SNOW Global fits to neutrino oscillation data. Thomas Schwetz SISSA, Trieste

SNOW 26 Global fits to neutrino oscillation data Thomas Schwetz SISSA, Trieste based on work in collaboration with M. Maltoni, M.A. Tortola, and J.W.F. Valle [hep-ph/3913, hep-ph/45172] T.S. is supported by an Intra-European Marie Curie fellowship of the European Commission within the 6th framework program T. Schwetz, SNOW26, Stockholm, 2 May 26 p.1

Outline Introduction T. Schwetz, SNOW26, Stockholm, 2 May 26 p.2

Outline Introduction Determination of m 2 21 and θ 12 global solar (SNO, SK, GNO, SAGE, Homestake) and KamLAND data T. Schwetz, SNOW26, Stockholm, 2 May 26 p.2

Outline Introduction Determination of m 2 21 and θ 12 global solar (SNO, SK, GNO, SAGE, Homestake) and KamLAND data Determination of m 2 31 and θ 23 SK atmospheric ν data, K2K, first results from MINOS The bound on θ 13 from global data Sub-leading effects in atmosheric neutrinos implications for θ 23 (deviations from maximal mixing) and the bound on θ 13 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.2

3-flavour oscillation parameters m 2 31 m 2 21 U = B @ 1 c 23 s 23 s 23 c 23 1 C A B @ c 13 e iδ s 13 1 e iδ s 13 c 13 1 C A B @ c 12 s 12 s 12 c 12 1 1 C A atmospheric solar T. Schwetz, SNOW26, Stockholm, 2 May 26 p.3

3-flavour oscillation parameters m 2 31 m 2 21 U = B @ 1 c 23 s 23 s 23 c 23 1 C A B @ c 13 e iδ s 13 1 e iδ s 13 c 13 1 C A B @ c 12 s 12 s 12 c 12 1 1 C A atmospheric solar known params. bounded params. unknown params. m 2 31 sin 2 θ 23 m 2 21 sin 2 θ 12 sin 2 θ 13 D 23 sin 2 θ 23.5 δ sign( m 2 31) T. Schwetz, SNOW26, Stockholm, 2 May 26 p.3

The solar parameters m 2 21, θ 12 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.4

Solar parameters global solar neutrino data: Homestake,SAGE,GNO,SK,SNO 2 15 χ 2 1 3σ 5 2σ SNO Φ CC / Φ NC contours m 2 SOL [1-5 ev 2 ] 2 15 1 5.5.45.4.35.3.25.2 2σ 3σ.1.2.3.4.5 5 1 15 2 25 sin 2 θ SOL χ 2 see also talk of A. McDonald T. Schwetz, SNOW26, Stockholm, 2 May 26 p.5

Solar parameters global solar neutrino data: Homestake,SAGE,GNO,SK,SNO χ 2 m 2 SOL [1-5 ev 2 ] 2 15 1 5 2 15 1 5 3σ 2σ.5.45.4.35.3.25.2 SNO Φ CC / Φ NC contours.1.2.3.4.5 5 1 15 2 25 sin 2 θ SOL χ 2 2σ 3σ see also talk of A. McDonald The SNO experiment: ν e + d p + p + e ν x + d p + n + ν x SNO-II 391d nucl-ex/5221 φ CC φ NC =.34±.23±.3 7σ evidence for a non-zero ν µ,τ flux from the sun constraint on θ 12 : φ CC Pee SNO sin 2 θ 12 φ NC T. Schwetz, SNOW26, Stockholm, 2 May 26 p.5

The KamLAND reactor neutrino experiment Kamioka Liquid scinitillator Anti-Neutrino Detector detection of ν e produced in surrounding nuclear power plants 7 GW of nuclear power (7% of world total) is generated at a distance 175 ± 3 km from Kamioka 258 events are observed, 365.2 ± 23.7 expected for no disappearance T. Schwetz, SNOW26, Stockholm, 2 May 26 p.6

The KamLAND energy spectrum 1.2 1 2.6 MeV no oscillations N i / N i no-osc.8.6.4.2 m 2 = 8.1 x 1-5 ev 2, s 2 12 =.29, s2 13 = m 2 = 1.6 x 1-5 ev 2, s 2 12 =.31, s2 13 = m 2 = 1.7 x 1-4 ev 2, s 2 12 =.25, s2 13 = m 2 = 8.1 x 1-5 ev 2, s 2 12 =.19, s2 13 =.1 2 3 4 5 6 7 8 E pr [MeV] evidence for flux suppression and spectral distortion T. Schwetz, SNOW26, Stockholm, 2 May 26 p.7

The KamLAND reactor neutrino experiment characteristics of our KamLAND data analysis: equal bins in 1/E pr instead of equal bins in E pr T. Schwetz, SNOW26, Stockholm, 2 May 26 p.8

