Neutrinos & Large Extra Dimensions. Renata Zukanovich Funchal Universidade de São Paulo, Brazil

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1 Neutrinos & Large Extra Dimensions Renata Zukanovich Funchal Universidade de São Paulo, Brazil What is ν? Workshop June 26, 2012

5 x 10-5 ev 2 Δm 2 32 Δm 2 31 2.5 x 10-3 ev 2 sin 2 θ12 0.

2 ν Masses & Mixings Majorana CP Violating phases solar atmospheric accelerator reactor Δm x 10-5 ev 2 Δm 2 32 Δm x 10-3 ev 2 sin 2 θ sin 2 θ sin 2 θ Normal Hierarchy ν 2 cosδ ν 3 = -1 ν 1 Inverted Hierarchy ν 2 ν 1 ν 3

3 Fermions Mass Hierarchy Elementary Particle Masses Span 11 orders of magnitude!? m0 = absolute neutrino mass scale for neutrinos the well motivated seesaw mechanism can provide an understanding of the smallness of neutrino mass if neutrinos are Majorana fermions

4 Neutrino Anomalies seem to indicate the need of extra species (see Steve Brice) Gallium Anomaly LSND/MiniBooNE Anomaly LSND(2001),MiniBooNE (2012) Gallex (2010), SAGE (2009) Mueller et al. (2011) Huber (2011) Reactor Anomaly Menton et al. (2011)

5 Extra Dimensions T. Kaluza (1919) O. Klein (1926)

flat extra dimensions Extra Dimensions more recently this was revisited by string inspired ideas designed to address the hierarchy problem Large Extra Dimensions (LED) : Arkani-Hamed, Dimopoulos,

6 flat extra dimensions Extra Dimensions more recently this was revisited by string inspired ideas designed to address the hierarchy problem Large Extra Dimensions (LED) : Arkani-Hamed, Dimopoulos, Dvali (1998) only gravity (and SM singlets) in the bulk Universal Extra Dimensions (UED): Appelquist, Cheng, Dobrescu (2001) all SM particles can propagate in the bulk Warped Extra Dimensions (WED): extra dimensions are curved Randall, Sundrum (1999)

Large Extra Dimensions assuming toroidal compactification of the δ extra dimensions of the same size R bulk 1+3+δ M PL = 1 10 16 TeV 8π GN

7 Large Extra Dimensions assuming toroidal compactification of the δ extra dimensions of the same size R bulk 1+3+δ M PL = TeV 8π GN brane M = M 2 PL (2πR) δ 1/(2+δ) new fundamental scale of gravity ds 2 = g µν dx µ dx ν δ ab dy a dy b δ 2 largest extra dimension < 0.2 mm

8 LED & Neutrinos Dvali, δ 2 but only one R1 = a >> R2, R3,... (effectively D) S = d 4 xdyiψ α Γ J J Ψ α + d 4 xdy(i ν Lγ α µ µ νl α + λ αβ H ν LΨ α β (x, y)δ(y)+h.c.) R SM particles propagate in the 1+3D brane bulk-brane coupling 3 families of SM singlets propagate in the 1+4D bulk Γ J J =0,..., 4 : the 5-D Dirac gamma matrices Dienes, Dudas, Gherghetta (1999) Smirnov (1999) Mohapatra, Nandi, Perez-Lorenzana (1999) Davoudiasl, Langacker, Perelstein (2002) Ψ α : SM singlet bulk fermion fields ν α L : SM neutrinos λ αβ = h αβ / M Dimensionless coupling

9 LED & Neutrinos to get chiral fermion compactify on an orbifold (S 1 /Z2 ) periodicity condition : y = y + 2π a allows a Fourier decomposition 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 +Ψ α( n) R Kaluza-Klein modes n =1,..., ν (n) αl 1 Ψ α(n) L 2 Ψ α( n) L even under Z2 n =1,..., odd under Z2

10 Effective Mass Lagrangian α,β m D αβ ν αl ν (0) βr + 2 SM neutrinos n=1 ν αl ν (n) βr + α n=1 n a ν(n) αl ν(n) αr m n KK = n a mass of KK modes KK modes sterile neutrinos m D αβ = h αβ v M M PL naturally small Dirac masses

11 Neutrino Mass Matrix 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 λ i πa 2 m 2 i cot(πλ i )=0 (W (n) i ) 2 = ν αl = 3 i=1 U αi 2 1+π 2 (am i ) 2 + λ (n)2 /(am i i ) 2 W (n) ν (n) i il n=0

12 Neutrino Oscillations P (ν α ν β ; L, E) = A να ν β (L, E) 2 A να ν β (L, E) = n=1 m n KK 3 standard oscillation U αi U βi A i (L, E) i=1 PMNS mixing A i (L, E) (1 π2 6 m2 i a 2 ) 2 exp i m2 i L 2E 2 i mi + 2 exp (2m2 i + mn2 KK )L 2E a single extra parameter m n KK = n a depends on : absolute neutrino mass scale mass hierarchy

13 Neutrino Oscillations P (ν α ν β ; L, E) = A να ν β (L, E) 2 A να ν β (L, E) = n=1 can be probed by current experiments m n KK 3 i=1 U αi U βi A i (L, E) in order to affect the standard probability by ~10% (since at least one mi ~ 0.05 ev) a ~ 5 ev -1 = 1μm A i (L, E) (1 π2 6 m2 i a 2 ) 2 exp i m2 i L 2E 2 i mi + 2 exp (2m2 i + mn2 KK )L 2E m n KK = n a depends on : absolute neutrino mass scale mass hierarchy

