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note
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We may alternatively consider a superpotential of the form [12]: Equation presented, with n > 1, where φ, φ can now transform nontrivially under a continuous symmetry group, e.g. under a global B-L symmetry. The choice n = 1 would typically not allow positive square masses for both waterfall fields during inflation. The choice n > 1 also allows "smooth" hybrid inflation driven by the S field [13].
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G. Lazarides and C. Panagiotakopoulos, Phys. Rev. D 52, R559 (1995); R. Jeannerot, S. Khalil, and G. Lazarides, Phys. Lett. B 506, 344 (2001).
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84927772586
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note
-
Henceforth we will consider one of the singlet sneutrinos as the inflaton for simplicity and drop family indices.
-
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32
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84927772585
-
-
note
-
More precisely S acquires a vev of order the soft masses after inflation and can be used to generate an effective μ-term by adding a coupling ŜĤuĤd to the superpotential, where Ĥu and Ĥd contain the Higgs doublets coupling to the up-type quarks and down-type quarks [16].
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84927772584
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note
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The dots in Eq. (1) include Z4-violating higher-dimensional operators such as, e.g., Ŝφ̂5/M′3 (or even Ŝφ̂5/mP3) which lift the degeneracy of the true vacuum and effectively blow away potential domain wall networks associated with Z4-breaking after inflation.
-
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36
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84927772583
-
-
note
-
Supergravity corrections to the inflaton mass can easily be of the order of the Hubble parameter, inducing η = O(1). In our example, we are going to solve this "η-problem" by explicit tuning. An alternative route could be an effective no-scale supergravity theory leading to zero soft scalar masses at high energy (see e.g. [19]).
-
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38
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84927772582
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note
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We have replaced the superfields in W and K by their bosonic components [3].
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84927772581
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note
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In general, after the second order phase transition ending inflation both involved fields, the waterfall field φ and the sneutrino inflaton Ñ, oscillate and can be relevant for leptogenesis and reheating. The sneutrino dominates leptogenesis and reheating if it decays later than φ. Leptogenesis and reheating via the decay of φ have been discussed e.g. in [24].
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43
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K. Hamaguchi, H. Murayama, and T. Yanagida, Phys. Rev. D 65, 043512 (2002); S. Davidson and A. Ibarra, Phys. Lett. B 535, 25 (2002).
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K. Hamaguchi, H. Murayama, and T. Yanagida, Phys. Rev. D 65, 043512 (2002); S. Davidson and A. Ibarra, Phys. Lett. B 535, 25 (2002).
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48
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84927772580
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note
-
For TRH ≈ 106 GeV, successful leptogenesis requires the upper bound on ε to be saturated. For quasidegenerate light neutrinos via an additional mass term from a triplet seesaw, TRH ≈ 105GeV is possible since the bound on the decay asymmetry is relaxed [28].
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50
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