Large Primordial Trispectra in General Single Field Inflation
- Chen, Xingang et al
- arXiv:0905.3494MIT-CTP-4039CAS-KITPC-ITP-111CERN-PH-TH-2009-064MAD-TH-09-04
 | Two diagrams that contribute to the large trispectra. |
 | This figure illustrates the tetrahedron weconsider. |
 | In this group of figures, we consider the equilateral limit $k_1=k_2=k_3=k_4$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that $T_{loc1}$ blows up when $k_{12}\ll k_1$ and $k_{14} \ll k_1$. $T_{loc1}$ also blows up in the other boundary, because this boundary corresponds to $k_{13}\ll k_1$. So $T_{loc1}$ is distinguishable from all other shapes in this limit. We also notethat $T_{c1}$ and $T_{loc2}$ are both independent of $k_{12}$ and $k_{14}$. |
 | In this group of figures, we consider the equilateral limit $k_1=k_2=k_3=k_4$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that $T_{loc1}$ blows up when $k_{12}\ll k_1$ and $k_{14} \ll k_1$. $T_{loc1}$ also blows up in the other boundary, because this boundary corresponds to $k_{13}\ll k_1$. So $T_{loc1}$ is distinguishable from all other shapes in this limit. We also notethat $T_{c1}$ and $T_{loc2}$ are both independent of $k_{12}$ and $k_{14}$. |
 | In this group of figures, we consider the equilateral limit $k_1=k_2=k_3=k_4$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that $T_{loc1}$ blows up when $k_{12}\ll k_1$ and $k_{14} \ll k_1$. $T_{loc1}$ also blows up in the other boundary, because this boundary corresponds to $k_{13}\ll k_1$. So $T_{loc1}$ is distinguishable from all other shapes in this limit. We also notethat $T_{c1}$ and $T_{loc2}$ are both independent of $k_{12}$ and $k_{14}$. |
 | In this group of figures, we consider the equilateral limit $k_1=k_2=k_3=k_4$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that $T_{loc1}$ blows up when $k_{12}\ll k_1$ and $k_{14} \ll k_1$. $T_{loc1}$ also blows up in the other boundary, because this boundary corresponds to $k_{13}\ll k_1$. So $T_{loc1}$ is distinguishable from all other shapes in this limit. We also notethat $T_{c1}$ and $T_{loc2}$ are both independent of $k_{12}$ and $k_{14}$. |
 | In this group of figures, we consider the equilateral limit $k_1=k_2=k_3=k_4$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that $T_{loc1}$ blows up when $k_{12}\ll k_1$ and $k_{14} \ll k_1$. $T_{loc1}$ also blows up in the other boundary, because this boundary corresponds to $k_{13}\ll k_1$. So $T_{loc1}$ is distinguishable from all other shapes in this limit. We also notethat $T_{c1}$ and $T_{loc2}$ are both independent of $k_{12}$ and $k_{14}$. |
 | In this group of figures, we consider the equilateral limit $k_1=k_2=k_3=k_4$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that $T_{loc1}$ blows up when $k_{12}\ll k_1$ and $k_{14} \ll k_1$. $T_{loc1}$ also blows up in the other boundary, because this boundary corresponds to $k_{13}\ll k_1$. So $T_{loc1}$ is distinguishable from all other shapes in this limit. We also notethat $T_{c1}$ and $T_{loc2}$ are both independent of $k_{12}$ and $k_{14}$. |
 | In this group of figures, we consider the folded limit $k_{12}=0$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$ and $T_{loc2}$, respectively, as functions of $k_{14}/k_1$ and $k_{4}/k_1$. $T_{loc1}$ blows up in this limit. Note that when $k_4\rightarrow 0$, allshape functions except $T_{loc1}$ and $T_{loc2}$ vanish. |
 | In this group of figures, we consider the folded limit $k_{12}=0$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$ and $T_{loc2}$, respectively, as functions of $k_{14}/k_1$ and $k_{4}/k_1$. $T_{loc1}$ blows up in this limit. Note that when $k_4\rightarrow 0$, allshape functions except $T_{loc1}$ and $T_{loc2}$ vanish. |
 | In this group of figures, we consider the folded limit $k_{12}=0$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$ and $T_{loc2}$, respectively, as functions of $k_{14}/k_1$ and $k_{4}/k_1$. $T_{loc1}$ blows up in this limit. Note that when $k_4\rightarrow 0$, allshape functions except $T_{loc1}$ and $T_{loc2}$ vanish. |
