M. Giorgini

University of Bologna, Italy, and INFN

Limits on Lorentz invariance violation in atmospheric neutrino oscillations

using MACRO data

From Colliders to Cosmic Rays 7 – 13 September 2005, Prague, Czech Republic

Outline

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

Mass-induced oscillations

23 ≡ mm

m3 2

es

Mass-induced atmospheric 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/E distribution

• ↔ oscillations favoured (> 99% C.L.) with respect to:• ↔ sterile

(MACRO Coll., Phys. Lett. B517 (2001) 59 ; SK Coll., Phys. Rev. Lett. 85 (2000) 3999)

• ↔ e

(SK Coll., Phys. Rev. Lett. 93 (2004) 101801)

• 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 oscillations : MACRO results

Category E Data MCno osc

Upthr. 50 857 1169 IU 4.2 157 285 ID+UGS 3.5 262 375

Upthroughgoing (857 events)

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

L/E distribution

E

LmP

222 27.1sin2sin1

From the shape of the muon zenith distribution

From the measurement of the muon energy using the Multiple Coulomb Scattering (PLB566 (2003) 35).

Upthr. data (~300 events)IU data

12% point-to-point syst. error

MC predictions for oscillations with the best

MACRO parameters

• Zenith distribution

Final results (Eur. Phys. J. C36 (2004) 357)

• E estimate by MCS

• IU, ID and UGS

R1= N(cos < -0.7) / N(cos> -0.4)

R2= N(low E) / N(high E)

R3= N(ID+UGS) / N(IU)

{H.E.

NO OSCILLATION HYPOTHESISRULED OUT BY ~ 5

L.E.

Adding the absolute flux information (Bartol96 correct within 17%)

NO OSCILLATION HYPOTHESISRULED OUT BY ~ 6

Only 3 ratios

Best parameters for m2 = 2.3 10-3 eV2 ; sin2 2 =1

3 ratios + 2 normalizations

90% C.L.

Violation of Lorentz Invariance (VLI)

If VLI is introduced, particles could have different Maximum Attainable Velocities (MAVs) vi (p=∞) ≠ c

3 2

Mixed oscillation scenario

Mixed oscillations scenario• While in the “pure” cases probabilities do not depend on the sign of v, m2 and mixing angles, in the mixed scenario relative signs are important

• Domain of variability : m2 ≥ 0v ≥ 0 0 ≤ m ≤ /4 -/4 ≤ v ≤ /4

• Oscillations induced by the Violation of the Equivalence Principle (VEP) may be treated similarly to VLI-induced oscillations

• Due to the L and E dependence, VLI effects are emphasized for large L and large E

Survival probability vs E

(L=10000 km , m2=2.3.10-3 eV2 , m= /4

+0.3

-0.3

+0.7 -0.7 +1 -1

Main effect are mass-induced oscillationsVLI is considered as a subdominant effect, at least for the accessible energies

Mixed scenario: MACRO data analyses

We used the data with E 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

χ2 analysis

η= 0

high>

Cuts optimizedwith MC

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

Likelihood analysis

Minimization of the function:

F = -2 ∑ ln f(Ei,Li ; m2,v,m23,v

23)i

f(x:a) = K × pMC × p( → )

Event by event analysis to exploit the full information

Analysis procedure

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

We used the events (106) with the most accurate energy reconstruction

25 GeV ≤ E ≤ 75 GeV

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 E 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 |v| upper limits of the order of 10-25

•Very large volume neutrino experiments could tell more in the next years…