Limits on the neutron-antineutron oscillation time from the stability of nuclei

We refute a recent claim by Nazaruk that the limits placed on the free--space neutron--antineutron oscillation time $\tau_{{n\bar n}}$ can be improved by many orders of magnitude with respect to the estimate $\tau_{{n\bar n}}>2(T_0/\Gamma)^{1/2}$, where $T_0$ is a measured limit on the annihilation lifetime of a nucleus and $\Gamma\sim 100$ MeV is a typical antineutron-nucleus annihilation width.Comment: 4 pages, Latex, submitted to Physics Letters

The Pion in Electromagnetic and Weak Neutral Current Nuclear Response Functions

The impact of pionic correlations and meson--exchange currents in determining the (vector) response functions for electroweak quasielastic lepton scattering from nuclei is discussed. The approach taken builds on previous work where the Fermi gas model is used to maintain consistency in treating forces and currents (gauge invariance) and to provide a Lorentz covariant framework. Results obtained in first-order perturbation theory are compared with infinite-order summation schemes (HF and RPA) and found to provide quite successful approximations for the quasielastic response functions. The role of pionic correlations in hardening the responses R_L and R_T is investigated in some detail, including studies of the relative importance of central and tensor pieces of the force and of exchange and self-energy diagrams; in addition, their role in significantly modifying the longitudinal parity-violating response R_{AV}^L is explored. The MEC are shown to provide a small, but non-negligible, contribution in determining the vector responses.Comment: TeX, 21 figures (Postscript, available from the authors), MIT preprint CTP\#219

Influence of nucleonic motion in Relativistic Fermi Gas inclusive responses

Impulsive hadronic descriptions of electroweak processes in nuclei involve two distinctly different elements: one stems from the nuclear many-body physics --- the medium --- which is rather similar for the various inclusive response functions, and the other embodies the responses of the hadrons themselves to the electroweak probe and varies with the channel selected. In this letter we investigate within the context of the relativistic Fermi gas in both the quasi-elastic and $N\to\Delta$ regimes the interplay between these two elements. Specifically, we focus on expansions in the one small parameter in the problem, namely, the momentum of a nucleon in the initial wave function compared with the hadronic scale, the nucleon mass. Both parity-conserving and -violating inclusive responses are studied and the interplay between longitudinal ($L$) and transverse ($T$ and $T'$) contributions is highlighted.Comment: 11 pages, 1 figur

Feynman Diagrams and Rooted Maps

The Rooted Maps Theory, a branch of the Theory of Homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The numerical correspondence between the number of this class of Feynman diagrams as a function of perturbative order and the number of rooted maps as a function of the number of edges is studied. A graphical procedure to associate Feynman diagrams and rooted maps is then stated. Finally, starting from rooted maps principles, an original definition of the genus of a Feynman diagram, which totally differs from the usual one, is given.Comment: 20 pages, 30 figures, 3 table

Conditions for detecting CP violation via neutrinoless double beta decay

Neutrinoless double beta decay data together with information on the absolute neutrino masses obtained from the future KATRIN experiment and/or astrophysical measurements give a chance to find CP violation in the lepton sector with Majorana neutrinos. We derive and discuss necessary conditions which make discovery of such CP violation possible for the future neutrino oscillation and mass measurements data.Comment: 15 pages, 4 figures, RevTe

Spontaneous symmetry breaking and response functions

We study the quantum phase transition occurring in an infinite homogeneous system of spin 1/2 fermions in a non-relativistic context. As an example we consider neutrons interacting through a simple spin-spin Heisenberg force. The two critical values of the coupling strength -- signaling the onset into the system of a finite magnetization and of the total magnetization, respectively -- are found and their dependence upon the range of the interaction is explored. The spin response function of the system in the region where the spin-rotational symmetry is spontaneously broken is also studied. For a ferromagnetic interaction the spin response along the direction of the spontaneous magnetization occurs in the particle-hole continuum and displays, for not too large momentum transfers, two distinct peaks. The response along the direction orthogonal to the spontaneous magnetization displays instead, beyond a softened and depleted particle-hole continuum, a collective mode to be identified with a Goldstone boson of type II. Notably, the random phase approximation on a Hartree-Fock basis accounts for it, in particular for its quadratic -- close to the origin -- dispersion relation. It is shown that the Goldstone boson contributes to the saturation of the energy-weighted sum rule for ~25% when the system becomes fully magnetized (that is in correspondence of the upper critical value of the interaction strength) and continues to grow as the interaction strength increases.Comment: 36 pages, 17 figure