Missing energy and the measurement of the CP-violating phase in neutrino oscillations

In the next generation of long-baseline neutrino oscillation experiments, aiming to determine the charge-parity violating phase $\delta_{CP}$ in the appearance channel, fine-grained time-projection chambers are expected to play an important role. In this Letter, we analyze an influence of realistic detector capabilities on the $\delta_{CP}$ sensitivity for a setup similar to that of the Deep Underground Neutrino Experiment. We find that the effect of the missing energy, carried out by undetected particles, is sizable. Although the reconstructed neutrino energy can be corrected for the missing energy, the accuracy of such procedure has to exceed 20\%, to avoid a sizable bias in the extracted $\delta_{CP}$ value.Comment: 6 pages, 2 figures. v2 matches the version published in PR

Gauge dependence in topological gauge theories

We parametrize the gauge-fixing freedom in choosing the Lagrangian of a topological gauge theory. We compute the gauge-fixing dependence of correlators of equivariant operators when the compactified moduli space has a non-empty boundary and verify that only a subset of these has a gauge independent meaning. We analyze in detail a simple example of such anomalous topological theories, 4D topological Yang-Mills on the four-sphere and instanton number k=1.Comment: 12 pages, TeX , harvma

A lagrangian formulation of 2-dimensional topological gravity and Cech-de Rham cohomology

We present a very simplified analysis of how one can overcome the Gribov problem in a non-abelian gauge theory. Our formulae, albeit quite simplified, show that possible breakdowns of the Slavnov-Taylor identity could in principle come from singularities in space of gauge orbits. To test these ideas we exhibit the calculation of a very simple correlation function of 2-dimensional topological gravity and we show how in this model the singularities of the moduli space induce a breakdown of the Slavnov-Taylor identity. We comment on the technical relevance of the possibility of including the singularities into a finite number of cells of the moduli space

Weak commutation relations of unbounded operators and applications

Four possible definitions of the commutation relation [S,T]=\Id of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space \H where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.Comment: In press in Journal of Mathematical Physic

Genus bounds for minimal surfaces arising from min-max constructions

In this paper we prove genus bounds for closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments. A stronger estimate was announced by Pitts and Rubistein but to our knowledge its proof has never been published. Our proof follows ideas of Simon and uses an extension of a famous result of Meeks, Simon and Yau on the convergence of minimizing sequences of isotopic surfaces. This result is proved in the second part of the paper.Comment: Accepted for publication on Journal for Pure and Applied Mathematic

Weak commutation relations of unbounded operators: nonlinear extensions

We continue our analysis of the consequences of the commutation relation [S,T]=\Id, where $S$ and $T$ are two closable unbounded operators. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space \H where the operators act. {We also consider what we call, adopting a physical terminology}, a {\em nonlinear} extension of the above commutation relations

Comparison of the calorimetric and kinematic methods of neutrino energy reconstruction in disappearance experiments

To be able to achieve their physics goals, future neutrino-oscillation experiments will need to reconstruct the neutrino energy with very high accuracy. In this work, we analyze how the energy reconstruction may be affected by realistic detection capabilities, such as energy resolutions, efficiencies, and thresholds. This allows us to estimate how well the detector performance needs to be determined a priori in order to avoid a sizable bias in the measurement of the relevant oscillation parameters. We compare the kinematic and calorimetric methods of energy reconstruction in the context of two muon-neutrino disappearance experiments operating in different energy regimes. For the calorimetric reconstruction method, we find that the detector performance has to be estimated with a ~10% accuracy to avoid a significant bias in the extracted oscillation parameters. On the other hand, in the case of kinematic energy reconstruction, we observe that the results exhibit less sensitivity to an overestimation of the detector capabilities.Comment: 16 pages, 14 figures, matches the version published in Phys. Rev.