- #1

Matt atkinson

- 116

- 1

## Homework Statement

The ##B^+## meson decays through the weak interaction. One of its decay channels is

## Homework Equations

Mass of ##B^+## is 5.279 GeV/

*c*2, mass of

*c*2,mass of ##\rho^+##is 0.770 GeV/

*c*2

## The Attempt at a Solution

max energy => when ##B^+ \parallel \bar{D^o}## and ##\rho^+## anti parallel to ##B^+##

min energy => when ##B^+ \parallel \bar{D^o}## and ##\rho^+\parallel B^+##

__Max__conservation of momentum ; ##E_{\beta}=E_{\rho}+E_{\bar{D}}##

conservation of energy ; ##p_{\beta}=-p_{\rho}+p_{\bar{D}}##

$$E_{\bar{D}}^2=m_{\bar{D}}^2+p_{\bar{D}}^2$$

$$E_{\bar{D}}^2=m_{\bar{D}}^2+(p_{\beta}+p_{\rho})^2$$

$$E_{\bar{D}}^2=m_{\bar{D}}^2+p_{\beta}^2+p_{\rho}^2+2p_{\rho}p_{\beta}$$

$$E_{\bar{D}}^2=m_{\bar{D}}^2+p_{\beta}^2+E_{\rho}^2-m_{\rho}^2+2p_{\rho}p_{\beta}$$

$$E_{\bar{D}}^2=m_{\bar{D}}^2+p_{\beta}^2+(E_{\beta}-E_{\bar{D}})^2-m_{\rho}^2+2p_{\rho}p_{\beta}$$

$$E_{\bar{D}}=\frac{m_{\bar{D}}^2+p_{\beta}^2+E_{\beta}^2-m_{\rho}^2+2p_{\rho}p_{\beta}}{2E_{\beta}}$$

but after this I am not sure how to get rid of the ##p_{\rho}## from the ##2p_{\rho}p_{\beta}}{2E_{\beta}## term.

also to do the case for minimum energy, i would just have ##p_{\beta}=p_{\rho}+p_{\bar{D}}## for my momentum conservation right?

edit;using momentum conservation on the ##p_{\beta}=p_{\rho}+p_{\bar{D}}## term;

$$E_{\bar{D}}=\frac{m_{\bar{D}}^2+m_{\beta}^2-m_{\rho}^2+2p_{\bar{D}}p_{\beta}}{2E_{\beta}}$$

but this doesn't help too much because i still don't know ##p_{\bar{D}}##

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