On capped Higgs positivity cone

Figure  1.  Positivity regions in the 2D subspaces of $ C_1, C_2 $, and $ C_3 $ by using linear and nonlinear unitarity conditions. Here, $ \bar{C_i}=C_i \Lambda^4 /(4\pi)^2 $. The orange and red regions are the results of the current paper using linear and nonlinear unitarity conditions respectively, while the blue region are from Ref. [24], which uses linear unitarity conditions but without using full Higgs symmetries. The orange and red regions are the same. We choose $ N=10,\ell_M=20 $ and use 42 null constraints.

Figure  2.  Convergence of positivity (upper and lower) bounds with the number of null constraint. We choose $ N=10,\ell_M=20 $.

Figure  3.  Convergence of positivity (upper and lower) bounds with the numerical truncations $ \ell_M $ and N. Here $ \bar{C_i}=C_i \Lambda^4 /(4\pi)^2 $. 42 null constraints are used.