 | In this group of figures, we consider the folded limit $k_{12}=0$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$ and $T_{loc2}$, respectively, as functions of $k_{14}/k_1$ and $k_{4}/k_1$. $T_{loc1}$ blows up in this limit. Note that when $k_4\rightarrow 0$, allshape functions except $T_{loc1}$ and $T_{loc2}$ vanish. |
 | In this group of figures, we consider the folded limit $k_{12}=0$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$ and $T_{loc2}$, respectively, as functions of $k_{14}/k_1$ and $k_{4}/k_1$. $T_{loc1}$ blows up in this limit. Note that when $k_4\rightarrow 0$, allshape functions except $T_{loc1}$ and $T_{loc2}$ vanish. |
 | In this group of figures, we consider the specialized planar limit with $k_1=k_3=k_{14}$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{2}/k_1$ and $k_{4}/k_1$. Again, in the $k_2\rightarrow 0$ or $k_4\rightarrow 0$ limit, our shape functions vanish as $\CO(k_2^2)$ and $\CO(k_4^2)$ respectively. This is different from that of the local shape. $T_{loc1}$ blows up when $k_2 \rightarrow k_4$. This is because inthis limit, $k_{13}\rightarrow 0$. |
 | In this group of figures, we consider the specialized planar limit with $k_1=k_3=k_{14}$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{2}/k_1$ and $k_{4}/k_1$. Again, in the $k_2\rightarrow 0$ or $k_4\rightarrow 0$ limit, our shape functions vanish as $\CO(k_2^2)$ and $\CO(k_4^2)$ respectively. This is different from that of the local shape. $T_{loc1}$ blows up when $k_2 \rightarrow k_4$. This is because inthis limit, $k_{13}\rightarrow 0$. |
 | In this group of figures, we consider the specialized planar limit with $k_1=k_3=k_{14}$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{2}/k_1$ and $k_{4}/k_1$. Again, in the $k_2\rightarrow 0$ or $k_4\rightarrow 0$ limit, our shape functions vanish as $\CO(k_2^2)$ and $\CO(k_4^2)$ respectively. This is different from that of the local shape. $T_{loc1}$ blows up when $k_2 \rightarrow k_4$. This is because inthis limit, $k_{13}\rightarrow 0$. |
 | In this group of figures, we consider the specialized planar limit with $k_1=k_3=k_{14}$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{2}/k_1$ and $k_{4}/k_1$. Again, in the $k_2\rightarrow 0$ or $k_4\rightarrow 0$ limit, our shape functions vanish as $\CO(k_2^2)$ and $\CO(k_4^2)$ respectively. This is different from that of the local shape. $T_{loc1}$ blows up when $k_2 \rightarrow k_4$. This is because inthis limit, $k_{13}\rightarrow 0$. |
 | In this group of figures, we consider the specialized planar limit with $k_1=k_3=k_{14}$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{2}/k_1$ and $k_{4}/k_1$. Again, in the $k_2\rightarrow 0$ or $k_4\rightarrow 0$ limit, our shape functions vanish as $\CO(k_2^2)$ and $\CO(k_4^2)$ respectively. This is different from that of the local shape. $T_{loc1}$ blows up when $k_2 \rightarrow k_4$. This is because inthis limit, $k_{13}\rightarrow 0$. |
 | In this group of figures, we consider the specialized planar limit with $k_1=k_3=k_{14}$, and plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{2}/k_1$ and $k_{4}/k_1$. Again, in the $k_2\rightarrow 0$ or $k_4\rightarrow 0$ limit, our shape functions vanish as $\CO(k_2^2)$ and $\CO(k_4^2)$ respectively. This is different from that of the local shape. $T_{loc1}$ blows up when $k_2 \rightarrow k_4$. This is because inthis limit, $k_{13}\rightarrow 0$. |
 | In this group of figures, we look at the shapes near the double squeezed limit: we consider the case where ${k}_3={k}_4=k_{12}$ and the tetrahedron is a planar quadrangle. We plot $T_{s1}/(\prod_{i=1}^4 k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$, $T_{c1}/(\prod k_i)$, $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that, taking the double-squeezed limit $k_4\rightarrow 0$, the scalar-exchange contributions $T_{s1}/(\prod k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$ are nonzero and finite, and the contact-interaction $T_{c1}/(\prod k_i)$ vanishes. As a comparison, the local form terms $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$ blow up. The different behaviors in the folded and squeezedlimit can also been seen from this figure (see the main text for details). |
