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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

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

CategoryEn DataMCno osc

Upthr. 50 857 1169

IU 4.2 157285

ID+UGS 3.5 262375

upthroughgoing m 857 events
qUpthroughgoing m (857 events)
  • Absolute flux : new MC codes have problems with
  • the new cosmic ray fit
  • Zenith angle distribution : shape known within 5%
l e n distribution
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

final results eur phys j c36 2004 357
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

violation of lorentz invariance vli
Violation of Lorentz Invariance (VLI)

If VLI is introduced, particles could have different

Maximum Attainable Velocities (MAVs) vi (p=∞) ≠ c

2

3

mixed oscillations scenario
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
survival probability vs e n l 10000 km d m 2 2 3 10 3 ev 2 q m p 4
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

mixed scenario macro data analyses
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
2 analysis
χ2 analysis

Cuts optimized

with MC

>

high

η= 0

likelihood analysis
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

analysis procedure
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

results
Results

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

conclusions
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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