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Affleck-Dine Leptogenesis from Higgs Inflation

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Affleck-Dine Leptogenesis from Higgs Inflation CTPU-PTC-21-21 Affleck-Dine Leptogenesis from Higgs Inflation Neil D. Barrie,1, ∗ Chengcheng Han,2, y and Hitoshi Murayama3, 4, 5, z 1Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon, 34126, Korea 2School of Physics, Sun Yat-Sen University, Guangzhou 510275, China 3Department of Physics, University of California, Berkeley, CA 94720, USA 4Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583, Japan 5Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA (Dated: June 8, 2021) We investigate the possibility of simultaneously explaining inflation, the neutrino masses and the baryon asymmetry through extending the Standard Model by a triplet Higgs. The neutrino masses are generated by the vacuum expectation value of the triplet Higgs, while a combination of the triplet and doublet Higgs' plays the role of the inflaton. Additionally, the dynamics of the triplet, and its inherent lepton number violating interactions, lead to the generation of a lepton asymmetry during inflation. The resultant baryon asymmetry, inflationary predictions and neutrino masses are consistent with current observational and experimental results. Introduction.|Despite the great successes of the [30{34]. However, to explain the existence of neutrino Standard Model (SM) at describing low energy scales, masses, only one triplet Higgs is required. We propose there remain many open problems that demand the ex- a mechanism by which successful Leptogenesis and istence of new physics. These issues include the mecha- neutrino mass generation can occur, with the addition nism for the epoch of rapid expansion in the early uni- of only a single triple Higgs. This triplet Higgs, in verse (inflation [1{5]), the origin of neutrino masses, and combination with the SM Higgs, will simultaneously give the source of the observed baryon asymmetry. Although rise to a Starobinsky-like inflationary epoch [35{41]. inflation is currently considered an integral component of standard cosmology, the exact nature of the inflation- Baryogenesis from a Complex Scalar| Following ary epoch remains unknown. The existence of non-zero [11], we consider a complex field φ with a global U(1) neutrino masses and the observed baryon asymmetry are charge Q and non-trivial potential V . Assuming it has a key pieces of evidence for physics beyond the SM. Each large initial field value in the early universe, φ will begin of these issues are tied to early universe physics, with any to oscillate once the Hubble parameter becomes smaller associated discoveries having significant implications for than its mass m. The dynamics of φ may give rise to both particle physics and cosmology. an asymmetry number density associated with its U(1) An exciting possibility to explore is whether each of charge, these unknowns could be explained within a unified y _ framework. There have been multiple attempts to do nφ = 2QIm[φ φ] ; (1) so in the past, but it is difficult to provide solutions to all three problems simultaneously with a single addition which satisfies the equation of motion, to the SM. For example, the SM plus three right-handed neutrinos can explain the neutrino masses via the see- @V n_ + 3Hn = Im φ : (2) saw mechanism [6{9] and generate the baryon asymme- φ φ @φ try through Leptogenesis [10], but not the inflationary arXiv:2106.03381v1 [hep-ph] 7 Jun 2021 sector. Inflationary Baryogenesis has been widely investi- To generate a non-vanishing U(1) asymmetry, the gated in the literature [11{22], but with few cases able to 1 potential V must contain an explicit U(1) breaking simultaneously explain each of the issues named above. term, which is generally assumed to be small. If the In this letter, we study the possibility that these three U(1) symmetry is composed of the global U(1) or problems can be solved through a simple extension to B U(1)L symmetries, a baryon number asymmetry can the SM by a single triplet Higgs. It has been known for a be generated prior to the Electroweak Phase Transition long time that with the addition of one triplet Higgs the (EWPT). In the following, we will consider a triplet baryon asymmetry cannot be generated through thermal Higgs which is doubly charged under the lepton number Leptogenesis, but rather requires the introduction of a symmetry U(1)L. There exist interaction terms between second triplet Higgs [25{29], or a right-handed neutrino the triplet and SM Higgs' that explicitly violate lepton number, providing a possible path for Leptogenesis. 