macro constraints on violation of lorentz invariance n.
Skip this Video
Loading SlideShow in 5 Seconds..
MACRO constraints on violation of Lorentz invariance PowerPoint Presentation
Download Presentation
MACRO constraints on violation of Lorentz invariance

MACRO constraints on violation of Lorentz invariance

158 Views Download Presentation
Download Presentation

MACRO constraints on violation of Lorentz invariance

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  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 M. Cozzi

  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(p=∞)≠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 M. Cozzi

  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 M. Cozzi

  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 θ23 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 M. Cozzi

  6. “Pure” VLI-induced neutrino oscillations • 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 (Dv≡ v2- v3≠ 0) and the mixing angle qv23 ≡ qv≠ 0, then the survival oscillation probability has the form: Note the L·E dependence M. Cozzi

  7. Mixed scenario • When both mass-induced and VLI-induced oscillations are simultaneously considered: • where • 2Q=atan(a1/a2) • W=√a12+ a22 oscillation “length” oscillation “strength” h = generic phase connecting mass and velocity eigenstates M. Cozzi

  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↔ |f|Dgwhere 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 L·E) M. Cozzi

  9. Energy dependence for P(νμνμ) assuming L=10000 km, Dm2 = 0.0023 eV2 and qm=p/4 Black line: no VLI Mixed scenario: VLI with sin2θv>0 VLI with sin2θv<0 M. Cozzi

  10. MACRO results on mass-induced neutrino oscillations M. Cozzi

  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 m nm m m 50/yr Internal Upgoing (IU) 35/yr Internal Downgoing (ID) + 35/yr Upgoing Stopping (UGS) 180/yr Up-throughgoing nm nm M. Cozzi <En(GeV)> 50 4.2 3.5

  12. Neutrino events detected by MACRO M. Cozzi

  13. Used for this analysis 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) M. Cozzi

  14. L/En distribution DATA/MC(no oscillation) as a function of reconstructed L/E: Internal Upgoing 300 Throughgoing events M. Cozzi

  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(cosq<-0.7)/N(cosq>-0.4) • Energy spectrum R2= N(low En)/N(high En) • Low energy R3= N(ID+UGS)/N(IU) • Null hypothesis ruled out by PNH~5s • 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): • Dm2=0.0023 eV2 • sin22qm=1 M. Cozzi

  16. 90% CL allowed region Based on the “shapes” of the distributions (14 bins) D Including normalization (Bartol flux with 17% sys. err.) q M. Cozzi

  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. M. Cozzi

  18. A subsample of 300 upthroughgoing muons (with energy estimated via MCS) are particularly favorable: <En> ≈ 50 GeV(as they are uptroughgoing) <L> ≈ 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 qv=p/4 M. Cozzi

  19. Analysis strategy Optimized with MC • 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 evts • Define the statistics: and (in the first step) fix mass-induced oscillation parameters Dm2=0.0023 eV2 and sin22qm=1 (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 χ2 in each point (Feldman & Cousins prescription) M. Cozzi

  20. Results of the analysis - I χ2 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 M. Cozzi

  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 (-π/4≤ qv ≤ π/4 ): |Dv|< 3 x 10-25 VLI VEP f|Dg|< 1.5 x 10-25 M. Cozzi

  22. Results of the analysis - III • A different and complementary analysis has been performed: • Select the central region of the energy spectrum 25 GeV < Enrec < 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 M. Cozzi

  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 |Dv|< 3 x 10-25 at 90% C.L.(or f|Dg|< 1.5 x 10-25 for the VEP case) M. Cozzi