14 Neutrino Oscillations LED in vacuum 735 km MINOS sin 2 θ 12 =0.319 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 m0 = m1 normal hierarchy (NH) m0 = m3 inverted hierarchy (NH)

15 Neutrino Oscillations LED in vacuum 180 km KamLAND sin 2 θ 12 =0.319 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 m0 = m1 normal hierarchy (NH) m0 = m3 inverted hierarchy (NH)

16 Neutrino Oscillations CHOOZ/DC/RENO/Daya Bay 1.0 LED in vacuum 1.05 km sin 2 θ 12 =0.319 sin 2 2θ 13 =0.07 sin 2 2θ 23 =1 PΝeΝe 0.8 Standard LED: m 0 0 a m Normal hierarchy Inverted hierarchy m 2 21 = ev 2 m 2 32 = ev Energy MeV m0 = m1 normal hierarchy (NH) m0 = m3 inverted hierarchy (NH)

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17 Neutrino Oscillations No sizable effect in disappearance ν µ ν s (n) ν e ν µ ν s (n)!"#$%&'()*(+,-&'("*-"*%(-'.(+,-&'("*#"/ *567*(+,-&'("*#"/ *567*%(-'.(+,-&'("*#"/+ ν e **********:;<+==>*8?019*@*3A1?*@*?413 :;<+==>*221A*BC.*3414*BC.*391?****************** #$%&'()*+!,"!-+.+/%)+!,"! Cannot explain MiniBooNE/LSND!"

18 Survival Probability P(ν e ν e ) or P(ν e ν e ) standard oscillation, sin 2 2θ 13 = 0.0 standard oscillation, sin 2 2θ 13 = 0.1 a = 0.08 µm, m 0 = 0.1 ev (Inverted), θ 13 =0 a = 0.3 µm, m 0 = 0 (Inverted), θ 13 = 0 a = 0.1 µm, m 0 = 0.2 ev (Inverted), θ 13 =0 SAGE SAGE GALLEX Ga (E = 0.43/0.75/0.81 MeV) GALLEX ILL Bugey-3/4 ROVNO91 SRP-I SRP-II ROVNO88-1I/2I ROVNO88-1S/3S ROVNO88-2S Reactor Krasnoyarsk-I Bugey-3 Goesgen-I Goesgen-II Krasnoyarsk-III Gosgen-III Krasnoyarsk-II sin 2 θ 12 =0.32 sin 2 2θ 23 =1 Δm 2 31 =2.46x10-3 ev 2 Δm 2 21 =7.59x10-5 ev 2 Palo Verde CHOOZ Distance from the Source (m) Bugey-3 Double Chooz RENO Daya Bay averaged survival probability To illustrate how LED can explain the short baseline anomalies PAN Machado, H. Nunokawa, F.A. Pereira dos Santos, RZF (2012)

19 Allowed Regions PAN Machado, H. Nunokawa, F.A. Pereira dos Santos, RZF (2012)

20 Some Comments if 1/a >> m 2 21 LED matter effects are not important, but LED can reduce the overall νe survival probability Terrestrial bounds imply very small reduction As long as we consider the terrestrial bounds LED does not observably affect the atmospheric neutrino oscillations

21 Effective νe Mass V. S. Basto-Gonzalez, A. Esmaili, O.L.G. Peres (2012) 3 H 3 He + +e + ν e KATRIN K(T e,m 0,a)= p k E k k 3 U ei 2 n=1 a (W (n) i n=0 ) 2 E 2 k (λ(n) i /a) 2 pk = transition probability of the k th excited state of the daughter nucleus E k = Q W k T e excitation energy a

22 Conclusions LED framework can provide naturally small Dirac masses LED framework can provide sterile neutrinos LED framework is testable (a single new parameter) LED can accommodate all current neutrino oscillation data (except for MiniBooNE/LSND)

23 Other Bounds model dependent KK gravitons M D (Fundamental Scale of Gravity) [TeV] Bounds on (Flat) Large Extra Dimensions for δ=2 NS heat [16] γ NS [16] excluded δ=4 δ=3 δ=1 δ=2 excluded by current data (normal, m 0 = 0.2 ev) Newton Law [17] excluded excluded by current data (normal, m 0 = 0) SN87A [16] excluded LHC LEP [15] a (Size of the Extra Dimention) [m] LEP (LHC): from KK graviton emission and exchange M = M D = M 2 PL (2π a) δ best bounds: due to over production/decays of KK gravitons in astrophysical environments Hall, Tucker-Smith (1999) Hannestad (2001, 2004) Hannestad, Raffelt (2003) 1/(2+δ)

24 Other Bounds model dependent KK neutrinos M D (Fundamental Scale of Gravity) [TeV] Bounds on (Flat) Large Extra Dimensions for δ=2 NS heat [16] γ NS [16] excluded δ=4 δ=3 δ=1 δ=2 excluded by current data (normal, m 0 = 0.2 ev) Newton Law [17] excluded excluded by current data (normal, m 0 = 0) SN87A [16] excluded LHC LEP [15] a (Size of the Extra Dimention) [m] BBN weaker than our bounds Cosmology M = M D = M 2 PL (2π a) δ Goh, Mohapatra (2002) Abazajian, Fuller, Patel (2003) very strong bounds from CMB, diffuse γ backgrounds, LSS but can be evaded 1/(2+δ)

25 Thank you!

Probing Extra-Dimensions with Neutrinos Oscillations

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