PHYSICAL REVIEW D 97, 115013 (2018) Big-bang nucleosynthesis and leptogenesis in the CMSSM † ‡ ∥ Munehiro Kubo,1,* Joe Sato,1, Takashi Shimomura,2, Yasutaka Takanishi,1,§ and Masato Yamanaka3, 1Department of Physics, Saitama University, Shimo-Okubo 255, 338-8570 Saitama Sakura-ku, Japan 2Faculty of Education, University of Miyazaki, Gakuen-Kibanadai-Nishi 1-1, 889-2192 Miyazaki, Japan 3Maskawa Institute, Kyoto Sangyo University, Kyoto 603-8555, Japan (Received 21 March 2018; published 8 June 2018) We have studied the constrained minimal supersymmetric standard model with three right-handed neutrinos, and investigated whether there still is a parameter region consistent with all experimental data/ limits such as the baryon asymmetry of the Universe, the dark matter abundance and the lithium primordial abundance. Using Casas-Ibarra parametrization, we have found a very narrow parameter space of the complex orthogonal matrix elements where the lightest slepton can have a long lifetime, which is necessary for solving the lithium problem. We have studied three cases of the right-handed neutrino mass ratio (i) M2 ¼ 2 × M1, (ii) M2 ¼ 4 × M1, (iii) M2 ¼ 10 × M1, while M3 ¼ 40 × M1 is fixed. We have obtained the mass range of the lightest right-handed neutrino that lies between 109 and 1011 GeV. The important result is that its upper limit is derived by solving the lithium problem and the lower limit comes from leptogenesis. Lepton flavor violating decays such as μ → eγ in our scenario are in the reach of MEG-II and Mu3e. DOI: 10.1103/PhysRevD.97.115013 I. INTRODUCTION type-I seesaw mechanism [4–8]. In this mechanism, the heavy Majorana right-handed (RH) neutrinos are introduced The standard models (SMs) of particle physics and and, thus, the Yukawa interactions of left-handed (LH) and cosmology have been successful at understanding most RH neutrinos can be formed with the Higgs scalar, which of the experimental and observational results obtained so gives rise to the flavor mixings in the neutrino sector. After far. Nonetheless, there are several phenomena which cannot integrating out the RH neutrinos, the LH neutrino masses be explained by these models. Among such phenomena, become very light due to the suppression factor which is the mass and mixing of neutrinos, the baryon asymmetry of proportional to the inverse of the Majorana mass scale. Thus, the Universe (BAU), the existence of the dark matter (DM), when we make use of the seesaw mechanism, we can and the so-called lithium (Li) problems are compelling successfully generate the phenomenologically required evidence that new physics laws are required. If all of these masses and mixings of LH neutrinos. phenomena are addressed in particle physics, the new Furthermore, the seesaw mechanism has another physics laws should be incorporated in a unified picture virtue, generating the baryon asymmetry [2] through beyond the SM of particle physics. leptogenesis [9]. At the early stage of the Universe, the Neutrino oscillation experiments (see Ref. [1] for recent RH Majorana neutrinos are produced in the thermal bath. review and global fit analysis) and cosmological observa- As the temperature decreases to their mass scale, these tions [2,3] revealed that the masses of neutrinos are much neutrinos go to out-of-thermal equilibrium, and at that lighter than those of other known SM particles. To generate time they decay into leptons with Higgs or antileptons such tiny masses, many mechanisms have been proposed, with anti-Higgs. If CP symmetry is violated in the among which the most well-studied and simplest is the neutrino Yukawa coupling, the decay rates into lepton and antilepton are obviously different. That means that the *[email protected] † lepton number asymmetry is generated through the decays [email protected] ‡ of the heavy Majorana RH neutrinos, and then the lepton [email protected] §[email protected] number asymmetry is converted to the baryon asymmetry ∥ [email protected] by the sphaleron process [10,11]: the seesaw mechanism explains two phenomena simultaneously. (see, e.g., Published by the American Physical Society under the terms of Refs. [12–18]) the Creative Commons Attribution 4.0 International license. The existence of DM is also a problem [19]. The dark Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, matter must be a massive and stable or a very long-lived and DOI. Funded by SCOAP3. particle compared with the age of the Universe and not 2470-0010=2018=97(11)=115013(15) 115013-1 Published by the American Physical Society MUNEHIRO KUBO et al. PHYS. REV. D 97, 115013 (2018) carry electric or color charges. LH neutrino is the only between 350 and 420 GeV in the constrained MSSM possible