New interactions: past and future experiments

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1 New interactions: past and future experiments Michele Maltoni Departamento de Física Teórica & Instituto de Física Teórica Universidad Autónoma de Madrid Neutrino 2008, Christchurch, New Zealand May 27, 2008 I. Non-standard interactions with matter II. Models with extra sterile neutrinos III. Neutrino decay and decoherence Summary Violation of fundamental principles Neutrino magnetic moment Long-range leptonic forces Mass-varying neutrinos...

2 I. Non-standard interactions with matter 2 Lagrangian formalism Effective low-energy Lagrangian for standard neutrino interactions with matter: LSM eff = 2 ( 2G F [ νβ γ µ Ll β ][ f γ µ L f ) ]+h.c. 2 2G F g f P [ ν βγ µ Lν β ][ f γ µ P f] β P,β where P {L,R}, ( f, f ) form an SU(2) doublet, and g f P is the Z coupling to fermion f : g ν L = 1 2, gl L = sin2 θ W 1 2, gu L = 2 3 sin2 θ W + 1 2, gd L = 1 3 sin2 θ W 1 2, g ν R = 0, gl R = sin2 θ W, g u R = 2 3 sin2 θ W, g d R = 1 3 sin2 θ W ; here we consider NC-like non-standard neutrino-matter described by: note that ε f P αβ is Hermitian; LNSI eff = 2 2G F ε f P αβ [ ν αγ µ Lν β ][ f γ µ P f]; P,α,β for convenience, we also define the vector component ε fv αβ = ε f L αβ + ε f R αβ.

3 I. Non-standard interactions with matter 3 Bounds from non-oscillation experiments (Flavor Conserving) 0.03 < ε el ee < < ε ul ee < < ε dl ee < < εer ee < 0.15 ν e e νe ν e e νe LSND Reactors good [1, 2] 0.4 < ε ur ee < 0.7 ν e q νq CHARM mild [3] 0.6 < εdr ee < 0.5 ν eq νq CHARM mild [3] ε el µµ < 0.03 ε er µµ < 0.03 ν µ e νe CHARM II good [1, 3] ε ul µµ < < εur µµ < ν µq νq NuTeV strong [3] ε dl µµ < < εdr µµ < ν µq νq NuTeV strong [3] 0.5 < ε el ττ < 0.2 ε ul ττ < 1.4 ε dl ττ < 1.1 (limits at 90% CL varying one parameter at a time) [1] J. Barranco et al., arxiv: < εer ττ < 0.4 e+ e ν νγ LEP mild [1, 4] [2] J. Barranco et al., Phys. Rev. D73 (2006) [hep-ph/ ]. [3] S. Davidson et al., JHEP 03 (2003) 011 [hep-ph/ ]. εur ττ < 3 rad. corrections τ decay poor [3] ε dr ττ < 6 rad. corrections τ decay poor [3] [4] Z. Berezhiani and A. Rossi, Phys. Lett. B535 (2002) 207 [hep-ph/ ].

4 I. Non-standard interactions with matter 4 Bounds from non-oscillation experiments (Flavor Changing) ε el eµ < ε ul eµ < ε dl eµ ε er eµ < rad. corrections µ 3e strong [3] ε ur eµ < rad. corrections Ti µ Ti e strong [3] < εdr eµ < rad. corrections Tiµ Tie strong [3] ε el eτ < 0.33 ε ul eτ < 0.5 ε dl eτ < 0.5 ε er eτ < 0.28 ν e e νe LEP+LSND+Rea mild [1, 4] εur eτ < 0.5 ν eq νq CHARM mild [3] εdr eτ < 0.5 ν eq νq CHARM mild [3] ε el µτ < 0.1 εer µτ < 0.1 ν µe νe CHARM II good [1, 3] ε ul µτ < 0.05 εur µτ < 0.05 ν µq νq NuTeV good [3] ε dl µτ < 0.05 ε dr µτ < 0.05 ν µ q νq NuTeV good [3] (limits at 90% CL varying one parameter at a time) WARNING: bounds become weaker when correlations among parameters are included! [1] J. Barranco et al., arxiv: [3] S. Davidson et al., JHEP 03 (2003) 011 [hep-ph/ ]. [4] Z. Berezhiani and A. Rossi, Phys. Lett. B535 (2002) 207 [hep-ph/ ].

