122319907
The propagation of an interacting spin one field
125191465
On the role of fixed angular-momentum-plane branch points, with regard to thet = 0 singularity structure of Reggeized scattering amplitudes
SummaryA generating function for the Feynman amplitude for the scattering of four massive spinless particles due to the exchange of a spin-J particle, described by a (J, 0) field of Weinberg, is obtained. The amplitude is then Reggeized by way of the Van Hove model, and the resulting Reggeized amplitude is found to receive contributions from a single Regge pole, and a sequence of fixedJ-plane branch points. The leading fixed branch point is shown to play an important role with regard to thet=0 singularity structure of the Reggeized amplitude, whilst the secondary fixed branch points are of no obvious significance. Also, within the context of the Van Hove model, connections between thet=0 singularity structure of Reggeized scattering amplitudes and the choice of interaction Hamiltonian density, are discussed.RiassuntoSi ottiene una funzione generatrice per l’ampiezza di Feynman dello scattering di quattro particelle senza spin, ma con massa, dovuto allo scambio di una particella con spinJ, descritto da un campo di Weinberg (J, 0). Si reggeizza poi l’ampiezza tramite il modello di Van Hove, e si trova l’ampiezza reggeizzata risultante ricevere contributi da un singolo polo di Regge, ed una sequenza di punti di ramificazione fissi del pianoJ. Si mostra che il punto di diramazione fisso principale giuoca un ruolo importante rispetto alla struttura della singolaritàt=0 dell’ampiezza reggeizzata, mentre i punti di diramazione fissi secondari non hanno un ovvio significato. Si discutono anche, nel contesto del modello di Van Hove, le connessioni fra la struttura della singolaritàt=0 delle ampiezze di scattering reggeizzate e la scelta delle densità dell’hamiltoniano di interazione.РеэюмеВыводится проиэводяшая функция для фейнмановской амплитуды для рассеяния четырех массивных бесспиновых частиц вследствие обмена частицей со спиномJ, которая описывается полем (J, 0) Вейнберга. Затем с помошью модели Ван Хова зта амплитуда реджеиэуется. Обнаружено, что реэультируюшая реджеи-эованная амплитуда содержит вклады от отдельного полюса Редже и последовательности фиксированных точек ветвления вJ-плоскости. Покаэывается, что главная фиксированная точка ветвления играет важную роль в структуре сингулярности приt=0 реджеиэованной амплитуды, тогда как вторичные фиксированные точки ветвления не имеют явного смысла. В свяэи с моделью Ван Хова также обсуждается свяэь между структурой сингулярности приt=0 реджеиэованных амплитуд рассеяния и выбором плотности Гамильтониана вэаимодействия.
121923701
Constraints, causality and Lorentz invariance
Simple theories of interacting classical relativistic massive spin-1 and spin-3/2 fields are studied. In these examples, it is found that if a theory is acausal in the sense of Velo and Zwanziger, it is also not Lorentz covariant. The breakdown of Lorentz covariance is seen to manifest itself in the constraints, which must be satisfied by the interacting fields, not determining all the dependent fields components simultaneously in all inertial frames of reference. Some remarks on the present state of massive spin-3/2 theories are made.
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.
118501099
Daughters and Weinberg field theory
SummaryA recurrence relation is obtained for the Feynman amplitude for the scattering of four spinless particles due to the exchange of a particle with spinJ, described by a (J, 0) field of Weinberg. It is shown that lower-spin contributions still occur in the amplitude, even though there are no redundant components in the spinor field.RiassuntoSi ottiene una relazione di ricorrenza per l'ampiezza di Feynmann dello scattering di quattro particelle prive di spin dovuto allo scambio di una particella di spinJ, descritto da un campo (J, 0) di Weinberg. Si dimostra che nell'ampiezza si ha ancora il contributo dello spin minore, anche se nel campo spinoriale non si hanno componenti ridondanti.РезюмеПолучается рекурентное соотношение для фейнмановской амплитуды рассеяния четырех бесспиновых частиц, обусловленное обменом частицы со спиномJ, которая описывается (J, 0) полем Вейнберга. Показывается, что в амплитуде все же имеется вклад от более низкого спина, даже если не существуют ишбыточные компоненты в спинорном поле.
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.
117798634
Non-oscillation probes of the neutrino mass hierarchy and vanishing |U(e3)|
One of the outstanding issues in neutrino physics is the experimental determination of the neutrino mass hierarchy: Is the order of the neutrino masses ``normal'' - m_1^2<m_2^2<m_3^2 - or is it inverted - m_3^2<m_1^2<m_2^2, with m_2^2-m_1^2 << m_2^2,m_1^2? While this issue can be resolved in next-generation long-baseline nu_{mu} to nu_e neutrino oscillation studies if |U_{e3}|^2 is large enough, a clear strategy on how to resolve it if |U_{e3}|^2 is sufficiently small is still lacking. We study the capability of non-oscillation probes of neutrino masses to determine the neutrino mass ordering. We concentrate on studies of m_{nu_e}, the kinematical neutrino mass to which precise studies of tritium beta-decay are sensitive, m_{ee}, the effective mass to which the rate for neutrinoless double-beta decay is sensitive if the neutrinos are Majorana fermions, and Sigma, the sum of the neutrino masses, to which cosmological probes of the energy budget of the Universe are sensitive. We find that combined measurements of m_{ee}, Sigma, and m_{nu_e} are capable of establishing the neutrino mass hierarchy if these measurements are precise enough and if one ``gets lucky.'' We quantify the previous sentence in detail by performing a numerical analysis of a large number of theoretical data sets, for different measured values of m_{nu_e}, m_{ee}, and Sigma, keeping in mind the ultimate sensitivity that can be reached by next (and next-to-next) generation experiments.
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.
118491521
Model independent explorations of Majorana neutrino mass origins
The scale of neutrino mass generation may be too large to explore directly, but useful information may still be extracted from independent experimental channels. Here I survey various model independent probes of Majorana neutrino mass origins. An introduction to the concepts relevant to the analysis is followed by a discussion of the physical ranges of neutrino parameters within the context of standard and non-standard interactions. Armed with this, I move on to systematically analyze the properties of radiatively generated neutrino masses induced by nonrenormalizable lepton number violating effective operators of mass dimensions five through eleven. By fitting these to the observed light mass scale, I extract predictions for neutrino mixing as well as neutrinoless double beta decay, rare meson/tau decays and collider phenomenology. I find that many such models are already constrained by current data and many more will be probed in the near future. I then move on demonstrate the utility of a low scale seesaw mechanism via a viable sterile neutrino model that satisfies all oscillation data as well as solves problems associated with supernova kicks and heavy element nucleosynthesis. From this I extract predictions for tritium and neutrinoless double beta decay searches.
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