arXiv subjects

D. C. Latimer

Publications and source records attributed to D. C. Latimer.

At least 19 recordsLinked to original sources

arXiv2014

Impact of approximate oscillation probabilities in the analysis of three neutrino experiments

As neutrino oscillation data becomes ever more precise, the use of approximate formulae for the oscillation probabilities ${\mathcal P}_{αβ}$ must be examined to ensure that the approximation is adequate. Here, the oscillation probability ${\mathcal P}_{ee}$ is investigated in the context of the Daya Bay experiment; the oscillation probability ${\mathcal P}_{μμ}$ is investigated in terms of the T2K disappearance experiment; and the probability ${\mathcal P}_{μe}$ is investigated in terms of the T2K appearance experiment. Daya Bay requires ${\mathcal P}_{ee}$ in vacuum and thus the simple analytic formula negates the need for an approximate formula. However, improved data from T2K will soon become sensitive to the hierarchy, and thus require a more careful treatment of that aspect. For the other cases, we choose an expansion by Akhmedov et al. which systematically includes all terms through second order in $\sinθ_{13}$ and in $α=: Δ_{21}/Δ_{31}$ ($Δ_{jk} =: m^2_j - m^2_k$). For the T2K disappearance experiment the approximation is quite accurate. However, for the T2K appearance experiment the approximate formula is not precise enough for addressing such questions as hierarchy or the existence of CP violation in the lepton sector. We suggest the use of numerical calculations of the oscillation probabilities, which are stable, accurate, and efficient and eliminate the possibility that differences in analyses are emanating from different approximations.

hep-ph↗

arXiv2013

Neutrino Oscillations: Hierarchy Question

The only experimentally observed phenomenon that lies outside the standard model of the electroweak interaction is neutrino oscillations. A way to try to unify the extensive neutrino oscillation data is to add a phenomenological mass term to the Lagrangian that is not diagonal in the flavor basis. The goal is then to understand the world's data in terms of the parameters of the mixing matrix and the differences between the squares of the masses of the neutrinos. An outstanding question is what is the correct ordering of the masses, the hierarchy question. We point out a broken symmetry relevant to this question, the symmetry of the simultaneous interchange of hierarchy and the sign of $θ_{13}$. We first present the results of an analysis of data that well determine the phenomenological parameters but are not sensitive to the hierarchy. We find $θ_{13} = 0.152\pm 0.014$, $θ_{23} = 0.25^{+0.03}_{-0.05} π$ and $Δ_{32} = 2.45\pm 0.14 \times 10^{-3}$ eV$^2$, results consistent with others. We then include data that are sensitive to the hierarchy and the sign of $θ_{13}$. We find, unlike others, four isolated minimum in the $χ^2$-space as predicted by the symmetry. Now that Daya Bay and RENO have determined $θ_{13}$ to be surprisingly large, the Super-K atmospheric data produce meaningful symmetry breaking such that the inverse hierarchy is preferred at the 97.2 % level.

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arXiv2012

Implications of nonzero $θ_{13}$ for the neutrino mass hierarchy

The Daya Bay, RENO, and Double Chooz experiments have discovered a large non-zero value for $θ_{13}$. We present a global analysis that includes these three experiments, Chooz, the Super-K atmospheric data, and the $ν_μ\rightarrow ν_e$ T2K and MINOS experiments that are sensitive to the hierarchy and the sign of $θ_{13}$. We report preliminary results in which we fix the mixing parameters other than $θ_{13}$ to those from a recent global analysis. Given there is no evidence for a non-zero CP violation, we assume $δ=0$. T2K and MINOS lie in a region of $L/E$ where there is a hierarchy degeneracy in the limit of $θ_{13}\rightarrow 0$ and no matter interaction. For non-zero $θ_{13}$, the symmetry is partially broken, but a degeneracy under the simultaneous exchange of both hierarchy and the sign of $θ_{13}$ remains. Matter effects break this symmetry such that the positions of the peaks in the oscillation probabilities maintain the two-fold symmetry, while the magnitude of the oscillations is sensitive to the hierarchy. This renders T2K and NO$ν$A, with different baselines and different matter effects, better able in combination to distinguish the hierarchy and the sign of $θ_{13}$. The large value of $θ_{13}$ yields effects from atmospheric data that distinguish hierarchies. We find for normal hierarchy, positive $θ_{13}$, $\sin^22θ_{13}=0.090\pm0.020$ and is 0.2% probable it is the correct combination; for normal hierarchy, negative $θ_{13}$, $\sin^22θ_{13}=0.108\pm0.023$ and is 2.2% probable; for inverse hierarchy, positive $θ_{13}$, $\sin^22θ_{13}=0.110\pm0.022$ and is 7.1% probable; for inverse hierarchy, negative $θ_{13}$, $\sin^22θ_{13}=0.113\pm0.022$ and is 90.5% probable, results that are inconsistent with two similar analyses.

