Erratum to: Relating the CMSSM and SUGRA models with GUT scale and super-GUT scale supersymmetry breaking

Erratum to: Eur. Phys. J. C (2012) 72:2138 DOI 10.1140/epjc/s10052-012-2138-3

In the original version of the paper, there was an ambiguity between the value of μ before and after the shift due to the Giudice–Masiero (GM) term. Here, we will clarify the equations which were affected. We define μ ₀ as the μ-term in the superpotential defined at the input universality scale M _in. μ(M _in) will refer to the μ-term after the shift induced by the GM contribution to the Kähler potential also defined at the input scale. Then Eq. (12) becomes

$$\mu(M_{\mathrm{in}}) = \mu_0 + c_H m_0 . $$

(12)

Similarly, μB(M _in) is defined as

$$\mu B (M_{\mathrm{in}}) = \mu_0 B_0 + 2 c_H m_0^2 , $$

(13)

which replaces Eq. (13). As a consequence, we would find

$$B(M_{\mathrm{in}}) = (A_0 - m_0) \mu_0/\mu(M_{\mathrm{in}}) + 2 c_H m_0^2/\mu(M_{\mathrm{in}}) . $$

(14)

This clarification affects the result only in Sect. 2 of the paper. For M _in=M _GUT, and when the Giudice-Masiero term (11) is included [15], one can deduce the (GUT) boundary conditions for μ and B:

(16)

(17)

This allows us to solve for c _H where we obtain an equation similar to Eq. (30):

$$\begin{aligned}[b] c_H &= (B(M_{\mathrm{GUT}}) - A_0 + m_0)\mu(M_{\mathrm{GUT}})/(3m_0^2 - A_0 m_0) . \end{aligned} $$

(18)

These changes affect the contours in Figs. 2–4. In Fig. 2, with A ₀=0, all contour labels should be multiplied by 2/3. In Fig. 3, with A ₀=2.5m ₀, all contours should be multiplied by 4.0. In Fig. 4a, with A ₀=0, all contour labels should be multiplied by 2/3. Finally, in Fig. 4b, with A ₀=2.0m ₀, all contour labels should be multiplied by 2.0.

All results and figures in Sects. 3 and 4 remain unaffected.