5 I. Non-standard interactions with matter 5 NSI and neutrino oscillations Equation of motion: lots of parameters: i d ν dt = H ν; H = U Hd 0 U +V SM +V NSI ; H0 d = 1 ( ) diag 0, m E 31 ; ν c 12 c 13 s 12 c 13 s 13 e iδ CP ν e U = s 12 c 23 c 12 s 13 s 23 e iδ CP c 12 c 23 s 12 s 13 s 23 e iδ CP c 13 s 23, ν = ν µ ; s 12 s 23 c 12 s 13 c 23 e iδ CP c 12 s 23 s 12 s 13 c 23 e iδ CP c 13 c 23 ν τ V SM = ± 2G F N e diag(1, 0, 0); V NSI = ± 2G F N e f N f N e εee fv εeµ fv εeτ fv note that only the vector couplings ε fv αβ = ε f L αβ + ε f R αβ appear in propagation; however, NC-like NSI can affect detection (e.g., νe νe elastic scattering); too much parameters only partial analyses so far... εeµ fv εeτ fv εµµ fv εµτ fv fv fv εµτ εττ ;

6 I. Non-standard interactions with matter 6 Solar neutrinos As in the SM case, solar neutrinos can be reduced to an effective 2ν problem [5]: [ ( ) i d ν dt = m 2 21 cos2θ 12 sin2θ 12 ± ( ) c 2 2G F N e (r) 13 0 ± ( )] 0 ε f 2G F N f (r) 4E ν sin2θ 12 cos2θ ε f ε ν, f ( ) ε ν f = c 13 (εeµ fv c 23 εeτ fv s 23 ) s 13 [εµτ fv (c 2 23 s2 fv 23 )+(εµµ εττ fv )c 23 s 23 ], e ν =, ε f ν a = ε µµc fv ε ττ fv s 2 23 ε ee fv 2εµτ fv c 23 s s 13 c 13 (εeτ fv c 23 + εeµ fv s 23 ) s 2 fv 13 (εττ c ε µµ fv s2 23 ε ee fv fv + 2εµτ s 23 c 23 ) (neglecting for simplicity δ CP and the complex phases in ε fv αβ ); Analyses in the literature [5, 6] focus on f = {u,d}, because (1) bounds on ε qv αβ are weaker, and (2) for f = e SK detection is also affected by NSI. pre-borexino solar data can be perfectly fitted by NSI only (i.e., m 2 21 = 0); however, KamLAND requires m 2 21 pure NSI solution no longer interesting. [5] M. Guzzo et al., Nucl. Phys. B629 (2002) 479 [hep-ph/ ]. [6] A. M. Gago et al., Phys. Rev. D65 (2002) [hep-ph/ ].

7 I. Non-standard interactions with matter 7 Solar neutrinos with both oscillations and NSI Solar LMA solution is unstable with respect to the introduction of NSI [7, 8, 9]; KamLAND is insensitive to NSI it determines m 2 21 ; bounds on ε q and ε q from combined Solar+KamLAND analysis are very weak. χ Present Future [7] [9] 90% C.L. 90% C.L. m 2 (ev 2 ) LMA-II LMA-II LMA-I LMA-I LMA ε ε tan 2 θ tan 2 θ 1 [7] O. G. Miranda, M. A. Tortola, and J. W. F. Valle, JHEP 10 (2006) 008 [hep-ph/ ]. [8] M. M. Guzzo, P. C. de Holanda, and O. L. G. Peres, Phys. Lett. B591 (2004) 1 [hep-ph/ ]. [9] A. Friedland, C. Lunardini, and C. Pena-Garay, Phys. Lett. B594 (2004) 347 [hep-ph/ ].

8 I. Non-standard interactions with matter 8 Atmospheric neutrinos: the ν µ ν τ channel We consider NSI in the µ τ sector [10] (note that εµµ fv 0 from LAB data): [ ( ) i d ν dt = m 2 31 cos2θ 23 sin2θ 23 ± ( )] ( fv 0 εµτ 2G F N f (r) ν, ν = 4E ν sin2θ 23 cos2θ 23 determination of oscillation parameters is very stable; εµτ fv ε fv ττ ν µ ν τ ) ; 90% (3σ) bounds on NSI [11]: { ε ev µτ (0.058), (e) 0.12 (0.19); (u) (d) { { ε ev ττ ε uv µτ (0.019), ε uv ττ (0.061); ε dv µτ (0.019), (0.060); ε dv ττ m 2 31 [10-3 ev 2 ] f = e sin 2 θ 23 Bounds on ε fv ττ F = ε e µτ 2 + ε e ττ εe µµ 2 / f = e [11] ε e µτ / F are much stronger than LAB ones. [10] N. Fornengo et al., Phys. Rev. D65 (2002) [hep-ph/ ]. [11] M. C. Gonzalez-Garcia and M. Maltoni, Phys. Rept. 460 (2008) 1 [arxiv: ].

