A How to find branching ratio after modelling Lagrangian?

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After modeling the Lagrangian and extracting Feynman rules, the decay width can be calculated from the matrix element, leading to the branching ratio (BR). The discussion explores whether alternative methods exist for calculating BR beyond the standard approach. It also considers the possibility of using the Lagrangian in the Euler-Lagrangian equation to derive the branching ratio. Participants emphasize the importance of understanding the relationship between the Lagrangian and decay processes. Ultimately, the conversation highlights the need for clarity on various methodologies for calculating branching ratios in particle physics.
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to find branching ratio after modelling Lagrangian
hi, we have learned that after modelling Lagrangian and extracting Feynman rules from it - we can find matrix element - from which decay width can be calculated - and than Branching ratio - my question is can we use some other way of calculatiing BR , or can we use our Lagrangain in our Euler -Lagrangian equation - from there we can find out Branching ratio ?
 

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