MACRO constraints on violation of Lorentz invariance

1
MACRO constraints on violation of Lorentz
invariance

• M. Cozzi
• Bologna University - INFN
• Neutrino Oscillation Workshop
• Conca Specchiulla (Otranto)
• September 9-16, 2006

2
Outline

• Violation of Lorentz Invariance (VLI)
• Test of VLI with neutrino oscillations
• MACRO results on mass-induced n oscillations
• Search for a VLI contribution in neutrino
  oscillations
• Results and conclusions

3
Violation of the Lorentz Invariance

• 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(p8)?c
• Renewed interest in this field. Recent works on
• VLI connected to the breakdown of GZK cutoff
• VLI from photon stability
• VLI from radioactive muon decay
• VLI from hadronic physics
• Here we consider only those violation of Lorentz
  Invariance conserving CPT

4
Test of Lorentz invariance with neutrino
oscillations

• The CPT-conserving Lorentz violations lead to
  neutrino oscillations even if neutrinos are
  massless
• However, observable neutrino oscillations may
  result from a combination of effects involving
  neutrino masses and VLI
• Given the very small neutrino mass ( eV),
  neutrinos are ultra relativistic particles
• Searches for neutrino oscillations can provide a
  sensitive test of Lorentz invariance

5
Pure mass-induced neutrino oscillations

• In the 2 family approximation, we have
• 2 mass eigenstates and with
  masses m2 and m3
• 2 flavor eigenstates and
• The mixing between the 2 basis is described by
  the ?23 angle
• If the states are not degenerate (Dm2 m22- m32
  ? 0) and the mixing angle q23 ? 0, then the
  probability that a flavor survives after a
  distance L is

Note the L/E dependence
6
Pure VLI-induced neutrino oscillations

• When VLI is considered, we introduce a new
  basisthe velocity basis and (2
  family approx)
• Velocity and flavor eigenstates are now connected
  by a new mixing angle
• If neutrinos have different MAVs (Dv v2- v3 ?
  0) and the mixing angle qv23 qv? 0, then the
  survival oscillation probability has the form

Note the LE dependence
7
Mixed scenario

• When both mass-induced and VLI-induced
  oscillations are simultaneously considered
• where
• 2Qatan(a1/a2)
• Wva12 a22

oscillation length
oscillation strength
h generic phase connecting mass and velocity
eigenstates
8
Notes

• In the pure cases, probabilities do not depend
  on the sign of Dv, Dm2 and mixing angles while in
  the mixed case relative signs are important.
  Domain of variability
• Dm2 0 0 qm p/2
• Dv 0 -p/4 qv p/4
• Formally, VLI-induced oscillations are equivalent
  to oscillations induced by Violation of the
  Equivalence Principle (VEP) after the
  substitution Dv/2 ? fDgwhere f is
  the gravitational potential and Dg 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
  LE)

9
Energy dependence for P(?µ??µ) assuming L10000
km, Dm2 0.0023 eV2 and qmp/4
Black line no VLI Mixed scenario VLI with
sin2?vgt0 VLI with sin2?v lt0
10
MACRO results on mass-induced neutrino
oscillations
11
Topologies of n-induced events

3 horizontal layers ot Liquid scintillators

nm
14 horizontal planes of limited streamer tubes
m
7 Rock absorbers 25 Xo
nm
m
m
m
35/yr Internal Downgoing (ID) 35/yr Upgoing
Stopping (UGS)
50/yr Internal Upgoing (IU)
180/yr Up-throughgoing
nm
nm
ltEn(GeV)gt
50 4.2 3.5
12
Neutrino events detected by MACRO
Data samples Data samples No-osc Expected (MC)
Topologies Measured No-osc Expected (MC)
Up Throughgoing 857 1169
Internal Up 157 285
Int. Down Up stop 262 375
13
Upthroughgoing muons

• Absolute flux
• Even if new MCs are strongly improved, there are
  still problems connected with CR fit ? large sys.
  err.
• Zenith angle deformation
• Excellent resolution (2 for HE)
• Very powerful observable (shape known to within
  5)
• Energy spectrum deformation
• Energy estimate through MCS in the rock absorber
  of the detector (sub-sample of upthroughgoing
  events) PLB 566 (2003) 35
• Extremely powerful, but poorer shape knowledge
  (12 error point-to-point)

14
L/En distribution
DATA/MC(no oscillation) as a function of
reconstructed L/E
Internal Upgoing
300 Throughgoing events
15
Final MACRO results

• The analysis was based on ratios (reduced
  systematic errors at few level) Eur. Phys.
  J. C36 (2004) 357
• Angular distribution R1 N(cosqlt-0.7)/N(cosqgt-0
  .4)
• Energy spectrum R2 N(low En)/N(high En)
• Low energy R3 N(IDUGS)/N(IU)
• Null hypothesis ruled out by PNH5s
• If the absolute flux information is added
  (assuming Bartol96 correct within 17) PNH 6s
• Best fit parameters for nm?nt oscillations
  (global fit of all MACRO neutrino data)
• Dm20.0023 eV2
• sin22qm1

16
90 CL allowed region
Based on the shapes of the distributions (14
bins)
D
Including normalization (Bartol flux with 17
sys. err.)
q
17
Search for a VLI contributionusing MACRO data
Assuming standard mass-induced neutrino
oscillations as the leading mechanism for flavor
transitions and VLI as a subdominant effect.
18
A subsample of 300 upthroughgoing muons (with
energy estimated via MCS) are particularly
favorable ltEngt 50 GeV (as they are
uptroughgoing) ltLgt 10000 km (due to analysis
cuts) Golden events for VLI studies!
Good sensitivity expected from the relative
abundances of low and high energy events
Dv 2 x 10-25 qvp/4
19
Analysis strategy

• Divide the MCS sample (300 events) in two
  sub-samples
• Low energy sample Erec lt 28 GeV ? Nlow 44
  evts
• High energy sample Erec gt 142 GeV ? Nhigh 35
  evts
• Define the statistics
• and (in the first step) fix mass-induced
  oscillation parameters Dm20.0023 eV2 and
  sin22qm1 (MACRO values) and assume eih real
• assume 16 systematic error on the ratio
  Nlow/Nhigh (mainly due to the spectrum slope of
  primary cosmic rays)
• Scan the (Dv, qv) plane and compute ?2 in each
  point (Feldman Cousins prescription)

Optimized with MC
20
Results of the analysis - I
?2 not improved in any point of the (Dv, qv)
plane
Original cuts
90 C.L. limits
Optimized cuts
Neutrino flux used in MC new Honda - PRD70
(2004) 043008
21
Results of the analysis - II

• Changing Dm2 around the best-fit point with Dm2
  30, the limit moves up/down by at most a factor
  2
• Allowing Dm2 to vary inside 30, qm 20 and any
  value for the phase h and marginalizing in qv
  (-p/4 qv p/4 )

Dvlt 3 x 10-25
VLI
VEP
fDglt 1.5 x 10-25
22
Results of the analysis - III

• A different and complementary analysis has been
  performed
• Select the central region of the energy spectrum
  25 GeV lt Enrec lt 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 lt 10-25, slowly varying with ?m2
23
Conclusions

• We 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 level
• We obtained the limit on VLI parameter Dvlt 3 x
  10-25 at 90 C.L. (or fDglt 1.5 x 10-25 for the
  VEP case)