The KamLAND reactor neutrino experiment characteristics of our KamLAND data analysis: equal bins in 1/E pr instead of equal bins in E pr include earth matter effects (few % effect) improved anti-neutrino flux parameterization P.Huber, TS, Phys. Rev. D 7 (24) 5311 [hep-ph/4726] uncertainties from fluxes, flux shapes, reactor fuel composition, individual reactor powers P.Huber, TS, Phys. Rev. D 7 (24) 5311 [hep-ph/4726] T. Schwetz, SNOW26, Stockholm, 2 May 26 p.8

KamLAND vs solar data 9% and 99.73% CL contours combined 1-4 m 2 21 [ev2 ] solar only KamLAND only 1-5.2.4.6.8 1 sin 2 θ 12 m 2 = 7.9 ±.3 1 5 ev 2, sin 2 θ 12 =.31 +.2.3 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.9

The atmospheric parameters m 2 31, θ 23 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.1

Atmospheric parameters Super-Kamiokande I atmospheric data hep-ex/5164 3 2 e-like Sub-GeV e-like P < 4 MeV/c 3 2 Sub-GeV µ-like P < 4 MeV/c µ-like 6 4 multi-ring Sub-GeV µ-like 1 1 2 Number of Events -1 -.5.5 1 3 Sub-GeV e-like P > 4 MeV/c 2 1 15 1-1 -.5.5 1 5 Multi-GeV e-like -1 -.5.5 1-1 -.5.5 1 4 Sub-GeV µ-like multi-ring 3 P > 4 MeV/c 1 Multi-GeV µ-like 2 1-1 -.5.5 1-1 -.5.5 1 2 15 Multi-GeV µ-like PC 1 5 5 15 1 5-1 -.5.5 1 cosθ -1 -.5.5 1 cosθ -1 -.5.5 1 cosθ T. Schwetz, SNOW26, Stockholm, 2 May 26 p.11

Oscillatory signal in atmospheric neutrinos Super-K Coll., Phys. Rev. Lett. 93 (24) 1181 Data/Prediction (null osc.) 1.8 1.6 1.4 1.2 1.8.6.4.2 1 1 1 2 1 3 1 4 L/E (km/gev) P 2ν = 1 sin 2 2θ sin 2 ( m 2 4 L E ν ) T. Schwetz, SNOW26, Stockholm, 2 May 26 p.12

Atmospheric parameters 1-2 m 2 atm [ev2 ] 1-3 best fit: m 2 32 = 2. 1 3 ev 2 sin 2 θ 23 =.5.25.5.75 1 sin 2 θ atm atmospheric neutrino data from SK-I (re-analysis of Maltoni et al., hep-ph/45172) T. Schwetz, SNOW26, Stockholm, 2 May 26 p.13

Atmospheric parameters 1-2 m 2 atm [ev2 ] 1-3 best fit: m 2 32 = 2.2 1 3 ev 2 sin 2 θ 23 =.5.25.5.75 1 sin 2 θ atm (K2K spectral analysis with 56 1-ring µ-like events) K2K: 25 km from KEK to SK, 1.3 GeV neutrinos 18 events observed, 15.9 +11.6 1. expected for no osc T. Schwetz, SNOW26, Stockholm, 2 May 26 p.13

Atmospheric parameters First results from MINOS see talk of E. Falk Harris NuMI beam produced at Fermilab 98.5% ν µ + ν µ, 6.5% ν µ, 1.5% ν e + ν e mean energy of 3 GeV far detector (5.4 kt) at Soudan Mine (L = 735 km) T. Schwetz, SNOW26, Stockholm, 2 May 26 p.14

First results from MINOS data taken from 2 May to 6 Dec 25 (.93 1 2 p.o.t.) presented in a talk at Fermilab on 3 March 26 http://www-numi.fnal.gov/talks/results6.html T. Schwetz, SNOW26, Stockholm, 2 May 26 p.15

First results from MINOS T. Schwetz, SNOW26, Stockholm, 2 May 26 p.15

Atmospheric parameters.6 9% CL regions.5 MINOS.4 m 2 [ev 2 ].3 K2K K2K + MINOS.2.1 SK atmospheric.5.6.7.8.9 1 sin 2 2θ T. Schwetz, SNOW26, Stockholm, 2 May 26 p.16

Atmospheric parameters 2 15 3 neutrino analysis CHOOZ + SOL + KAML incl. m 2 [1 3 ev 2 ] χ 2 1 3σ exp. bf 3σ int. 5 2σ K2K + MINOS ATM SK 2. 1.-3.8 6 SK+K2K 2.4 1.4-3.3 m 2 atm [1 3 ev 2 ] K2K + MINOS 4 2 ATM.25.5.75 1 sin 2 θ atm 2σ 3σ 5 1 15 2 χ 2 SK+K2K 2.5 1.8-3.3 +MINOS sin 2 θ 23 SK.5 3.4-6.8 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.17

