macro constraints on violation of lorentz invariance
DESCRIPTION
MACRO constraints on violation of Lorentz invariance. M. Cozzi Bologna University - INFN Neutrino Oscillation Workshop Conca Specchiulla (Otranto) September 9-16, 2006. Outline. Violation of Lorentz Invariance (VLI) Test of VLI with neutrino oscillations - PowerPoint PPT PresentationTRANSCRIPT
1
MACRO constraints on MACRO constraints on violation of Lorentz violation of Lorentz
invarianceinvarianceM. Cozzi
Bologna University - INFN
Neutrino Oscillation WorkshopConca Specchiulla (Otranto)
September 9-16, 2006
NOW 2006NOW 2006 M. CozziM. Cozzi 2
OutlineOutline
Violation of Lorentz Invariance (VLI)Test of VLI with neutrino oscillationsMACRO results on mass-induced oscillationsSearch for a VLI contribution in neutrino oscillationsResults and conclusions
NOW 2006NOW 2006 M. CozziM. Cozzi 3
Violation of the Lorentz Violation of the Lorentz InvarianceInvariance
In general, when Violation of the Lorentz Invariance (VLI) perturbations are introduced in the Lagrangian, particles have different Maximum Attainable Velocities (MAVs), i.e. Vi(p=∞)≠c
Renewed interest in this field. Recent works on:VLI connected to the breakdown of GZK cutoffVLI from photon stabilityVLI from radioactive muon decayVLI from hadronic physics
Here we consider only those violation of Lorentz Invariance conserving CPT
NOW 2006NOW 2006 M. CozziM. Cozzi 4
Test of Lorentz invariance with Test of Lorentz invariance with neutrino oscillationsneutrino oscillations
The CPT-conserving Lorentz violations lead to neutrino oscillations even if neutrinos are masslessHowever, observable neutrino oscillations may result from a combination of effects involving neutrino masses and VLIGiven the very small neutrino mass ( eV), neutrinos are ultra relativistic particlesSearches for neutrino oscillations can provide a sensitive test of Lorentz invariance
1m
NOW 2006NOW 2006 M. CozziM. Cozzi 5
““Pure” mass-induced neutrino Pure” mass-induced neutrino oscillationsoscillations
In the 2 family approximation, we have2 mass eigenstates and with masses m2 and m3
2 flavor eigenstates and
The mixing between the 2 basis is described by the θ23 angle:
If the states are not degenerate (m2 ≡ m22- m3
2 ≠ 0) and the mixing angle ≠ 0, then the probability that a flavor “survives” after a distance L is:
m23
m3
m23
m2
m23
m3
m23
m2
cossin
sincos
E/Lm27.1sin2sin1P 22m
2
m2
m3
Note the L/E dependence
NOW 2006NOW 2006 M. CozziM. Cozzi 6
““Pure” VLI-induced neutrino Pure” VLI-induced neutrino oscillationsoscillations
When VLI is considered, we introduce a new basis:the velocity basis: and (2 family approx)Velocity and flavor eigenstates are now connected by a new mixing angle:
If neutrinos have different MAVs (v ≡ v2- v3 ≠ 0)
and the mixing angle v≡ v≠ 0, then the survival
oscillation probability has the form:
v23
v3
v23
v2
v23
v3
v23
v2
cossin
sincos
ELv1054.2sin2sin1P 182v
2
v2
v3
Note the L·E dependence
NOW 2006NOW 2006 M. CozziM. Cozzi 7
Mixed scenarioMixed scenarioWhen both mass-induced and VLI-induced oscillations are simultaneously considered:
where2=atan(a1/a2)
=√a12+ a2
2
22 sin2sin1 P
)LE 2 cos v2·10 L/Ecos2 m(1.27 a
e LE 2 sin v2·10 L/Esin2 m1.27 a
v18
m2
2
iv
18m
21
oscillation“strength”
oscillation“length”
= generic phase connecting mass and velocity eigenstates
NOW 2006NOW 2006 M. CozziM. Cozzi 8
Notes:Notes:In the “pure” cases, probabilities do not depend on the sign of v, m2 and mixing angles while in the “mixed” case relative signs are important. Domain of variability:
m2 ≥ 0 0 ≤ m ≤ /2v ≥ 0 /4 ≤ v ≤ /4
Formally, VLI-induced oscillations are equivalent to oscillations induced by Violation of the Equivalence Principle (VEP) after the substitution:
v/2↔ ||where is the gravitational potential and is the difference of the neutrino coupling to the gravitational field.Due to the different (L,E) behavior, VLI effects are emphasized for large L and large E (large L·E)
NOW 2006NOW 2006 M. CozziM. Cozzi 9
Energy dependence for P(Energy dependence for P(ννμμννμμ) assuming ) assuming L=10000 km, L=10000 km, mm2 2 = 0.0023 eV= 0.0023 eV2 2 and and mm==/4/4
252 10 ,sin 2 0vv 252 10 ,sin 2 0.3vv
252 10 ,sin 2 0.7vv 252 10 ,sin 2 1vv
Black line: no VLI
Mixed scenario:
VLI with sin2θv>0
VLI with sin2θv <0
NOW 2006NOW 2006 M. CozziM. Cozzi 10
MACRO results on mass-induced MACRO results on mass-induced neutrino oscillationsneutrino oscillations
NOW 2006NOW 2006 M. CozziM. Cozzi 11
7 Rock absorbers~ 25 Xo
35/yr Internal Downgoing (ID) +35/yr Upgoing Stopping (UGS)
180/yr Up-throughgoing
3 horizontal layers ot Liquid
scintillators
14 horizontal planes of limited
streamer tubes
<E(GeV)>50 4.2 3.550 4.2 3.5
Topologies of Topologies of -induced -induced eventsevents
50/yr Internal Upgoing (IU)
NOW 2006NOW 2006 M. CozziM. Cozzi 12
Neutrino events Neutrino events detected by MACROdetected by MACRO
Data samples No-osc Expected (MC)Topologies Measure
d
Up Throughgoing 857 1169
Internal Up 157 285
Int. Down + Up stop
262 375
50E GeV
3.5E GeV
4.2E GeV
NOW 2006NOW 2006 M. CozziM. Cozzi 13
Upthroughgoing muonsUpthroughgoing muonsAbsolute flux
Even if new MCs are strongly improved, there are still problems connected with CR fit → large sys. err.
