1. Search for exotic contributions to Atmospheric Neutrino Oscillations Search for exotic contributions to Atmospheric Neutrino Oscillations - Introduction - Monte Carlos - Final oscillation analyses - Search for LIV contributions - Conclusions G. Giacomelli, V. Popa, M. Sioli University of Bologna and INFN Venezia, 22-25/2/2005, “ Neutrino Telescopes ”

2. Upstop In down In up Upthroughgoing Absorber Streamer Scintillator 1) 2) 3) 4) DATA SAMPLES (measured) (Bartol96 expected) __________________________ Upthrough(1) 857 1169 In up(2) 157 285 In down(3)+ Up stop(4) 262 375 MACRO

3. 1984 MACRO Proposal

4. Early analyses Upthrough  only Angular distribution Absolute value (Bartol96 MC)  m 2 =0.0025 eV 2 Phys.Lett. B434(1998)451 Maximal mixing Phys.Lett. B517(2001)59 Lower energy topologies consistent with upthrough  { {  energy estimate through Multiple Coulomb Scattering of upthroughgoing muons Phys.Lett. B566(2003)35

5. - After 2001 FLUKA2001-3 (Honda2001-3) Both 3-dimensional improved interaction models new cosmic ray fit,..... They agree to ~5% But: Predictions of new Honda and FLUKA MCs H.E. 25% low ; L.E. 12% low - Angular distributions of Bartol96, new Honda and FLUKA MCs agree to ~<6% New L3cosmic data favor Bartol96, … astro-ph0502380 Atmospheric flux. Monte Carlos - Until 2001 Bartol96 (Honda96)

6. n1 MACRO data MonteCarlos Upthroughgoing

7.  energy estimate through Multiple Coulomb Scattering of upthroughgoing muons in rock in lower MACRO (Phys. Lett. B566 (2003) 35) E = 13 GeVE = 36 GeV E = 88 GeV E =146 GeV No oscillation Bartol96 MC predictions for    oscillations with the MACRO parameters 300 events with θ<60 degrees

8. From the muon zenith distribution From the measurement of the muon energy using Multiple Coulomb Scattering Upthr.  data IU  data 12% point-to-point syst. error MC predictions for    oscillations with the best MACRO parameters L/E distribution

9. Low Energy Neutrino Events Internal Up Internal Down + Up-stopping  Measured (points) and expected number (dashed lines: MC Bartol96) of upgoing semicontained events (left) and up-stopping plus downgoing semicontained  (right). Solid lines: oscillations with the best fit parameters sin 2 2  =1 and  m 2 =0.0023 eV 2. =2.3 GeV. Monte Carlo scale uncertainty 21%

10. Final oscillation analyses R 1 = N(cos  -0.4) { H.E. Zenith distribution E estimate IU, ID and UGS  R 2 = N(low E ) / N(high E ) R 3 = N(ID+UGS) / N(IU) No oscillation hypothesis ruled out by ~ 5  Best fit parameters for       m 2 = 2.3 10 -3 eV 2 ; sin 2 2  =1 Eur. Phys. J. C36(2004)357 L.E. Absolute values referred to Bartol96 MC : R 4 =(Data/MC) H.E. ; R 5 =(Data/MC) L.E. With these informations, the no oscillation hypothesis is ruled out by ~ 6  Use ratios with uncertainties of ~5%, independent of MCs

11. MACRO  

12. 2 flavor interpretation:induced by the mixing of 2 mass eigenstates, and 2 weak eigenstates,: The survival probability is Mass induced oscillations

13. For LIV oscillations: there is mixing between 2 flavor eigenstates and 2 velocity eigenstates: (asymptotic v  different from c) The survival probability is: (  v=v 3 -v 2 ) Exotic oscillations Lorentz invariance violation (LIV) Notice the dependence LE   LIV is not dominant Violation of the equivalence principle Similar results as for LIV, but with parameter   = difference of coupling constants of to gravitational pot  )

14. If both mass-induced and LIV-induced transitions are considered simultaneously: where and Mixed oscillations

16. P(    ) Mixed oscillations

17. We computed upper limits of LIV parameters  v, sin 2 2θ v -using the formalism of Coleman-Glashow PL B405(1997)249; hep-ph/0407087, -taking the N low, N high samples of low and high energy muon upthroughgoing data with cuts - as for MACRO mass oscillation analysis - optimized for LIV search -fixing  m 2 =0.0023 eV 2 and maximal mixing (MACRO values) -minimize with respect to  v, θ v the function 90% C.L. limits on  v and θ v computed with Feldman–Cousins prescription  2 analysis

18. (30,130) GeV (28,142) GeV

19. Maximum Likelihood analysis in intermediate E region Minimization of the negative log-likelihood function: Event-by-event analysis  best use of existing information 106 events with Method tested on “mass-induced” oscillations  MACRO parameters well reproduced Average  v < 10 -25, slowly varying with  m 2

20. Conclusions The inclusion of LIV effects does not improve the fits to the muon energy data The limits for LVI parameters at 90% CL are at sin 2 2θ v = 0 :  v/2 < 3 10 -24 at sin 2 2θ v = 1 :  v/2 < 1.4 10 -26