9 I. Non-standard interactions with matter 9 { Atmospheric ν: the ν e ν τ channel Nu /N e = (core),3.012 (mantle) N d /N e = (core),3.024 (mantle) Let us now turn to the e τ sector [12, 13, 14]: 4 1 ε V ee 0 ε V eτ ε V αβ N f ε fv ε V ee = 0.15 V NSI = f N αβ 3 e 0.5 ε V eτ 0 ε V ττ ε ev αβ + 3εuV αβ + 3εdV 2 αβ 0 a dramatic cancellation [12] occurs along the parabola (1+ε V ee)ε V ττ = ε V eτ 2 ; determination of osc. parameters is still stable; but the previous bound on ε V ττ no longer applies; however, the bound is still strong; Correlations among different ε V αβ can have very important consequences! m 2 31 [10-3 ev 2 ] m 2 31 [10-3 ev 2 ] Normal Inverted sin 2 θ 23 ε ττ V 0.5 ε ττ V 1 0 Normal Inverted V ε eτ [12] A. Friedland, C. Lunardini, and M. Maltoni, Phys. Rev. D70 (2004) [hep-ph/ ]. [13] A. Friedland and C. Lunardini, Phys. Rev. D72 (2005) [hep-ph/ ]. [14] A. Friedland and C. Lunardini, Phys. Rev. D74 (2006) [hep-ph/ ].

10 I. Non-standard interactions with matter 10 Future experiments: degeneracies at ν factories Ε eτ a Ε eτ b Neutrino factories data will provide complementary information to atmospheric neutrinos [15]; however, in a ν-factory critical degeneracies may arise between NSI and oscillation parameters; Ε eτ s 13 s 13 c Ε eτ d s 13 s 13 in particular, NSI may spoil the sensitivity to θ 13 of a neutrino factory [16, 17]; ΕeΤ ΕeΤ c d a b the situation somewhat improves if data from two different base- 10 lines are combined [16] sin 2 2Θ 13 [16] sin 2 2Θ 13 [15] P. Huber and J. W. F. Valle, Phys. Lett. B523 (2001) 151 [hep-ph/ ]. [16] P. Huber, T. Schwetz, and J. W. F. Valle, Phys. Rev. Lett. 88 (2002) [hep-ph/ ]. [17] P. Huber, T. Schwetz, and J. W. F. Valle, Phys. Rev. D66 (2002) [hep-ph/ ].

11 I. Non-standard interactions with matter 11 NSI at ν factories: recent studies Single baseline (3000 km) [18]: the correlation between arg(ε V eµ) and δ CP is crucial. Sensitivity to ε V eτ is considerably worse than to ε V eµ ; sin 2 2Θ Two baselines ( & km): degeneracies solved: NSI don t spoil θ 13 and δ CP [19]; better sin 2 2Θ13 5Σ NH for true CP 3Π 2 5Σ CPV for true CP 3Π 2 5Σ sin 2 2Θ13 reach no NSI sensitivities: ε V eτ O(10 3 ) and ε V eµ O(10 4 ), independently of θ 13 [19]; sin 2 2Θ13 5Σ NH for true CP 3Π 2 5Σ CPV for true CP 3Π 2 5Σ sin 2 2Θ13 reach m fit includingε eτ energy: performances drop for E µ < 25 GeV [20]; Ε m ee 3Σ ν µ ν µ important to resolve degeneracies [20]; in contrast, ν e ν τ contributes very little [20] GLoBES 2008 Improvement by Silver 4000 km 5 GeV 25 GeV 50 GeV Ε m eτ 3Σ Ε m ΜΤ 3Σ Ε m ΤΤ 3Σ [20] m Ε ΑΒ reach [18] J. Kopp, M. Lindner, and T. Ota, Phys. Rev. D76 (2007) [hep-ph/ ]. [19] N. C. Ribeiro et al., JHEP 12 (2007) 002 [arxiv: ]. [20] J. Kopp, T. Ota, and W. Winter, arxiv: Ε m ΑΒ