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arXiv2012

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%.

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arXiv2010

Dark Matter Constraints from a Cosmic Index of Refraction

The dark-matter candidates of particle physics invariably possess electromagnetic interactions, if only via quantum fluctuations. Taken en masse, dark matter can thus engender an index of refraction which deviates from its vacuum value. Its presence is signaled through frequency-dependent effects in the propagation and attenuation of light. We discuss theoretical constraints on the expansion of the index of refraction with frequency, the physical interpretation of the terms, and the particular observations needed to isolate its coefficients. This, with the advent of new opportunities to view gamma-ray bursts at cosmological distance scales, gives us a new probe of dark matter and a new possibility for its direct detection. As a first application we use the time delay determined from radio afterglow observations of distant gamma-ray bursts to realize a direct limit on the electric-charge-to-mass ratio of dark matter of |varepsilon|/M < 1 x 10^{-5} eV^{-1} at 95% CL.

hep-ph↗

arXiv2010

The impact of hierarchy upon the values of neutrino mixing parameters

A neutrino-oscillation analysis is performed of the more finely binned Super-K atmospheric, MINOS, and CHOOZ data in order to examine the impact of neutrino hierarchy in this data set upon the value of $θ_{13}$ and the deviation of $θ_{23}$ from maximal mixing. Exact oscillation probabilities are used, thus incorporating all powers of $θ_{13}$ and $ε:=θ_{23}-π/4$. The extracted oscillation parameters are found to be dependent on the hierarchy, particularly for $θ_{13}$. We find at 90% CL are $Δ_{32} = 2.44^{+0.26}_{-0.20}$ and $2.48^{+0.25}_{-0.22}\times 10^{-3} {\rm eV}^2$, $ε=θ_{23}-π/4=0.06^{+0.06}_{-0.16}$ and $0.06^{+0.08}_{-0.17}$, and $θ_{13}=-0.07^{+0.18}_{-0.11}$ and $-0.13^{+0.23}_{-0.16}$, for the normal and inverted hierarchy respectively. The inverted hierarchy is preferred at a statistically insignificant level of 0.3 $σ$.

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arXiv2009

Atmospheric, long baseline, and reactor neutrino data constraints on $θ_{13}$

A new atmospheric neutrino oscillation tool which utilizes full three neutrino oscillation probabilities and a full three neutrino treatment of the MSW effect is combined with a standard analysis of the K2K, MINOS, and CHOOZ data to examine the bounds on $θ_{13}$ implied by existing data, including the recent, more finely binned, Super-K atmospheric data. In the region $L/E_ν\gtrsim 10^4$ km/GeV, we have previously found that the sub-dominant expansion does not converge and that terms linear in $θ_{13}$ can be significant. The current analysis confirms this and leads to the conclusion that $θ_{13}$ is bounded from above by the atmospheric data while CHOOZ provides the lower bound. We trace the origin of this result to fully contained data in the previously mentioned very long baseline region, to a combination of a quadratic in $θ_{13}$ term in ${\mathcal P}_{ee}$ and a linear term in ${\mathcal P}_{eμ}$ and their contribution to $R_e$, a broad MSW resonance for the solar mass-squared difference at 180 MeV, and an increase in $θ_{12}$ due to this resonant matter effect which alters the sign of the linear in $θ_{13}$ term. Assuming CP is conserved in the lepton sector, we find $θ_{13}=-0.07^{+0.18}_{-0.11}$, the asymmetry being a reflection of the importance of the linear in $θ_{13}$ terms.

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arXiv2009

Implications of the Super-K atmospheric data for the mixing angles $θ_{13}$ and $θ_{23}$

A three-neutrino analysis of oscillation data is performed using the recent, more finely binned Super-K oscillation data, together with the CHOOZ, K2K, and MINOS data. The solar parameters, $Δ_{21}$ and $θ_{12}$, are fixed from a recent analysis, and $Δ_{32}$, $θ_{13}$, and $θ_{23}$ are varied. We utilize the full three-neutrino oscillation probability and an exact treatment of the Earth's MSW effect with a castle-wall density. By including terms linear in $θ_{13}$ and $\varepsilon := θ_{23} - π/4$, we find asymmetric errors for these parameters $θ_{13}=-0.07^{+0.18}_{-0.11}$ and $\varepsilon=0.03^{+0.09}_{-0.15}$. For $θ_{13}$, we see that the lower bound is primarily set by the CHOOZ experiment while the upper bound is determined by the low energy $e$-like events in the Super-K atmospheric data. We find that the parameters $θ_{13}$ and $\varepsilon$ are correlated -- the preferred negative value of $θ_{13}$ permits the preferred value of $θ_{23}$ to be in the second octant, and the true value of $θ_{13}$ affects the allowed region for $θ_{23}$.

