Changes between Version 6 and Version 7 of anomalyfreeZprime

Timestamp:

Jun 5, 2020, 4:22:19 PM (5 years ago)

Author:

MartinBauer

Comment:

--

anomalyfreeZprime

@@ -27 +27 @@
 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
 $\mbox{Var}[\tau(X_p,X_d)]=\mbox{Var}[E(\tau(X_p,X_d)|X_p)]+E[\mbox{Var}(\tau(X_p,X_d)|X_p)]$
 }}}
+