The amplitude of B decay into tau neutrino

[Safinaz]

Hi there,

In Reference as hep-ph/0306037v2, we see the effective Hamiltonian of ## B \to l \nu ## equ. 1, which has the SM and the NP parts. In equ. 4, it seems that ## m_l ## comes from ## P^\mu_B ## equ. 3.

The question that how ## P^\mu_B ## yields ## m_l ## ? Where ## P^\mu_B = ( E_B, 0, 0, \bf{p} )## , or ## P^\mu_B = ( m_B, 0, 0, 0)## in B rest frame ..

Bests.

 

[Hepth]

## P^{\mu} \bar{\ell} \gamma_{\mu} (1-\gamma_5) \nu = (p^{\mu}_{\ell} + p^{\mu}_{\bar{\nu}} ) \bar{\ell} \gamma_{\mu} (1-\gamma_5) \nu ##
## = \bar{\ell} (\not p_{\ell} + \not p_{\bar{\nu}} )(1-\gamma_5) \nu ##

and
## \bar{\ell} \not p_{\ell} = -m_{\ell} \bar{\ell} ##

 

[Safinaz]

Many thanks .. May I ask another question about " the vacuum saturation approximation ", that why

## < 0 | \bar{u} \gamma_\mu b | B > ~ and ~ < 0 | \bar{u} b | B > = 0 ## ? , and for ## [ \bar{l} \gamma^\mu (1-\gamma_5) \nu ] ##, why didn't say:
## < l^- \bar{ \nu} | \bar{l} \gamma^\mu (1-\gamma_5) \nu | 0 > ## ?