12 I. Non-standard interactions with matter 12 Forthcoming facilities Borexino: precise measurement of the 7 Be line can have a strong impact on NSI [21]; MINOS (future): degeneracy with ε V eτ spoils sensitivity to θ 13. External input on either parameter helps measuring the other [22]; OPERA: data sample is too small to gain sensitivity to ε V eτ and εv ττ, even if combined with MINOS and Double-CHOOZ [23]. However, it may help in the determination of ε V µτ [24]; Coherent ν scattering: very sensitive to NSI interactions with quarks; present limits on ε qv ee and ε qv eτ could be improved dramatically [25, 26]. [21] Z. Berezhiani, R. S. Raghavan, and A. Rossi, Nucl. Phys. B638 (2002) 62 [hep-ph/ ]. [22] M. Blennow, T. Ohlsson, and J. Skrotzki, Phys. Lett. B660 (2008) 522 [hep-ph/ ]. [23] A. Esteban-Pretel, J. W. F. Valle, and P. Huber, arxiv: [24] M. Blennow et al., arxiv: [25] J. Barranco, O. G. Miranda, and T. I. Rashba, JHEP 12 (2005) 021 [hep-ph/ ]. [26] J. Barranco, O. G. Miranda, and T. I. Rashba, Phys. Rev. D76 (2007) [hep-ph/ ].

13 I. Non-standard interactions with matter 13 Other long-term facilities T2KK: good sensitivity to ε V µτ [27] (analysis restricted to the µ τ sector only); βb: also affected by degeneracies between ε V αβ and θ 13 [28]. Reactors+superbeams: widely complementary, since reactors are insensitive to ε V αβ, hence determine θ 13 irrespectively of NSI [29]. Warning In this talk we have focused only on neutral-current NSI. If NSI are considered also for charged-current interactions, so far neglected in most phenomenological studies, the problem of degeneracies may become more serious [17, 18, 29]. [17] P. Huber, T. Schwetz, and J. W. F. Valle, Phys. Rev. D66 (2002) [hep-ph/ ]. [18] J. Kopp, M. Lindner, and T. Ota, Phys. Rev. D76 (2007) [hep-ph/ ]. [27] N. C. Ribeiro et al., Phys. Rev. D77 (2008) [arxiv: ]. [28] R. Adhikari, S. K. Agarwalla, and A. Raychaudhuri, Phys. Lett. B642 (2006) 111 [hep-ph/ ]. [29] J. Kopp, M. Lindner, T. Ota, and J. Sato, Phys. Rev. D77 (2008) [arxiv: ].

14 II. Models with extra sterile neutrinos 14 The LSND problem LSND observed ν e appearance in a ν µ beam (E ν 30 MeV, L 35 m); the signal is compatible with ν µ ν e oscillations provided that m ev 2 ; on the other hand, other data give (at 3σ): [11] m 2 = SOL ev 2, m 2 = ev 2 (IH), ATM ev 2 (NH); m 2 (ev 2 /c 4 ) Karmen Bugey 90% (L max -L < 2.3) 99% (L max -L < 4.6) CCFR NOMAD sin 2 2θ in order to explain LSND with mass-induced neutrino oscillations one needs at least one more neutrino mass eigenstate. These new states must be sterile in order not to spoil the Z width measurement. [11] M. C. Gonzalez-Garcia and M. Maltoni, Phys. Rept. 460 (2008) 1 [arxiv: ].

15 II. Models with extra sterile neutrinos 15 Four neutrino mass models Approximation: m 2 SOL m2 ATM m2 LSND 6 different mass schemes: LSND LSND ATM SOL SOL ATM ATM SOL LSND (a) ATM SOL (b) SOL ATM (c) LSND (d) LSND (A) LSND SOL (B) ATM (3+1) (2+2) Total: 3 m 2, 6 angles, 3 phases. Different set of experimental data partially decouple: m 2 SOL m 2 ATM m 2 LSND ϕ 13 η s SOL ATM NEV d µ LSND ϕ 34 θ SOL θ ATM θ LSND η e ϕ 12

