Wave Functions for Particles of Higher Spin

Two-component spinors are the basic ingredients for describing fermions in quantum field theory in 3 + 1 spacetime dimensions. We develop and review the techniques of the twocomponent spinor formalism and provide a complete set of Feynman rules for fermions using two-component spinor notation. These rules are suitable for practical calculations of crosssections, decay rates, and radiative corrections in the Standard Model and its extensions, including supersymmetry, and many explicit examples are provided. The unified treatment presented in this review applies to massless Weyl fermions and massive Dirac and Majorana fermions. We exhibit the relation between the two-component spinor formalism and the more traditional four-component spinor formalism, and indicate their connections to the spinor helicity method and techniques for the computation of helicity amplitudes.

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“…Hence, in this convention χ s (ŝ) = D(φ , θ)χ s (ẑ), which is the most common choice for the spinor wave function [36,254,255].…”

Section: C1 Fixed-axis Spinor Wave Functionsmentioning

confidence: 99%

Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry

Dreiner¹,

Haber²,

Martin³

2010

Physics Reports

434

462

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“…where we use the Jacob-Wick convention for the helicity polarization four-vectors as written down in [25]. The z-direction is defined by the momentum of the J/ψ.…”

Section: Appendix A: Helicity and Multipole Amplitudesmentioning

confidence: 99%

One-photon decay of the tetraquark stateX(3872)→γ+J/ψin a relativistic constituent quark model with infrared confinement

et al. 2011

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We further explore the consequences of treating the X(3872) meson as a tetraquark bound state by analyzing its one-photon decay X → γ +J/ψ in the framework of our approach developed in previous papers which incorporates quark confinement in an effective way. To introduce electromagnetism we gauge a nonlocal effective Lagrangian describing the interaction of the X(3872) meson with its four constituent quarks by using the P-exponential path-independent formalism. We calculate the matrix element of the transition X → γ + J/ψ and prove its gauge invariance. We evaluate the X → γ + J/ψ decay width and the longitudinal/transverse composition of the J/ψ in this decay. For a reasonable value of the size parameter of the X(3872) meson we find consistency with the available experimental data. We also calculate the helicity and multipole amplitudes of the process, and describe how they can be obtained from the covariant transition amplitude by covariant projection.

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“…The gravitino in the general theory with spontaneously broken supersymmetry will be massive. The states of a free massive spin-3 2 particle were studied by Auvil and Brehm in [37] (see also [24] for a nice review). A free massive gravitino has γ · ψ = 0.…”

Section: Introductionmentioning

confidence: 99%

Superconformal symmetry, supergravity and cosmology

Каллош

Kofman

Linde

et al. 2000

Class. Quantum Grav.

172

300

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We introduce the general N = 1 gauge theory superconformally coupled to supergravity. The theory has local SU (2, 2|1) symmetry and no dimensional parameters. The superconformal origin of the Fayet-Iliopoulos (FI) terms is clarified. The phase of this theory with spontaneously broken conformal symmetry gives various formulations of N = 1 supergravity interacting with matter, depending on the choice of the R-symmetry fixing.We have found that the locally superconformal theory is useful for describing the physics of the early universe with a conformally flat FRW metric. Few applications of superconformal theory to cosmology include the study of i) particle production after inflation, particularly the nonconformal helicity-1 2 states of gravitino, ii) the super-Higgs effect in cosmology and the derivation of the equations for the gravitino interacting with any number of chiral and vector multiplets in the gravitational background with varying scalar fields, iii) the weak-coupling limit of supergravity M P → ∞ and gravitino-goldstino equivalence. This explains why gravitino production in the early universe is not suppressed in the limit of weak gravitational coupling.We discuss the possible existence of an unbroken phase of the superconformal theories, interpreted as a strong-coupling limit of supergravity M P → 0. † On leave of absence from Stanford University until 1 September 2000 ‡ Onderzoeksdirecteur, FWO, Belgium

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Wave Functions for Particles of Higher Spin

Abstract: A simple method is presented for constructing wave functions for particles of arbitrary spin. These are helicity eigenstates and satisfy the Rarita-Schwinger equation. The wave functions are given explicitly.

Cited by 85 publications

References 6 publications

Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry

Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry

One-photon decay of the tetraquark stateX(3872)→γ+J/ψin a relativistic constituent quark model with infrared confinement

Superconformal symmetry, supergravity and cosmology

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