Sterile neutrinos at future long-baseline experiments

Transcription

1 Davide Meloni, Dip. Fisica Roma Tre & INFN sez. Roma Tre, Friday 12, NOW 2008

2 1 Introduction Sterile neutrinos today 2 Current limits on new mixing angles The question of the parameterization Current allowed regions for θ i4 The relevant probabilities in matter 3 Physics at LBL experiments: coming soon (the present...) The OPERA experiment Sensitivity to (3+1) sterile neutrinos at OPERA 4 Physics at LBL exps (the future) Sterile neutrinos at Neutrino Factories Numerical results CP violation degeneracies 5 Conclusions

3 Sterile neutrinos today introduction Neutrino conversion has been confirmed in many experiments three flavours accompanying e, µ and τ leptons number of light neutrinos coupled with the Z boson ± ALEPH collaboration, Phys. Rept. 427(2006) 257 there is only space for neutrinos with no electroweak interactions: STERILE NEUTRINOS since their properties are not completely known, there is parameter space to investigate ( they attracted people from ν s in BBN (Miele) in this workshop = different areas ν s in CMB + LSS (Cirelli)

4 Sterile neutrinos today in this talk... since visible effects in mixing with active neutrinos we need to introduce several more parameters to account for extra mixings new mass differences & new mixing angles the simplest scenario: only one more mass eigenstate in the game this give rise to the (3 + 1) and (2 + 2) schemes These scenarios are LSND-inspired : m 2 SBL is a large mass difference O(1) ev 2 probed by this experiment

5 Sterile neutrinos today the simplest scenario but it turns out that no satisfactory description of all neutrino data Bilenky98,Giunti00, Gonzalez-Garcia01,Maltoni02, Strumia02... strong constrains from SOL, ATM and null-result short baseline exps Maltoni04, Gonzalez-Garcia07 in the (2+2) the extra sterile state cannot be simultaneously decoupled from both solar and atmospheric oscillation the (3+1) suffers from a tension between LSND and null-result SBL disappearance experiments This is even worse after the MiniBooNE results Giunti00, Gonzalez-Garcia01,Maltoni03... Okada97, Bilenky98,Barger98, Peres01,Grimus01,Maltoni01... the LSND anomaly cannot be explained using sterile neutrinos however disregarding the LSND result the (3+1) is still is a perfectly viable extension of the Standard Model

6 The question of the parameterization How to parametrize the new mixing matrix An unitary 4 4 matrix has 6 mixing angles and 3 CP-violating phases we need to accomodate these new parameters Different parameterizations available, we choose the one useful for long baseline experiments M.Maltoni and T.Schwetz, arxiv: U LBL = R 34(θ 34) R 24(θ 24) R 23(θ 23, δ 3) R 14(θ 14) R 13(θ 13, δ 2) R 12(θ 12, δ 1) one phase (δ 1) is in R 12 = it drops in the two-mass dominance regime the other (δ 2) is in R 13 = it reduces to the standard Dirac phase in the three-family limit the other can be put anywhere

7 Current allowed regions for θ i4 The bounds on θ 13 θ 14 A. Donini et al., JHEP12 (2007) 013 ν e disappearance at L/E such that sol can be safely neglected We use the vacuum approximation, useful for Bugey and Chooz P ee = 1 sin 2 2θ 14 sin 2 sbll 2 c 4 14 sin 2 2θ 13 sin 2 atml 2 90%, 95%, 99% and 3 σ CL correlation between θ 13, θ 14 the three-family Chooz bound on θ 13 is slightly modulated by θ 14 both angles cannot be much larger than 10

8 Current allowed regions for θ i4 The bounds on θ 24 θ 34 A. Donini et al., JHEP12 (2007) 013 ν µ disappearance at atmospheric L/E In the vacuum approximation (useful for K2K...) P µµ = 1 2s s 2 23 ˆc2 23 (1 2s 2 24) s 2 13 sin 2 atml 2 θ 24 cannot be much larger than 10 the upper bound on θ 34 comes from indirect searches for ν µ ν s in atmospheric experiments