Atmospheric parameters 2 15 3 neutrino analysis CHOOZ + SOL + KAML incl. m 2 [1 3 ev 2 ] χ 2 1 3σ exp. bf 3σ int. 5 2σ ATM + K2K ATM + K2K + MINOS SK 2. 1.-3.8 6 SK+K2K 2.4 1.4-3.3 m 2 atm [1 3 ev 2 ] 4 2 ATM + K2K ATM + K2K + MINOS.25.5.75 1 sin 2 θ atm 2σ 3σ 5 1 15 2 χ 2 SK+K2K 2.5 1.8-3.3 +MINOS sin 2 θ 23 SK.5 3.4-6.8 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.17

The bound on θ 13 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.18

The bound on θ 13 The bound on θ 13 emerges from an interplay of the global data 1-2 9% CL (2 dof) m 2 31 [ev2 ] CHOOZ 1-3 1-2 1-1 sin 2 θ 13 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.19

The bound on θ 13 The bound on θ 13 emerges from an interplay of the global data 1-2 9% CL (2 dof) m 2 31 [ev2 ] CHOOZ 1-3 SOL+KAML +CHOOZ 1-2 1-1 sin 2 θ 13 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.19

The bound on θ 13 The bound on θ 13 emerges from an interplay of the global data 1-2 9% CL (2 dof) m 2 31 [ev2 ] SK+K2K+MINOS CHOOZ 1-3 SOL+KAML +CHOOZ 1-2 1-1 sin 2 θ 13 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.19

The bound on θ 13 The bound on θ 13 emerges from an interplay of the global data 1-2 GLOBAL 9% CL (2 dof) m 2 31 [ev2 ] SK+K2K+MINOS CHOOZ 1-3 SOL+KAML +CHOOZ 1-2 1-1 sin 2 θ 13 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.19

The bound on θ 13 χ 2 2 15 1 5 dashed: w/o MINOS 3σ 9% CL Total Atm + LBL + Chooz Solar + KamLAND 3σ bounds with (w/o) MINOS: Solar+KamLAND: sin 2 θ 13 <.79 Atm+Chooz+LBL: sin 2 θ 13 <.58 (.67) 1-2 1-1 sin 2 θ 13 Global: sin 2 θ 13 <.44 (.46) T. Schwetz, SNOW26, Stockholm, 2 May 26 p.2

The bound on θ 13 and MINOS sin 2 θ 13.8.6.4 Global 3ν analysis with and w/o MINOS (Atm, Sol, KamL, Chooz, K2K).2 1-2 m 2 31 [ev2 ] 1-3.2.4.6.8 1 sin 2 θ 23.2.4.6.8 sin 2 θ 13 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.21

The θ 13 bound from KamLAND and Solar complementarity between solar and KamLAND data.2.15 Solar KamLAND Maltoni et al., hep-ph/45172 sin 2 θ 13.1 see also Goswami and Smirnov, hep-ph/411359.5.25.5.75 1 KamLAND spectrum sin 2 θ 12 P KL ( 1 2 sin 2 θ 13 ) ( 1 sin 2 2θ 12 sin 2 m2 21L 4E ν ) P Sol ( 1 2 sin 2 θ 13 ) { sin 2 θ 12 high E ν (1.5 sin 2 2θ 12 ) low E ν T. Schwetz, SNOW26, Stockholm, 2 May 26 p.22

Sub-leading effects in atmospheric neutrino data T. Schwetz, SNOW26, Stockholm, 2 May 26 p.23

Sub-leading effects in atmospheric neutrino data Incomplete list: Petcov, Phys. Lett. B434, 321 (1998), hep-ph/985262 Akhmedov, Nucl. Phys. B538, 25 (1999), hep-ph/985272 Akhmedov, Dighe, Lipari, Smirnov, Nucl. Phys. B542, 3 (1999), hep-ph/98827 Kim, Lee, Phys. Lett. B444, 24 (1998), hep-ph/989491 Peres, Smirnov, Phys. Lett. B456, 24 (1999), hep-ph/992312 Bernabeu, Palomares-Ruiz, Perez, Petcov, Phys. Lett. B531, 9 (22), hep-ph/1171 Gonzalez-Garcia, Maltoni, Eur. Phys. J. C26, 417 (23), hep-ph/22218 Bernabeu, Palomares-Ruiz, Petcov, Nucl. Phys. B669, 255 (23), hep-ph/35152 Peres, Smirnov, Nucl. Phys. B68, 479 (24), hep-ph/39312 Gonzalez-Garcia, Maltoni, Smirnov, Phys. Rev. D7, 935 (24), hep-ph/4817 Fogli, Lisi, Marrone, Palazzo, hep-ph/5683 Huber, Maltoni, Schwetz, Phys. Rev. D71, 536 (25), hep-ph/5137 T. Kajita (Super-K), see e.g. talks at NuFact5, NuInt5 Petcov, Schwetz, Nucl. Phys. B74, 1 (26) 1, hep-ph/511277 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.23

