Affleck-Dine leptogenesis via multiscalar evolution in a seesaw - PowerPoint PPT Presentation

宇宙線研究所理論研究会「初期宇宙と標準模型を超える物理」 高山 務 東京大学宇宙線研究所 Affleck-Dine leptogenesis via multiscalar evolution in a seesaw model (ICRR, Univ of Tokyo) Dec. 11. 2007 共同研究者 : 瀬波大土 JCAP11(2007)015 M.Senami, TT

・ Outline １ Introduction ・ Leptogenesis via Affleck-Dine mechanism: an alternative to thermal leptogenesis in SUSY N only (Allahverdi & Drees, 2004) ˜ multiscalar -direction and RH-sneutrino LH u ２ Set-up ・ Scalar potential ・ initial condition ３ Evolution of scalar fields ４ Evolution of asymmetry ５ Constraints ６ Resultant baryon asymmetry ７ Summary

１ . Introduction Standard Model (SM) + Heavy right-handed Majorana neutrino possible solution of two unsolved problem of SM Origin of small neutrino mass 1) m ν � O (0 . 1)eV seesaw mechanism Majorana mass: Dirac mass: m ¯ M ¯ L ν R ν R : right-handed neutrino ν R ν R lighter mass eigenvalue ∼ m 2 M 2) Origin of baryon asymmetry − 0 . 4 × 10 − 11 (WMAP) n B baryon-to-entropy ratio: = 8 . 7 +0 . 3 s example: thermal leptogenesis

１ . Introduction ・ sufficient baryon asymmetry requires T R > M > 10 9 GeV in SUSY, gravitino is overproduced unless T R < 10 8 GeV alternatives ？ many non-thermal leptogenesis scenarios are considered... Affleck-Dine leptogenesis from right-handed sneutrino � � � � 1 1 φ 0 ・ -flat direction LH u L = , H u = √ 0 √ φ 2 2  LH u -flat direction has large vev   AD mechanism in multiscalar evolution (Senami & Yamamoto, 2003)  LH u -flat direction has vanishing vev   - flat direction is irrelevant? (Allahverdi & Drees, 2004) LH u 

１ . Introduction: Affleck-Dine mechanism complex scalar field with baryon (or lepton) number φ 1 total baryon (or lepton) number in homogeneous condensate of φ φ ∗ φ − φ ∗ ˙ φ ) = 2 | φ | 2 ˙ n φ = i ( ˙ φ = | φ | e i θ n = n φ − ¯ θ “angular momentum” of φ baryon (lepton) number rotational motion after inflation Im( φ ) baryon (lepton) number in condensate φ - ( -) conserving decay B L Re( φ ) baryon (lepton) number in SM particles

１ . Introduction Allahverdi & Drees’s scenario (brief review) N | 2 + C I H 2 | ˜ N | 2 + ( Bm 3 / 2 ˜ N 2 + h.c. ) + ( bH ˜ N 2 + h.c. ) V ( ˜ 0 | ˜ N ) = m 2 ・ asymmetry is produced via Affleck-Dine mechanism n ˜ N − n ˜ N ∗ ・ SM sector lepton number n ˜ N − n ˜ N ∗ -violating decay of ˜  N CP  or SUSY-breaking from thermal effect  thermal mass ∆ m 2 B = 2 ∆ m 2 L � = Γ ˜ Γ ˜ N → ¯ N → H u ˜ F H u ¯ ˜ L bosonic, fermionic, ∆ L = 1 ∆ L = − 1 ・ asymmetry is oscillating: n ˜ N ∗ ≃ t − 2 M − 1 N N 2 0 sin(2 Bm 3 / 2 t ) δ e ff N − n ˜ tuning is needed (decay at maximum) | B | m 3 / 2 ≃ Γ ˜ N assumption: -direction does not contribute (always ) � φ � = 0 LH u due to interaction with , -flat direction gets large value! ˜ N LH u

２ . Set-up of the model: scalar potential ２ . Set-up superpotential: W = W MSSM + y ν NLH u + M N λ 2 N 2 + N 4 4 M Pl m ν = y 2 ν v 2 seesaw mechanism: · M N N ) = y 2 N | 2 + λ 2 4 | φ | 4 + M N | ˜ N | 2 + y 2 V ( φ , ˜ ν | φ | 2 | ˜ | ˜ N | 6 ν M 2 F-term Pl �� y ν � � N ∗ + y ν λ N ∗ 3 + λ M N cross term 2 M N φ 2 ˜ φ 2 ˜ N ˜ ˜ N ∗ 3 + h.c. + in F-term 2 M Pl M Pl + c φ H 2 | φ | 2 − c N H 2 | ˜ N | 2 Hubble-induced SUSY breaking mass term �� bH � � N 2 + a y y ν N + a λ λ H φ 2 ˜ 2 M N ˜ H ˜ N 4 + + h.c. 2 4 M Pl Hubble-induced SUSY breaking + V th ( φ ) thermal-mass correction A- and B-term ※ , | a | ∼ 1 , | b | ∼ 1 c φ ∼ 1 > 0 , c N ∼ 1 > 0 � � � � 1 1 φ 0 φ ˜ LH u ： direction N ： RH-sneutrino L = , H u = √ 0 √ φ 2 2

２ . Set-up of the model: initial conditions NR F-term can not be during the inflation, H ≫ M N used to trap ˜ N ini N : displaced from the origin ˜ ・ radial direction: | ˜ N ini | = M GUT D-term (Hubble-induced mass and D-term) +Hubble ※ is assumed M N / λ > 1 . 2 × 10 14 GeV NR F-term +Hubble ・ phase direction can either be randomly displaced from B-term minima  ( case)  H inf ≫ M N F-term | ˜ N | or, trapped at B-term minima ( case)  H inf � M N M GUT ※ hereafter, M GUT = 10 16 GeV : fixed at the origin due to large effective mass φ m e ff ∼ y ν M GUT � φ � hor ∼ H H φ has quantum fluctuation around the origin 2 π m e ff

