Electroweak Breaking MSSM- D-term pot. question

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SUMMARY

The discussion centers on the D-term potential in the Minimal Supersymmetric Standard Model (MSSM) and its relation to the Fayet-Iliopoulos model. The scalar potential is expressed as V_{D}= \frac{1}{2} |ξ+ g \phi^{*} \phi|^{2}, raising questions about the absence of the field ξ and the conditions under which it can be set to zero. Additionally, the implications of the chiral Higgs scalar fields and their interaction with the vector superfield V are explored, referencing Howard Baer and Xerxes Tata's work in "Weak Scale Supersymmetry" (2006).

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ChrisVer
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Looking at the attachment, I see that the scalar potential coming from the D-term of the Higgs sector is given as shown in (8.14b).
However shouldn't there also be a field ξ as in Fayet-Iliopoulos model?
V_{D}= \frac{1}{2} |ξ+ g \phi^{*} \phi|^{2}
Is there a reason I don't see, that allows us to set ξ=0?
Also here:
http://staff.science.uva.nl/~jdeboer/education/projects/projects/mscthesis.pdf
page 34 as you scroll down, equation 1.4.12 (or even under 1.4.10) the D term for the potential are given differently...

Also a second question, the chiral Higgs scalar sfields as denoted in the attachment... what happens to the V vector sfield in S^{\dagger} e^{V} S=S^{\dagger} e^{\frac{1}{2}g_{2}T^{a}V^{a}-2i \theta \sigma^{\mu} \bar{\theta} \partial_{\mu}} S |_{Left}?

(the attachment is from Howard Baer, Xerxes Tata- Weak scale Supersymmetry (2006), chapter 8.2)
 

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