Sub-leading effects in atmospheric neutrinos excess of electron-like events: N e N e 1 (r s 2 23 1) P 2ν( m 2 31, θ 13) θ 13 -effects + (r c 2 23 1) P 2ν( m 2 21, θ 12) m 2 21-effects 2s 13 s 23 c 23 r Re(A ee A µe) interference: δ CP r = r(e ν ) F µ(e ν ) F e (E ν ) r 2 r 2.6 4.5 (sub-gev) (multi-gev) T. Schwetz, SNOW26, Stockholm, 2 May 26 p.24

θ 13 -effects N e Ne 1 (r s 2 23 1) P 2ν( m 2 31, θ 13) resonant matter effect in P 2ν ( m 2 31, θ 13 ) for multi-gev events (r 2.6 4.5) normal hierarchy: enhancement for neutrinos inverted hierarchy: enhancement for anti-neutrinos detection cross sections are different for neutrinos and anti-neutrinos sensitivity to the neutrino mass hierarchy T. Schwetz, SNOW26, Stockholm, 2 May 26 p.25

θ 13 -effects N e Ne 1 (r s 2 23 1) P 2ν( m 2 31, θ 13) for multi-gev events N e / N e 1.4 1.3 1.2 1.1.84 < cosθ ν nadir < 1 sin 2 θ 23 =.64 normal inverted normal sin 2 θ 23 =.36 inverted 1.2.4.6.8.1 sin 2 2θ 13 Bernabeu, Palomares-Ruiz, Petcov, hep-ph/35152 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.25

m 2 21-effects N e Ne 1 (r c 2 23 1) P 2ν( m 2 21, θ 12) m 2 21(eV 2 ) 1-3 -.5% -1.% -2.% -3.% 3.% 2.% 1.%.5% Peres, Smirnov, hep-ph/39312 contours of N e N e 1 1-4 current best fit 3% 2% 2% 1% 1% 3% relevant for sub-gev events sensitivity to the octant of θ 23 1-5 -.2 -.15 -.1 -.5.5.1.15.2 D 23.5 sin 2 θ 23 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.26

Sub-leading effects in atmospheric neutrinos Fogli et al., hep-ph/5683 all 3 terms are important for sub-gev, also the interference term depending on δ CP multi-gev are dominated by the θ 13 term effects at the level of few % T. Schwetz, SNOW26, Stockholm, 2 May 26 p.27

Sub-leading effects in atmospheric neutrinos These effects can be explored in future Mt scale detectors, see talk of M. Maltoni, but... Are these effects visible in present (SK-I) data? T. Schwetz, SNOW26, Stockholm, 2 May 26 p.28

Sub-leading effects in atmospheric neutrinos Currently there are three groups performing a 3-flavour analysis of SK data (to my knowledge): SK collaboration, hep-ex/6411 ( m 2 21 = ) Talks by T. Kajita (including m 2 21 ) Bari group, E. Lisi et al., hep-ph/5683 (δ CP =, π) M. Maltoni et al. T. Schwetz, SNOW26, Stockholm, 2 May 26 p.29

Taking into account m 2 21.5 SK + K2K θ 13 =.4 m 2 21 = 8 x 1-5 ev 2 m 2 21 = m 2 31 [ev2 ].3.2.1.3.4.5.6.7 sin 2 θ 23 Gonzalez-Garcia, Maltoni, Smirnov, hep-ph/4817 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.3

Is there an indication for a non-max θ 23? Super-K Coll. Gonzalez-Garcia, Maltoni, Smirnov Fogli et al., T. Kajita, NuFact5 hep-ph/4817 hep-ph/5683 best fit: sin 2 θ 23 =.51 sin 2 θ 23 =.46 sin 2 θ 23 =.44 max θ 23 : χ 2.1 χ 2.3 χ 2.8 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.31

Is there an indication for a non-max θ 23?.5.4 SK + CHOOZ + K2K + MINOS sub GeV 1-ring (e+µ) χ 2 =.2,.5, 1, 4.6 m 2 21 = 8 x 1-5 ev 2.3 sin 2 θ 13.2.1.3.4.5.6.7 sin 2 θ 23 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.32

Is there an indication for a non-max θ 23?.5.4 SK + CHOOZ + K2K + MINOS sub GeV 1-ring (e+µ) χ 2 =.2,.5, 1, 4.6 m 2 21 = 8 x 1-5 ev 2 sin 2 θ 13.3.2.1.5.4.3.4.5.6.7 sin 2 θ 23 multi GeV 1-ring (e+µ) χ 2 =.2,.5, 1, 4.6 m 2 21 = 8 x 1-5 ev 2 sin 2 θ 13.3.2.1.3.4.5.6.7 sin 2 θ 23 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.32