 | In this group of figures, we look at the shapes near the double squeezed limit: we consider the case where ${k}_3={k}_4=k_{12}$ and the tetrahedron is a planar quadrangle. We plot $T_{s1}/(\prod_{i=1}^4 k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$, $T_{c1}/(\prod k_i)$, $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that, taking the double-squeezed limit $k_4\rightarrow 0$, the scalar-exchange contributions $T_{s1}/(\prod k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$ are nonzero and finite, and the contact-interaction $T_{c1}/(\prod k_i)$ vanishes. As a comparison, the local form terms $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$ blow up. The different behaviors in the folded and squeezedlimit can also been seen from this figure (see the main text for details). |
 | In this group of figures, we look at the shapes near the double squeezed limit: we consider the case where ${k}_3={k}_4=k_{12}$ and the tetrahedron is a planar quadrangle. We plot $T_{s1}/(\prod_{i=1}^4 k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$, $T_{c1}/(\prod k_i)$, $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that, taking the double-squeezed limit $k_4\rightarrow 0$, the scalar-exchange contributions $T_{s1}/(\prod k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$ are nonzero and finite, and the contact-interaction $T_{c1}/(\prod k_i)$ vanishes. As a comparison, the local form terms $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$ blow up. The different behaviors in the folded and squeezedlimit can also been seen from this figure (see the main text for details). |
 | In this group of figures, we look at the shapes near the double squeezed limit: we consider the case where ${k}_3={k}_4=k_{12}$ and the tetrahedron is a planar quadrangle. We plot $T_{s1}/(\prod_{i=1}^4 k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$, $T_{c1}/(\prod k_i)$, $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that, taking the double-squeezed limit $k_4\rightarrow 0$, the scalar-exchange contributions $T_{s1}/(\prod k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$ are nonzero and finite, and the contact-interaction $T_{c1}/(\prod k_i)$ vanishes. As a comparison, the local form terms $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$ blow up. The different behaviors in the folded and squeezedlimit can also been seen from this figure (see the main text for details). |
 | In this group of figures, we look at the shapes near the double squeezed limit: we consider the case where ${k}_3={k}_4=k_{12}$ and the tetrahedron is a planar quadrangle. We plot $T_{s1}/(\prod_{i=1}^4 k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$, $T_{c1}/(\prod k_i)$, $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that, taking the double-squeezed limit $k_4\rightarrow 0$, the scalar-exchange contributions $T_{s1}/(\prod k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$ are nonzero and finite, and the contact-interaction $T_{c1}/(\prod k_i)$ vanishes. As a comparison, the local form terms $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$ blow up. The different behaviors in the folded and squeezedlimit can also been seen from this figure (see the main text for details). |
 | In this group of figures, we look at the shapes near the double squeezed limit: we consider the case where ${k}_3={k}_4=k_{12}$ and the tetrahedron is a planar quadrangle. We plot $T_{s1}/(\prod_{i=1}^4 k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$, $T_{c1}/(\prod k_i)$, $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that, taking the double-squeezed limit $k_4\rightarrow 0$, the scalar-exchange contributions $T_{s1}/(\prod k_i)$, $T_{s2}/(\prod k_i)$, $T_{s3}/(\prod k_i)$ are nonzero and finite, and the contact-interaction $T_{c1}/(\prod k_i)$ vanishes. As a comparison, the local form terms $T_{loc1}/(\prod k_i)$ and $T_{loc2}/(\prod k_i)$ blow up. The different behaviors in the folded and squeezedlimit can also been seen from this figure (see the main text for details). |
