A prescription for projectors to compute helicity amplitudes in D dimensions

This article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor decomposition and avoids also dimensional splitting. Because of the latter, commutation between Lorentz index contraction and loop integration is preserved within this prescription, which entails certain technical advantages. The usage of these D-dimensional polarized amplitude projectors results in helicity amplitudes that can be expressed solely in terms of external momenta, but different from those defined in the existing dimensional regularization schemes. Furthermore, we argue that despite being different from the conventional dimensional regularization scheme (CDR), owing to the amplitude-level factorization of ultraviolet and infrared singularities, our prescription can be used, within an infrared subtraction framework, in a hybrid way without re-calculating the (process-independent) integrated subtraction coefficients, many of which are available in CDR. This hybrid CDR-compatible prescription is shown to be unitary. We include two examples to demonstrate this explicitly and also to illustrate its usage in practice.

A NEW APPROACH TO THE RELATIVISTIC TREATMENT OF THE FERMION–BOSON SYSTEM, BASED ON THE EXTENSION OF THE SL(2, C) GROUP

A new technique for constructing the relativistic wave equation for the two-body system composed of the spin-1/2 and spin-0 particles is proposed. The method is based on the extension of the SL (2, C) group to the Sp (4, C) one. The obtained equation includes the interaction potentials, having both the Lorentz-vector and Lorentz-tensor structure, exactly describes the relativistic kinematics and possesses the correct one-particle limits. The comparison with results of other approaches to this problem is discussed.

Lorentz Multiplet Structure of Baryon Spectra and Relativistic Description

The pole positions of the various baryon resonances are known to reveal well-pronounced clustering, so-called Höhler clusters. For nonstrange baryons, the Höhler clusters are shown to be identical to Lorentz multiplets of the type {j,j}⊗[{1/2,0} ⊕ {0,1/2}] with j being a half-integer. For the Λ hyperons below 1,800 MeV, these clusters are shown to be of the type {1,0} ⊕ {0,1} ⊗ [{1/2,0} ⊕ {0,1/2}] while above 1,800 MeV they are parity duplicated {J,0} ⊕ {0,J} higher-spin (Weinberg–Ahluwalia) states. Therefore, for Λ hyperons the restoration of chiral symmetry takes place above 1,800 MeV. Finally, it is demonstrated that the description of spin-3/2 particles in terms of a second rank antisymmetric Lorentz tensor with Dirac spinor components does not contain any off-shell parameters and avoids the main difficulties of the Rarita–Schwinger description based on a four-vector with Dirac spinor components.