ABSTRACT
As mentioned, the Higgs sector of the MSSM consists of two complex Higgs doublets, H u $ H_u $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315367903/c2682a74-a79a-4ae8-b55f-fb03894f6bcd/content/inline-math6_1.tif"/> and H d $ H_d $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315367903/c2682a74-a79a-4ae8-b55f-fb03894f6bcd/content/inline-math6_2.tif"/> . After EWSB, three of the eight degrees of freedom contained in H u $ H_u $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315367903/c2682a74-a79a-4ae8-b55f-fb03894f6bcd/content/inline-math6_3.tif"/> and H d $ H_d $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315367903/c2682a74-a79a-4ae8-b55f-fb03894f6bcd/content/inline-math6_4.tif"/> are acquired in the usual way by the W ± $ W^{\pm } $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315367903/c2682a74-a79a-4ae8-b55f-fb03894f6bcd/content/inline-math6_5.tif"/> and Z in order to become massive. The five physical degrees of freedom that remain form a neutral pseudoscalar (or CP-odd) Higgs boson, A, two neutral scalars (or CP-even), h and H, plus a charged Higgs boson pair (with mixed CP quantum numbers), H ± $ H^{\pm } $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315367903/c2682a74-a79a-4ae8-b55f-fb03894f6bcd/content/inline-math6_6.tif"/> . This varied spectrum is to be compared with the single physical neutral scalar Higgs boson of the SM. From Eq. (4.32), the scalar potential V ( H u , H d ) $ V(H_u,H_d) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315367903/c2682a74-a79a-4ae8-b55f-fb03894f6bcd/content/inline-math6_7.tif"/> can be written as V ( H u , H d ) = m 2 2 | H u + | 2 + | H u 0 | 2 + m 1 2 | H d - | 2 + | H d 0 | 2 + m 3 2 H u + H d - - H u 0 H d 0 + h . c . + g 1 2 + g 2 2 8 | H u + | 2 + | H u 0 | 2 - | H d 0 | 2 - | H d - | 2 2 + g 2 2 2 H u + H d 0 ∗ + H u 0 H d - ∗ 2 . $$ \begin{aligned} V(H_u,H_d)&= m_2^2 \left(\vert H_u^+ \vert ^2 + \vert H_u^0 \vert ^2 \right) + m_1^2 \left(\vert H_d^- \vert ^2 + \vert H_d^0 \vert ^2 \right) \nonumber \\&+ \left[m_3^2 \left( H_u^+ H_d^- - H_u^0 H_d^0 \right) + \mathrm{h.c.} \right] + \frac{g_1^2 + g_2^2}{8} \left[\vert H_u^+ \vert ^2 + \vert H_u^0 \vert ^2 \right. \nonumber \\&-&\left. \vert H_d^0 \vert ^2 - \vert H_d^- \vert ^2 \right]^2 +\frac{g_2^2}{2}\left|H_u^+ {H_d^0}^* + H_u^0 {H_d^-}^* \right|^2. \end{aligned} $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315367903/c2682a74-a79a-4ae8-b55f-fb03894f6bcd/content/math6_1.tif"/>
