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The amplitude of B decay into tau neutrino

  1. Mar 18, 2015 #1
    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.
     
  2. jcsd
  3. Mar 20, 2015 #2

    Hepth

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    ## 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} ##
     
  4. Mar 21, 2015 #3
    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 > ## ?
     
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