Changes between Version 1 and Version 2 of DMEffFerm

Timestamp:

May 8, 2023, 8:15:45 AM (15 months ago)

Author:

Ayse Kuday

Comment:

--

DMEffFerm

@@ -1 @@
-To be continued
+Interaction operators for fermionic WIMP of 6-dimensional Effective Field Theory in tree level, which contains four-fermion interactions and vector, scalar, fermion interactions, are implemented.
+
+For 6-dimensional EFT, fermionic DM is a SM gauge singlet and odd under global Z2 symmetry. The tree level
+interactions between this fermionic DM and SM particles can be chosen as the Lagrangian form of the operators given [1,2,3] 
+
+\begin{itemize}
+\item 4-fermion vectoral interactions:
+\begin{eqnarray}
+                \mathcal{L}_{(uR,dR,eR)\chi}=\frac{g^u_{R}}{2 \Lambda^2}(\bar{u}\gamma^{\mu}u)(\bar{\chi}\gamma_{\mu}\chi) +\frac{g^d_{R}}{2 \Lambda^2}(\bar{d}\gamma^{\mu}d)(\bar{\chi}\gamma_{\mu}\chi) + \frac{g^e_{R}}{2\Lambda^2}(\bar{e}\gamma^{\mu}e)(\bar{\chi}\gamma_{\mu}\chi)  \label{eq-lag-4ferm-vekt}
+                \end{eqnarray}
+                
+\item   4-fermion scalar interactions:
+\begin{eqnarray}
+                \mathcal{L}_{(\ell,q)\chi}=\frac{g^{\ell}_L}{\Lambda^2}(\bar{\ell}\chi)(\bar{\chi}\ell)  + \frac{g^q_L}{\Lambda^2} (\bar{q}\chi)(\bar{\chi}q) \label{eq-lag-4ferm-sca}
+                \end{eqnarray}
+
+\item Fermion-vector-scalar interactions:
+\begin{eqnarray}
+                \mathcal{L}_{\phi\chi}=\frac{i \alpha_{\phi \chi}}{\Lambda^2}({\phi}^{\dagger}D^{\mu}\phi)(\bar{\chi}\gamma_{\mu}\chi)+h.c.
+                \label{eq-lag-ferm-vec-sca}
+                \end{eqnarray}
+                \end{itemize}
+
+where, $\chi$ is fermionic DM field, $u,d,e$'s are right-handed fermions, $\gamma$'s are gamma matrices, $q,\ell$ denotes left-handed quarks and leptons, $\phi$ is Higgs field  $\Lambda$ is cut-off scale of new physics,  $g_{R}^{u(d,e)}$ and $g_L^{\ell(q)}$'s are the coupling parameters related to dark operators $\alpha$'s. The apparent relation between $g$'s and $\alpha$'s are given as:
+                
+\begin{eqnarray}
+g^{u}_{L}=-\frac{1}{2}\alpha_{q\chi}, \qquad g^{u}_{R}=\frac{1}{2}\alpha_{u\chi} \nonumber
+\end{eqnarray}
+\begin{eqnarray}
+g^{d}_{L}=-\frac{1}{2}\alpha_{q \chi}, \qquad g^{d}_{R}=\frac{1}{2}\alpha_{d\chi} \nonumber
+\end{eqnarray}
+\begin{eqnarray}
+g^{e}_{L}=-\frac{1}{2}\alpha_{\ell \chi},\qquad g^{e}_{R}=\frac{1}{2}\alpha_{e\chi} \nonumber
+\end{eqnarray}
+\begin{eqnarray}
+g^{\nu}_{L}=-\frac{1}{2}\alpha_{\ell \chi}, \qquad g^{\nu}_{R}=0 \nonumber
+\end{eqnarray}
+
+[1] Ayşe Elçiboğa KUDAY, Erdinç Ulaş SAKA, Ferhat ÖZOK. June 2022. Analysis of Direct and Indirect Detection of Fermionic Dark Matter of 6-Dimensional Effective Field Theory. International Journal of Geometric Methods in Modern Physics, Vol. 19, No. 13 (2022) 2250202,[ArXiV: 2305.02302 [hep_ph]. 
+[2] Ayşe Elçiboğa KUDAY, Erdinç Ulaş SAKA, Ferhat ÖZOK. 2020. Probing Dark Matter via Effective Field Theory Approach. International Journal of Geometric Methods in Modern Physics, Vol. 17, No. 2 (2020) 2050028, [ArXiV: 2305.02592 [hep_ph]]. 
+[3] Zhang, H., Cao, QH., Chen, CR. et al. Effective dark matter model: relic density,
+CDMS II, Fermi LAT and LHC. J. High Energ. Phys. (2011) 2011: 18 [ArXiV: 0912.4511v2 [hep_ph]]