Probing Extra Dimensions with Neutrino Oscillations P. A. N. Machadoa, H. Nunokawab and R. Zukanovich Funchala ∗ 1 1 aInstituto de F´ısica, Universidade de S˜ao Paulo, 0 2 C. P. 66.318, 05315-970 S˜ao Paulo, Brazil n bDepartamento de F´ısica, Pontif´ıcia Universidade Cat´olica do Rio de Janeiro, a C. P. 38071, 22452-970 Rio de Janeiro, Brazil J 9 We consider a model where sterile neutrinos can propagate in a large compactified extra dimension (a) giving ] rise to Kaluza-Klein (KK) modes and the Standard Model left-handed neutrinos are confined to a 4-dimensional h spacetimebrane. TheKKmodesmixwiththestandardneutrinosmodifyingtheiroscillationpattern. Weexamine p current experiments in this framework obtaining stringent limits on a. - p e h [ 1. Introduction toDiracmassesandmixingsamongactivespecies 1 and sterile KK modes. This can be derived from v The introduction of singlet neutrino fields the action (cid:90) 6 which can propagate in extra spatial dimen- S = d4xdyıΨαΓ ∂JΨα 8 sions as well as in the usual three dimensional J 6 space may lead to naturally small Dirac neutrino (cid:90) 1 + d4xıν¯αγ ∂µνα masses,duetoavolumesuppression. Ifthosesin- L µ L . 1 glets mix with standard neutrinos they may have (cid:90) 10 an impact on neutrino oscillations, even if the + d4xλαβHν¯LαΨβR(x,0)+h.c., sizeofthelargestextradimensionissmallerthan 1 where Γ ,J = 0,..,4 are the 5-dimensional : 2×10−4m(thecurrentlimitfromCavendish-type J v Dirac matrices, that after dimensional reduction experiments which test the Newton Law). i and electroweak symmetry breaking gives rise to X the effective neutrino mass Lagrangian ar 2. Theoretical Framework L = (cid:88)mD (cid:34)ν(0)ν(0)+√2 (cid:88)∞ ν(0)ν(N)(cid:35) HereweconsiderthemodeldiscussedinRef.[1] eff αβ αL βR αL βR where the 3 standard model (SM) left-handed α,β N=1 neutrinos νLα and the other SM fields, including + (cid:88) (cid:88)∞ N ν(N)ν(N)+h.c., the Higgs (H), are confined to propagate in a a αL αR α N=1 4-dimensional spacetime, while 3 families of SM wheretheGreekindicesα,β =e,µ,τ, thecap- singlet fermions (Ψα) can propagate in a higher ital Roman index N = 1,...,∞, mD is a Dirac dimensionalspacetimewithatleasttwocompact- αβ ified extra dimensions, one of these (y) compact- mass matrix, ν(0) , ν(N) and ν(N) are the linear αR αR αL ified on a circle of radius a, much larger than the combinations of the singlet fermions that couple size of the others so that we can in practice use a to the SM neutrinos ν(0). αL 5-dimensional treatment. Inthiscontextonecancomputetheactiveneu- The singlet fermions have Yukawa couplings trino transition probabilities λ withtheHiggsandtheSMneutrinosleading αβ P(ν(0) →ν(0);L)= ∗CToanlckagSivpeenccahtiNulOlaW, O20tr1a0n,tNo,euIttarilny,oSOespctiellmatbieorn4W-1o1r,ks2h0o1p0., (cid:12)(cid:12)(cid:12)(cid:12)(cid:88) (cid:88)∞ UααiUβ∗kWβ i(j0N)∗Wk(j0N)exp(cid:32)iλ2(jEN)a22L(cid:33)(cid:12)(cid:12)(cid:12)(cid:12)2 E-mail: [email protected] i,j,kN=0 1 2 where U and W are the mixing matrices for ac- LEDinVacuum tive and KK modes, respectively. Here λ(N) is 1.0 j 735km a dimensionless eigenvalue of the evolution equa- 0.8 tion [1] which depends on the j-th neutrino mass (mj), hence on the mass hierarchy, L is the base- (cid:174)Ν(cid:76)Μ 0.6 Standard linTeoanildlusEtriastethwehnaetuitsrienxopeecnteerdgyw.e plot in Fig. 1 (cid:72)ΝPΜ 0.4 LED: ma0(cid:61)(cid:61)0510(cid:45)7m the survival probabilities for ν → ν and ν¯ → 0.2 Normalhierarchy µ µ e ν¯ as a function of E. We show the behavior for Invertedhierarchy e 0.0 the normal and inverted mass hierarchy assum- 1 2 3 4 5 ingthelightestneutrinotobemassless(m =0). E(cid:72)GeV(cid:76) 0 The effect of this large extra dimension (LED) 1.0 depends on the product m a. We observe that j 180km in the ν →ν channel the effect of LED is basi- 0.8 µ µ callythesamefornormal(NH)andinverted(IH) hierarchies, since in this case all the amplitudes Ν(cid:76)e 0.6 (cid:174) involved are rather large. On the other hand, for (cid:72)ΝPe 0.4 ν¯ →ν¯ theeffectissmallerforNHasinthiscase e e 0.2 the dominant m a term is suppressed by θ . j 13 0.0 2 3 4 5 6 7 8 3. Results