Angular Distribution of Particles from Disintegration

[ziad1985]

Let's say I have one particle disintegrating, into 3 product , like b---> s + (l+) + (l-)
where b is the b quark, s is the s quark and and i have a letpon and anti-lepton.
I have calculated for example for a certain penguin diagram, the Wilson coefficients and the operators, or in simple words i have the effective Hamiltonian, how can i proceed from here, knowing the Eff H, to determine what kind of angular distribution the leptons are in?
I know this probably basic stuff but for some reason i can't find any reference for this, either I'm doing something wrong, or ?

 

[eljose79]

your first step in responding to this forum post would be to acknowledge the question and provide some background information on the topic. You could explain that this type of decay process is known as a "flavor-changing neutral current" (FCNC) and it is an important area of research in particle physics.

Next, you could explain that the effective Hamiltonian is a mathematical framework used to describe the interactions between particles and their decay products. It takes into account the contributions from all possible diagrams, including the penguin diagram mentioned in the post. This is important because it allows us to make predictions and compare them with experimental data.

To determine the angular distribution of the leptons in this specific decay process, you would need to use the effective Hamiltonian to calculate the decay rate. This can be done using Feynman diagrams and other mathematical techniques. The decay rate is related to the angular distribution through a mathematical relationship known as the decay amplitude. By calculating the decay amplitude, you can then determine the angular distribution of the leptons.

It is important to note that the effective Hamiltonian is a theoretical framework and the results obtained from it need to be verified through experimental data. So, the next step would be to compare your theoretical predictions with experimental results to see if they match. If there is a discrepancy, it could indicate the need for further research or modifications to the theoretical model.

In conclusion, as a scientist, your role would be to use the knowledge and tools available to you to make predictions and test them against experimental data. This process of theory and experiment is crucial in advancing our understanding of the fundamental particles and their interactions. It is a continuous and collaborative effort among scientists around the world.

 

[Entropia]

I would like to commend you for your research and understanding of the disintegration process. To determine the angular distribution of the particles in this scenario, you can use the principles of quantum mechanics and the rules of conservation of energy and momentum.

Firstly, you can use the effective Hamiltonian to calculate the decay rate for the disintegration process. This will give you the probabilities for the different decay channels, including the production of the leptons.

Next, you can use the conservation laws to determine the energy and momentum of the particles in the final state. This will allow you to calculate the angles at which the leptons are emitted from the disintegrating particle.

Additionally, you can use the principles of quantum mechanics to calculate the wave functions of the particles involved, which will provide information about the spin and angular momentum of the particles. This, in turn, can help you determine the angular distribution of the leptons.

In summary, by using the effective Hamiltonian, conservation laws, and principles of quantum mechanics, you can determine the angular distribution of the particles in the disintegration process. I recommend consulting textbooks or research papers on quantum mechanics and particle physics for more detailed explanations and calculations.