 | In this group of figures, we plot the $\tilde T_{c1}/{\rm Re}(C_-)$ (the left column) and $\tilde T_{s1}/{\rm Re}(C_-)$ (the right column) in the equilateral limit, specialized planar limit, and near double squeezed limit (we plot $\tilde T_{c1}/[{\rm Re}(C_-)\Pi_i k_i]$ and $\tilde T_{s1}/[{\rm Re}(C_-)\Pi_i k_i]$ in near double squeezed limit) respectively. Note that, in order to show clearly the locations of the divergence, in some figures we have taken thecutoffs of the z-axes to be extremely large. |
 | In this group of figures, we plot the $\tilde T_{c1}/{\rm Re}(C_-)$ (the left column) and $\tilde T_{s1}/{\rm Re}(C_-)$ (the right column) in the equilateral limit, specialized planar limit, and near double squeezed limit (we plot $\tilde T_{c1}/[{\rm Re}(C_-)\Pi_i k_i]$ and $\tilde T_{s1}/[{\rm Re}(C_-)\Pi_i k_i]$ in near double squeezed limit) respectively. Note that, in order to show clearly the locations of the divergence, in some figures we have taken thecutoffs of the z-axes to be extremely large. |
 | In this group of figures, we plot the $\tilde T_{c1}/{\rm Re}(C_-)$ (the left column) and $\tilde T_{s1}/{\rm Re}(C_-)$ (the right column) in the equilateral limit, specialized planar limit, and near double squeezed limit (we plot $\tilde T_{c1}/[{\rm Re}(C_-)\Pi_i k_i]$ and $\tilde T_{s1}/[{\rm Re}(C_-)\Pi_i k_i]$ in near double squeezed limit) respectively. Note that, in order to show clearly the locations of the divergence, in some figures we have taken thecutoffs of the z-axes to be extremely large. |
 | In this group of figures, we plot the $\tilde T_{c1}/{\rm Re}(C_-)$ (the left column) and $\tilde T_{s1}/{\rm Re}(C_-)$ (the right column) in the equilateral limit, specialized planar limit, and near double squeezed limit (we plot $\tilde T_{c1}/[{\rm Re}(C_-)\Pi_i k_i]$ and $\tilde T_{s1}/[{\rm Re}(C_-)\Pi_i k_i]$ in near double squeezed limit) respectively. Note that, in order to show clearly the locations of the divergence, in some figures we have taken thecutoffs of the z-axes to be extremely large. |
 | In this group of figures, we plot the $\tilde T_{c1}/{\rm Re}(C_-)$ (the left column) and $\tilde T_{s1}/{\rm Re}(C_-)$ (the right column) in the equilateral limit, specialized planar limit, and near double squeezed limit (we plot $\tilde T_{c1}/[{\rm Re}(C_-)\Pi_i k_i]$ and $\tilde T_{s1}/[{\rm Re}(C_-)\Pi_i k_i]$ in near double squeezed limit) respectively. Note that, in order to show clearly the locations of the divergence, in some figures we have taken thecutoffs of the z-axes to be extremely large. |
 | In this group of figures, we plot the $\tilde T_{c1}/{\rm Re}(C_-)$ (the left column) and $\tilde T_{s1}/{\rm Re}(C_-)$ (the right column) in the equilateral limit, specialized planar limit, and near double squeezed limit (we plot $\tilde T_{c1}/[{\rm Re}(C_-)\Pi_i k_i]$ and $\tilde T_{s1}/[{\rm Re}(C_-)\Pi_i k_i]$ in near double squeezed limit) respectively. Note that, in order to show clearly the locations of the divergence, in some figures we have taken thecutoffs of the z-axes to be extremely large. |
 | The quadrangles in black and blue represents the solution (\ref{planark2}) with minus and plus sign respectively. The term with plus sign corresponds to the blue quadrangle, and can be transformed into another quadrangle corresponding to the minus solution by a symmetry discussed in Eq.\eqref{symeq}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |
 | In the six rows, we plot $T_{s1}$, $T_{s2}$, $T_{s3}$, $T_{c1}$, $T_{loc1}$ and $T_{loc2}$ respectively as functions of $k_{12}/k_1$ and $k_{14}/k_1$ in the planar limit. Within each row, the momenta configuration is $(k_3/k_1,k_4/k_1)=\{(0.6,0.6),(0.6,1.0),(1.0,0.6),(1.0,1.0)\}$ respectively in the four columns, as given in \eqref{groupfigk}. |