9 The relevant probabilities in matter Probabilities in matter The previous results give the way to simplify the analytical expressions for the probabilites in matter, useful to analyze long baseline experiments A. Dighe and S.Ray, Phys. Rev. D 76, (2007) S. Goswami and T. Ota, Phys. Rev. D 78, (2008) A. Donini, F. Ken-ichi, D. M., J. Lopez-Pavon, O. Yasuda, in preparation i d dt να = [U ε U 8 + A] αβ ν β s 13 s 14 s 24 s 2 34! ε = diag 0, m E, m E, m2 41 >< m 2 2 E since = 21 / m2 41 <= 10 4 A = m G F diag(n e, 0, 0, n n/2) = diag(a e, 0, 0, A / m2 41 <= 10 3 n) >: A e/ m 2 41 <= 10 3 we expand up to quadratic order in s 13, s 14, s 24, s 2 34 and neglect terms 1/ m 2 41

10 The relevant probabilities in matter Probabilities in matter Using these approximations we get simple and elegant expressions: P ee = 1 + O(s 2 13) P eµ P eτ P es O(s 2 13) ff electron neutrino decouples!!! P µµ = 1 sin 2 2θ 23 sin 2 m2 L 4E P µτ = sin 2 2θ 23(1 s 2 34) sin 2 m2 L 4E 2(AnL)s24s34 sin2 2θ 23 cos δ 3 sin m2 L 2E + s24s34 [sin δ3 + 2(AnL) cos δ3] sin m2 L 2E 9 >= >; main dependence on θ 24 and θ 34 in P µµ and P µτ we focus on ν µ ν τ and ν µ ν µ

11 The OPERA experiment A brief reminder on OPERA and CNGS In this workshop: Ronga, Scotto-Lavina, Sala Cern-to-Gran Sasso ν µ beam L 732 km, < E ν > 17 GeV 10 6 (A n L) and m 2 L/(2E ν) small ν µ flux (arbitrary units) anti ν µ anti ν e ν e Main goal: detect ν µ ν τ oscillations E ν (GeV) This is very important because new physics mainly affects this channel

12 Sensitivity to (3+1) sterile neutrinos at OPERA sensitivities A. Donini et al., JHEP12 (2007) 013 The sensitivity is defined as the region for which a (poissonian) 2 dof χ 2 is compatible with a null result at the given CL we assumed pot/year 5 years, detector mass=1.8 Kton both ν µ ν τ and ν µ ν e have been considered the θ i4 not shown are marginalized, the others are fixed to their best fit values colored regions: bounds at 90 and 99% CL with the nominal flux, OPERA can improve a little the bound but it has no sensitivity to θ i4 increasing the nominal intensity, a significant improvement can be obtained, for any θ i4 but θ 14, since it appears at higher orders in P µτ and P µµ

13 Sensitivity to (3+1) sterile neutrinos at OPERA combined analysis of present data + null results of the OPERA experiment A. Donini et al., JHEP12 (2007) 013 We show the allowed regions at 99% CL in the (θ 13, θ 14) plane (left) and in the (θ 24, θ 34) plane (right) from the combined analysis of present data and a null result of the OPERA experiment the sensitivity of OPERA strongly benefits from the complementary information on the neutrino parameters provided by other experiments even with the nominal beam intensity the extension of the allowed regions is reduced by a moderate but non-negligible amount.

14 Sterile neutrinos at Neutrino Factories Sterile neutrinos at Neutrino Factories Short baseline neutrino factory can easily probe the effect of large mass differences L O(1) ev 2 K. Dick et al.,nucl. Phys. B 562, 29 (1999); A. Donini et al., Nucl. Phys. B 574, 23 (2000); A. Donini and D. Meloni, Eur. Phys. J. C 22, 179 (2001) Here we study the physics reach of long baseline neutrino factories but previous studies for the scheme in: S. M. Bilenky et al., Phys. Rev. D 58, (1998); A. Kalliomaki et al.,phys. Lett. B 469, 179 (1999); K. Dick et al.,nucl. Phys. B 562, 29 (1999); C. Giunti,JHEP 0001, 032 (2000); T. Hattori et al., Phys. Rev. D 62, (2000). We assume: muon decay/year 4 yr, E µ = 50 GeV two different baselines: L = 3000 Km and L = 7500 Km We consider the combination of P µµ and P µτ PRELIMINARY ANALYSIS