Is there an indication for a non-max θ 23?.5.4 SK + CHOOZ + K2K + MINOS sub GeV 1-ring (e+µ) χ 2 =.2,.5, 1, 4.6 m 2 21 = 8 x 1-5 ev 2.5.4 SK + CHOOZ + K2K + MINOS sub+multi GeV 1-ring (e+µ) m 2 21 = 8 x 1-5 ev 2 χ 2 =.2,.5, 1, 4.6.3.3 sin 2 θ 13.2 sin 2 θ 13.2.1.1.5.4.3.4.5.6.7 sin 2 θ 23 multi GeV 1-ring (e+µ) χ 2 =.2,.5, 1, 4.6 m 2 21 = 8 x 1-5 ev 2.3.4.5.6.7 sin 2 θ 23.3 sin 2 θ 13.2.1.3.4.5.6.7 sin 2 θ 23 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.32

Is there an indication for a non-max θ 23?.5.4 SK + CHOOZ + K2K + MINOS sub GeV 1-ring (e+µ) χ 2 =.2,.5, 1, 4.6 m 2 21 = 8 x 1-5 ev 2.5.4 SK + CHOOZ + K2K + MINOS sub+multi GeV 1-ring (e+µ) m 2 21 = 8 x 1-5 ev 2 χ 2 =.2,.5, 1, 4.6.3.3 sin 2 θ 13.2 sin 2 θ 13.2.1.1.5.4.3.4.5.6.7 sin 2 θ 23 multi GeV 1-ring (e+µ) χ 2 =.2,.5, 1, 4.6 m 2 21 = 8 x 1-5 ev 2.5.4.3.4.5.6.7 sin 2 θ 23 all SK (sub,mul,stop,through) m 2 21 = 8 x 1-5 ev 2 χ 2 =.2,.5, 1, 4.6.3.3 sin 2 θ 13.2 sin 2 θ 13.2.1.1.3.4.5.6.7 sin 2 θ 23.3.4.5.6.7 sin 2 θ 23 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.32

Is there an indication for a non-max θ 23? sub-leading effects are significantly smaller than statistical and systematical uncertainties too small to account for the sub-gev e-like excess results depend on the fine-details of the analysis T. Schwetz, SNOW26, Stockholm, 2 May 26 p.33

Sub-leading effects in ATM and θ 13 8 ATM+CHOOZ+K2K 6 Maltoni et al. hep-ph/45172 χ 2 4 2 2σ 9% CL.1.2.3.4.5 sin 2 θ 13 reference χ 2 from Maltoni, Schwetz, Tortola, Valle ( m 2 21 = and NH) T. Schwetz, SNOW26, Stockholm, 2 May 26 p.34

Sub-leading effects in ATM and θ 13 8 ATM+CHOOZ+K2K 6 Maltoni et al. hep-ph/45172 2ν ATM χ 2 4 2 2σ 9% CL.1.2.3.4.5 sin 2 θ 13 θ 13 -effects in ATM do contribute to the bound T. Schwetz, SNOW26, Stockholm, 2 May 26 p.34

Sub-leading effects in ATM and θ 13 8 ATM+CHOOZ+K2K 6 Maltoni et al. hep-ph/45172 different systematics χ 2 4 2 2σ 9% CL.1.2.3.4.5 sin 2 θ 13 black: systematics treatment from Kameda thesis magenta: flux and CS systematics developed in Gonzalez-Garcia, Maltoni, hep-ph/4485 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.34

Sub-leading effects in ATM and θ 13 8 ATM+CHOOZ+K2K χ 2 6 4 2σ Maltoni et al. hep-ph/45172 different systematics with solar osc (NH) with solar osc (IH) 9% CL 2.1.2.3.4.5 sin 2 θ 13 m 2 21 has an important impact on the bound (shown for NH and IH, minimized over δ CP ) T. Schwetz, SNOW26, Stockholm, 2 May 26 p.34

Sub-leading effects in ATM and θ 13 8 ATM+CHOOZ+K2K χ 2 6 4 2σ Maltoni et al. hep-ph/45172 different systematics SK 2nu SK 3nu NH SK 3nu IH 9% CL 2.1.2.3.4.5 sin 2 θ 13 Super-K 3ν analysis from hep-ex/6411 ( m 2 21 = ) big effect for NH T. Schwetz, SNOW26, Stockholm, 2 May 26 p.34

Sub-leading effects in ATM and θ 13 8 ATM+CHOOZ+K2K χ 2 6 4 2σ Maltoni et al. hep-ph/45172 with solar osc (NH) with solar osc (IH) Fogli et al., hep-ph/5683 9% CL 2.1.2.3.4.5 sin 2 θ 13 comparison with Bari group ( m 2 21, minimized over NH/IH, and δ CP =, π) T. Schwetz, SNOW26, Stockholm, 2 May 26 p.34

