# Last on B-mesons and CPV (for now)

• ChrisVer
In summary, the conversation discusses the parameterization of the mass matrix for B meson oscillations and how it relates to the eigenstates |B_L> and |B_H>. It also explains how to determine the values of p and q using the eigenvectors, which leads to the equation \frac{q}{p}= -\dfrac{ \Delta m_B - (i/2) \Delta \Gamma_B}{2 [M_{12} - (i/2) \Gamma_{12}]} in question.
ChrisVer
Gold Member
Last one before my exam tomorrow...
I was wondering. If we have B meson oscillations we can write the light/heavy eigenstates:
$|B_L> = p |B^0> + q |\bar{B}^0>$
$|B_H> = p |B^0> - q |\bar{B}^0>$
with $|p|^2 + |q|^2 =1$...
How can I see that:
$\frac{q}{p}= -\dfrac{ \Delta m_B - (i/2) \Delta \Gamma_B}{2 [M_{12} - (i/2) \Gamma_{12}]}$
??

Last edited:
You can parameterize the mass matrix in real and imaginary parts as

$$\mathcal{M} = \begin{pmatrix} M_{11} - i\frac{\Gamma_{11}}{2} & M_{12} - i\frac{\Gamma_{12}}{2} \\ M_{12} + i\frac{\Gamma_{12}}{2} & M_{22} - i\frac{\Gamma_{2}}{2} \end{pmatrix}.$$

Then find the eigenvectors to determine ##p,q##.

## 1. What are B-mesons and why are they important in physics?

B-mesons are subatomic particles made up of a bottom quark and an anti-quark. They are important in physics because they can provide information about the fundamental forces and laws that govern the behavior of matter. They also play a crucial role in studying the symmetry and asymmetry of particles, particularly in the field of CP violation.

## 2. What is CP violation and why is it significant in the study of B-mesons?

CP violation refers to the violation of the combined symmetry of charge (C) and parity (P) in certain subatomic particles. This phenomenon is significant in the study of B-mesons because it can help explain why there is an imbalance of matter and antimatter in the universe, which is one of the biggest mysteries in physics.

## 3. How do scientists study B-mesons and CP violation?

Scientists study B-mesons and CP violation through various experiments and analyses using particle accelerators, such as the Large Hadron Collider (LHC). They observe the decay patterns and properties of B-mesons to gather data and look for any deviations from the expected behavior, which could indicate CP violation.

## 4. What have scientists discovered about B-mesons and CP violation so far?

Scientists have discovered that B-mesons exhibit a small but measurable amount of CP violation, which supports the Standard Model of particle physics. However, there are still many unanswered questions and ongoing research in this field, as the level of CP violation observed is not enough to fully explain the matter-antimatter asymmetry in the universe.

## 5. What are the implications of further research on B-mesons and CP violation?

Further research on B-mesons and CP violation can lead to a better understanding of the fundamental forces and laws of nature. It can also potentially provide insights into the mysteries of the universe, such as the existence of dark matter and the dominance of matter over antimatter. This research also has practical applications in technology, such as improving particle accelerators and medical imaging techniques.

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