Helicity-coupling amplitudes in tensor formalism

Journal Article · Sun Aug 01 04:00:00 EDT 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.48.1225· OSTI ID:6379775

Chung, S U ^[1]

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1. Institut fuer Physik, Johannes-Gutenberg-Universitaet, 6500 Mainz (Germany)

The decay of a particle with spin to two other particles with spin is best described in the helicity formalism. It is the purpose of this paper to show that the helicity-coupling amplitudes, which appear in the angular distributions, can be expressed in terms of the covariant amplitudes in the tensor formalism. This allows for a systematic derivation for the energy dependence of the helicity-coupling amplitudes within the framework of the tensor formalism. The concept of pure intrinsic spin has been developed in the tensor formalism, for decays involving two spins in the final state, in order to bring the formalism to a form comparable to the standard [ital lS]-coupling scheme. Among several examples worked out in this paper are those involving spin-0, spin-1, or spin-2 states in the initial and the final systems and, in particular, a spin-1 state coupling to two spin-1 final states. The latter example is then specialized to the [ital J]/[psi] radiative decays into a pseudovector ([ital J][sup [ital P][ital C]]=1[sup ++]) or into a vector ([ital J][sup [ital P][ital C]]=1[sup [minus]+]) which is exotic, i.e., not a quarkonium. Orbital angular momenta up to [ital l]=4 have been included in the examples; in particular, the decay [pi][sub 2](1670)[r arrow][ital f][sub 2](1270)+[pi], which involves three [ital l]'s ([ital l]=0, 2, and 4), is shown to exhibit a complicated energy-dependent form for the helicity-coupling amplitude.

• OSTI ID: 6379775
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 48:3; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ANGULAR DISTRIBUTION
ANGULAR MOMENTUM
DECAY AMPLITUDES
DISTRIBUTION
ENERGY DEPENDENCE
FUNCTIONS
HELICITY
INVARIANCE PRINCIPLES
LORENTZ INVARIANCE
PARTICLE PROPERTIES
SPIN
TENSORS
TRANSITION AMPLITUDES
WAVE FUNCTIONS