Sub-leading effects in ATM and θ 13 8 ATM+CHOOZ+K2K χ 2 6 4 2 2σ 9% CL Maltoni et al. hep-ph/45172 2ν ATM different systematics with solar osc (NH) with solar osc (IH) SK 2nu SK 3nu NH SK 3nu IH Fogli et al., hep-ph/5683.1.2.3.4.5 sin 2 θ 13 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.34

Sub-leading effects in ATM and θ 13 6 Fogli et al., hep-ph/5683 NH 4 δ CP = π δ CP = χ 2 2 -.2 -.1.1.2 cos(δ CP ) sinθ 13 Bari: best fit: sin 2 θ 13.1, χ 2.85 for θ 13 = T. Schwetz, SNOW26, Stockholm, 2 May 26 p.34

Sub-leading effects in ATM and θ 13 6 Fogli et al., hep-ph/5683 NH δ CP = π δ CP = 4 χ 2 2 code of M. Maltoni -.2 -.1.1.2 cos(δ CP ) sinθ 13 Bari: best fit: sin 2 θ 13.1, χ 2.85 for θ 13 = Maltoni: best fit: sin 2 θ 13.5, χ 2.16 for θ 13 = T. Schwetz, SNOW26, Stockholm, 2 May 26 p.34

Sub-leading effects in ATM and θ 13 6 Fogli et al., hep-ph/5683 NH δ CP = π δ CP = 4 χ 2 2 sin 2 2θ 13 =.88 code of M. Maltoni -.2 -.1.1.2 cos(δ CP ) sinθ 13 Bari: best fit: sin 2 θ 13.1, χ 2.85 for θ 13 = Maltoni: best fit: sin 2 θ 13.5, χ 2.16 for θ 13 = T. Schwetz, SNOW26, Stockholm, 2 May 26 p.34

The LSND puzzle T. Schwetz, SNOW26, Stockholm, 2 May 26 p.35

The LSND result evidence for ν µ ν e oscillations Aguilar et al., PRD 64 (21) 1127 87.9±22.4±6. excess events P = (.264 ±.67 ±.45)% 3.3σ away from zero T. Schwetz, SNOW26, Stockholm, 2 May 26 p.36

The LSND result evidence for ν µ ν e oscillations Aguilar et al., PRD 64 (21) 1127 87.9±22.4±6. excess events P = (.264 ±.67 ±.45)% 3.3σ away from zero m 2 ev 2 not consistent with solar and atmospheric mass splittings for 3 neutrinos! T. Schwetz, SNOW26, Stockholm, 2 May 26 p.36

4-neutrino oscillations? T. Schwetz, SNOW26, Stockholm, 2 May 26 p.37

Adding a sterile neutrino 4-neutrino mass schemes: m 2 i (2+2) (3+1) m 2 atm m 2 LSND m 2 LSND m 2 atm m 2 sol m 2 sol ν e ν µ ν τ ν s T. Schwetz, SNOW26, Stockholm, 2 May 26 p.38

(2+2): ruled out by solar and atmospheric data Maltoni, Schwetz, Tortola, Valle, hep-ph/27157, hep-ph/45172 5 χ 2 4 3 2 1 solar solar + KamLAND solar pre-sno salt.2.4.6.8 1 η s T. Schwetz, SNOW26, Stockholm, 2 May 26 p.39

(2+2): ruled out by solar and atmospheric data Maltoni, Schwetz, Tortola, Valle, hep-ph/27157, hep-ph/45172 5 χ 2 4 3 2 solar + KamLAND χ 2 PC 1 atm + K2K + SBL.2.4.6.8 1 η s T. Schwetz, SNOW26, Stockholm, 2 May 26 p.39

(2+2): ruled out by solar and atmospheric data Maltoni, Schwetz, Tortola, Valle, hep-ph/27157, hep-ph/45172 5 χ 2 4 3 2 global solar + KamLAND χ 2 PG χ 2 PC 1 atm + K2K + SBL.2.4.6.8 1 η s χ 2 = 26 (2+2) ruled out at the 5σ level T. Schwetz, SNOW26, Stockholm, 2 May 26 p.39

(3+1): strongly disfavoured by SBL data disappearance experiments Bugey, CDHS: d e, d µ 1 (3+1): sin 2 2θ LSND = 4 d e d µ Bilenky, Giunti, Grimus, 96, 98; Okada, Yasuda, 1997; Barger et al., 1998, 2; Bilenky, Giunti, Grimus, Schwetz, 1999; Giunti, Laveder, 21; Peres, Smirnov, 21; Grimus, Schwetz, 21; Maltoni, Schwetz, Valle, 22 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.4

