Abstract
An efficient algorithm is developed for compactly weaving all the Lorentz covariant three-point vertices in relation to the decay of a massive particle $X$ of mass $m_X$ and spin $J$ into two particles $ M_{1,2}$ with equal mass $m$ and spin $s$. The closely-related equivalence between the helicity formalism and the covariant formulation is utilized so as to identify the basic building blocks for constructing the covariant three-point vertex corresponding to each helicity combination explicitly. The massless case with $m=0$ is worked out straightforwardly and the (anti)symmetrization of the three-point vertex required by spin statistics of identical particles is made systematically. It is shown that the off-shell electromagnetic photon coupling to the states $M_1$ and $M_2$ can be accommodated in this framework. The power of the algorithm is demonstrated with a few typical examples with specific $J$ and $s$ values.
Highlights
The Standard Model (SM) [1,2,3,4] of particle physics has been firmly established by the discovery of the spin-0 resonance of about 125 GeV mass at the Large Hadron
Even though a lot of high-energy experiments have searched for new phenomena beyond the SM (BSM) and they have tested the SM with great precision for decades, none of any BSM
We show that the massless (m 1⁄4 0) case treated previously [30] can be worked out straightforwardly and thesymmetrization of the vertex required by the spin statistics of identical particles [43] can be made systematically
Summary
The Standard Model (SM) [1,2,3,4] of particle physics has been firmly established by the discovery of the spin-0 resonance of about 125 GeV mass at the Large Hadron. We adopt the conventional description of the integer and half-integer wave tensors [33,34,35,36,37,38,39] and we effectively utilize the closely related equivalence between the helicity formalism in the Jacob-Wick (JW) convention [40,41] and the standard covariant formulation Their one-to-one correspondence enables us to identify every basic building block for constructing the covariant three-point vertex corresponding to each helicity combination explicitly.. Another convenient procedure for describing the three-point vertex of on-shell massive particles of any spin is to use a spinor formalism developed in Ref. [42]
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