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Дата индексирования: Mon Oct 1 22:46:54 2012
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Leptoquarks

In this section we present an example of Lagrangian which contains the matrix of C-conjugation. Such matrix appears in interactions violating the fermion number conservation. Let $\Psi_e$ and $\Psi_u$ be the fermion fields of electron and u-quark, respectively, interacting with the scalar complex leptoquark field F

$$L = \lambda \bar{\Psi}_u^c (1+\gamma^5) \Psi_e F + \lambda \bar{\Psi}_e (1+\gamma^5) \Psi_u^c F^+$$

where $\bar{\Psi}_u^c=\Psi_u^T C$ and $\Psi_e^c=C \bar{\Psi}_e^T$.

In the Majorana basis which is used in CompHEP  the charge conjugation operator $C=-\gamma^0$. So the Lagrangian can be presented in the form

$$\begin{eqnarray*} L &=& - \lambda \Psi_u^T \gamma^0 (1+\gamma^5) \Psi_e F - \la... ...si_e F + \lambda \Psi_u^+ \gamma^0 (1+\gamma^5) \Psi_e^+ F^+\;. \end{eqnarray*}$$

Direct implementation of the definition (8) gives us the Vertex table

A1	A2	A3	A4	Factor	Lorentz part
u	e1	F		-lambda	(1+G5)
E1	U	F+		lambda	(1+G5)

By means of equation (11) we can rewrite this table in the equivalent form:

A1	A2	A3	A4	Factor	Lorentz part
e1	u	F		-lambda	(1+G5)
U	E1	F+		lambda	(1+G5)