Moduli mediation without moduli-induced gravitino problem

Published for SISSA by Springer Received: April 5, 2016 Accepted: May 13, 2016 Published: May 30, 2016 Kensuke Akita,a Tatsuo Kobayashi,b Akane Oikawaa and Hajime Otsukaa a Department of Physics, Waseda University, Tokyo, 169-8555 Japan b Department of Physics, Hokkaido University, Sapporo, 060-0810 Japan E-mail: , , , Abstract: We study the moduli-induced gravitino problem within the framework of the phenomenologically attractive mirage mediations. The huge amount of gravitino generated by the moduli decay can be successfully diluted by introducing an extra light modulus field which does not induce the supersymmetry breaking. Since the lifetime of extra modulus field becomes longer than usually considered modulus field, our proposed mechanism is applied to both the low- and high-scale supersymmetry breaking scenarios. We also point out that such an extra modulus field appears in the flux compactification of type II string theory. Keywords: Cosmology of Theories beyond the SM, Supergravity Models ArXiv ePrint: 1603.08399 Open Access, c The Authors. Article funded by SCOAP3 . doi:10.1007/JHEP05(2016)178 JHEP05(2016)178 Moduli mediation without moduli-induced gravitino problem Contents 1 Introduction 1 2 Brief review of the moduli-induced gravitino problem in the mirage mediation 2 7 4 The dilution mechanism in effective action of type II string theory 4.1 F -term uplifting 4.1.1 Model 1 4.1.2 Model 2 4.1.3 Model 3 4.2 Uplifting with anti D-brane 4.3 The dilution mechanism 10 11 11 13 14 15 15 5 Conclusion 19 A Moduli-dependent uplifting scenario 20 1 Introduction Supersymmetry (SUSY) is a not only a phenomenologically plausible symmetry beyond the standard model (SM), but also is expected to appear in the low-energy effective theory of superstring theory. However, the lack of evidence of supersymmetry particles implies that the SUSY is broken above the TeV scale. In order to build in the SUSY-breaking scenario, we have to take care of the constraints from the collider experiments and cosmological observations, simultaneously. In particular, the mirage mediation [1–4], which is the mixture of modulus [5–8] and anomaly mediations [9, 10], predicts the characteristic sparticle spectrum in contrast to the other SUSY-breaking scenarios. The modulus mediation is achieved by the framework of Kachru-Kallosh-Linde-Trivedi (KKLT)-type moduli stabilization [11], where the volume modulus T is stabilized at the AdS vacuum by the non-perturbative effects such as gaugino condensation on hidden D7-branes and Euclidean D-brane instanton, and the AdS vacuum is lifted to dS vacuum by anti D-branes. Since the F -term of T is one-loop suppressed, the modulus mediation is comparable to the anomaly mediation. In this setup, the anomaly mediation and renormalization group effects cancel each other at a certain energy scale [3], and the pure modulus mediation appears at that energy scale. Such an energy scale is called as the mirage scale. In particular, the TeV scale mirage mediation is important, because one can relax the fine-tuning problem on the Higgs mass [12–14]. For example, in the next-to-minimal supersymmetric standard model with the TeV scale mirage mediation, one needs O(10)% tuning for 1.5 TeV gluino mass and O(1)% fine-tuning even for several TeV of gluino mass to realize the weak scale [15, 16].1 1 See also ref. [17]. –1– JHEP05(2016)178 3 The dilution mechanism in 4D N = 1 SUGRA 2 Brief review of the moduli-induced gravitino problem in the mirage mediation We start with the 4D SUGRA originating from the type IIB string theory on CY orientifold. The moduli Kähler potential is described in the reduced Planck unit, 2 K = −3 ln(−i(T − T̄ )) − ln(−i(τ − τ̄ )) h i − ln 2i(F − F̄ ) − i(U i − Ū i )(∂i F + ∂ī F̄ ) , 2 In this paper, we work the reduced Planck unit MPl = 2.4 × 1018 GeV, unless we specify it. –2– (2.1) JHEP05(2016)178 In this paper, we focus on the cosmological aspects of pure modulus and mirage mediations. In the inflationary regime, the moduli fields are generically stabilized at the minimum away from those of KKLT-type moduli stabilization. This is because the moduli fields would receive the Hubble-induced masses due to the positive vacuum energy density or they couple to the inflaton field through the Planck-suppressed operators. Even if the moduli fields do not receive the Hubble-correction due to the shift symmetry, the quantum fluctuations deviate the minimum of moduli fields during the inflation. In any cases, when the Hubble scale is comparable to the masses of moduli fields, the moduli fields would oscillate around the true minima and such oscillating energy density dominates the energy density of the Universe. This is problematic from a cosmological point of view. First of all, the moduli fields should decay into the light particles before the start of Big Bang Nucleosynthesis (BBN) not to spoil the success of BBN. In addition, the moduli fields produce the huge amount of gravitinos. When the gravitino is unstable, the non-thermal lightest supersymmetric particle (LSP) is overproduced by the gravitino decay [18–20]. Since this moduli-induced gravitino problem occurs in both low-and high-scale SUSY-breaking scenarios, it motivates us to explore dilution of the gravitino abundance. There are several studies to dilute the overproduced LSP by the thermal inflation [21, 22], Q-ball [23] and unstable domain-wall [24], or the introduction of the axion sector [25]. The modulus oscillation may be suppressed by the adiabatic oscillation [26, 27]. Note that the heavier gravitino compared with the volume modulus is not relevant for the above moduli-induced gravitino problem, as can be shown in the large volume scenario [28, 29]. In this paper, we propose a new dilution mechanism by an inclusion of the extra light modulus field, which does not break the SUSY at the vacuum. In the framework of flux compactification of type IIB string theory on Calabi-Yau (CY) manifold, it was argued that on general grounds all the complex structure moduli and axion-dilaton are stabilized at the compactification scale [30]. However, it depends on the choice of three-form fluxes. We consider that one of the complex structure moduli remains massless under the flux compactification, and it can be stabilized by the instanton effects without breaking the SUSY. Since such complex structure modulus is lighter than Kähler modulus, it plays an important role of diluting the gravitino produced by the Kähler modulus. After briefly reviewing the cosmological aspects of mirage mediation, such as moduli-induced gravitino problem in section 2, we study the dilution mechanism based on the 4D effective N = 1 supergravity (SUGRA) in section 3 and the effective action of type II string theory in section 4, respectively. Finally, we conclude in section 5. where T is the simplified overall Kähler modulus, τ is the axion-dilaton, and F is the prepotential as functions of (...truncated)