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arXiv2007

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 $ν_e$--$ν_μ$ 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 $θ_{13}$ were known.

hep-ph↗

arXiv2007

Comment on ``Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty''

In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del Castillo consider various symplectic structures on the classical phase space of the two-dimensional isotropic harmonic oscillator. Using Dirac's quantization condition, the authors investigate how these alternative symplectic forms affect this system's quantization. They claim that these symplectic structures result in mutually inequivalent quantum theories. In fact, we show here that there exists a unitary map between the two representation spaces so that the various quantizations are equivalent.

quant-ph↗

arXiv2007

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 $Δm^2 \cong 0.9$ 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 $Δm^2 \cong 1.9$ 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.

hep-ex↗

arXiv2005

Correlations between $θ_{13}$ and $θ_{23}$ in a very long baseline neutrino oscillation experiment

A very long baseline experiment, with $L/E$ of $1.6 \times 10^4$ m/MeV, has been proposed as the ideal means to measure $θ_{13}$, including its sign, for neutrino energies less than 50 MeV. Higher energies require consideration of the earth MSW effect. Approximating a constant density mantle, we examine the $ν_e$--$ν_μ$ and $ν_μ$--$ν_μ$ oscillation channels at very long baselines with particular focus upon the deviation of $θ_{23}$ from maximal mixing and the sign of $θ_{13}$. It is demonstrated that measurements of these oscillation channels in this region are sensitive to $θ_{13}$, including its sign, and to $θ_{23}$, including its octant, with a significant correlation between the value of $θ_{13}$ and the difference of $θ_{23}$ from maximal mixing.

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arXiv2005

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 $θ_{13}$. This is done with a mass ordering that permits the map $Δ_{31} \mapsto -Δ_{31}$. 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.

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arXiv2005

Neutrino oscillations: measuring $θ_{13}$ including its sign

In neutrino phenomenology, terms in the oscillation probabilities linear in $\sin θ_{13}$ lead naturally to the question ``How can one measure $θ_{13}$ including its sign?'' Here we demonstrate analytically and with a simulation of neutrino data that ${\mathcal P}_{eμ}$ and ${\mathcal {P}_{μμ}$ at $L/E = 2π/Δ_{21}$ exhibit significant linear dependence on $θ_{13}$ in the limit of vacuum oscillations. Measurements at this particular value of $L/E$ can thus determine not only $θ_{13}$ but also its sign, if CP violation is small.

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arXiv2004

Analysis of three-neutrino oscillations in the full mixing angle space

We use a model, with no CP violation, of the world's neutrino oscillation data, excluding the LSND experiments, and search the full parameter space ($0\leqθ_{12} \le π/2$; $-π/2 \le θ_{13} \le π/2$; and 0\leqθ_{23} \le π/2$) for the best fit values of the mixing angles and mass-squared differences. We find that the mixing angle $θ_{13}$ is bounded by $-0.15<θ_{13}<0.20$ with an absolute minimum at $θ_{13}=0.12$ and a local minimum at $-0.04$. The importance of the negative $θ_{13}$ region and this structure in the chi-square space has heretofore been overlooked because the factorization approximation commonly employed yields oscillation probabilities that are a function of $\sin^2θ_{13}$.

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arXiv2004

Quantizing the damped harmonic oscillator

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.

quant-ph↗

arXiv2004

Physical region for three-neutrino mixing angles

We derive a set of symmetry relations for the three-neutrino mixing angles, including the MSW matter effect. Though interesting in their own right, these relations are used to choose the physical region of the mixing angles such that oscillations are parameterized completely and uniquely. We propose that the preferred way of setting the bounds on the mixing angles should be $θ_{12} \in [0,π/2]$, $θ_{13} \in [-π/2,π/2]$, $θ_{23}\in [0,π/2]$, and $δ\in [0,π)$. No CP violation then results simply from setting $δ=0$. In the presence of the MSW effect, this choice of bounds is a new result. Since the size of the asymmetry about $θ_{13} = 0$ is dependent on the details of the data analysis and is a part of the results of the analysis, we argue that the negative values of $θ_{13}$ should not be ignored.

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arXiv2004

Bounds on the angles for the parameterization of three neutrino mixing

An algebraic approach is used to derive symmetry relations for the parameterization of the three neutrino mixing matrix. The symmetry relations imply bounds on the mixing angles. Including a CP violating phase $δ$, the mixing angles $θ_{jk}$ lie in the range [0,$π$/2], and $δ$ lies within [0,$2π$). If one restricts the CP phase $δ\in [0,π)$, then one must extend the range of either $θ_{12}$ {\it or} $θ_{23}$ to $[0, π)$. In particular, for no CP violation, one can set $δ=0$ {\it and} $δ=π$ with $θ_{jk}$ in the range [0,$π$/2]. Alternatively, one can set $δ=0$ only, and allow either $θ_{12}$ {\it or} $θ_{23}$ to lie within [0,$π$).

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