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Limits on Lorentz invariance violation in atmospheric neutrino oscillations using MACRO data

Limits on Lorentz invariance violation in atmospheric neutrino oscillations using MACRO data. From Colliders to Cosmic Rays 7 – 13 September 2005, Prague, Czech Republic. M. Giorgini University of Bologna, Italy, and INFN. Outline. Mass-induced n oscillations :

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Limits on Lorentz invariance violation in atmospheric neutrino oscillations using MACRO data

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  1. Limits on Lorentz invariance violation in atmospheric neutrino oscillations using MACRO data From Colliders to Cosmic Rays 7 – 13 September 2005, Prague, Czech Republic M. Giorgini University of Bologna, Italy, and INFN

  2. Outline • Mass-induced n oscillations : • MACRO atmospheric n results • Violation of Lorentz Invariance (VLI) • VLI-induced n oscillations • Mixed oscillation scenario : MACRO results • Conclusions

  3. q23 ≡qm m Mass-induced n oscillations es 2 3 m

  4. Mass-induced atmospheric n oscillations • Strong evidence for mass-induced oscillations given by • MACRO, SK, Soudan 2 : • Deficit of muon events with respect to the predictions • Distortion of the zenith distribution • Energy spectrum • First dip in the L/En distribution • nm↔ nt oscillations favoured (> 99% C.L.) with respect to: • nm ↔ nsterile • (MACRO Coll., Phys. Lett. B517 (2001) 59 ; SK Coll., Phys. Rev. Lett. 85 (2000) 3999) • nm ↔ ne • (SK Coll., Phys. Rev. Lett. 93 (2004) 101801) • n decay, decoherence, CPT violation,… • (A. Habig, 28th ICRC, Japan, 2003) • Violation of Lorentz Invariance (VLI) • (Phys. Rev. D60 (1999) 053006 ; Phys. Rev. D70 (2004) 033010 ; hep-ph/0407087)

  5. Mass-induced n oscillations : MACRO results CategoryEn DataMCno osc Upthr. 50 857 1169 IU 4.2 157285 ID+UGS 3.5 262375

  6. q Upthroughgoing m (857 events) • Absolute flux : new MC codes have problems with • the new cosmic ray fit • Zenith angle distribution : shape known within 5%

  7. MC predictions for nm nt oscillations with the best MACRO parameters L/En distribution From the shape of the muon zenith distribution From the measurement of the muon energy using the m Multiple Coulomb Scattering (PLB566 (2003) 35). Upthr. m data (~300 events) IU m data 12% point-to-point syst. error

  8. Best parameters for nm nt Dm2 = 2.3 10-3 eV2 ; sin2 2q =1 Final results(Eur. Phys. J. C36 (2004) 357) { R1= N(cos Q < -0.7) / N(cosQ > -0.4) • Zenith distribution H.E. • En estimate by MCS R2= N(low En) / N(high En) R3= N(ID+UGS) / N(IU) • IU, ID and UGS m L.E. NO OSCILLATION HYPOTHESIS RULED OUT BY ~ 5s 90% C.L. Only 3 ratios Adding the absolute flux information (Bartol96 correct within 17%) 3 ratios + 2 normalizations NO OSCILLATION HYPOTHESIS RULED OUT BY ~ 6s

  9. Violation of Lorentz Invariance (VLI) If VLI is introduced, particles could have different Maximum Attainable Velocities (MAVs) vi (p=∞) ≠ c 2 3

  10. Mixed oscillation scenario

  11. Mixed oscillations scenario • While in the “pure” cases probabilities do not depend on the sign • of Dv, Dm2 and mixing angles, in the mixed scenario relative signs • are important • Domain of variability : • - Dm2≥ 0 • - Dv ≥ 0 • - 0 ≤ qm ≤ p/4 • - -p/4 ≤ qv ≤ p/4 • Oscillations induced by the Violation of the Equivalence Principle • (VEP) may be treated similarly to VLI-induced oscillations • Due to the L and En dependence, VLI effects are emphasized for • large L and large En

  12. Survival probability vs En(L=10000 km , Dm2=2.3.10-3 eV2 , qm= p/4 +0.3 -0.3 Main effect are mass-induced oscillations VLI is considered as a subdominant effect, at least for the accessible energies +0.7 -0.7 +1 -1

  13. Mixed scenario: MACRO data analyses We used the data with En reconstructed by Multiple Coulomb Scattering (~300 events). Phys. Lett. B566 (2003) 35 Two different techniques were used to estimate the upper limits of possible exotic contributions to atmospheric neutrino oscillations • Conventional Feldman-Cousins analysis based on the χ2 criterion • Analysis based on the Maximum Likelihood function

  14. χ2 analysis Cuts optimized with MC > high η= 0

  15. Neutrino flux used in MC: Honda et al., Phys Rev. D70 (2004) 043008 Results (Phys. Lett. B615 (2005) 14)

  16. Likelihood analysis Minimization of the function: F = -2 ∑ ln f(Eni,Li ; Dm2,Dv,qm23,qv23) i f(x:a) = K × pMC × p(nm → nm) Event by event analysis to exploit the full information

  17. Analysis procedure We used the events (106) with the most accurate energy reconstruction 25 GeV ≤ En ≤ 75 GeV We allowed the oscillation mass parameters to vary along the 90% C.L. contour of the final MACRO solution without normalization. For each point of the contour we performed maximum likelihood fits for the VLI parameters

  18. Results The 90% C.L. limits obtained from the convolution of the local 90% C.L. upper/lower limits.

  19. Conclusions • We re-analyzed the L and En distributions of MACRO • neutrino data to include the possibility of exotic effects • (Violation of Lorentz Invariance) • Two different analyses were performed on 2 different • data subsamples, both yielding |Dv| upper limits of the • order of 10-25 • Very large volume neutrino experiments could tell more • in the next years…

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