# Changes between Version 6 and Version 7 of anomalyfreeZprime

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Timestamp:
06/05/20 16:22:19 (4 months ago)
Comment:

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Unmodified
 v6 between the lepton and baryon numbers The $Z'$ couplings to currents of SM fermionsare given by:[[BR]] {{{#!latex \begin{alignat}{9} \mathcal{L}_\text{fermion} = -g_{Z'} j'_\mu & {Z'}^\mu \notag \\ j'_\mu&= 0 \qquad && U(1)_X \notag  \\ j'_\mu&= \bar L_i \gamma_\mu L_i + \bar \ell_i\gamma_\mu \ell_i - \bar L_j \gamma_\mu L_j -\bar\ell_j\gamma_\mu \ell_j \qquad && U(1)_{L_i-L_j} \notag \\ j'_\mu&=  \frac{1}{3}\bar Q \gamma_\mu Q + \frac{1}{3}\bar u_R\gamma_\mu u_R + \frac{1}{3}\bar d_R\gamma_\mu d_R - \bar L \gamma_\mu L + \bar \ell\gamma_\mu \ell \qquad && U(1)_{B-L} \; , \end{alignat} }}} where $g_{Z'}$ denotes the dark gauge coupling.  The different coupling structures shown above can be understood in terms of a flavor structure of a dark gauge coupling matrix. The fermion current structure can be generalized to include the dark matter current. To couple to the gauge mediator the dark matter fermion has to be a Dirac fermion. To avoid new anomalies, the dark matter candidate cannot be chiral and its charges under the new gauge group are $q_{\chi_L}=q_{\chi_R}$. This defines a dark fermion Lagrangian with a vector mass term {{{#!latex \begin{align*} \mathcal{L}_\text{DM}= i \bar \chi \not{D} \chi - m_\chi \bar \chi \chi \; , \end{align*} }}} with the covariant derivative of the SM-singlet fermion {{{#!latex $D_\mu=\partial_\mu -ig_{Z'} q_\chi \hat Z'_\mu$. }}} In all cases, the kinetic term for the $U(1)$ gauge bosons is not canonically normalized {{{#!latex $\mbox{Var}[\tau(X_p,X_d)]=\mbox{Var}[E(\tau(X_p,X_d)|X_p)]+E[\mbox{Var}(\tau(X_p,X_d)|X_p)]$ }}}