The Soft Supersymmetry-Breaking Lagrangian: Theory and Applications
- Chung, D.J.H. et al
- hep-ph/0312378CERN-TH-2003-182FERMILAB-PUB-03-228-TMCTP-03-39SHEP-03-25
| mSUGRA/CMSSM parameter space exclusion plots taken from \cite{Ellis:2003cw}, in which \protect\( A_{0}=0\protect \) and other parameters are as shown. The darkest ``V'' shaped thin strip corresponds to the region with \protect\( 0.094\leq \Omega h^{2}\leq 0.129\protect \), while a bigger strip with a similar shape corresponds to the region with \protect\( 0.1\leq \Omega h^{2}\leq 0.3\protect \). (There are other dark strips as well when examined carefully.) The triangular region in the lower right hand corner is excluded by \protect\( m_{\widetilde{\tau }_{1}}<m_{\widetilde{\chi }^{0}}\protect \), since DM cannot be charged and hence is a neutralino \protect\( \widetilde{\chi }^{0}\protect \)). Other shadings and lines correspond to accelerator constraints. In the lower figure ( \protect\( \mu <0\protect \)), most of the DM favored region below \protect\( m_{1/2}<400\protect \) GeV is ruled out by the \protect\( b\rightarrow s\gamma \protect \) constraint. In the upper figure, the medium shaded band encompassing the bulge region shows that the region favored by dark matter constraints is in concordance with the region favored by \protect\( g_{\mu }-2\protect \) measurements. The Higgs and chargino mass bounds are also as indicated: the parameter space left of these bounds is ruled out. Unless excluded by accelerator constraints, the region below the darkest {}``V'' region is not excluded, but is not cosmologically interesting due to the small relic abundance. |
| mSUGRA/CMSSM parameter space exclusion plots taken from \cite{Ellis:2003cw}, in which \protect\( A_{0}=0\protect \) and other parameters are as shown. The darkest ``V'' shaped thin strip corresponds to the region with \protect\( 0.094\leq \Omega h^{2}\leq 0.129\protect \), while a bigger strip with a similar shape corresponds to the region with \protect\( 0.1\leq \Omega h^{2}\leq 0.3\protect \). (There are other dark strips as well when examined carefully.) The triangular region in the lower right hand corner is excluded by \protect\( m_{\widetilde{\tau }_{1}}<m_{\widetilde{\chi }^{0}}\protect \), since DM cannot be charged and hence is a neutralino \protect\( \widetilde{\chi }^{0}\protect \)). Other shadings and lines correspond to accelerator constraints. In the lower figure ( \protect\( \mu <0\protect \)), most of the DM favored region below \protect\( m_{1/2}<400\protect \) GeV is ruled out by the \protect\( b\rightarrow s\gamma \protect \) constraint. In the upper figure, the medium shaded band encompassing the bulge region shows that the region favored by dark matter constraints is in concordance with the region favored by \protect\( g_{\mu }-2\protect \) measurements. The Higgs and chargino mass bounds are also as indicated: the parameter space left of these bounds is ruled out. Unless excluded by accelerator constraints, the region below the darkest {}``V'' region is not excluded, but is not cosmologically interesting due to the small relic abundance. |
| Typical exclusion plot taken from \cite{Benoit:2001zu}. The region above the curves are excluded. The closed curve represents the \protect\( 3\sigma \protect \) positive detection region of DAMA experiment. |
| Taken from \cite{Bertin:2002ky}, the left figure shows the direct detection scalar elastic scattering cross section for various neutralino masses, and the right figure shows the indirect detection experiments' muon flux for various neutralino masses. The scatter points represent ``typical'' class of models. Specifically, the model parameters are \protect\( A_{0}=0,\tan \beta =45,\mu >0,m_{0}\in [40,3000],m_{1/2}\in [40,1000].\protect \) The dotted curve, dot dashed curved, and the dashed curve on the right figure represents the upper bound on the muon flux coming from Macro, Baksan, and Super-Kamiokande experiments, respectively. This plot should be taken as an optimistic picture, because the threshold for detection was set at 5 GeV, where the signal-to-noise ratio is very low in practice. |
