Abstract
Using elementary considerations of Lorentz invariance, Bose symmetry and BRST invariance, we argue why the decay of a massive color-octet vector state into a pair of on-shell massless gluons is possible in a non-Abelian SU(N) Yang–Mills theory, we constrain the form of the amplitude of the process and offer a simple understanding of these results in terms of effective-action operators.
Highlights
The Landau–Yang theorem states that a massive vector particle cannot decay into two on-shell massless photons
In this note we analyze in depth the origin of the cancellation at tree level and the structure of the amplitude in full generality, we explore where the proof of a would-be Landau–Yang theorem for colored states fails, and derive constraints on the form of the amplitude for the decay of a massive vector color-octet in two massless gluons
In this note we have considered the process where a massive, color-octet vector state decays into two on-shell massless gluons
Summary
The Landau–Yang theorem states that a massive vector (i.e. spin 1) particle cannot decay into two on-shell massless photons. This process is of phenomenological interest for models predicting the existence of colored massive vector particles, and for heavy quarkonium physics, e.g. for the hadroproduction of a J /ψ particle or its decay into hadrons.1 Evidence that this amplitude vanishes at tree-level has been given many times in Quantum Chromodynamics (QCD), usually by explicitly calculating the two-gluon decay of a quark–antiquark pair projected onto a massive coloroctet spin-1, S-wave state that we denote as (Q Q )(J8=), see e.g. Refs. For a number of years no attempt was apparently made to study the color-octet case in more detail or to explicitly check if the vanishing of the amplitude at tree level still held at higher orders This situation began to change only recently, when two calculations found non-zero results for the one-loop amplitude of the transition between a massive color-octet vector state and two massless gluons: Ref. Cacciari et al / Physics Letters B 753 (2016) 476–481 one-loop and beyond, and show how the LY theorem (or its failure) can be understood in a very direct and simple way at the operator level
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