16 II. Models with extra sterile neutrinos 16 (2+2): ruled out by solar and atmospheric data χ solar + KamLAND solar solar (pre SNO salt) Real atm + LBL Restricted (2+2) global solar + KamLAND χ 2 PG χ 2 PC 10 3σ 3σ atm + LBL 3σ η s d s η s = d s in (2+2) models, the fractions of ν s in solar (η s ) and atmospheric (1 d s ) oscillations add to one η s = d s ; 3σ allowed regions η s 0.31 (solar) and d s 0.64 (atmospheric) do not overlap; superposition occurs only above 4.6σ (χ 2 = 20.8); PC the χ 2 increase due to the combination of solar and atmospheric data is χ 2 PG dof), corresponding to a PG = = 30.7 (1

17 II. Models with extra sterile neutrinos 17 (3+1): ruled out by short-baseline data m 2 41 [ev 2 ] Bugey Chooz U e4 2 CDHS atmospheric U µ4 2 (3+1) 90%, 99% CL LSND DAR atm + NEV + MB sin 2 2θ LSND = 4 U e4 U µ4 2 In (3+1) schemes, the SBL appearance probability is P 4ν µe = 4 U e4u µ4 2 sin 2 φ 41 ; disappearance experiments put upper bounds on U e4 2 and U µ4 2 ; { with other appearance experiments (Karmen, Nomad, MiniBooNE); LSND is in conflict: with disappearance experiments; quantitatively: χ 2 PG = 24.8 (4 dof) PG = ; Conclusion: four-neutrino models cannot explain LSND.

18 II. Models with extra sterile neutrinos 18 Reconciling MiniBooNE and LSND in (3+2) models MeV MB300 MB475 MB data app data incl. MB best fit LSND only excess events per MeV excess events CCQE E ν [GeV] 0 background L/E ν [m/mev] Trick: use the CP phase δ = arg(ue4 U µ4u e5 Uµ5 ) to differentiate ν (MB) from ν (LSND) [30]: Pµe 5ν = 4 U e4 U µ4 2 sin 2 φ U e5 U µ5 2 sin 2 φ U e4 U e5 U µ4 U µ5 sinφ 41 sinφ 51 cos(φ 54 δ); Also: δ = π+ε and U e4 U µ4 m 2 41 U e5u µ5 m 2 51 suppress MB probability. [30] M. Maltoni and T. Schwetz, Phys. Rev. D76 (2007) [arxiv: ].

19 II. Models with extra sterile neutrinos 19 Fitting all appearance data in (3+2) models m 2 51 [ev2 ] 10 0 m 2 51 [ev2 ] (3+2) fit: 10-1 (3+2) fit: 10-2 MB475 + LSND + KARMEN + NOMAD m 2 41 [ev2 ] 10-2 MB300 + LSND + KARMEN + NOMAD m 2 41 [ev2 ] data set U e4 U µ4 m 2 41 U e5 U µ5 m 2 51 δ χ 2 min /dof gof appearance (MB475) π 16.9/(29 5) 85% appearance (MB300) π 18.5/(31 5) 85%

20 II. Models with extra sterile neutrinos 20 The doom of disappearance data As for (3+1) models, disappearance data imply bounds on U ei 2 and U µi 2 (i = 4,5); these bounds are in conflict with the large values of U ei U µi required by appearance data; U e5 U µ %, 99% (4 dof) χ 2 PC = 9.3, m 2 41 = 0.87, m 2 51 = 19.9 disappearance appearance (MB475) again, a tension between APP and DIS arises: χ 2 PG = 17.5 (4 dof) PG = [no MB]; χ 2 = 17.2 (4 dof) PG PG = [MB475]; %, 99% (4 dof) χ 2 PC = 12.6, m 2 41 = 0.87, m 2 51 = 1.9 χ 2 = 25.1 (4 dof) PG = 4.8 PG 10 5 [MB300]; alternatively, compare LSND and NEV as in (3+1): U e5 U µ appearance (MB300) χ 2 PG = 19.6 (5 dof) PG = [before MB]; χ 2 PG = 21.2 (5 dof) PG = [after MB]. Conclusion: (3+2) models fail exactly as (3+1) do disappearance U e4 U µ4

21 II. Models with extra sterile neutrinos 21 Adding a third sterile neutrino: (3+3) models Improvements: (3+1) (3+2) [MB475]: χ 2 = 6.1/4 dof (81% CL) (3+2) (3+3) [MB475]: χ 2 = 1.7/4 dof (21% CL) (3+2) (3+3) [MB300]: χ χ 2 = 3.5/4 dof (52% CL) (3+2) (3+3) (3+1) MB m 2 41 [ev2 ] (3+3) (3+2) MB m 2 41 [ev2 ] (3+3) models do not offer qualitatively new effects with respect to (3+2) models; in particular, the improvement in χ 2 is very modest [30]. In brief: it is not possible to explain LSND with sterile neutrinos. [30] M. Maltoni and T. Schwetz, Phys. Rev. D76 (2007) [arxiv: ].

