13 (sin 2  13 ) Significance (1.12Mtonyr) 7 deg (0.015) 1.6  9 (0.025) (0.036) (0.05)4.5

Can we discriminate positive and negative  m 2 in water Ch.?  (total) and d  /dy are different between and anti-.  If  m 23 2 is positive, resonance for   If  m 23 2 is negative, resonance for anti- + CC e Others Multi-ring e-like y=(E -E  )/E d  /dy CC e Others 1-ring e-like Fraction E (GeV) SK atm. MC

Electron appearance for positive and negative  m 2 Single-ring e-like Multi-ring e-like Positive  m 2 Negative  m 2 null oscillation cos  Relatively high anti- e fraction Lower anti- e fraction. Small (Large) effect for  m 2 0).

 2 difference (true – wrong hierarchy)  m 2 : fixed,  23 : free,  13 : free Exposure: 1.8Mtonyr = 80yr SK = 3.3yr HK  m 2 : fixed,  23 : free,  13 : free Exposure: 1.8Mtonyr = 80yr SK = 3.3yr HK 33 True= 33  Water Ch. and magnetized muon detectors have similar sensitivity

Octant of  23

Solar oscillation effect in atmospheric neutrinos e     So far,  m 12 2 has been neglected, because  m 12 2 (8.0×10 -5 ) <<  m 23 2 (2.5×10 -3 )  m 23 2  m 12 2 However, Diameter of the Earth (L) = 12,800km, Typical atmospheric neutrino energy (E) = 1GeV  (L/E) -1 = 8×10 -5 (km/GeV) -1 However, Diameter of the Earth (L) = 12,800km, Typical atmospheric neutrino energy (E) = 1GeV  (L/E) -1 = 8×10 -5 (km/GeV) -1 Solar oscillation terms cannot be neglected ! ●matter effect must be taken into account ●  13 = 0 assumed.

s 2 2  12 =0.825  m 2 12 =8.3×10 -5  m 2 23 =2.5×10 -3 sin 2  13 =0 Atmospheric neutrinos oscillation by (  12,  m 12 2 ). Peres & Smirnov NPB 680 (2004) 479 Solar term effect to atmospheric Solar term effect to atmospheric w/o matter effect with matter effect

Oscillation probability is different between s 2  23 =0.4 and 0.6  discrimination between  23 >  /4 and <  /4 might be possible by studying low energy atmospheric e and  events. However, due to the cancellation between   e and e  x, the change in the e flux is small. Solar term effect to atmospheric Solar term effect to atmospheric P 2 : 2 transition prob. e    x by m 12 2 P( e  e ) = 1 – P 2 P( e   ) = P(   e ) = cos 2  23 P 2 e flux (osc) = f( e 0 ) ・ (1-P 2 )+f(  0 ) ・ cos 2  23 P 2

Effect of the solar terms to the sub-GeV  /e ratio (zenith angle dependence) Below 1.3GeVP , e < 400 MeVP , e > 400 MeV  m 2 12 = 8.3 x eV 2  m 2 23 = 2.5 x eV 2 sin 2 2  12 = 0.82 sin 2  13 =0 (  e) (3 flavor) (  e) (2 flavor full-mixing) sin 2  23 = 0.6 sin 2  23 = 0.4 sin 2  23 = flavor (sin 2 2  23 =.96) It could be possible to discriminate the octant of  23, if sin 2  23 is significantly away from 0.5.

Solar terms off : best-fit : sin 2  23 = 0.50 Solar terms on : best-fit : sin 2  23 = 0.52 (sin 2 2 23 = ) Constraint on sin 2  23 with and without the solar terms w/o solar terms w/ solar terms (preliminary) Still (almost) maximum mixing is most favored.

Future  23 octant determination with the (12) and (13) terms s 2  23 =0.40 ~ 0.60 s 2  13 =0.00~0.04  cp=45 o Discrimination between  23 >  /4 and <  /4 is possible for all  Mtonyr = SK 80 yrs = 3.3 HK yrs Discrimination between  23 >  /4 and sin 2  23 sin 2  13 sin 2 2  23 =0.96sin 2 2  23 = %CL Test point Fit result

 23 octant determination and syst. errors  m 2 12 = 8.3 x eV 2  m 2 23 = 2.5 x eV 2 sin 2 2  12 = 0.82 sin 2  13 =0 P , e < 400 MeV sin 2  23 = 0.6 sin 2  23 = 0.4 sin 2  23 = flavor (sin 2 2  23 =.96) (  e) (3 flavor) (  e) (2 flavor full-mixing) true 0.8 Mtonyr = SK 20yr = HK 0.8yr S.Nakayama, RCCN Int. Workshop on sub-dom. Atm. Osc. 2004

Present atmospheric neutrino data are nicely explained by    oscillations. L/E analysis has shown evidence for “oscillatory” signature. The data are consistent with tau neutrino appearance. So far, no evidence for sub-dominant oscillations. Future atmospheric neutrino experiments (magnetized detector, very large water Cherenkov) are likely to give unique contribution to this field (especially if sin 2 2  13 is close to the present limit). Detecting solar oscillation effect is also an interesting possibility. Summary of atmospheric neutrino-2

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