Zenith angle deformationExcellent resolution (2% for HE)Very powerful observable (shape known to within 5%)
Energy spectrum deformationEnergy estimate through MCS in the rock absorber of the
detector (sub-sample of upthroughgoing events) PLB 566 (2003) 35PLB 566 (2003) 35
Extremely powerful, but poorer shape knowledge (12% error point-to-point)
Used for this analysis
NOW 2006NOW 2006 M. CozziM. Cozzi 14
L/EL/E distribution distributionDATA/MC(no oscillation) as a function
of reconstructed L/E:
Internal Upgoing
300 Throughgoing events
NOW 2006NOW 2006 M. CozziM. Cozzi 15
The analysis was based on ratios (reduced systematic errors at few % level): Eur. Phys. J. C36 (2004) 357
Angular distribution R1= N(cos<-0.7)/N(cos>-0.4)
Energy spectrum R2= N(low E)/N(high E)
Low energy R3= N(ID+UGS)/N(IU)
Null hypothesis ruled out by PNH~5If the absolute flux information is added (assuming Bartol96 correct within 17%): PNH~ 6Best fit parameters for ↔ oscillations (global fit of all MACRO neutrino data):m2=0.0023 eV2
sin22m=1
Final MACRO resultsFinal MACRO results
NOW 2006NOW 2006 M. CozziM. Cozzi 16
90% CL allowed region90% CL allowed region
Based on the “shapes” of the distributions (14 bins)
Including normalization (Bartol flux with 17% sys. err.)
NOW 2006NOW 2006 M. CozziM. Cozzi 17
Search for a VLI contributionSearch for a VLI contributionusing MACRO datausing MACRO data
Assuming standard mass-induced neutrino oscillations as the leading mechanism for flavor transitions and VLI as a subdominant effect.
NOW 2006NOW 2006 M. CozziM. Cozzi 18
A subsample of 300 upthroughgoing muons (with energy estimated via MCS) are particularly favorable:<E> ≈ 50 GeV (as they are uptroughgoing)<L> ≈ 10000 km (due to analysis cuts)
Golden events for VLI studies!
v= 2 x 10-25
v=/4
Good sensitivity expected from the
relative abundancesof low and high energy events
NOW 2006NOW 2006 M. CozziM. Cozzi 19
Divide the MCS sample (300 events) in two sub-samples:Low energy sample: Erec < 28 GeV → Nlow= 44 evts
High energy sample: Erec > 142 GeV → Nhigh= 35 evtsDefine the statistics:
and (in the first step) fix mass-induced oscillation parameters m2=0.0023 eV2 and sin22m=1 (MACRO values) and assume ei realassume 16% systematic error on the ratio Nlow/Nhigh (mainly due to the spectrum slope of primary cosmic rays)Scan the (v, v) plane and compute χ2 in each point (Feldman & Cousins prescription)
Analysis strategyAnalysis strategy
Optimizedwith MC
22
22 2
, ; ,MChigh i i v m
i low stat syst
N N v m
NOW 2006NOW 2006 M. CozziM. Cozzi 20
Results of the analysis - IResults of the analysis - I
Original cuts
Optimized cuts
χ2 not improved in any point of
the (v, v) plane:
90% C.L. limits
Neutrino flux used in MC: “new Honda” - PRD70 (2004) 043008
NOW 2006NOW 2006 M. CozziM. Cozzi 21
Results of the analysis - IIResults of the analysis - IIChanging m2 around the best-fit point with m2± 30%, the limit moves up/down by at most a factor 2Allowing m2 to vary inside ±30%, m± 20% and any value for the phase and marginalizing in v
(-π/4≤ v ≤ π/4 ):
|v|< 3 x 10-25
||< 1.5 x 10-25
VLI
VEP
NOW 2006NOW 2006 M. CozziM. Cozzi 22
Results of the analysis - IIIResults of the analysis - IIIA different and complementary analysis has been performed:
Select the central region of the energy spectrum 25 GeV < E
rec < 75 GeV (106 evts)Negative log-likelihood function was built event by event and fitted to the data.Mass-induced oscillation parameters inside the MACRO 90% C.L. region; VLI parameters free in the whole plane.
Average v < 10-
25, slowly varying with m2
NOW 2006NOW 2006 M. CozziM. Cozzi 23
ConclusionsConclusionsWe re-analyzed the energy distribution of MACRO neutrino data to include the possibility of exotic effects (Violation of the Lorentz Invariance)The inclusion of VLI effects does not improve the fit to the muon energy data → VLI effects excluded even at a sub-dominant levelWe obtained the limit on VLI parameter |v|< 3 x 10-25 at 90% C.L.
(or ||< 1.5 x 10-25 for the VEP case)