Probing Extra-Dimensions with Neutrinos Oscillations

Transcription

1 Probing Extra-Dimensions with Neutrinos Oscillations Renata Zukanovich Funchal Universidade de São Paulo, Brazil work in collaboration with P. A.N. Machado and H. Nunokawa (in preparation) 12: 1HXWULQR 2VFLOODWLRQ :RUNVKRS &RQFD 6SHFFKLXOOD 2WUDQWR /HFFH,WDO\ 6HSWHPEHU

2 Introduction introduction of singlet bulk neutrinos in LED model can lead to naturally small Dirac masses m D = hvm /M Pl M Pl = M M V δ fenomenology imposes δ 2 Cavendish type experiments that the Newton Law impose constraints on the size of the largest extradimension a as [C.D. Hoyle et al., Phys. Rev. Lett. 86, 1418 (2001)] a m So it is possible that the largest extra spacial dimension can impact neutrino oscillations

3 Introduction limits from experiments: CHOOZ a<10 5 m Solar Atmosferic a<10 5 m a< m [H. Davoudiasl and P. Langacker, PRD 65, (2002)]

4 Framework SM particles propagate in the 3-D brane S = 3 families of SM singlets propagate in the 4-D bulk d 4 xdyiψ α Γ J J Ψ α + d 4 x (i ν Lγ α µ µ νl α + λ αβ H ν LΨ α β (x, 0) + h.c.) R Γ J J =0,..., 4 : the 5-D Dirac gamma matrices Ψ α : SM singlet bulk fermion fields νl α : SM flavor neutrinos Yukawa couplings to SM H λ αβ = h αβ / M [G.R. Dvali and A.Y. Smirnov, Nucl. Phys. B563, 63 (1999); R.N. Mohapatra and A. Perez-Lorenzana, Nucl. Phys. B576,466 (2000); B593, 451(2001); R. Barbieri, P. Creminelli, and A. Strumia, Nucl. Phys. B585,28 (2000); H. Davoudiasl and P. Langacker, PRD 65, (2002)]

5 Framework One can decompose Ψ α (x, y) in KK-modes a = radius of the compact extra dimension Ψ α (x, y) = 1 2πa N= Ψ α(n) (x) e iny/a ν (0) αr Ψα(0) R ν (N) αr 1 Ψ α(n) R 2 ν (N) αl 1 Ψ α(n) L 2 ν (0) αl να L +Ψ α( N) N =1,..., R Ψ α( N) L N =1,...,

6 Framework α,β = h αβ vm /M Pl m D αβ ν (0) αl ν(0) βr + 2 N=1 ν (0) αl ν(n) βr + α N=1 N a ν(n) αl ν(n) αr + g 2 α l α γ µ (1 γ 5 ) ν (0) α W µ + h.c. ν (0) αl = i U αi ν (0) il 3 SM flavor neutrinos: KK-modes: ν (0) αl ν (N) αr α = e, µ, τ and ν(n) αl ν (0) αr = i R αi ν (0) ir ν (N) αr,αl = i R αi ν (N) ir,il, N 1

7 M i M i = lim N m 2 i 2am i 2am i 2am i... 2m 2am i (1/a) am i 0 (2/a) am i (N/a) 2 m 1 = m 0 i =1, 2, 3 m 3 = m 0

8 ν i = i d dt ν 1 ν 2 ν 3 L = 1 2E Neutrino Oscillation with LED Evolution Eq. in terms of the mass eigenstates where V α = T ν (0) i ν (1) i ν (2) i..., i =1, 2, 3 Vα = M 1 M M 2 M M 3 M 3 δeα V CC + V NC U V CC = 2G F N e V NC = 2G F N n /2 V e V µ V τ U ν 1 ν 2 ν 3 : matter potential L U : mixing matrix ν e ν µ ν τ = U ν 1 ν 2 ν 3 U = U e1 0 U e2 0 U e3 0 0 R e1 0 R e2 0 R e3 U µ1 0 U µ2 0 U µ3 0 0 R µ1 0 R µ2 0 R µ3 U τ1 0 U τ2 0 U τ3 0 0 R τ1 0 R τ2 0 R τ3 ν α = ν (0) α ν (1) α ν (2) α... T, α = e, µ, τ : flavor eigenstates U αi, α = e, µ, τ,i=1, 2, 3 R αi, α = e, µ, τ,i=1, 2, 3 : standard 3 flavor mixing : mixing due to KK states

9 Neutrino Oscillations with LED 1.0 L= 180 km LED in vacuum 180 km sin 2 θ 12 = sin 2 2θ 13 =0.07 PΝeΝe Standard LED: m 0 0 a m Normal hierarchy Inverted hierarchy sin 2 2θ 23 =1 m 2 21 = ev 2 m 2 32 = ev Energy MeV

10 Neutrino Oscillations with LED 1.0 L= 735 km LED in vacuum 735 km sin 2 θ 12 = sin 2 2θ 13 =0.07 PΝΜΝΜ Standard LED: m 0 0 a m Normal hierarchy Inverted hierarchy sin 2 2θ 23 =1 m 2 21 = ev 2 m 2 32 = ev Energy GeV