22 II. Models with extra sterile neutrinos 22 Sterile neutrinos: what next? Once LSND is dropped, there is no reason to make any assumption on the mass of the sterile states. However, this general case has been considered only in a very few works [31, 32, 33]; most of the works performed so far still assume heavy sterile neutrinos, in the context of Opera [34], of future ν factories [35, 36, 37, 38], and of neutrino telescopes [39, 40]. [31] P. C. de Holanda and A. Y. Smirnov, Phys. Rev. D69 (2004) [hep-ph/ ]. [32] V. Barger, S. Geer, and K. Whisnant, New J. Phys. 6 (2004) 135 [hep-ph/ ]. [33] M. Cirelli, G. Marandella, A. Strumia, and F. Vissani, Nucl. Phys. B708 (2005) [hep-ph/ ]. [34] A. Donini, M. Maltoni, D. Meloni, P. Migliozzi, and F. Terranova, JHEP 12 (2007) 013 [arxiv: ]. [35] V. D. Barger, S. Geer, R. Raja, and K. Whisnant, Phys. Rev. D63 (2001) [hep-ph/ ]. [36] A. Donini, M. B. Gavela, P. Hernandez, and S. Rigolin, hep-ph/ [37] A. Donini, M. Lusignoli, and D. Meloni, Nucl. Phys. B624 (2002) [hep-ph/ ]. [38] A. Dighe and S. Ray, Phys. Rev. D76 (2007) [arxiv: ]. [39] R. L. Awasthi and S. Choubey, Phys. Rev. D76 (2007) [arxiv: ]. [40] S. Choubey, JHEP 12 (2007) 014 [arxiv: ].

23 III. Neutrino decay and decoherence 23 Two phenomenologically situations: Neutrino decay (1) ν i ν j + X: the decay products include one (or more) detectable neutrinos. A theoretical model is needed to fix the energy distribution of the daughter neutrino(s); (2) ν i X: the decay products are completely invisible. The process is completely described by the neutrino lifetime τ i. We will discuss mainly Case (2). Neglecting possible interference effects [41] between oscillations and decay: i d ν [ ] dt = H 0 ν; H 0 = U H0 d iγd 0 U ; U as usual; H0 d = 1 ( ) diag 0, m E, m2 31 ; Γ d 0 = 1 ( m1 diag, m 2, m ) 3 ; ν 2E ν τ 1 τ 2 τ 3 analyses performed so far are restricted to 2ν scenarios. [41] M. Lindner, T. Ohlsson, and W. Winter, Nucl. Phys. B607 (2001) 326 [hep-ph/ ].

24 III. Neutrino decay and decoherence 24 Neutrino decoherence Origin: finite-size neutrino wave-packet, averaging due to finite detector resolution, neutrino interactions with space-time foam,... Approach: use density-matrix formalism: dρ dt most conservative assumptions on D[ρ]: = i[h, ρ] D[ρ]; complete positivity Lindblad form: D[ρ] = {ρ, D l D l } 2D lρd l ; unitarity & increase of Von Neumann entropy [ Tr(ρlnρ)] D l = D l ; conservation of energy in vacuum [H 0, D l ] = 0; lead tod[ρ] = [D l, [D l, ρ]], with D l = diag(d l1,..., d ln ) in the vacuum mass basis; l in this case the evolution equation (in vacuum) can be solved analytically. For n neutrinos ( ) 2, there are n(n 1)/2 new parameters, γ ji = dl j d li in addition to the usual ones; l note that γ ji can depend on the neutrino energy: γ ji = γ ji (E ν ). l

