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

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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 :
- MACRO atmospheric n results
- Violation of Lorentz Invariance (VLI)
- VLI-induced n oscillations
- Mixed oscillation scenario : MACRO results
- Conclusions

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

CategoryEn DataMCno osc

Upthr. 50 857 1169

IU 4.2 157285

ID+UGS 3.5 262375

qUpthroughgoing m (857 events)

- Absolute flux : new MC codes have problems with
- the new cosmic ray fit
- Zenith angle distribution : shape known within 5%

MC predictions for nm nt

oscillations with the best

MACRO parameters

L/En distributionFrom 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

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)

If VLI is introduced, particles could have different

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

2

3

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 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

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

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

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

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

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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