C. Latimer (until Spring 2005, now at the University of
graduate students:Jesus Escamilla
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.
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
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
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
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,
D.C. Latimer and D.J. Ernst, "Neutrino oscillations: measuring theta13
including its sign," Phys. Rev. C 71, 062501(R) (2005)
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
August 16, 2005
Volker Oberacker Vanderbilt