search for exotic contributions to atmospheric neutrino oscillations
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Search for exotic contributions Search for exotic contributions to to AtmosphericAtmospheric NeutrinoNeutrino OscillationsOscillations
- Introduction
- Monte Carlos
- Final oscillation analyses
- Search for LIV contributions
- Conclusions
G. Giacomelli, V. Popa, M. SioliG. Giacomelli, V. Popa, M. SioliUniversity of Bologna and INFNVenezia, 22-25/2/2005, “Neutrino Telescopes”
UpstopIn down
In up
Upthroughgoing
Absorber
Streamer
Scintillator
1) 2) 3) 4)
DATA SAMPLES(measured)(Bartol96 expected)
__________________________
Upthrough(1) 857 1169
In up(2) 157 285
In down(3)+ Up stop(4) 262
375
MACRO
- After 2001 FLUKA2001-3 (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
Atmospheric flux. Monte Carlos
- Until 2001 Bartol96 (Honda96)
n1
MACRO data
MonteCarlos
Upthroughgoing
energy estimate through Multiple Coulomb Scattering of upthroughgoing muons in rock in lower MACRO
(Phys. Lett. B566 (2003) 35) E = 13 GeV E = 36 GeV
E = 88 GeV E =146 GeV
No oscillation Bartol96
MC predictions for oscillations with the MACRO parameters
300 events with θ<60 degrees
E
LmP
222 27.1sin2sin1
From the muon zenith distribution
From the measurement of the muon energy using Multiple Coulomb Scattering
Upthr. dataIU data
12% point-to-point syst. error
MC predictions for oscillations with the best MACRO parameters
L/E distribution
Final oscillation analyses
R1= N(cos < -0.7) /N(cos> -0.4) {H.E.
Zenith distribution
E estimate
IU, ID and UGS
R2= N(low E) / N(high E)
R3= N(ID+UGS) / N(IU)
No oscillation hypothesisruled out by ~ 5
Best fit parameters for m2 = 2.3 10-3 eV2 ; sin2 2 =1Eur. Phys. J. C36(2004)357
L.E.
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
Use ratios with uncertainties of ~5%, independent of MCs
MACRO
2 flavor interpretation: induced by the mixing
mmmm
mmmm
233232
233232
cossin
sincos
ELmP m /.sinsin 222 27121
of 2 mass eigenstatesm2
m3,
and 2 weak eigenstates , :
The survival probability is
Mass induced oscillations
For LIV oscillations: there is mixing between 2 flavor eigenstates and 2 velocity eigenstates: (asymptotic vdifferent from c)
vvvv
vvvv
233232
233232
cossin
sincos
The survival probability is: ( v=v3-v2 )
LE
vP v 2
10521 1822 sinsin
Exotic oscillationsLorentz invariance violation (LIV)
Notice the dependence LE LIV is not dominant Violation of the equivalence principleSimilar results as for LIV, but with parameter = difference of coupling constants of to gravitational pot )
If both mass-induced and LIV-induced transitions are
considered simultaneously:
22 21 sinsin P
22
21
12 /tana2
aa
aa
where
im
m
eELELma
ELELma
v
v
cosv/cos.
sinv/sin.
21022271
21022271
1822
1821
and
Mixed oscillations
P()
Mixed
oscillations
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 m2=0.0023 eV2 and maximal mixing (MACRO values)
-minimize with respect to v, θv the function
high
lowi syststat
mvMCii mvNN
22
222
,;,
90% C.L. limits on v and θv computed with Feldman–Cousins prescription
2 analysis
(30,130) GeV
(28,142) GeV
Maximum Likelihood analysis in intermediate E region
Minimization of the negative log-likelihood function:
),,,;,(ln)(
v
i
mii mLEfF 2323
22
)();( ppKaxf MC
Event-by-event analysis best use of existing information
106 events with GeVEGeV 7525
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 : v/2 < 3 10-24
at sin22θv = 1 : v/2 < 1.4 10-26
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