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A Minimal Model of Neutrino Flavor Introduction T7 Model NLO Which Group? Conclusions Introduction T7 Model NLO Which Group? Conclusions Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Introduction T7 Model NLO Which Group? Conclusions A Minimal Model of Neutrino Flavor Akın Wingerter Laboratoire de Physique Subatomique et de Cosmologie UJF Grenoble 1, CNRS/IN2P3, INPG, Grenoble, France July 12, 2012 Work in progress w/Christoph Luhn (IPPP, Durham) & Krishna Mohan Parattu (IUCAA, Pune) Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Introduction T7 Model NLO Which Group? Conclusions Neutrino Mixing Matrix ã Neutrinos have mass and the different flavors can mix Super-Kamiokande Collaboration, Y. Fukuda et al., \Evidence for oscillation of atmospheric neutrinos," Phys. Rev. Lett. 81 (1998) 1562{1567, hep-ex/9807003 SNO Collaboration, Q. R. Ahmad et al., \Direct evidence for neutrino flavor transformation from neutral-current interactions in the Sudbury Neutrino Observatory," Phys. Rev. Lett. 89 (2002) 011301, nucl-ex/0204008 ã Charged lepton and neutrino mass matrices cannot be simultaneously diagonalized ^ y ^ y M`+ = DLM`+ DR ; Mν = ULMνUR ã Pontecorvo-Maki-Nakagawa-Sakata matrix B. Pontecorvo, \Mesonium and antimesonium," Sov. Phys. JETP 6 (1957) 429 Z. Maki, M. Nakagawa, and S. Sakata, \Remarks on the unified model of elementary particles," Prog. Theor. Phys. 28 (1962) 870{880 0 1 0 1 νe ν1 y @νµA = DLUL @ν2A ντ | {z } ν3 UPMNS Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Introduction T7 Model NLO Which Group? Conclusions Neutrino Mixing Matrix What we know about the mixing angles . −iδ 1 0 0 c13 0 e s13 c12 s12 0 UPMNS = 0 c23 s23 0 1 0 -s12 c12 0 iδ 0 -s23 c23 -e s13 0 c13 0 0 1 −iδ c12c13 s12c13 s13e iδ iδ = -c23s12−s13s23c12e c23c12−s13s23s12e s23c13 iδ iδ s23s12−s13c23c12e -s23c12−s13c23s12e c23c13 D. Forero, M. Tortola, and J. Valle, \Global status of neutrino oscillation parameters after recent reactor measurements," 1205.4018 Parameter Best Fit 1σ range 3σ range ◦ ◦ ◦ ◦ ◦ θ12 34:45 33:40 − 35:37 31:31 − 37:46 ◦ ◦ ◦ ◦ ◦ θ23 44:43 41:55 − 49:02 38:65 − 53:13 ◦ ◦ ◦ ◦ ◦ θ13 9:28 8:53 − 9:80 7:03 − 10:94 Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Introduction T7 Model NLO Which Group? Conclusions Tribimaximal Mixing ã Until recently, our best guess was tribimaximal mixing (TBM) P. F. Harrison, D. H. Perkins, and W. G. Scott, \Tri-bimaximal mixing and the neutrino oscillation data," Phys. Lett. B530 (2002) 167, hep-ph/0202074 0p p 1 ? 2p=3 1=p3 0p UPMNS = UHPS = @-1=p6 1=p3 -1=p2A -1= 6 1= 3 1= 2 ◦ ◦ ◦ ,! θ12 = 35:26 ; θ23 = 45 ; θ13 = 0 ◦ ã Agreement still quite good for θ12, θ23, but θ13 = 0 excluded @5σ Forero et al, 1205.4018, DAYA-BAY Collaboration, 1203.1669, RENO Collaboration, 1204.0626 Parameter Tribimaximal Global fit 1σ Daya Bay Reno ◦ ◦ ◦ θ12 35:26 33:40 − 35:37 - - 3 ◦ ◦ ◦ θ23 45:00 41:55 − 49:02 - - 3 ◦ ◦ ◦ ◦ ◦ θ13 0:00 8:53 − 9:80 8:8 9:8 7 Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Introduction T7 Model NLO Which Group? Conclusions Tribimaximal Mixing ã Until recently, our best guess was tribimaximal mixing (TBM) P. F. Harrison, D. H. Perkins, and W. G. Scott, \Tri-bimaximal mixing and the neutrino oscillation data," Phys. Lett. B530 (2002) 167, hep-ph/0202074 0p p 1 ? 2p=3 1=p3 0p UPMNS = UHPS = @-1=p6 1=p3 -1=p2A -1= 6 1= 3 1= 2 ◦ ◦ ◦ ,! θ12 = 35:26 ; θ23 = 45 ; θ13 = 0 ◦ ã Agreement still quite good for θ12, θ23, but θ13 = 0 excluded @5σ Forero et al, 1205.4018, DAYA-BAY Collaboration, 1203.1669, RENO Collaboration, 1204.0626 Parameter Tribimaximal Global fit 1σ Daya Bay Reno ◦ ◦ ◦ θ12 35:26 33:40 − 35:37 - - 3 ◦ ◦ ◦ θ23 45:00 41:55 − 49:02 - - 3 ◦ ◦ ◦ ◦ ◦ θ13 0:00 8:53 − 9:80 8:8 9:8 7 Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Introduction T7 Model NLO Which Group? Conclusions Post-Daya Bay Confusion ã Regular patter UPMNS is suggestive of a family symmetry 0p p 1 0 1 ? 2p=3 1=p3 0p 2 1 0 UPMNS = UHPS = @-1=p6 1=p3 -1=p2A ∼ @1 1 1A -1= 6 1= 3 1= 2 1 1 1 ã Daya bay and Reno rule out tribimaximal Mixing ã What are our options? Give up family symmetries? Some remarks towards the end . ◦ Look for groups that give θ13 6= 0 R. d. A. Toorop, F. Feruglio, and C. Hagedorn, \Discrete Flavour Symmetries in Light of T2K," Phys.Lett. B703 (2011) 447{451, 1107.3486 Keep TBM and calculate higher corrections ! This talk! Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Introduction T7 Model NLO Which Group? Conclusions Discrete Flavor Symmetries ã Introduce relations between families of quarks and leptons ã But which discrete group do we take for the family symmetry? Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Introduction T7 Model NLO Which Group? Conclusions Discrete Flavor Symmetries ã Introduce relations between families of quarks and leptons ã But which discrete group do we take for the family symmetry? Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Discrete Flavor Symmetries Introduction 1012.2842 K. M. Parattu and A. Wingerter, \Tribimaximal Mixing From Small Groups," ã ã ã ã T We identified the smallest group∆(96) that gives gives TBM! Many papers on We scanned 76 discrete groups 7 Model NLO Which Group? Akın Wingerter, LPSC Grenoble θ 13 Conclusions 6= 0 A 4 × ◦ Z but is large n , n ≥ 3. Connection between A Minimal Model of Neutrino Flavor 105 Phys.Rev. 104 103 D84 102 Number of Models A (2011) 013011, 1 10 4 and TBM? (12,3) (21,1) (24,3) (27,3) (27,4) (36,3) (39,1) (42,2) (48,3) (54,8) (57,1) (60,5) (60,9) (63,1) (63,3) (72,3) (75,2) (78,2) (81,7) (81,8) (81,9) (84,2) (84,9) (93,1) (96,3) (24,12) (24,13) (36,11) (48,28) (48,29) (48,30) (48,31) (48,32) (48,33) (48,48) (48,49) (48,50) (72,15) (72,25) (72,42) (72,43) (72,44) (81,10) (84,11) (96,64) (96,65) (96,66) (96,67) (96,68) (96,69) (96,70) (96,71) (96,72) (96,74) (96,185) (96,186) (96,187) (96,188) (96,189) (96,190) (96,191) (96,192) (96,193) (96,194) (96,195) (96,197) (96,198) (96,199) (96,200) (96,201) (96,202) (96,203) (96,204) (96,226) (96,227) (96,229) Discrete Flavor Symmetries Introduction 1012.2842 K. M. Parattu and A. Wingerter, \Tribimaximal Mixing From Small Groups," ã ã ã ã T ∆(96) gives Many papers on We scanned 76 discrete groups We identified the smallest group that gives TBM! 7 Model NLO Which Group? Akın Wingerter, LPSC Grenoble θ 13 Conclusions 6= 0 A 4 × ◦ Z but is large n , n ≥ 3. Connection between A Minimal Model of Neutrino Flavor 105 Phys.Rev. 104 103 D84 102 Number of Models A (2011) 013011, 1 10 4 and TBM? (12,3) (21,1) (24,3) (27,3) (27,4) (36,3) (39,1) (42,2) (48,3) (54,8) (57,1) (60,5) (60,9) (63,1) (63,3) (72,3) (75,2) (78,2) (81,7) (81,8) (81,9) (84,2) (84,9) (93,1) (96,3) (24,12) (24,13) (36,11) (48,28) (48,29) (48,30) (48,31) (48,32) (48,33) (48,48) (48,49) (48,50) (72,15) (72,25) (72,42) (72,43) (72,44) (81,10) (84,11) (96,64) (96,65) (96,66) (96,67) (96,68) (96,69) (96,70) (96,71) (96,72) (96,74) (96,185) (96,186) (96,187) (96,188) (96,189) (96,190) (96,191) (96,192) (96,193) (96,194) (96,195) (96,197) (96,198) (96,199) (96,200) (96,201) (96,202) (96,203) (96,204) (96,226) (96,227) (96,229) Altarelli/Feruglio and most others Discrete Flavor Symmetries Introduction 1012.2842 K. M. Parattu and A. Wingerter, \Tribimaximal Mixing From Small Groups," ã ã ã ã T We identified the smallest group∆(96) that gives gives TBM! Many papers on We scanned 76 discrete groups 7 Model NLO Which Group? Akın Wingerter, LPSC Grenoble θ 13 Conclusions 6= 0 A 4 × ◦ Z but is large n , n ≥ 3. Connection between A Minimal Model of Neutrino Flavor 105 Phys.Rev. 104 103 D84 102 Number of Models A (2011) 013011, 1 10 4 and TBM? (12,3) (21,1) (24,3) (27,3) (27,4) (36,3) (39,1) (42,2) (48,3) (54,8) (57,1) (60,5) (60,9) (63,1) (63,3) (72,3) (75,2) (78,2) (81,7) (81,8) (81,9) (84,2) (84,9) (93,1) (96,3) (24,12) (24,13) (36,11) (48,28) (48,29) (48,30) (48,31) (48,32) (48,33) (48,48) (48,49) (48,50) (72,15) (72,25) (72,42) (72,43) (72,44) (81,10) (84,11) (96,64) (96,65) (96,66) (96,67) (96,68) (96,69) (96,70) (96,71) (96,72) (96,74) (96,185) (96,186) (96,187) (96,188) (96,189) (96,190) (96,191) (96,192) (96,193) (96,194) (96,195) (96,197) (96,198) (96,199) (96,200) (96,201) (96,202) (96,203) (96,204) (96,226) (96,227) (96,229) Adelhart Toorop et al Altarelli/Feruglio and most others Discrete Flavor Symmetries Introduction 1012.2842 K.
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