・ ・ ・ ３ . Evolution of scalar fields ① during inflation: H = H inf > M N � bH � N | 2 + N 2 + h.c. N ∼ − c N H 2 | ˜ 2 M N ˜ V ˜ + D − term due to balance between ˜ N Hubble-induced mass and D-term, | ˜ N | ∼ M GUT phase-direction is assumed to be trapped at the minimum of B-term contribution V φ ≃ c φ H 2 | φ | 2 + y 2 ν | ˜ N | 2 | φ | 2 is trapped at the origin φ φ

３ . Evolution of scalar fields ※ in general, Hubble-induced A- and B-terms ② after inflation: H < M N are effective only during inflation � λ M N � N | 2 + N ∗ 3 + h.c. N | ˜ N ˜ ˜ N ≃ M 2 V ˜ M Pl | ˜ ・ oscillates with ˜ N | ∝ H N ˜ N ・ cross term in F-term contribution serves as a source of asymmetry ・ displacement between B-term and cross term gives -violation CP � y ν � V φ ≃ c φ H 2 | φ | 2 + y 2 N | 2 | φ | 2 + 2 M N φ 2 ˜ N ∗ + h.c. ν | ˜ is trapped at the origin φ ・ φ

３ . Evolution of scalar fields in general, m 2 I, e ff | δ I | 2 inflaton: , : oscillating H 2 ≃ I = � I � + δ I δ I 3 M 2 Pl “Hubble-induced” - or -terms A ∝ δ I B due to rapid oscillation of , these terms effectively vanish δ I ※ higher order terms of can give effectively non-vanishing - or -terms ∝ ( δ I ) 2 ∂ I W A B however, these terms decrease rapidly � � a  for example, K ( I, φ ) = I † I + φ † φ + I † φφ + h.c. 2 M Pl  W ( I ) = I { v 2 − gI n / ( n + 1) } (new inflation)  V ∋ − aW φ φ † e K F ∗ + h.c. = aW φ φ † e K 2 v δ I † − aW φ φ † e K ( δ I † ) 2 ¯  I + h.c. M Pl M Pl M Pl  H 2 ≃ 4 v 2 | δ I | 2  3 M 2 Pl

・ ・ ・ ３ . Evolution of scalar fields ③ destabilization: ※ Allahverdi & Drees did not consider this process � λ M N � N | 2 + N ∗ 3 + h.c. N | ˜ N ˜ ˜ N ≃ M 2 V ˜ M Pl | ˜ after and decrease sufficiently, N | H ˜ N N | 2 + c φ H 2 y ν M N | ˜ ν | ˜ N | ∼ y 2 � y ν � N | 2 | φ | 2 + 2 M N φ 2 ˜ N ∗ + h.c. ν | ˜ V φ ≃ y 2 + y 2 ν | φ | 4 / 4 two minima appear in opposite directions φ minimize the cross term these two minima are determined by ˜ N position of these minima rotate together with the rotation of ˜ N

・ ・ ３ . Evolution of scalar fields N | 2 + c φ H 2 ④ after destabilization: H < M N , y ν M N | ˜ ν | ˜ N | > y 2 � y ν � N | 2 + y 2 N | 2 | φ | 2 + 2 M N φ 2 ˜ N ∗ + h.c. N | ˜ ν | ˜ N ≃ M 2 V ˜ oscillates around the minimum ˜ N ˜ N determined by rotating φ � y ν � N | 2 | φ | 2 + 2 M N φ 2 ˜ N ∗ + h.c. ν | ˜ V φ ≃ y 2 + y 2 ν | φ | 4 / 4 oscillates around one of minima φ φ determined by the cross term ・ to which minima falls is determined by φ quantum fluctuation spatially inhomogeneous

・ ・ ３ . Evolution of scalar fields ˜ N = y 2 ⑤ after decay of : N H < Γ ˜ ν M N / (4 π ) ˜ （ friction term dominates the evolution of ） N after the condensate of decays, ˜ N ˜ N is fixed at the minima ˜ N V φ , e ff ≃ y 4 | φ | 6 ν + V th ( φ ) M 2 4 N oscillates around the origin φ φ ・ the direction of rotation is determined by the rotation of at ② ˜ N

⑤ ① ② ③ ④ ３ . Evolution of scalar fields: numerical result evolution of scalar fields (numerical calculation) 10 17 10 16 | ˜ N | 10 15 10 14 field [GeV] 10 13 10 12 10 11 | φ | 10 10 10 9 10 8 10 7 10 6 10 13 10 12 10 11 10 10 10 9 10 8 10 7 10 6 10 5 10 4 H [GeV] M N = 10 11 GeV , y ν = 10 − 1 , T R = 2 × 10 6 GeV c φ = c N = 1 , λ = 10 − 4

３ . Evolution of scalar fields: remarks ※ Remarks: Allahverdi & Drees did not consider destabilization of φ we reconsidered this scenario in ② , must not be trapped at the minima of F-term contribution ˜ N N | 4 + λ 2 N | 2 − 2 λ M N N | ˜ | ˜ | ˜ V N,F NR = M 2 N | 6 M 2 M Pl Pl M N / λ > 1 . 2 × 10 14 GeV is needed φ final direction of rotation of is determined by the rotation of in ② ˜ N non-vanishing is generated L φ after averaging over initial quantum fluctuation of φ