25 III. Neutrino decay and decoherence 25 Decay of solar neutrinos Since Sun-Earth distance solar radius, ν decay inside the Sun can be neglected; ν 1 is usually assumed to be stable. Also, present bounds on θ 13 show that ν 3 mixes very little with ν e. Hence solar data imply limits on ν 2 lifetime; ν decay produces (A) model-independent ν 2 disappearance, and (B) model-dependent ν 1 appearance. The mean ν 1 energy is higher for quasi-degenerate masses [42]; limits on ν 2 disappearance have been studied in [43, 44]. The strongest limit is τ 2 /m 2 > s/ev (99% CL) [44]. This bound may not hold for quasi-degenerate masses [42]; limits on solar ν e appearance have been set by KamLAND [45] and by SNO [46], giving τ 2 /m 2 > (0.0011) s/ev for quasi-degenerate (hierarchical) masses [45]. [42] J. F. Beacom and N. F. Bell, Phys. Rev. D65 (2002) [hep-ph/ ]. [43] A. S. Joshipura, E. Masso, and S. Mohanty, Phys. Rev. D66 (2002) [hep-ph/ ]. [44] A. Bandyopadhyay, S. Choubey, and S. Goswami, Phys. Lett. B555 (2003) [hep-ph/ ]. [45] KamLAND Collaboration, K. Eguchi et al., Phys. Rev. Lett. 92 (2004) [hep-ex/ ]. [46] SNO Collaboration, B. Aharmim et al., Phys. Rev. D70 (2004) [hep-ex/ ].

26 III. Neutrino decay and decoherence 26 Decoherence in solar and reactor neutrinos In the 2ν limit, the explicit formula for the survival probability in vacuum is: P surv = 1 1 [ ( m 2 sin2 (2θ) 1 e γl 2 )] ( ) L n Eν cos. We assume γ(e ν ) = κ n ; 2E ν GeV this formula properly describes decoherence effects in KamLAND [47]. In contrast, for solar neutrinos matter effects cannot be neglected [48]; combined solar+kamland analysis [48]: κ sol 2 < GeV, κ sol 1 < GeV, 95% CL: κ sol 0 < GeV, κ sol +1 < GeV, κ sol +2 < GeV; determination of solar parameters is reasonably stable. [47] T. Schwetz, Phys. Lett. B577 (2003) [hep-ph/ ]. [48] G. L. Fogli et al., Phys. Rev. D76 (2007) [arxiv: ]. [48]

27 III. Neutrino decay and decoherence 27 Pure decay and decoherence in atmospheric neutrinos Focus on effective 2ν oscillations in the µ τ sector; a 2ν pure decoherence solution (κ atm 1 = GeV) to the ATM problem was first proposed in [49], and later found to be disfavored although not excluded [50]; similarly, a pure ν 3 decay solution to the ATM problem was proposed in [51] (note that from solar data ν 1 and ν 2 are stable for atmospheric L/E); a more recent analysis of SK-I data ruled out both possibilities at more than 3σ [52]; hence we will focus on combined osc+decay and osc+decoherence analysis. Data/Prediction (null osc.) [52] L/E (km/gev) [49] E. Lisi, A. Marrone, and D. Montanino, Phys. Rev. Lett. 85 (2000) [hep-ph/ ]. [50] G. L. Fogli et al., Phys. Rev. D67 (2003) [hep-ph/ ]. [51] V. D. Barger et al., Phys. Lett. B462 (1999) [hep-ph/ ]. [52] Super-Kamiokande Collaboration, Y. Ashie et al., Phys. Rev. Lett. 93 (2004) [hep-ex/ ].

28 III. Neutrino decay and decoherence 28 Present bounds on decay and decoherence from ATM+LBL data First osc+decoh analysis reported in [49]; pure decay and pure decoherence fits now excluded, in agreement with SK; an alternative oscill+decay solution with τ 3 /m s/ev gives a good fit χ ATM+LBL ATM only 3σ 2σ to ATM data, but is ruled out by LBL [53]; % CL: τ 3 /m 3 > s/ev; 90% CL: κ atm 2 < GeV, κ atm 1 < GeV, κ atm 0 < GeV, κ atm +1 < GeV, κ atm +2 < GeV; determination of osc. parameters stable. m 2 32 [10-3 ev 2 ] Decay τ 3 /m 3 [s/ev] Decoherence κ -1 [GeV] [49] E. Lisi, A. Marrone, and D. Montanino, Phys. Rev. Lett. 85 (2000) [hep-ph/ ]. [53] M. C. Gonzalez-Garcia and M. Maltoni, Phys. Lett. B (in press) [arxiv: ].