(3+1): strongly disfavoured by SBL data disappearance experiments Bugey, CDHS: d e, d µ 1 Maltoni, Schwetz, Tortola, Valle, hep-ph/45172 (3+1): sin 2 2θ LSND = 4 d e d µ 1 1 NEV + atm + K2K Bilenky, Giunti, Grimus, 96, 98; Okada, Yasuda, 1997; Barger et al., 1998, 2; Bilenky, Giunti, Grimus, Schwetz, 1999; Giunti, Laveder, 21; Peres, Smirnov, 21; Grimus, Schwetz, 21; Maltoni, Schwetz, Valle, 22 m 2 LSND [ev2 ] LSND global LSND DAR 1 1-1 95% CL 99% CL 1-4 1-3 1-2 1-1 1 sin 2 2θ LSND T. Schwetz, SNOW26, Stockholm, 2 May 26 p.4

Global 4-neutrino analysis SOL ATM LSND NEV χ 2 PG parameter GOF (PG) (3+1)..4 5.7 1.9 17. 1.9 1 3 3.1σ (2+2) 5.3 2.8.6 7.3 33.9 7.8 1 7 4.9σ T. Schwetz, SNOW26, Stockholm, 2 May 26 p.41

More sterile neutrinos? T. Schwetz, SNOW26, Stockholm, 2 May 26 p.42

5-neutrino oscillations (3+2) mass schemes, Sorel, Conrad, Shaevitz, hep-ph/35255 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.43

5-neutrino oscillations (3+2) mass schemes, Sorel, Conrad, Shaevitz, hep-ph/35255 m 2 LSND [ev2 ] 1 1 1 m 2 51 2 ev 2 m 2 41.9 ev 2 1-1 1-3 1-2 sin 2 2θ LSND PG (3+2) = 2.1% PG (3+1) =.32% T. Schwetz, SNOW26, Stockholm, 2 May 26 p.43

5-neutrino oscillations (3+2) mass schemes, Sorel, Conrad, Shaevitz, hep-ph/35255 m 2 LSND [ev2 ] 1 1 1 m 2 51 2 ev 2 m 2 41.9 ev 2 1-1 1-3 1-2 sin 2 2θ LSND cosmology? PG (3+2) = 2.1% PG (3+1) =.32% T. Schwetz, SNOW26, Stockholm, 2 May 26 p.43

5-neutrino oscillations Conflict with atmospheric neutrinos? best fit: U µ4 =.24, U µ5 =.224 d µ = U µ4 2 + U µ5 2.9 3 χ 2 2 (3+2) best fit atmospheric + K2K 1 99% CL (1 dof).5.1.15.2 d µ Maltoni, Schwetz, Tortola, Valle, hep-ph/45172 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.44

More exotic proposals T. Schwetz, SNOW26, Stockholm, 2 May 26 p.45

More exotic proposals 3-neutrinos and CPT violation Murayama, Yanagida 1; Barenboim, Borissov, Lykken 2; Gonzalez-Garcia, Maltoni, Schwetz 3 4-neutrinos and CPT violation Barger, Marfatia, Whisnant 3 Exotic muon-decay Babu, Pakvasa 2 CPT violating quantum decoherence Barenboim, Mavromatos 4, 6 mass varying neutrinos Kaplan, Nelson, Weiner 4; Zurek 4; Barger, Marfatia, Whisnant 5 shortcuts of sterile neutrinos in extra dimensions Paes, Pakvasa, Weiler 5 decaying sterile neutrinos Palomares-Riuz, Pascoli, Schwetz 5 3 neutrinos and Lorentz violation degouvea, Grossmann 6 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.46

LSND and a decaying sterile neutrino T. Schwetz, SNOW26, Stockholm, 2 May 26 p.47

LSND and a decaying sterile neutrino oscillation interpretation π + µ + + ν µ e + + ν e + ν µ oscillations ν e T. Schwetz, SNOW26, Stockholm, 2 May 26 p.48

LSND and a decaying sterile neutrino oscillation interpretation π + µ + + ν µ e + + ν e + ν µ oscillations ν e Palomares-Riuz, Pascoli, Schwetz, hep-ph/55216 π + µ + + ν µ e + + ν e + ν µ U µ4 2 ν h decay ν e + Φ T. Schwetz, SNOW26, Stockholm, 2 May 26 p.48

The decay model postulate heavy neutrino ν h, which decays into light neutrinos ν l and a scalar Φ L = 3 l=1 g l ν ll ν hr Φ + h.c. T. Schwetz, SNOW26, Stockholm, 2 May 26 p.49

The decay model postulate heavy neutrino ν h, which decays into light neutrinos ν l and a scalar Φ L = 3 l=1 g l ν ll ν hr Φ + h.c. assume m 1,2,3 m Φ m h light neutrinos are stable T. Schwetz, SNOW26, Stockholm, 2 May 26 p.49

The decay model postulate heavy neutrino ν h, which decays into light neutrinos ν l and a scalar Φ total decay rate of ν h : L = 3 l=1 g l ν ll ν hr Φ + h.c. Γ = ḡ2 m 2 h 16πE νh with ḡ 2 = l g l 2 branching ratio for ν h ν α : R α g α 2 ḡ 2 with g α = l U αl g l T. Schwetz, SNOW26, Stockholm, 2 May 26 p.49