candidate for the DM within the SM; however, this (CMSSM). This result is consistent with nonobservation possibility already has been ruled out because neutrino of SUSY particle at the LHC experiment so far. However, it masses are too light. Thus, one should extend the SM so is in the reach of the LHC Run-II. that the DM is incorporated. Supersymmetry (SUSY) with In this article, we consider the CMSSM with the type I R parity is one of the attractive extensions in this regard, seesaw mechanism as a unified picture which successfully where the lightest SUSY particle (LSP) becomes absolutely explains all phenomena as we have mentioned above. We stable. In many SUSY models, the LSP is the lightest aim to examine this model through searches of the long- neutralino that is a linear combination of neutral compo- lived charged particles at the LHC and lepton flavor nents of gauginos and Higgsinos that are SUSY partners of violation (see, e.g., Refs. [14,33–47]) at MEG-II, Mu3e electroweak gauge bosons and the Higgses, respectively. and Belle-II experiments. This paper is organized as Therefore, the lightest neutralino LSP is a good candidate follows. In Sec. II, we review the CMSSM with the heavy for the DM, and in fact the abundance of the neutralino LSP RH Majorana neutrinos. In Sec. III, we show cosmological can be consistent with observational ones of the DM [19] constraints such as dark matter, BBN and BAU, which we in specific parameter regions. In particular, the so-called require to the model in our analysis. Then, we present the coannihilation region is very interesting, in which the parameter sets of the CMSSM and RH Yukawa coupling neutralino DM and the lighter stau, SUSY partner of the which satisfies all requirements in Sec. IV. Predictions on tau lepton, as the next-LSP (NLSP) are degenerate in mass lepton flavor violating decays are shown in Sec. V. The last [20]. When the mass difference of the neutralino LSP and section is devoted to a summary and discussion. the stau NLSP is smaller than Oð100Þ MeV, the stau NLSP becomes long-lived so that it can survive during the big- II. MODEL AND NOTATION bang nucleosynthesis (BBN) [21–23]. Thus, the existence of the stau NLSP affects the primordial abundance of light We consider the MSSM with RH Majorana neutrinos elements. One can expect to find evidence of the stau NLSP (MSSMRN). The superpotential for the lepton sector is in the primordial abundance of the light elements. given by It has been reported that there are disagreements on the 1 7 6 W ˆ c ˆ ˆ λ ˆ ˆ ˆ c − ˆ c ˆ c primordial abundance of Li and Li between the standard l ¼ EαðYEÞαβLβ · Hd þ βiLβ · HuNi 2 ðMNÞijNi Nj : BBN prediction and observations. The prediction of the 7Li abundance is about 3 times larger than the observational ð1Þ −10 one 1.6 0.3 × 10 [24–26]. This discrepancy hardly ˆ ˆ c ð Æ Þ Here, Lα and Eα (α ¼ e; μ; τ; i; j ¼ 1, 2, 3) are the chiral seems to be solved in the standard BBN with the meas- 2 7 6 supermultiplets, respectively, of the SUð ÞL doublet lepton urement errors. This is called the Li problem. The Li 2 and of the SUð ÞL singlet charged lepton in the flavor basis abundance also disagrees with the observations. The which is given as the mass eigenstate of the charged lepton, 103 predicted abundance is about smaller than the obser- that is, the eigenstate of Y and hence implicitly ðY Þαβ ¼ 6 7 −2 E E vational abundance Li= Li ≃ 5 × 10 [27]. Although this ˆ c yαδαβ is assumed. Similarly N ði ¼ 1; 2; 3Þ is that of the disagreement is less robust because of uncertainties in the i RH neutrino and the indices denote the mass eigenstate, observations, it is called the 6Li problem. that is, the eigenstate of M , and implicitly M ¼ M δ Since the disagreements cannot be attributed to nuclear N Nij i ij is assumed, and the superscript C denotes the charge physics in the BBN [28], one needs to modify the standard ˆ ˆ BBN reactions. In Ref. [29], the authors have shown in the conjugation. Hu and Hd are the supermultiplets of the minimal SUSY standard model (MSSM) that negatively two Higgs doublet fields Hu and Hd. charged stau can form bound states with light nuclei and Below the lightest RH seesaw mass scale, the singlet ˆ c immediately destroy the nuclei through internal conversion supermultiplets Ni containing the RH neutrino fields are processes during the BBN. Further, a detailed analysis [30] integrated out, the Majorana mass term for the LH has shown that in the coannihilation region, where the neutrinos in the flavor basis is obtained, lightest neutralino LSP is the DM and the stau NLSP has a 1 lifetime of O 103 sec, Li and beryllium (Be) nuclei are Lν − ν ν ð Þ m ¼ 2 LαðmνÞαβ Lβ þ H:c:; ð2Þ effectively destroyed.