29 III. Neutrino decay and decoherence 29 Explaining LSND with decoherence Recent suggestion [54]: 3ν oscillations + decoherence, with γ 21 = 0, γ 31 = γ 32 = γ and γ(e) = κ 4 (E ν /GeV) 4 ; only 1 new parameter. Probabilities: P µe (γ,l) = P eµ (γ,l) = 2 U µ3 2 U e3 2[ 1 e γl cos( 31 L) ], P ee (γ,l) = 1 2 U e3 2 (1 U e3 2 ) [ 1 e γl cos( 31 L) ], P µµ (γ,l) = 1 2 U µ3 2 (1 U µ3 2 ) [ 1 e γl cos( 31 L) ] ; Best fit: κ atm 4 = GeV; Explicit prediction: sin 2 θ 13 > (2.6 ± 0.8) 10 3 ; µ 2 [ev 2 ] [54] LSND KARMEN U e3 2 MiniBooNE Other possibilities: decay + sterile neutrinos [55], decoherence + CPT-violation [56], decoherence with unusual L dependence [57],... Reactor [54] Y. Farzan, T. Schwetz, and A. Y. Smirnov, arxiv: [55] S. Palomares-Ruiz, S. Pascoli, and T. Schwetz, JHEP 09 (2005) 048 [hep-ph/ ]. [56] G. Barenboim and N. E. Mavromatos, JHEP 01 (2005) 034 [hep-ph/ ]. [57] G. Barenboim et al., Nucl. Phys. B758 (2006) [hep-ph/ ].

30 III. Neutrino decay and decoherence 30 Decay and decoherence at future facilities Damping effects at future reactors and ν-factories have been discussed in [58]. Results: decay scenarios can easily be recognized at a ν factory; decoherence effects can fake the determination of θ 13 by reactor experiments; the sensitivity of a ν factory to decoherence depends on the shape of γ(e ν ); the sensitivity to decoherence of near-future accelerator experiments CNGS and T2K is discussed in [59]. It is shown that the bounds on κ atm n which can be put by these experiments are comparable to those derived with atmospheric neutrinos; similar results hold for T2KK configuration [27], which in the context of decoherence models it is shown to be systematically better than the separate Kamioka-only and Korea-only configurations. [27] N. C. Ribeiro et al., Phys. Rev. D77 (2008) [arxiv: ]. [58] M. Blennow, T. Ohlsson, and W. Winter, JHEP 06 (2005) 049 [hep-ph/ ]. [59] N. E. Mavromatos et al., Phys. Rev. D77 (2008) [arxiv: ].

31 III. Neutrino decay and decoherence 31 Decay and decoherence at neutrino telescopes The impact of ν decay on high-energy neutrinos has been discussed in a number of papers (see, e.g., [60, 61, 62, 63] and references therein). In particular: due to the extremely long distance traveled by astrophysical neutrinos, the sensitivity to decay effects is many orders of magnitude larger than terrestrial experiments; neutrino decay can break the 1 : 1 : 1 flavor ratio expected from a π-decay source, hence opening the possibility to measure oscillation parameters at ν telescopes; Under our restrictive assumptions, decoherence is indistinguishable from averaged oscillations. However, more general scenarios may exhibit unique signatures [64, 65]. [60] J. F. Beacom et al., Phys. Rev. Lett. 90 (2003) [hep-ph/ ]. [61] J. F. Beacom et al., Phys. Rev. D69 (2004) [hep-ph/ ]. [62] D. Meloni and T. Ohlsson, Phys. Rev. D75 (2007) [hep-ph/ ]. [63] M. Maltoni and W. Winter, arxiv: [64] D. Hooper, D. Morgan, and E. Winstanley, Phys. Lett. B609 (2005) [hep-ph/ ]. [65] L. A. Anchordoqui et al., Phys. Rev. D72 (2005) [hep-ph/ ].

32 Summary 32 Non-standard interactions with matter present bounds on NSI parameters are affected by strong degeneracies; these degeneracies may spoil the sensitivity to θ 13 of future LBL experiments; for ν factories, the problem can be solved by combining data from two different baselines. Models with extra sterile neutrinos four-neutrino models fail to reconcile LSND with MiniBooNE; five-neutrino models avoid this problem, but severe tension with disapp. data spoil the fit; six-neutrino models does not add any qualitatively new feature to the 5ν case. Neutrino decay and decoherence We have reviewed the present limits on neutrino decay and decoherence parameters; future reactor and accelerator facilities can further constraint these parameters; presence of ν decay can enhance the sensitivity of ν telescopes to oscillation parameters. Thank you for your attention!