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Search for exotic contributions to Atmospheric Neutrino Oscillations. G. Giacomelli, V. Popa, M. Sioli University of Bologna and INFN Venezia, 22-25/2/2005, “ Neutrino Telescopes ”. - Introduction - Monte Carlos - Final oscillation analyses - Search for LIV contributions
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Search for exotic contributions to AtmosphericNeutrino Oscillations G. Giacomelli, V. Popa, M. Sioli University of Bologna and INFN Venezia, 22-25/2/2005, “NeutrinoTelescopes” - Introduction - Monte Carlos - Final oscillation analyses - Search for LIV contributions - Conclusions
Upthroughgoing In up Absorber Streamer Scintillator In down Upstop 1) 4) 3) 2) MACRO DATA SAMPLES(measured) (Bartol96 expected) __________________________ Upthrough(1) 857 1169 In up(2) 157 285In down(3)+ Up stop(4) 262 375
Atmospheric n flux. Monte Carlos - Until 2001 Bartol96 (Honda96) - After 2001FLUKA2001-3 (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
MACRO data MonteCarlos Upthroughgoing n1
En = 13 GeV En = 36 GeV MC predictions for nm nt oscillations with the MACRO parameters En = 88 GeV En =146 GeV nm energy estimate through Multiple Coulomb Scattering of upthroughgoing muons in rock in lower MACRO(Phys. Lett. B566 (2003) 35) 300 events with θ<60 degrees No oscillation Bartol96
MC predictions for nm nt oscillations with the best MACRO parameters L/En distribution From the muon zenith distribution From the measurement of the muon energy using Multiple Coulomb Scattering Upthr. m data IU m data 12% point-to-point syst. error
Best fit parameters for nm nt Dm2 = 2.3 10-3 eV2 ; sin2 2q =1 Eur. Phys. J. C36(2004)357 Final oscillation analyses Use ratios with uncertainties of ~5%, independent of MCs { Zenithdistribution R1= N(cos Q < -0.7) /N(cosQ > -0.4) H.E. R2= N(low En) / N(high En) En estimate IU, ID and UGS m R3= N(ID+UGS) / N(IU) L.E. No oscillation hypothesis ruled out by ~ 5 s Absolute values referred to Bartol96 MC : R4=(Data/MC)H.E. ; R5=(Data/MC)L.E. With these informations, the no oscillation hypothesis is ruled out by ~ 6 s
MACRO D q
Mass induced oscillations 2 n flavor interpretation: induced by the mixing of 2 mass eigenstates , and 2 weak eigenstates , : The survival probability is
Exotic oscillations Lorentz invariance violation (LIV) For LIV oscillations: there is mixing between 2 flavor eigenstates and 2 velocity eigenstates: (asymptotic vn different from c) The survival probability is: ( v=v3-v2 ) Notice the dependence LEn LIV is not dominant Violation of the equivalence principle Similar results as for LIV, but with parameter fD (fD= difference of coupling constants of n to gravitational pot f)
Mixed oscillations If both mass-induced and LIV-induced transitions are considered simultaneously: where and
P(nmnt) Mixed oscillations
2 analysis We computed upper limits of LIV parameters v , sin2 2θv -using the formalism of Coleman-Glashow PL B405(1997)249; hep-ph/0407087 , -taking the Nlow, Nhigh samples of low and high energy muon upthroughgoing data with cuts - as for MACRO mass oscillation analysis - optimized for LIV search -fixing Dm2=0.0023 eV2 and maximal mixing (MACRO values) -minimize with respect to Dv, θv the function 90% C.L. limits on v and θv computed with Feldman–Cousins prescription
(30,130) GeV (28,142) GeV
Maximum Likelihood analysis in intermediate En region Event-by-event analysis best use of existing information 106 events with Minimization of the negative log-likelihood function: Method tested on “mass-induced” oscillations MACRO parameters well reproduced Average v < 10-25, slowly varying with m2
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 sin22θv = 0 : Dv/2 < 3 10-24 at sin22θv = 1 : Dv/2 < 1.4 10-26