11 KamLAND ν e ν e Analysis :17 energy bins from MeV Selection efficiency sys. uncertainty = 6.5% (MeV) E p KamLAND data no oscillation best-fit osci. accidental C(!,n) O best-fit Geo " e best-fit osci. + BG + best-fit Geo " e priors: sin 2 θ 23 =(0.46 ± 0.08) m 2 32 =(2.46 ± 0.12) 10 3 ev 2 sin 2 2θ 13 < 0.1 [M. C. Gonzalez-Garcia, M. Maltoni, and J. Salvado arxiv: ] [KamLAND Collaboration, Phys. Rev. Lett. 100, (2008)]

12 KamLAND ν e ν e KamLAND 2 generations 10 4 standard fit: ev 2 2 m C.L. 99 C.L. 95 C.L. Best fit tan 2 θ 12 =0.62 m 2 21 = ev 2 χ 2 min/dof = 20.8/15 = tan 2 Θ 12 this reproduces well KamLAND results in [KamLAND Collaboration, Phys. Rev. Lett. 100, (2008)]

13 KamLAND ν e ν e KamLAND with LED ev 2 2 m C.L. 99 C.L. 95 C.L. Best fit tan 2 Θ 12 fit with LED: tan 2 θ 12 =0.42 m 2 21 = ev 2 a = m m 0 = ev for normal hierarchy χ 2 min/dof = 17.9/13 = 1.38

14 KamLAND Limits on LED 10 0 KamLAND Preliminary m 0 0: a<8.5 (9.8) (99)% CL 10 1 IH m0 ev 10 2 Normal hierarchy Inverted hierarchy a(m) R m m 0 =0.2 ev : a<2.0 (2.3) (99)% CL any hierarchy

15 MINOS ν µ ν µ Analysis :16 energy bins from 1-5 GeV Flux from NuMI beam MC simulation (M. Bishai) : effect of unfocused high energy pions in the secondary beam not included sys. uncertainties: 4% (3%) normalization on the signal (background) gaussian energy smearing with: σ Eν =0.16 (E ν /GeV) ( E ν /GeV) GeV priors: sin 2 θ 12 =0.319 ± m 2 21 =(7.59 ± 0.30) 10 5 ev 2 sin 2 2θ 13 < 0.09 [M. C. Gonzalez-Garcia, M. Maltoni, and J. Salvado arxiv: ] [P. Vahle (MINOS Collab.), Presentation at the XXIV International Conference on Neutrino Physics and Astrophysics (Neutrino 2010)]

16 MINOS ν µ ν µ 3.0 MINOS standard 2.8 standard fit: m ev sin 2 2θ 23 =1 m 2 32 = ev C.L. 68 C.L. [P. Vahle (Neutrino 2010)] χ 2 min/dof = 12.3/12 = 1.02 Best fit sin 2 2Θ 23 this reproduces well MINOS results (see J. Kopp, P.A.N. Machado and S. Parke, arxiv: )

17 MINOS ν µ ν µ 3.0 MINOS with LED fit with LED: 2.8 sin 2 2θ 23 =1 2 m ev m 2 32 = ev 2 a =0 m 0 = anything C.L. 68 C.L. Best fit χ 2 min/dof = 12.3/10 = sin 2 2Θ 23

18 MINOS Limits on LED MINOS Ν Μ Ν Μ 10 0 Preliminary m 0 0: a<7.2 (9.8) (99)% CL m0 ev Normal hierarchy Inverted hierarchy R m a(m) any hierarchy m 0 =0.2eV : a<1.3 (1.8) (99)% CL any hierarchy

19 MINOS+KamLAND Combined MINOS KamLAND 10 0 Preliminary m 0 0: a<5.0 (7.1) (99)% CL NH m0 ev Normal hierarchy a<7.6 (8.3) (99)% CL IH m 0 =0.2 ev : a<1.3 (1.6) (99)% CL Inverted hierarchy any hierarchy a(m) R m

20 Double CHOOZ Sensitivity to LED 1.0 L= 1.05 km LED in vacuum 1.05 km 10 0 Double Chooz Ν e Ν e 3yr Preliminary 10 1 PΝeΝe Standard LED: m 0 0 a m Normal hierarchy Inverted hierarchy Energy MeV m0 ev Normal hierarchy m 0 =0.2eV : Inverted hierarchy m 0 =0.2 ev : a(m) R m a<9.0 (13.0) (99)% CL

21 T2K & NOvA Sensitivity to LED T2K Ν Μ Ν Μ 5yr NOΝA Ν Μ Ν Μ 3yr 10 0 Preliminary 10 0 Preliminary m0 ev m0 ev Normal hierarchy Inverted hierarchy a(m) R m Normal hierarchy Inverted hierarchy R m a(m)

22 Summary We have performed a detailed analysis on the effect of LED in neutrino oscillations in current (MINOS and KamLAND) and future (Double CHOOZ, T2K and NOvA) We have established limits on the size of the largest extra dimension a Results (Preliminary): NH a<5.0 (7.1) (99)% CL m 0 0: Double CHOOZ can improve (IH) by a factor 2 IH a<7.6 (8.3) (99)% CL