1 Inflation with Leptogenesisesis by the right-handed sneutrino has Model Framework| Consider the general La- been considered in [23, 24]. grangian describing the SM Higgs doublet H, and triplet 2 Higgs ∆, non-vanishing ∆0 VEV can be approximated in the limit M∆ vEW as, L 1 2 µν y p = − MP R − f(H; ∆)R − g (DµH) (Dν H) 2 −g 2 0 µvEW h∆ i ' 2 ; (8) µν y 2m −g (Dµ∆) (Dν ∆) − V (H; ∆) + LYukawa;(3) ∆ where the SM Higgs VEV is v = 246 GeV. Note that y y EW where f(H; ∆) = ξ H H + ξ ∆ ∆ + :::, M is the re- 0 0 H ∆ p the ∆ VEV is bounded by O(1) GeV > h∆ i & 0:05 duced Planck mass, and R is the Ricci scalar. The Higgs' eV, in order to generate the observed neutrino masses, H and ∆ can be parameterized by, while ensuring yν is perturbative up to Mp. The upper p 0 h+ ∆+= 2 ∆++ bound on the ∆ VEV is derived from T-parameter H = ; ∆ = p ; (4) h ∆0 −∆+= 2 constraints determined by precision measurements [42]. where h and ∆0 are the neutral components of H and Trajectory of Inflation| The inflationary setting ∆ respectively. The LYukawa term contains not only will be induced by both Higgs' through there non- the Yukawa interactions of the SM fermions, but also minimal couplings to gravity. These couplings act to a new interaction between the left-handed leptons and flatten the scalar potential for large field values. This the triplet Higgs ∆, form of inflationary mechanism has been utilized in stan- dard Higgs inflation, and results in a Starobinsky-like in- SM 1 ¯c LY ukawa = LYukawa − yijLi ∆Lj + h:c: (5) flationary epoch [35, 43{54]. We consider the following 2 non-minimal coupling, The neutrino mass matrix will be generated through 1 1 0 f(H; ∆) = ξ jhj2 + ξ j∆0j2 = ξ ρ2 + ξ ρ2 ; (9) this interaction term, once ∆ obtains a non-zero vacuum H ∆ 2 H H 2 ∆ ∆ expectation value (VEV). Through this interaction we where we have utilized the polar coordinate parametriza- assign a lepton charge of QL = −2 to the triplet Higgs, tion h ≡ p1 ρ eiη, ∆0 ≡ p1 ρ eiθ. An inflation- thus opening the possibility that it may play a role in the 2 H 2 ∆ origin of the baryon asymmetry. ary framework consisting of two non-minimally coupled The potential for the Higgs' V (H; ∆) is given by, scalars has been considered in the past, and found to ex- hibit a unique inflationary trajectory [52]. In the large 2 y y 2 2 y V (H; ∆) = −mH H H + λH (H H) + m∆Tr(∆ ∆) field limit the ratio of the two scalars is fixed by, +λ Tr(∆y∆)2 + λ (HyH)Tr(∆y∆) s 3 1 ρ 2λ ξ − λ ξ y 2 y y H ∆ H H∆ ∆ +λ2(Tr(∆ ∆)) + λ4H ∆∆ H ≡ tan α ' ; (10) ρ∆ 2λH ξ∆ − λH∆ξH λ + µ(HT iσ2∆yH) + 5 (HT iσ2∆yH)(HyH) M where the derivation of this trajectory is given in Section P IB. The inflaton can then be defined as ' which is related 0 λ5 T 2 y y + (H iσ ∆ H)(∆ ∆) + h:c: + ::: ; (6) to ρH and ρ∆ through, MP ρH = ' sin α; ρ∆ = ' cos α; where the terms given in the square brackets [:::] violate ξ ≡ ξ sin2 α + ξ cos2 α : (11) lepton number, in which we have included dimension five H ∆ operators that are suppressed by MP . Even if they play We utilise the following Lagrangian, no role in low energy physics, they could be important L 1 1 1 p = − M 2 R − ξ'2R − gµν @ '@ ' during the early universe epochs of inflation and reheat- −g 2 P 2 2 µ ν ing. Note, the LHC has placed a lower limit on m∆ 1 of ∼ 800 GeV from searches for the associated doubly- − '2 cos2 α gµν @ θ@ θ − V ('; θ) ; (12) 2 µ ν charged Higgs. To simplify our analysis, we only focus on the neutral where components of ∆ and H, which have non-trivial VEVs. ~ ! 1 2 2 λ 4 3 λ5 2 Thus, V can be simplified as follows, V ('; θ) = m ' + ' + 2' µ~ + ' cos θ ;(13) 2 4 MP 0 2 2 2 0 2 4 0 4 V (h; ∆ )= −mH jhj + m∆j∆ j + λH jhj + λ∆j∆ j and 2 0 2 2 0∗ λ5 2 2 0∗ 2 2 2 2 2 +λH∆jhj j∆ j − µh ∆ + jhj h ∆ m = (m∆ cos α − mH sin α) ; MP 4 2 2 4 0 λ = λH sin α + λH∆ sin α cos α + λ∆ cos α ; λ ∗ + 5 j∆0j2h2∆0 + h:c: + ::: ; (7) 1 M µ~ = − p µ sin2 α cos α ; P 2 2 where λ∆ = λ2 + λ3 ; and λH∆ = λ1 + λ4 . All of the ~ 1 4 0 2 3 λ5 = − p (λ5 sin α cos α + λ sin α cos α) : (14) parameters must satisfy the stability condition, and the 4 2 5 3 Since the value of lepton asymmetry is dependent upon Lepton Number Density| Now that we have de- the motion of θ, we consider it to be a dynamical field.
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