1. 1 3+2 Neutrino Phenomenology and Studies at MiniBooNE PHENO 2007 Symposium May 7-9, 2007 U. Wisconsin, Madison Georgia Karagiorgi, Columbia University

2. Georgia Karagiorgi, Columbia U.2 Outline Motivation for 3+2 models 3+2 phenomenology and oscillation formalism The MiniBooNE result and experimental constraints for 3+2 models CP violation studies in 3+2 models and prospects for CPV measurement at MiniBooNE Current status of 3+2 analysis and future plans Conclusions G. Karagiorgi et al., “Leptonic CP violation studies at MiniBooNE in a (3+2) sterile neutrino oscillation hypothesis,” Phys. Rev. D. 75, 013011 (2007) [hep-ph/0609177].

3. Georgia Karagiorgi, Columbia U.3 The LSND Signal Δm 2 LSND >> Δm 2 atm >> Δm 2 sol Δm 2 LSND ~ 0.1- 10 eV 2 + small mixing  one option: 3 active + n “sterile” neutrinos  other options: neutrino decay, extra-D, etc.

4. Georgia Karagiorgi, Columbia U.4 3+2 Model Phenomenology 3 active + 2 sterile neutrinos light sterile neutrinos they can interact thru non-standard weak couplings they have very small active flavor content (U e4,…, U e5,…)  can participate in neutrino oscillations νeνμντνsνeνμντνs increasing m 2 (not to scale) Why n=2? 3+1 models: SBL and LSND marginally consistent with each other 3+2: next natural step… [M. Sorel, et al. hep-ph/0305255]

5. Georgia Karagiorgi, Columbia U.5 3+2 Model Phenomenology GUT’s Mohapatra, Nasri, & Yu [hep-ph/0505021] De Gouvea, Jenkins, & Vasudevan [hep-ph/0608147] Extra-D Pas, Pakvasa, & Weiler [hep-ph/0504096] Ma, Rajasekaran, & Sarkar [hep-ph/0006340] SUSY Kang, & Li [hep-ph/0501101] Dvali, & Nirb [hep-ph/9810257]

6. Georgia Karagiorgi, Columbia U.6 3+2 Neutrino Oscillation Formalism General neutrino oscillation formula: P(ν α  ν β ) = δ αβ – 4 Σ Re ( U* αi U βi U αj U* βj ) sin 2 x ij + 2 Σ Im (U* αi U βi U αj U* βj ) sin2x ij P(ν μ  ν e ) = 4|U μ4 | 2 |U e4 | 2 sin 2 x 41 + 4|U μ5 | 2 |U e5 | 2 sin 2 x 51 + + 8 |U μ5 ||U e5 ||U μ4 ||U e4 |sinx 41 sinx 51 cos(x 54 +φ 45 ) Assumptions for 3+2 model analysis: approximate m 1 = m 2 = m 3 = 0 * two independent mass splittings: Δm 2 41, Δm 2 51 four moduli: |U e4 |, |U μ4 |, |U e5 |, |U μ5 | one CPV phase: φ 54 = arg(U* μ5 U e5 U μ4 U* e4 ) * This allows for 6  1 CPV phase in a (3+2) hypothesis (3  0 CPV phases in a (3+1) hypothesis) (1  0 CPV phases in a (3+0) hypothesis) 3+2 model = most minimal model for CPV studies! x ij = 1.27Δm 2 ij L/E

7. Georgia Karagiorgi, Columbia U.7 First Results from MiniBooNE “A Search for Electron Neutrino Appearance at the Δm 2 ~ 1eV 2 Scale,” The MiniBooNE Collaboration [hep-ex/0704.1500]. MiniBooNE result excludes the LSND 90%CL allowed region at > 90% CL…

8. Georgia Karagiorgi, Columbia U.8 First Results from MiniBooNE …MiniBooNE result assumes: CP-conserving, 2-neutrino oscillation scenario E > 475 MeV Excess of ν e events at low energies: Currently investigating if this is a detector effect, or SM background… Could be a manifestation of beyond the SM physics… For more information on this, see talk by Chris Polly

9. Georgia Karagiorgi, Columbia U.9 Experimental Constraints We are interested in: studying the compatibility of null SBL results with LSND and MiniBooNE results in a 3 active + 2 sterile neutrino hypothesis constraining the 3+2 model parameters ChannelExperiment Lowest Δm 2 Reach (90%CL) High Δm 2 Optimal Δm 2 ν μ  ν e LSND KARMEN NOMAD MiniBooNE 3x10 -2 6x10 -2 4x10 -1 2.5x10 -2 > 2.5x10 -3 < 1.7x10 -3 < 1.4x10 -3 > 1.2x10 -3 < 1.0x10 -3 < 1.0x10 -3 ν e  ν e Bugey Chooz 1x10 -2 7x10 -4 < 1.4x10 -1 < 1.0x10 -1 < 1.3x10 -2 < 5x10 -2 ν μ  ν μ CCFR84 CDHS 6x10 0 3x10 -1none < 2x10 -1 < 5.3x10 -1 sin 2 θ constraint (90%CL)