E(cid:72)MeV(cid:76) As we can observe in Fig. 1 the main effect of Figure 1. In the top (bottom) panel we show the LED is a shift in the oscillation maximum with survival probability for ν (ν¯ ) as a function of µ e a decrease in the survival probability due to os- the neutrino energy for L=735 km (180 km) for cillations to KK modes. This makes experiments a = 0 (no LED, black curve) and a = 5×10−7 such as KamLAND and MINOS, which are cur- m for normal hierarchy (dashed blue curve) and rentlythebestexperimentstomeasure∆m2 and inverted hierarchy (dotted red curve). (cid:12) |∆m2 |, respectively, also the best experiments atm to test for LED. generate neutrinos with m = 0.2 eV. We have 0 We have used the recent MINOS [2] and Kam- verified that the inclusion of LED in the fit of LAND [3] results and reproduced their allowed the standard atmospheric oscillation parameters regions for the standard oscillation parameters. doesnotmodifyverymuchtheregionintheplane For this and the LED study we have modified sin22θ ×|∆m2 | allowed by MINOS data. In 23 atm GLoBES[4]accordingtoourpreviousanalysisof fact the best fit point as well as the χ2 remain min these experiments in [5] and [6]. the same as in the case without LED. In Fig. 2, we present the excluded region in KamLAND data provide, for hierarchical neu- the plane m × a, by MINOS, KamLAND and trinos with m → 0, a competitive limit only for 0 0 their combined data at 90 and 99% CL (2 dof). IH, in this case one gets a < 8.5(9.8)×10−7 m When finding these regions all standard oscilla- at 90 (99)% CL. For degenerate neutrinos with tion parameters where considered free. To ac- m = 0.2 eV one also gets from KamLAND 0 count for our previous knowledge of their values a < 2.0(2.3)×10−7 m at 90 (99)% CL. The in- [7],wehaveaddedGaussianpriorstotheχ2func- clusion of LED in the fit of the standard solar tion. As expected the limits provided by MINOS oscillation parameters here enlarges the region (ν →ν ) are basically the same for NH and IH. in the plane tan2θ × ∆m2 allowed by Kam- µ µ 12 (cid:12) From their data we obtain a < 7.3(9.7)×10−7 LAND data. The best fit point changes from m in the hierarchical case for m → 0 and ∆m2 = 7.6×10−5 eV2 and tan2θ = 0.62 to 0 (cid:12) 12 a < 1.2(1.6)×10−7 m at 90 (99)% CL for de- ∆m2 =8.6×10−5 eV2 andtan2θ =0.42,how- (cid:12) 12 3 4. Conclusions 100 MINOSΝ (cid:174)Ν Μ Μ We have investigated the effect of LED in neu- excluded trinooscillationdataderivinglimitsonthelargest extra dimension a provided by the most recent 10(cid:45)1 data from MINOS and KamLAND experiments. (cid:76)V For hierarchical neutrinos with m0 → 0, MINOS e (cid:72) and KamLAND constrain a < 6.8(9.5) × 10−7 m0 m for NH and a < 8.5(9.8) × 10−7 m at 90 10(cid:45)2 (99)% CL for IH. For degenerate neutrinos with m = 0.2 eV their combined data constrain a < 0 2.1(2.3)×10−7 m at 90 (99)% CL. 10(cid:45)3 We can estimate that the future Double KamLAND CHOOZexperimentwillbeabletoimprovethese limits by a factor 2 for the IH and by a factor excluded 1.5forthedegeneratecase. UnfortunatelyNOνA and T2K cannot improve MINOS limits. See [8] 10(cid:45)1 for any detail. (cid:76)V RZF and HN thank Profs. Fogli and Lisi for e (cid:72) m0 thecordialinvitationtoparticipateofNOW2010. 10(cid:45)2 This work has been supported by FAPESP, FAPERJ and CNPq Brazilian funding agencies. REFERENCES 10(cid:45)3 MINOS(cid:43)KamLAND 1. H. Davoudiasl, P. Langacker and M. Perel- stein, Phys. Rev. D 65, (2002) 105015 excluded [arXiv:hep-ph/0201128]. 2. P. Vahle [MINOS Collaboration], these pro- 10(cid:45)1 ceedings. (cid:76)eV 3. S. Abe et al. [KamLAND Collaboration], (cid:72) m0 Phys. Rev. Lett. 100, (2008) 221803 10(cid:45)2 [arXiv:0801.4589 [hep-ex]]. Normalhierarchy 4. P. Huber et al., Comput. Phys. Commun. 99(cid:37),90(cid:37)C.L. 177, (2007) 432 [arXiv:hep-ph/0701187], Invertedhierarchy 99(cid:37),90(cid:37)C.L. URL http://www.mpi-hd.mpg.de/˜ globes. 10(cid:45)3 5. H. Minakata, H. Nunokawa, W. J. C. Teves 10(cid:45)8 10(cid:45)7 10(cid:45)6 and R. Zukanovich Funchal, Nucl. Phys. a(cid:72)m(cid:76) Proc. 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