# Dominant Feynman diagram for ##b \to s ~l^+ l^−##

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• Safinaz
In summary, the conversation is discussing a Feynman diagram for the decay of b to s l+ l- and comparing two possible diagrams. The first diagram has two heavy propagators in the loop while the second has only one, making it seem like the second diagram would be dominant. However, the first diagram is actually dominant because it is proportional to VibVis and in the best case scenario, the CKM matrix elements are Vtb Vts or Vcb Vcs. The conversation also discusses the Z u b and u c bar vertices.
Safinaz
Hi all,

It's written in QFT books, see for instance George_W._S. book "Flavor Physics and the TeV Scale" that the following Feynman diagram (1)

is the dominant Feynman diagram for ## b \to s ~l^+l^− ## decay. Actually I compare this diagram via another possible diagram (2)

Both (1) and (2) are proportional to## G_F^2##, so they are on equal coupling order, also (1) proportional to

\begin{align}
\Big(\frac{1}{k\!\!/ - m_t}\Big)^2 ~ \frac{1}{k^2 - m_w^2},
\end{align}

while (2) proportional to

\begin{align}
\frac{1}{k\!\!/ - m_t} ~ \Big(\frac{1}{k^2 - m_w^2}\Big)^2 ,
\end{align}

I mean (1) has two heavy propagtors in the loop, while (2) has only one heavy propagator, so for the first sight, it seems (2) is the dominant diagram, but this is not the fact .. so anyone can explain why (1) is dominant one ?

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Why do you assume the loop contains top quarks?

because ## \mathcal {M} \propto V_{ib} V_{is} ##, so in the best cases the ##V_{CKM}## matrix elements are ## V_{tb} V_{ts}## or ##V_{cb} V_{cs}## . the first choice is the best because ## \mathcal {M} ## also proportional to ## m_i ##

aren't you supposed to add them (each individual flavor within the loop)?

Hi,

If you asking about ##Z u_b \bar{u }_c## vertex, there is ##\delta_{bc} ##, i.e., Z couples to the same quark flavor.

## What is a Feynman diagram?

A Feynman diagram is a visual representation of a mathematical expression that describes the behavior of subatomic particles in particle physics. It shows the interaction between particles and their corresponding antiparticles through lines and vertices.

## What is the "Dominant Feynman diagram for ##b \to s ~l^+ l^−##"?

The "Dominant Feynman diagram for ##b \to s ~l^+ l^−##" is a specific Feynman diagram that represents the decay process of a bottom quark (b) into a strange quark (s) and a pair of opposite-charged leptons (l+ and l-). It is important in studying the properties of the bottom quark and the Standard Model of particle physics.

## Why is the study of "Dominant Feynman diagram for ##b \to s ~l^+ l^−##" significant?

The study of the "Dominant Feynman diagram for ##b \to s ~l^+ l^−##" is significant because it helps us understand the behavior of subatomic particles and their interactions. It also provides valuable information about the fundamental forces and laws of nature, which can lead to advancements in technology and our understanding of the universe.

## How is the "Dominant Feynman diagram for ##b \to s ~l^+ l^−##" related to the Standard Model?

The "Dominant Feynman diagram for ##b \to s ~l^+ l^−##" is related to the Standard Model because it is one of the processes described by the model. The Standard Model is a theory that explains the behavior of subatomic particles and their interactions, and the "Dominant Feynman diagram for ##b \to s ~l^+ l^−##" is an example of this behavior.

## What are the implications of the "Dominant Feynman diagram for ##b \to s ~l^+ l^−##" in the field of particle physics?

The "Dominant Feynman diagram for ##b \to s ~l^+ l^−##" has important implications in the field of particle physics as it helps us understand the behavior and properties of subatomic particles. It also provides a way to test the predictions of the Standard Model and search for new physics beyond it. The study of this diagram can lead to new discoveries and advancements in our understanding of the fundamental building blocks of the universe.

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