15 Sterile neutrinos at Neutrino Factories Limits on mixing angles For the moment we assume that all the CP-phases are vanishing the (θ 13, θ 14)-plane we do not expect any sensitivity because of the scarse dependence of P µµ and P µτ on these angles we can slightly improve the situation adding P eµ and P eτ to the analysis the (θ 24, θ 34)-plane since δp µµ = P 4fam µµ P 3fam µµ A n s 24s 34 δp µτ = P 4fam µτ P 3fam µτ s s 24s 34 + A n s 24s 34 we expect: largest sensitivity to θ 34 from P µτ, especially at small baselines where δp µµ tends to vanish a similar sensitivity to both θ 24 and θ 34 for the largest baseline

16 Numerical results Results for a single baseline, 90% CL Θ we look for muons with a Magnetized Iron Calorimeter assuming εµ = 0.9, sys.error=0.05 we look for taus with a Magnetized Emulsion Cloud Chamber assuming εµ = 0.1 (efficiency BR(τ µ)), sys.error=0.1 P ΜΜ P ΜΤ P ΜΜ P ΜΤ Θ P ΜΜ P ΜΤ P ΜΜ P ΜΤ L 7500 Km 5 L 3000 Km Θ Θ24 For a single baseline: the pattern is understood in terms of transition probabilities θ 34 can be probed down 15 o the limits on θ 24 can be improved by a factor of 2

17 CP violation Looking for CP violation The formulae show that the dependence on CP violation in the sterile sectors comes from the only phase δ 3 In particular: CP asymmetry in the P µµ channel are obviously due to matter effects, since P µ µ(δ i, A e,n) = P µµ( δ i, A e,n) and δ 3 appears under cosinus in the µ τ channel pure CP effects arise due to the sin δ 3 dependence It is possible to build normalized CP asymmetries in both channels and comparing their values among 3-ν and 4-ν framework A. Dighe and S. Ray, Phys. Rev. D 76, (2007) far A µ(e) N µ far (E) Nµ near (E) N µ (E) N near µ (E) A τ (E) N τ far (E) N near µ (E) N far τ (E) N near µ (E) Nα near,far = leptons of type α produced at the near or far detectors

18 CP violation Looking for CP violation A. Dighe and S. Ray, Phys. Rev. D 76, (2007) slightly different parameterization used = not important for us Aµ perfect efficiencies and no backgrounds only quoted are statistical errors in red: spread in the 3-family scenario large deviation from 3-ν in some particular energy range where the 4ν predictions are quite different IH; θ 24 =θ 34 =0.10 NH; θ 24 =θ 34 =0.10 IH; θ 24 =θ 34 =0.16 NH; θ 24 =θ 34 = E (GeV) Aτ IH; θ 24 =θ 34 =0.10 NH; θ 24 =θ 34 =0.10 IH; θ 24 =θ 34 =0.16 NH; θ 24 =θ 34 = E (GeV) asymmetries turn out to be an efficient discriminator between standard and 4ν models

19 degeneracies The problem of the degeneracies When discussing CP violation, we also have to deal with degeneracies P µτ = sin 2 2θ 23(1 s 2 34) sin 2 m 2 L 4E in this workshop, already discussed by Walter Winter Let us study the ν µ ν τ S. Goswami and T. Ota, Phys. Rev. D 78, (2008) + s24s34 [sin δ3 + 2(AnL) cos δ3] sin m2 L 2E degeneracy vacuum matter octant : P µτ (θ 23) = P µτ (π/2 θ 23) yes yes sign[ m 2 23] δ 3 : P µτ ( m 2 23 > 0, δ 3) = P µτ ( m 2 23 < 0, δ 3) yes milder δ 3 (π δ 3) : P µτ (δ 3) = P µτ (π δ 3) yes milder (s 24 s 34 δ 3) : P µτ ((s 24 s 34), δ 3) = P µτ ((s 24 s 34), δ 3) yes yes

20 degeneracies The problem of the degeneracies: numerical results figures modified from S. Goswami and T. Ota, Phys. Rev. D 78, (2008) allowed regions in the ((s 24 s 34) δ 3) plane different combination of detector masses and baselines for an OPERA-like and liquid argon (LAr) detectors OPERA like 5.0 kt, L 130 km 1Σ 2Σ 3Σ OPERA like 5.0 kt L 130 km LAr near 1Σ 2Σ 3Σ 3 Degrees Degrees GLoBES Θ Θ 0 GLoBES Θ Θ upper region is due to the sign-degeneracy for each hierarchy, also visible the δ 3 (π δ 3) better with two detectors, because of the averaged term (s 24 s 34) 2