| Reheating temperature upper bound constraints from BBN as a function of the gravitino mass taken from \cite{Holtmann:1998gd}. The various ``high'' and ``low'' values refer to the usage of observationally deduced light nuclei abundances in deducing the upper bound. Hence, the discrepancy can be seen as an indication of the systematic error in the upper bound constraint from observational input uncertainties. |
| The leading diagrams contributing to the CP-violating currents that eventually sources the quark chiral asymmetry. The diagram a) corresponds to the right-handed squark current $J_R^\mu$ and the diagram b) corresponds to the higgsino current $J_{{\tilde H}}^\mu$. The effective mass terms correspond to $m_{LR}^2 =Y_t (A_t H_u - \mu^* H_d)$ and $\mu_a = g_a (H_d P_L + \frac{\mu}{|\mu|}H_u P_R)$ where $P_{L,R}$ are chiral projectors and $g_a=g_2$ for $a=1,2,3$ and $g_a=g_1$ for $a=4$. |
| Possible mechanisms for chargino decay. |
| Feynman Rules after redefining the gluino filed so that gluino mass is real and the phase shows up at the vertices. |
| How phases enter from gluino production. |
| Gluino production and decay. Phase factors enter at the vertices, as described in the text. |
| \normalsize $-g_2(V^{CKM})_{IJ}(\Gamma_{DL}^{SCKM})_{J\alpha}U_{i1} \cdot P_R$ $+\frac{g_2}{\sqrt{2} m_W cos\beta}(V^{CKM})_{IJ}(\Gamma_{DR}^{SCKM})_{J\alpha}m_J^d U_{i2} \cdot P_R$ +$\frac{g_2}{\sqrt{2}m_W \sin\beta}(V^{CKM})_{IJ}(\Gamma_{DL}^{SCKM})_{J\alpha}m_I^u V_{i2}^* \cdot P_L$ |
| Caption not extracted |
| $-g_2 (V_{IJ}^{CKM})^*(\Gamma_{DL}^{SCKM})_{J\alpha}^* U_{i1}^* \cdot P_L +\frac{g_2}{\sqrt{2}m_W \cos\beta} (V_{IJ}^{CKM})^* (\Gamma_{DR}^{SCKM})^*_{J\alpha}m_J^d U_{22}^* \cdot P_L$ $+\frac{g_2}{\sqrt{2} m_W \sin\beta} (V_{IJ}^{CKM})^* (\Gamma_{DL}^{SCKM})_{J\alpha}^* m_I^u V_{i2} \cdot P_R$ |
| $+g_2 V_{JI}^{CKM} (\Gamma_{UL}^{SCKM})_{J\alpha}^* V_{i1}^* \cdot C^{-1} P_L -\frac{g_2}{\sqrt{2}m_W \cos\beta} V_{JI}^{CKM}(\Gamma_{UL}^{SCKM})_{J\alpha}^* m_I^d U_{i2} \cdot C^{-1} \cdot P_R$ $-\frac{g_2}{\sqrt{2}m_W \sin\beta} V_{JI}^{CKM} (\Gamma_{UR}^{SCKM})^* m_J^u V_{i2}^*\cdot C^{-1} P_L$ |
| $-\sqrt{2} g_2 {(\Gamma_{UL}^{SCKM})}_{I\alpha}[T_{3I}N_{i2} - \tan \theta_W(T_{3I} - e_I)N_{i1}] \cdot P_R + \sqrt{2} g_2 \tan \theta_W{(\Gamma_{UR}^{SCKM})}_{I\alpha} N^*_{i1} \cdot P_L$ -$ \frac{g_2\;m_I^u}{\sqrt{2} m_W \sin\beta}(N^*_{i4}{(\Gamma_{UL}^{SCKM})}_{I\alpha} \cdot P_L +N^*_{i4}{(\Gamma_{UR}^{SCKM})^*}_{I\alpha} P_R.)$ |
| $-\sqrt{2} g_2 {(\Gamma_{UL}^{SCKM})}_{I\alpha}^*[T_{3I}N_{i2}^* - \tan\theta_W(T_{3I} - e_I)N_{i1}^*] \cdot P_L + \sqrt{2} g_2 \tan\theta_W{(\Gamma_{UR}^{SCKM})}_{I\alpha}^* N_{i1} \cdot P_R$ -$ \frac{g_2\;m_I^u}{\sqrt{2} m_W \sin\beta}(N_{i4}{(\Gamma_{UL}^{SCKM})}_{I\alpha}^* \cdot P_R +N_{i4}{(\Gamma_{UR}^{SCKM})}_{I\alpha} P_L.)$ |
| $-\sqrt{2}g_3 {T^a}_{jk} \big[ G^{-1}( {\Gamma^{SCKM}_{qL})}_{I\alpha} \cdot P_R - G{({\Gamma^{SCKM}}_{qR})}_{I\alpha} P_L\big]$ |
| $- \sqrt{2} g_3 {T^a}_{kj}(G{(\Gamma^{SCKM}_{qL})}_{I\alpha}^* P_L - G^{-1}{(\Gamma^{SCKM}_{qR})}^*_{I\alpha} P_R)$ |
| $g_2 \gamma^{\mu}(O_{ij}^L P_L + O_{ij}^R P_R)$ |
| $-e\gamma^{\mu}$ |
| $\frac{g_2}{\cos\theta_W} \gamma^\mu[O_{ij}^{\prime L} P_L + O_{ij}^{\prime R} P_R]$ |
| $\frac{g}{\cos\theta_W} \gamma^u(O_{ij}^{\prime \prime L}P_L + O_{ij}^{\prime \prime R}P_R)$ |
| $ ig_3 f_{abc}\gamma^\mu $ |
| $ -i\frac{g_2}{\sqrt{2}}{(P_d - P_u)}^\mu F_{\alpha\beta}^{1}$ |
| Caption not extracted |
| $ -i \frac{g_2}{\cos\theta_W}F_{\alpha\beta}^{2I}(P_\beta - P_\alpha)^\mu(T_{3I} - e_I \sin^2\theta_W)$ |
| $ \frac{g_{2}^{2}}{2} \eta_{\mu\nu} (\Gamma_{qL}^{SCKM})_{I\alpha}^{*}(\Gamma_{qL}^{SCKM})_{I\beta}$ |
| Caption not extracted |
| $-\frac{g_{2}^{2}}{\sqrt{2}} \frac{y_{Q}\sin^2\theta_W}{\cos\theta_W} \eta_{\mu\nu}F_{\alpha\beta}^{1}$ |
| Caption not extracted |
| $\frac{g^2}{\cos^2\theta_W}F_{\alpha\beta}^{2I}(T_{3I} - e_{I} \sin^2\theta_W)^2 $ |
| Caption not extracted |
| $ g_{3}^{2}(\frac{1}{3}\delta_{ab} {\mathbf{1} }+ d_{abc}T^c)g_{\mu\nu} $ |
| Caption not extracted |
| $2g_{3}e e_{\widetilde{q}_\alpha}T_{ij}^{a} $ |
| Caption not extracted |
| The annihilation of a pair of photinos into an electron-positron pair via a $t$-channel exchange of a left-handed scalar electron. The arrows on the lines label the direction of fermion number propagation. The arrows appearing together with the momenta label the direction of momentum flow. |
| One-loop diagram which can induce FCNCs. |