1,529 research outputs found

### On the degeneracies of the mass-squared differences for three-neutrino oscillations

Using an algebraic formulation, we explore two well-known degeneracies
involving the mass-squared differences for three-neutrino oscillations assuming
CP symmetry is conserved. For vacuum oscillation, we derive the expression for
the mixing angles that permit invariance under the interchange of two
mass-squared differences. This symmetry is most easily expressed in terms of an
ascending mass order. This can be used to reduce the parameter space by one
half in the absence of the MSW effect. For oscillations in matter, we derive
within our formalism the known approximate degeneracy between the standard and
inverted mass hierarchies in the limit of vanishing $\theta_{13}$. This is done
with a mass ordering that permits the map $\Delta_{31} \mapsto -\Delta_{31}$.
Our techniques allow us to translate mixing angles in this mass order
convention into their values for the ascending order convention. Using this
dictionary, we demonstrate that the vacuum symmetry and the approximate
symmetry invoked for oscillations in matter are distinctly different.Comment: 5 pages, revised manuscrip

### Vacuum-UV negative photoion spectroscopy of CH3F, CH3Cl and CH3Br

Using tunable vacuum-UV radiation from a synchrotron, negative ions are detected by quadrupolar mass spectrometry following photoexcitation of three gaseous halogenated methanes CH$_3$X (X = F,Cl,Br). The anions X$^-$, H$^-$, CX$^-$, CHX$^-$ and CH$_2$X$^-$ are observed, and their ion yields recorded in the range 8-35 eV. The anions show a linear dependence of signal with pressure, showing that they arise from unimolecular ion-pair dissociation, generically described as AB + h$v$ $\rightarrow$ A$^-$ + B$^+$ (+ neutrals). Absolute cross sections for ion-pair formation are obtained by calibrating the signal intensities with those of F$^-$ from both SF$_6$ and CF$_4$. The cross sections for formation of X$^-$ + CH$_3$$^+$ are much greater than for formation of CH$_2$X$^-$ + H$^+$. In common with many quadrupoles, the spectra of $m$/$z$ 1 (H$^-$) anions show contributions from all anions, and only for CH$_3$Br is it possible to perform the necessary subtraction to obtain the true H$^-$ spectrum. The anion cross sections are normalised to vacuum-UV absorption cross sections to obtain quantum yields for their production. The appearance energies of X$^-$ and CH$_2$X$^-$ are used to calculate upper limits to 298 K bond dissociation energies for D$^o$ (H$_3$C-X) and D$^o$ (XH$_2$C-H) which are consistent with literature values. The spectra suggest that most of the anions are formed indirectly by crossing of Rydberg states of the parent molecule onto an ion-pair continuum. The one exception is the lowest-energy peak of F$^-$ from CH$_3$F at 13.4 eV, where its width and lack of structure suggest it may correspond to a direct ion-pair transition

### On detecting CP violation in a single neutrino oscillation channel at very long baselines

We propose a way of detecting CP violation in a single neutrino oscillation
channel at very long baselines (on the order of several thousands of
kilometers), given precise knowledge of the smallest mass-squared difference.
It is shown that CP violation can be characterized by a shift in $L/E$ of the
peak oscillation in the $\nu_e$--$\nu_\mu$ appearance channel, both in vacuum
and in matter. In fact, matter effects enhance the shift at a fixed energy. We
consider the case in which sub-GeV neutrinos are measured with varying baseline
and also the case of a fixed baseline. For the varied baseline, accurate
knowledge of the absolute neutrino flux would not be necessary; however,
neutrinos must be distinguishable from antineutrinos. For the fixed baseline,
it is shown that CP violation can be distinguished if the mixing angle
$\theta_{13}$ were known.Comment: 8 pages, 9 figures; minor typos correcte

### Measuring the mass of a sterile neutrino with a very short baseline reactor experiment

An analysis of the world's neutrino oscillation data, including sterile
neutrinos, (M. Sorel, C. M. Conrad, and M. H. Shaevitz, Phys. Rev. D 70,
073004) found a peak in the allowed region at a mass-squared difference $\Delta
m^2 \cong 0.9$ eV$^2$. We trace its origin to harmonic oscillations in the
electron survival probability $P_{ee}$ as a function of L/E, the ratio of
baseline to neutrino energy, as measured in the near detector of the Bugey
experiment. We find a second occurrence for $\Delta m^2 \cong 1.9$ eV$^2$. We
point out that the phenomenon of harmonic oscillations of $P_{ee}$ as a
function of L/E, as seen in the Bugey experiment, can be used to measure the
mass-squared difference associated with a sterile neutrino in the range from a
fraction of an eV$^2$ to several eV$^2$ (compatible with that indicated by the
LSND experiment), as well as measure the amount of electron-sterile neutrino
mixing. We observe that the experiment is independent, to lowest order, of the
size of the reactor and suggest the possibility of a small reactor with a
detector sitting at a very short baseline.Comment: 4 pages, 2 figure

### Calculating error bars for neutrino mixing parameters

One goal of contemporary particle physics is to determine the mixing angles
and mass-squared differences that constitute the phenomenological constants
that describe neutrino oscillations. Of great interest are not only the best
fit values of these constants but also their errors. Some of the neutrino
oscillation data is statistically poor and cannot be treated by normal
(Gaussian) statistics. To extract confidence intervals when the statistics are
not normal, one should not utilize the value for chisquare versus confidence
level taken from normal statistics. Instead, we propose that one should use the
normalized likelihood function as a probability distribution; the relationship
between the correct chisquare and a given confidence level can be computed by
integrating over the likelihood function. This allows for a definition of
confidence level independent of the functional form of the !2 function; it is
particularly useful for cases in which the minimum of the !2 function is near a
boundary. We present two pedagogic examples and find that the proposed method
yields confidence intervals that can differ significantly from those obtained
by using the value of chisquare from normal statistics. For example, we find
that for the first data release of the T2K experiment the probability that
chisquare is not zero, as defined by the maximum confidence level at which the
value of zero is not allowed, is 92%. Using the value of chisquare at zero and
assigning a confidence level from normal statistics, a common practice, gives
the over estimation of 99.5%.Comment: 9 pages, 6 figure

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