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