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.
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.
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.
122319907
The propagation of an interacting spin one field
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.
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.
119278741
Some radiative corrections to neutrino scattering: Neutral currents
With the advent of high precision neutrino scattering experiments comes the need for improved radiative corrections. We present a phenomenological analysis of some contributions to the production of photons in neutrino neutral current scattering that are relevant to experiments subsuming the 1 % level of accuracy.
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.
12442898
What can we learn from neutrino electron scattering
Precision tests of the standard model are essential for constraining models of new physics. Neutrino-electron elastic scattering offers a clean probe into many electroweak effects that are complimentary to the more canonical measurements done at collider facilities. Such reactions are rare, even as compared with the already tiny cross sections for neutrino-nucleon scattering, and competitive precision measurements have historically been challenging to obtain. Because of new existing and proposed high-flux neutrino sources, this is about to change. We present a topical survey of precision measurements that can be done with neutrino-electron scattering in light of these new developments. Specifically, we consider four distinct neutrino sources: nuclear reactors, neutrino factories, beta beams, and conventional beams. For each source we estimate the expected future precision of several representative observables, including the weak mixing angle, neutrino magnetic moments, and potential leptonic ${Z}^{\ensuremath{'}}$ couplings. We find that future neutrino-electron scattering experiments should add nontrivially to our understanding of fundamental physics.
118402093
Minimally Allowed beta beta 0 nu Rates From Approximate Flavor Symmetries
Neutrinoless double beta decay ({beta}{beta}0{nu}) is the only realistic probe of Majorana neutrinos. In the standard scenario, dominated by light neutrino exchange, the process amplitude is proportional to m{sub ee} , the e - e element of the Majorana mass matrix. This is expected to hold true for small {beta}{beta}{nu} rates ({Gamma}{sub {beta}{beta}0{nu}}), even in the presence of new physics. Naively, current data allows for vanishing m{sub ee} , but this should be protected by an appropriate flavor symmetry. All such symmetries lead to mass matrices inconsistent with oscillation phenomenology. Hence, Majorana neutrinos imply nonzero {Gamma}{sub {beta}{beta}0{nu}}. I perform a spurion analysis to break all possible abelian symmetries that guarantee {Gamma}{sub {beta}{beta}0{nu}} = 0 and search for minimally allowed m{sub ee} values. Specifically, I survey 259 broken structures to yield m{sub ee} values and current phenomenological constraints under a variety of scenarios. This analysis also extracts predictions for both neutrino oscillation parameters and kinematic quantities. Assuming reasonable tuning levels, I find that m{sub ee} > 4 x 10{sup -6} eV at 99% confidence. Bounds below this value would indicate the Dirac neutrino nature or the existence of new light (eV-MeV scale) degrees of freedom that can potentially be probed elsewhere.more » This limit can be raised by improvements in neutrino parameter measurements, particularly of the reactor mixing angle, depending on the best fit parameter values. Such improvements will also significantly constrain the available model space and aid in future constructions.« less
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