Transcript Document 7676211

From Colliders to Cosmic Rays
7 – 13 September 2005, Prague, Czech Republic
Limits on Lorentz invariance violation
in atmospheric neutrino oscillations
using MACRO data
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 n oscillations
es
m
q23
≡ qm
3
m
2
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
Category
En
Data
Upthr.
IU
ID+UGS
50
4.2
3.5
857
157
262
MCno osc
1169
285
375
Upthroughgoing m (857 events)
q
• Absolute flux : new MC codes have problems with
the new cosmic ray fit
• Zenith angle distribution : shape known within 5%
L/En distribution
Pn mn m
2


m
 L
2
2
 1  sin 2q  sin 1.27

En 

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
MC predictions for nm
oscillations with the best
nt
MACRO parameters
12% point-to-point syst. error
Final results
(Eur. Phys. J. C36 (2004) 357)
{
H.E.
L.E.
• Zenith distribution
R1= N(cos Q < -0.7) / N(cosQ > -0.4)
• En estimate by MCS
R2= N(low En) / N(high En)
• IU, ID and UGS m
R3= N(ID+UGS) / N(IU)
NO OSCILLATION HYPOTHESIS
RULED OUT BY ~ 5s
90% C.L.
Only 3 ratios
3 ratios + 2 normalizations
Adding the absolute flux information
(Bartol96 correct within 17%)
NO OSCILLATION HYPOTHESIS
RULED OUT BY ~ 6s
Best parameters for nm
nt
m2 = 2.3 10-3 eV2 ; sin2 2q =1
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 ≥ 0
 v ≥ 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 , m2=2.3.10-3 eV2 , qm= p/4
+0.3
-0.3
oscillations
Main effect are mass-induced
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
χ2 analysis
>
high
η= 0
Cuts
optimized
with 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(Eni,Li ; m2,v,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 |v| upper limits of the
order of 10-25
•Very large volume neutrino experiments could tell more
in the next years…