122775679
An equivalence theorem for a massive spin one particle interacting with Dirac particles in quantum field theory
The (1,0)(+)(0,1) massive spin one field phi mu nu (x) is quantized following the method of Takahashi and Umezawa (1953). The interaction Hamiltonian in the interaction picture is then calculated for such a field interacting in a simple way with Dirac fields. In contrast with a remark of Kyriakopoulos (1969) the generalized Matthews' theorem is found to apply to the calculation of S matrix elements. The analogous theory in terms of the Proca field is given in outline, and the two theories are found to be inequivalent. A discussion of how the inequivalence arises is given; then it is demonstrated how equivalent theories may be constructed, and the equivalence is proved.
120287965
Some remarks on causality, Lorentz invariance and the generalized Matthews' rule for a massive spin one vector field in an external potential
A massive spin one vector field is quantized in the presence of an external potential, with source linear in the vector field, to provide an illustration of the aspects of a quantum theory in an external potential, which are reflections of the causal nature of the corresponding classical theory. In the examples considered, the S operator of the quantum theory is found to be Lorentz invariant or not, according as the corresponding classical theory is causal or not. The normal dependence of the interaction hamiltonian, and the applicability of the generalized Matthews' rule are also discussed.
120856316
The electromagnetic interaction of a massive spin one particle: some equivalence theorems and remarks
The minimal electromagnetic interaction is introduced into various free, quantum mechanical spin one formalisms, and it is found that the resulting theories are essentially equivalent. The situation does not prevail when, in addition, magnetic dipole or electric quadrupole interactions are considered. For simple such interactions in one formalism are found, in general, to be equivalent to structurally more complicated interactions in the other formalisms considered. Some known results on the acausal propagation of solutions of wave equations for a classical spin one particle in an external electromagnetic field are, with the aid of the above equivalence theorems, which are easily seen to apply to the classical case also, extended to include all the spin one formalisms considered herein.
122271673
Discrete symmetries and supersymmetry
The charge conjugation and parity transformation properties of the supersymmetry algebra with SU(N), of Dondi (1975), are discussed. It is shown when and how this algebra may be modified to accommodate charge conjugation or parity invariance.
122658441
On the possibility of breakdown of Lorentz invariance in the Takahashi-Umezawa quantization method
The Stuckelberg formalism for a massive spin-one field interacting with external potentials is quantized following the method of Takahashi and Umezawa. It is shown how the characteristic determinant of the field equations, which, in an earlier paper, was shown to have the same form as the Lee-yang determinant, for such a theory, determines the possibility of breakdown of Lorentz invariance in the procedure of the Takahashi-Umezawa quantization method.
123580085
The relationship between causality, in a classical relativistic field theory, and Lorentz invariance in the corresponding quantum theory, for a massive spin-one field in external potentials
A massive spin-one field, interacting with external potentials, is described in terms of the Stuckelberg formalism (1938). Some points, concerning necessary and sufficient conditions for the classical theory to be causal, in the sense of Velo and Zwanziger (1969 and 1971) are clarified. It is then shown that with a simple restriction on the type of interaction considered, the classical theory is causal, in the above sense, if and only if the corresponding quantum theory is Lorentz invariant, in that the S operator in the interaction picture is normal independent. Incidental in this demonstration is the result that the characteristic and Lee-Yang determinants share the same form. It is indicated how this result generalized to interactions between Stuckelberg, Klein-Gordon and electromagnetic fields and the validity of the result, in the more usual vector formalism is established.
121227319
What is the Energy Scale of the Physics Responsible for Neutrino Masses
The observed tiny but non-zero neutrino masses are often interpreted as evidence for new physics at energy scales above 1010 TeV. This statement is based on several assumptions, including (a) neutrinos are Ma-jorana fermions, (b) the physics responsible for neutrino masses is not very weakly coupled, and (c) the new physics sector – responsible for lepton number breaking – couples to the Standard Model in a 'simple' way. We point out that the issue of the energy scale associated to neutrino masses is far from a resolved and that we should turn to data in order to elucidate it. In particular, if one opts out of (c), the new physics responsible for neutrino masses could be associated to energy scales anywhere between 0.1 and 1012 TeV, even if one assumes that the new physics couplings to the standard model are order one. We study the neutrino phenomenology of all possible effective operators that break lepton number by two units and use those as estimates of the effect of 'all' models of high energy lepton-number breaking. We then estimate the effects of these different types of new physics on other lepton-number violating observables, including neutrinoless double-beta decay, collider signatures, and rare meson decays.
119609735
Survey of lepton number violation via effective operators
We survey 129 lepton number violating effective operators, consistent with the minimal standard model gauge group and particle content, of mass dimension up to and including 11. Upon requiring that each one radiatively generates the observed neutrino masses, we extract an associated characteristic cutoff energy scale which we use to calculate other observable manifestations of these operators for a number of current and future experimental probes, concentrating on lepton number violating phenomena. These include searches for neutrinoless double-beta decay and rare meson, lepton, and gauge boson decays. We also consider searches at hadron/lepton collider facilities in anticipation of the CERN LHC and the future ILC. We find that some operators are already disfavored by current data, while more are ripe to be probed by next-generation experiments. We also find that our current understanding of lepton mixing disfavors a subset of higher dimensional operators. While neutrinoless double-beta decay is the most promising signature of lepton number violation for the majority of operators, a handful is best probed by other means. We argue that a combination of constraints from various independent experimental sources will help to pinpoint the ''correct'' model of neutrino mass, or at least aid in narrowing down the setmore » of possibilities.« less
119095778
Initial optical results for the ChaMPlane Survey
We provide a brief description of the optical survey being conducted under the NOAO Long Term Surveys program in support of the Chandra Multiwavelength Plane (ChaMPlane) Survey (see paper by Grindlay et al. in this Volume). A representative photometry result is shown, along with spectroscopic followup.
118891248
Neutrino mass hierarchy, vacuum oscillations, and vanishing|Ue3|
Is the relatively isolated member of the neutrino mass spectrum heavier or lighter than the two closely-spaced members? This question--the character of the neutrino mass hierarchy--is of great theoretical interest. All previously identified experiments for addressing it via neutrino oscillations require that the currently unknown size of the U{sub e3} element of the leptonic mixing matrix (parameterized by the unknown {theta}{sub 13} mixing angle) be sufficiently large, and will utterly fail in the limit {theta}{sub 13}{yields}0. For this reason, we explore alternative oscillation approaches that would still succeed even if {theta}{sub 13} vanishes. We identify several alternatives that require neither a nonzero vertical bar U{sub e3} vertical bar nor the presence of significant matter effects (even if the latter are unavoidable in the case of long-baseline, Earth-based experiments). All include multiple percent-level neutrino oscillation measurements, usually involving muon-neutrino (or antineutrino) disappearance and very long baselines. We comment on the degree of promise that these alternative approaches show.
1539910
A phenomenological study of photon production in low energy neutrino nucleon scattering
Low energy photon production is an important background to many current and future precision neutrino experiments. We present a phenomenological study of t-channel radiative corrections to neutral current neutrino nucleus scattering. After introducing the relevant processes and phenomenological coupling constants, we will explore the derived energy and angular distributions as well as total cross-section predictions along their estimated uncertainties. This is supplemented throughout with comments on possible experimental signatures and implications. We conclude with a general discussion of the analysis in the context of complimentary methodologies.