Lorentz Violation and an E xperimental Limit

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

6. Earth Centered Frame Z-up 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. Y-east X-south

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 • Since we are looking for upper limits we can consider either the or the case separately in this work only the case will be considered • We can also neglect the mass term because it does not contribute a sidereal time dependency

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

11. We have reduced the problem to three parameters that we can compare to experimental data • In Double Chooz Geometry the parameters are connected to Standard Model Extensions by [4]

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 • Oscillation is Sidereal time is smaller than error bars • Data is consistent with no sidereal time oscillation • [] are constrained to <GeV

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