10. Georgia Karagiorgi, Columbia U.10 Combined NSBL+LSND+MiniBooNE 3+2 analysis (including MB ν e background disappearance) and compatibility tests are currently in progress… Recent studies: Leptonic CP violation studies at MiniBooNE in a 3+2 sterile neutrino oscillation hypothesis Expected oscillation probability at MiniBooNE Potential of CP-violation measurement at MiniBooNE [hep-ph/0609177] Dataset: NSBL + LSND only (no atmospheric or solar experiment data) + Super-K atm. constraint

11. Georgia Karagiorgi, Columbia U.11 Oscillation Analysis for CPV Studies at MiniBooNE Generate masses and mixing parameters (models): –0.1eV 2 ≤ Δm 2 41, Δm 2 51 ≤ 100eV 2 Δm 2 51 ≥ Δm 2 41 –|U e4 |, |U μ4 |, |U e5 |, |U μ5 | U ei 2 + U μi 2 ≤ 0.5, U α4 2 + U α5 2 ≤ 0.5 –atmospheric constraint: d μ = ½ - √(1-4A) /2 where A = (1 - |U μ4 | 2 - |U μ5 | 2 )(|U μ4 | 2 + |U μ5 | 2 ) + |U μ4 | 2 |U μ5 | 2 CP violation option: Fix φ 54 = 0, π, or allow to vary within (0,2π) Calculate expected oscillation probabilities in neutrino and anti-neutrino running mode at MiniBooNE (using expected full ν μ  ν e transmutation rates) Determine allowed regions by Gaussian approximation Importance sampling via Markov chain: P(x i  x i+1 ) = min{1,exp[-(χ 2 i+1 -χ 2 ι )/Τ]} x i+1 = x i + e P(ν μ  ν e ) = 4|U μ4 | 2 |U e4 | 2 sin 2 x 41 + 4|U μ5 | 2 |U e5 | 2 sin 2 x 51 + + 8 |U μ5 ||U e5 ||U μ4 ||U e4 |sinx 41 sinx 51 cos(x 54 +φ 45 )

12. Georgia Karagiorgi, Columbia U.12 Oscillation probability expected at MiniBooNE CP-violating 3+2 modelsCP-conserving 3+2 models 90%CL 99%CL Best fit models: CPC: χ 2 /dof = 141.4/145 CPV: χ 2 /dof = 140.8/144

13. Georgia Karagiorgi, Columbia U.13 Potential observation of CP-violation at MiniBooNE All CP-violating phase values allowed at 99%CL by the NSBL+LSND data are measurable at MiniBooNE Small degrees of CPV preferred Large asymmetries allowed, but not required 90%CL 99%CL

14. Georgia Karagiorgi, Columbia U.14 First global fit results Analysis by Maltoni & Schwetz Fig. 7 [hep-ph/0705.0107] Best fit parameters for global fit with full MiniBooNE E range: Δm 2 41 = 0.87eV 2 x 2 min /dof = 104.4/(109-7) Δm 2 51 = 1.91eV 2 gof = 41% cpv-phase = 1.44 π χ 2 PG = 17.5, PG = 1.5 x 10 −3 (no MB) χ 2 PG = 25.1, PG = 4.8 x 10 −5 (MB300)

15. Georgia Karagiorgi, Columbia U.15 Potential observation of CP-violation at MiniBooNE MiniBooNE expected oscillation probability asymmetry  based on calculated best fit model parameters from hep-ph/0705.0107 global 3+2 analysis (MB300 and MB475) MB300 A p/p = -0.448 φ 45 = 1.44π MB475 A p/p = -0.207 φ 45 = 1.64π

16. Georgia Karagiorgi, Columbia U.16 First global fit results Maltoni & Schwetz Fig. 3 [hep-ph/0705.0107] MB signal prediction from best fit points from SBL appearance data (LSND, KARMEN, NOMAD, MB) in a 3+2 oscillation analysis 3+2 neutrino models: provide a good fit to LSND and the recent MB data can account for the low energy event excess in MB However: there is significant tension between appearance and disappearance data (according to the PG test at the level of 3σ for MB475 and 4σ for MB300). Note: analysis done without full MiniBooNE error matrix

17. Georgia Karagiorgi, Columbia U.17 Our next 3+2 steps… More detailed combined NSBL + LSND + MiniBooNE 3+2 oscillation analysis and compatibility tests, that take into consideration: Full MiniBooNE error matrix Disappearance of MiniBooNE ν e background

18. Georgia Karagiorgi, Columbia U.18 Conclusions Original motivation: accommodate null SBL and LSND results within the framework of neutrino oscillations MiniBooNE data: key in addressing the viability of 3+2 models with sterile neutrinos Leptonic CP-violation possibility opened up in the 3+2 sterile neutrino hypothesis could have large measurable effects at MiniBooNE