Department of Physics and Astronomy

Neutrino Oscillations

Faculty:  David J. Ernst

Research Associate:  David C. Latimer (until Spring 2005, now at the University of Louisville)

current graduate students:  
Jesus Escamilla

Formal Developments

We investigated the bounds for the mixing angles in the presence of the MSW effect. In  the absence of the MSW effect, this was addressed extensively in the 1970's. Utilizing a new formalism, we found that the preferred choice of bounds on the angles is theta13 between -pi/2 and +pi/2, the CP phase delta between 0 and pi and the two other angles between 0 and pi/2. The common choice is theta13 between 0 and pi/2 and delta between 0 and 2 pi. For CP conservation, the complete space conventionally requires delta to be 0 and pi. The second delta=pi branch was pointed out by J. Gluza and M. Zralek in 2001, but has been largely ignored. For our choice, the allowed values of the parameters lie for all cases in one connected region, rather than two disconnected regions. This work is pubished in Phys. Rev. D.

The mass-hierarchy symmetry is a symmetry between having the small mass-square difference lie below or above the large mass-square difference. We found that there are two separate and distinct symmetries which in the literature are viewed as one. One symmetry is exactly valid in vacuum and is broken by the MSW effect. The second is exact in the limit of theta13 ---> 0. There is no limit of one which leads to the other. Both of these works also develop an elegant formalism and a number of possibly useful identities. This work has been submitted to the J. Math Phys.

Simulations and Analytic Work

The Particle Data Group and those doing the phenomenology of neutrino oscillations parameterize neutrino oscillations in terms of sin2 theta13. The dependence on the square results from the ``one mass-squared dominance'' approximation. We have developed a simulation of the world's data and find present data include linear effects in sin theta13. We traced the origin of these effects to the large L/E atmospheric data. This has been previously pointed out by O. L. G. Peres and A. Yu. Smirnov in 2004. We are writing an article that describes in detail the simulation and demonstrates the origin and implications of the linear terms.

Given linear terms in theta13, we investigated the oscillation probabilities to find where the linear terms might be largest. We find algebraically that Pe mu and Pmu mu at the particular values of L/E given by L/E=2 pi/ Delta m221, n an integer, have large linear terms. Our simulations show that the linear terms are actually dominant, suggesting a way to measure theta13 and its sign.


C.M. Chen, D.J. Ernst, and M.B. Johnson, "Extracting Forward Strong Amplitudes from Elastic Differential Cross Sections," submitted to Nucl. Phys.

D.C. Latimer and D.J. Ernst, "Physical region for three-neutrino mixing angles," Phys. Rev. D 71, 017301 (2005)

D.C. Latimer and D.J. Ernst, "On the degeneracies of the mass-squared differences for three neutrino oscillations," Mod. Phys. Lett. A 20, 1663 (2005)

D.C. Latimer and D.J. Ernst, "Neutrino oscillations: measuring theta13 including its sign," Phys. Rev. C 71, 062501(R) (2005)

former graduate students:

Stephen Jacobson, (Ph.D. Dec. 2000, "Crossing symmetry in pion-nucleon scattering", Adviser: Prof. Ernst), now Staff Scientist, GATS Inc., Newport News, VA

Dennis Malov,
(Ph.D. Dec. 1999, "String-parton model of heavy-ion collisions", Adviser: Profs. Ernst and Umar), now at Computer Modelling Firm, Phoenix, AZ

Last update: August 16, 2005
Volker Oberacker
  Vanderbilt University