21 degeneracies Looking for CP violation II- what about golden and silver channels? A. Donini, M. Lusignoli and D. Meloni, Nucl. Phys. B 624, 405 (2002) In principle less promising than P µµ and P µτ due to the weak dependence on new mixing angles however detection of P eµ P eτ have been extensively studied let us use our knowledge! is it possible to fit a CP-conserving scenario with a 3-family model? for the points in which confusion is possible, which value of standard δ? we answer the questions using: - three different baselines L = 732 Km, L = 3500 Km and L = 7300 Km - the same neutrino factory setup as before - slightly different parametrization used but similar behaviour of P eµ and P eτ with new mixing angles

22 degeneracies Is it possible to fit a CP-conserving scenario with a 3-family model? data are generated in the CP-conserving scheme for some value of θ 14 and θ 24 whereas θ 13 and θ 34 are left free for any (θ 13-θ 34) we fit this data with the 3-family model if successful, the point (θ 13-θ 34) is a dot on the same plane θ 14 = θ 24 = 2 o = 732: the averaged LSND term is not enough 3500: 3 and 4-ν probs are very similar 7300: large matter effects = θ 14 = θ 24 = 5 o better for larger θ 14 and θ 24 also: combination of baselines more useful to eliminate the ambiguity

23 degeneracies Which value of standard δ in the confusion points? answer: generally not too large example for θ 14 = θ 24 = 2 o and a θ 34 in the black region % CL 90% CL 68% CL % CL 90% CL 68% CL 0 99% CL 90% CL 68% CL ϑ ϑ ϑ13 the best fit is always close to δ = 0 the best determination is at L = 3500 Km, a part from a possible intrinsic degenerate solution for 6000 successful fits, we get 15 o < δ < 15 o in the 31%, 50% and 37% of the cases

24 Conclusion disregarding the LSND results, there is still space for 3+1 model of neutrino masses in principle, this model cannot be falsified, being a perturbation of the Standard Model the new angles are constrained from disappearance experiments; in particular: θ 14 θ o and θ 14 < 35 o an improved version of the Cern-to-Gran Sasso facility can further improve the bounds however, a neutrino factory seems to be more appropriate to strongly constrain the new mixing angles thanks to P µµ and P µτ transitions also, new CP-phases can be probed the old P eµ can be used to tell 3 from 4 neutrinos for some value of the new mixing angles

25 backup slides The problem of the degeneracies: numerical results figures modified from S. Goswami and T. Ota, Phys. Rev. D 78, (2008) allowed regions in the ((s 24 s 34) δ 3) plane different combination of detector masses and baselines for an OPERA-like and liquid argon (LAr) detectors LAr 100 kt, L 3000 km 1Σ 2Σ 3Σ LAr 100 kt, L 3000 km LAr near 1Σ 2Σ 3Σ 3 Degrees Degrees GLoBES Θ Θ 0 GLoBES Θ Θ

26 backup slides strong constrains from SOL, ATM and null-result short baseline exps Maltoni, Schwetz, Tortola and Valle, New J.Phys.6:122,2004 it is useful to introduce the following quantities: η α = X U αi 2 i runs on solar mass states d α = 1 X U αi 2 i runs on atmospheric mass states in such a way η α is the fraction of ν α participating in solar oscillations and 1 d α is the fraction of ν α participating in atmospheric oscillations in the (2+2) scheme: rules out by solar and atmospheric data η s 0.25 from solar+kamland data but η s 0.75 from Super-K, K2K and SBL neutrino data. 50 χ solar + KamLAND solar solar (pre SNO salt) global solar + KamLAND χ 2 PG χ 2 PC atm + K2K + SBL atmospheric + K2K 10 99% CL (1 dof) 99% CL (1 dof) η s η s d µ

27 backup slides 99% CL sterile vs active neutrinos II the (3+1) scheme: suffers from a tension between LSND and null-result SBL disappearance experiments Okada97, Bilenky98,Barger98, Peres01,Grimus01,Maltoni01 This is even worse after the MiniBooNE results The reason is that sin 2 2θ LSND = 4 d e d µ and the parameters d e and d µ are strongly constrained by ν e and ν µ disappearance 10 1 NEV + atm + K2K NEV + atm(1d) m 2 LSND [ev2 ] 10 0 LSND global LSND DAR % CL sin 2 2θ LSND

