1. Lorentz Violation and an Experimental Limit Ben Rybolt 12/10/2012

2. Goal Test the Standard Model Extension using neutrino oscillation data from the Double Chooz Experiment [3]. Place upper limit on possible SME terms Neutrino Oscillations act like interferometers and over large distances may be sensitive to very small Lorentz Violating Terms

3. Standard Model Extension[1] What is it? – Does not assume that the universe is Lorentz invariant. Includes terms that Violate CPT and maintain CPT symmetries – Can occur through spontaneous Lorentz symmetry breaking – Simple frame work to go beyond the standard model

4. Lagrangian Standard model for leptons Including Lorentz Violating Terms[2]

5. Sun Centered Frame Lorentz violating terms choose a preferred direction in space We assume the Lorentz violating field is a fixed in the Sun centered frame Z X Y Possible direction of Lorentz violating field

6. Earth Centered Frame Z-up X-south Y-east Neutrino propagation direction Is measured in the Earth centered Frame If a Lorentz Violating Field is fixed in the Sun centered Frame then Sidereal Time Variations in the earth Centered Frame would be a clear signal for Standard Model Extension.

7. Double Chooz Experiment We have established that Lorentz violating terms cause Sidereal time variations in neutrino oscillations No sidereal time variations were found in the Double Chooz data but we can place upper limits on the strength of possible Standard Model Extension Coefficients

8. General Oscillations Given the standard model Extension Lagrangian The Effective Hamiltonian for neutrino Oscillation is The probability of oscillation then can be written

9. Simplifying Assumptions

10. Simplified Oscillation Probability Transforming into an Earth based frame Grouping terms with sidereal time dependence

12. Results The Double Chooz detector measures Neutrinos created from 2 nuclear reactors ~ 1 km away We observe ~ 40 neutrino events/day Data set represents ~230 days of detector data All events were placed into 24 bins per sidereal day (23.934 hours)

13. Results

14. References [1]D. Colladay and A. Kostelecky, CPT Violation and the Standard Model, Phys. Rev. D 55, 6760 (1997). [2]V.A. Kostelecky and M. Mewes, Lorentz and CPT violation in the neutrino sector, Phys Rev D 70, 031902 [3]Y. Abe et al., First Test of Lorentz Violation with a Reactor-Based Antineutrino Experiment, arXiv:1209.5810[hep-ex] [4] V.A. Kostelecky and M. Mewes Phys., Lorentz Violation and Short-baseline Neutrino Experiments, Phys Rev D 70, 076002