Delta decuplet in a helicity basis

[metter]

Does anyone has any idea how the spinors of the 3/2 particles look in the helicity basis?
Basically, I'm trying to calculate a Feynman diagram for a nucleon Delta scattering, keeping the helicity inices explitly.

I've had a look at this:

http://arxiv.org/PS_cache/hep-th/pdf/0108/0108030v1.pdf

and

http://www.iop.org/EJ/article/0370-1328/91/3/308/prv91i3p577.pdf?request-id=a221633a-40c5-4f19-a3ec-a3e42bb988b3

but it's still not clear to me.
Thank you for the help.

 

[AndyW]

As a scientist familiar with particle physics and Feynman diagrams, I can offer some insight into the spinors of 3/2 particles in the helicity basis.

Firstly, it is important to understand that spinors represent the intrinsic angular momentum (spin) of a particle. In the helicity basis, spin is measured along the direction of motion of the particle.

For 3/2 particles, there are four spin states corresponding to four different helicities: +3/2, +1/2, -1/2, and -3/2. These states can be represented by four-component spinors, also known as Rarita-Schwinger spinors.

The Rarita-Schwinger spinor can be written as a linear combination of two Weyl spinors, corresponding to the left- and right-handed components of the particle's spin. The explicit form of the spinor can be found in the papers you have referenced, but it is a complex four-component vector with specific coefficients for each helicity state.

Now, in order to calculate a Feynman diagram for a nucleon Delta scattering, you will need to use the Feynman rules for spinors. These rules dictate how to manipulate the spinors in the diagram to calculate the amplitude of the process. These rules can also be found in the papers you have referenced, or in textbooks on quantum field theory.

In summary, the spinors of 3/2 particles in the helicity basis are complex four-component vectors that represent the different spin states of the particle. Understanding the Feynman rules for spinors will allow you to calculate the Feynman diagram for the nucleon Delta scattering process. I hope this helps clarify the concept for you. Best of luck with your calculations!

 

[sir-pinski]

The Delta decuplet is a group of baryon particles consisting of four Delta resonances, each with a spin of 3/2. In the helicity basis, the spin states of these particles are described by helicity spinors, which are two-component spinors that represent the particle's spin along the direction of motion.

To calculate a Feynman diagram for a nucleon Delta scattering in the helicity basis, you will need to use the helicity spinors for the Delta particles. These spinors can be derived from the Dirac spinors, which describe the spin states of fermions in the standard basis. The helicity spinors can also be found in the papers you have referenced, but it may take some time and effort to understand them fully.

One way to understand the helicity spinors is to think of them as representing the projection of the particle's spin onto the direction of motion. In the case of the Delta decuplet, the spin is always aligned with the direction of motion, so the helicity spinors will have a definite value of +1/2 or -1/2.

In order to calculate the Feynman diagram, you will also need to understand the interaction between the nucleon and the Delta particles, which is described by the relevant coupling constants. These coupling constants can be found in the literature or calculated using theoretical models.

Overall, understanding the helicity spinors and the interaction between the particles will be crucial in calculating the Feynman diagram accurately. It may take some time and effort to fully comprehend these concepts, but with persistence and further research, you will be able to successfully calculate the diagram.