28 backup slides Results for the combination of baselines PΜΜ PΜΜ PΜΤ PΜΤ 25 PΜΜ PΜΤ 25 PΜΜ PΜΤ Θ34 15 Θ34 15 L 7500 Km L 3000 Km Θ Θ P ΜΜ P ΜΤ the combination improves a little the single baseline results however, not a significant synergy when combining the two experiments

29 backup slides The appearance channels at the CNGS ν µ ν τ and ν µ ν e transitions A. Donini et al., JHEP12 (2007) 013 we studied the possibility to further constrain the θ i4 angles using both ν µ ν τ and ν µ ν e transitions expected rates Z N µα = A ε µα=detection efficiencies ν µ ν τ dφνµ (E) de P µα(e)σν CC α (E) ε µα de ν µ ν e ε µτ 13% ε µτ 30 40% main backgrounds: main backgrounds: charm decays and hadronic ν e beam contamination, O(19) reinteractions, O(1) event events we assumed pot/year 5 years, detector mass=1.8 Kton

30 backup slides The appearance channels at the CNGS ν µ ν τ and ν µ ν e transitions A. Donini et al., JHEP12 (2007) 013 we studied the possibility to further constrain the θ i4 angles using both ν µ ν τ and ν µ ν e transitions expected rates Z N µα = A ε µα=detection efficiencies ν µ ν τ dφνµ (E) de P µα(e)σν CC α (E) ε µα de ν µ ν e ε µτ 13% ε µτ 30 40% main backgrounds: main backgrounds: charm decays and hadronic ν e beam contamination, O(19) reinteractions, O(1) event events we assumed pot/year 5 years, detector mass=1.8 Kton

31 backup slides The appearance channels at the CNGS Expected events at OPERA (θ 13; θ 14; θ 24; θ 34) N τ background (θ 13; θ 14; θ 24; θ 34) N τ background (5 ; 5 ; 5 ; 20 ) (10 ; 5 ; 5 ; 20 ) (5 ; 5 ; 5 ; 30 ) (10 ; 5 ; 5 ; 30 ) (5 ; 5 ; 10 ; 20 ) (10 ; 5 ; 10 ; 20 ) (5 ; 5 ; 10 ; 30 ) (10 ; 5 ; 10 ; 30 ) families families Table: Event rates and expected background for the ν µ ν τ channel in the OPERA detector, for different values of θ 14, θ 24 and θ 34 in the (3+1) scheme. The other unknown angle, θ 13 has been fixed to: θ 13 = 5, 10. The CP-violating phases are: δ 1 = δ 2 = 0; δ 3 = 90. As a reference, the expected value in the case of standard three-family oscillation (i.e., for θ i4 = 0) is shown for maximal CP-violating phase δ.

32 backup slides The appearance channels at the CNGS Numerical accuracy We check the goodness of these formulae computing the quantity P αβ = Abs P exact αβ P approx αβ /Pαβ exact 10 4 Θ13 Θ14 Θ24 3 o Θ34 10 o P ΜΜ 20% 10 4 Θ13 Θ14 Θ24 3 o Θ34 10 o L Km 10 3 L Km EΝ GeV 10 2 P ΜΤ 20% EΝ GeV black regions satisfy the constrain P αβ < 20% P µτ a bit worse than P µµ in my opinion, good accuracy obtained with first-order formulae

33 backup slides The appearance channels at the CNGS Expected events at ν-fact (θ 13; θ 14; θ 24; θ 34) N τ /10 4 N µ/10 4 (5 ; 5 ; 5 ; 20 ) (5 ; 5 ; 5 ; 30 ) (5 ; 5 ; 10 ; 20 ) (5 ; 5 ; 10 ; 30 ) families Table: Event rates for the ν µ ν τ channel at the Neutrino Factory at L=3000 Km and 50 Kton detector mass, for different values of θ 14, θ 24 and θ 34 in the (3+1) scheme. The other unknown angle, θ 13 has been fixed to: θ 13 = 5, 10. The CP-violating phases are: δ 1 = δ 2 = 0; δ 3 = 90. No efficiencies included.