Reconciling LSND and no-evidence SBL data (3+1) oscillations decay 1 1 1 1 m 2 [ev 2 ] 1 g m 4 [ev] 1 1-1 1-3 1-2 1-1 sin 2 2θ eff ( P osc = 2 U e4 2 U µ4 [1 2 cos P dec = 1 2 U µ4 2 R e [1 exp m 2 2 ( ḡ2 m 2 h 16π 1-1 )] L E L E )] 1-3 1-2 1-1 1 U µ4 2 U e4 2 =, R e 1 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.5

Reconciling LSND and no-evidence SBL data (3+1) oscillations decay 1 1 1 1 m 2 [ev 2 ] 1 g m 4 [ev] 1 1-1 1-3 1-2 1-1 sin 2 2θ eff 1-1 1-3 1-2 1-1 1 U µ4 2 LSND vs the rest: PG (3+1) =.2% PG (3+2) = 2.1% PG decay = 4.6% T. Schwetz, SNOW26, Stockholm, 2 May 26 p.5

Reconciling LSND and no-evidence SBL data (3+1) oscillations decay 1 1 1 1 m 2 [ev 2 ] 1 g m 4 [ev] 1 1-1 1-3 1-2 1-1 sin 2 2θ eff 1-1 1-3 1-2 1-1 1 U µ4 2 appearance vs disappearance: PG (3+1) =.3% PG decay = 55% T. Schwetz, SNOW26, Stockholm, 2 May 26 p.5

LSND and a decaying sterile neutrino the global best fit point: U µ4 2 =.16, ḡm h = 3.4 ev need ḡ 1 6 1 3, m h kev MeV T. Schwetz, SNOW26, Stockholm, 2 May 26 p.51

LSND and a decaying sterile neutrino the global best fit point: U µ4 2 =.16, ḡm h = 3.4 ev need ḡ 1 6 1 3, m h kev MeV oscillations in solar and KamLAND are un-affected very small effects in atmospheric oscillations the values for g, m h, U µ4 2 are consistent with various existing bounds T. Schwetz, SNOW26, Stockholm, 2 May 26 p.51

Predictions for MiniBooNE Signal in MiniBooNE (arb. units) m 2 = 2 ev 2 decay m 2 =.9 ev 2 large or small m 2.5 1 1.5 2 2.5 E ν [GeV] T. Schwetz, SNOW26, Stockholm, 2 May 26 p.52

Summary T. Schwetz, SNOW26, Stockholm, 2 May 26 p.53

Summary: 3-flavour oscillation parameters mass-squared differences: parameter bf±1σ 1σ acc. 3σ range m 2 21 [1 5 ev 2 ] 7.9 ±.3 4% 7.1 8.9 m 2 31 [1 3 ev 2 ] 2.5 +.2.25 1% 1.8 3.3 mixing angles: parameter bf±1σ 1σ acc. 3σ range sin 2 θ 12.31 +.2.3 9%.24.4 sin 2 θ 23.5 +.8.7 16%.34.68 sin 2 θ 13.44 very small correlations among the parameters updated from Maltoni, Schwetz, Tortola, Valle, hep-ph/45172 T. Schwetz, SNOW26, Stockholm, 2 May 26 p.54

Summary: First results from MINOS 2 15 3 neutrino analysis CHOOZ + SOL + KAML incl. χ 2 1 3σ m 2 atm [1 3 ev 2 ] 5 2σ 6 4 2 ATM + K2K ATM + K2K + MINOS.25.5.75 1 sin 2 θ atm 2σ ATM + K2K ATM + K2K + MINOS 3σ 5 1 15 2 χ 2 χ 2 2 15 1 5 dashed: w/o MINOS 3σ 9% CL Total 1-2 1-1 sin 2 θ 13 Atm + LBL + Chooz Solar + KamLAND T. Schwetz, SNOW26, Stockholm, 2 May 26 p.55

Summary: the 3 neutrino mass spectrum Two possibilities for the neutrino mass spectrum: NORMAL INVERTED ν 3 ν 2 ν 1 ν e ν µ [mass] 2 ντ ν 2 ν 1 ν 3 m 2 31 > m2 31 < T. Schwetz, SNOW26, Stockholm, 2 May 26 p.56

Summary: LSND The LSND signal remains an open issue A confirmation from MiniBooNE would require new ideas (or the re-consideration of other SBL data) T. Schwetz, SNOW26, Stockholm, 2 May 26 p.57

Thanks to...... the SNOW26 organizers for the invitation to give this talk T. Schwetz, SNOW26, Stockholm, 2 May 26 p.58

Thanks to...... the SNOW26 organizers for the invitation to give this talk... Michele Maltoni for the permission to use his atmospheric neutrino code for the preparation of this talk, and for many illuminating discussions T. Schwetz, SNOW26, Stockholm, 2 May 26 p.58