AFFLECK-DINE LEPTOGENESIS WITH VARYING PQ SCALE Kyu Jung Bae, - PowerPoint PPT Presentation

AFFLECK-DINE LEPTOGENESIS WITH VARYING PQ SCALE Kyu Jung Bae, Center for Theoretical Physics of the Universe, 
 based on JHEP 1702 (2017) 017 with H. Baer, K. Hamaguchi and K. Nakayama "Testing CP-Violation for Baryogenesis" @UMass-Amherst Mar. 29, 2018

INTRODUCTION • Baryogenesis via Leptogenesis - Due to (B-L)-conserving and (B+L)-violating process makes Lepton asymmetry Baryon asymmetry - Neutrino physics can show its footprints. • Affleck-Dine mechanism - scalar field dynamics in SUSY: CPV in SUSY breaking parameters - Along LHu direction: lepton number generation light neutrino mass required <10 -9 eV; neutrinoless double beta decay • Varying PQ scale - PQ scale ~ M p during leptogenesis but f a ~10 9-12 GeV afterwards neutrino mass ~10 -4 eV; suppress axion isocurvature

INTRODUCTION • Dine-Fischler-Srednicki-Zhitnitsky model - SUSY DFSZ model provides strong CP solution, mu-term, also RHN mass - Dilution from saxion decay determines final lepton(baryon) asymmetry - suppress unwanted lepton number violation during saxion oscillation � � � [ �� ] �������� ��� � � = � � ��� � � = �� � ��� � � � [ �� ] �������� ��� � � = � / � ��� � � = �� � ��� 10 12 10 12 10 - 5 10 - 8 10 - 7 10 - 6 10 - 5 10 - 4 10 - 4 10 - 3 10 - 3 T � < 1 GeV V e G 0 10 - 8 1 10 - 2 < T � 10 - 2 10 11 10 11 10 - 7 10 - 1 10 - 1 � � [ ��� ] � � [ ��� ] T � < 10 GeV 10 - 6 m � > 0.17eV m � > 0.17eV 10 10 10 10 m � > 0.48eV m � > 0.48eV f a � N DW < 5 × 10 8 GeV f a � N DW < 5 × 10 8 GeV 10. 10 9 10 9 10 5 10 5 10 2 10 3 10 4 10 2 10 3 10 4 � [ ��� ] � [ ��� ]

OUTLINE 1. Leptogenesis 2. AD mechanism along LHu direction 3. AD leptogenesis in DFSZ model with varying PQ scale 4. Summary

OUTLINE 1. Leptogenesis 2. AD mechanism along LHu direction 3. AD leptogenesis in DFSZ model with varying PQ scale 4. Summary

BARYON ASYMMETRY Baryon Asymmetry of the Universe: n B = n ¯ n B cf) if universe were observed: B s ' 10 − 10 ≃ 10 − 18 . symmetric n γ n γ • Inflation dilutes all pre-existing particles. • We need a source of B asym. after inflation . Sakharov’s conditions: • B violation • C & CP violation • departure from thermal equilibrium

B & L VIOLATION • In the SM, baryon & lepton number are (accidental) symmetry at the tree-level. • Due to chiral nature of leptons & quarks, B & L have anomalies ∂ µ J B ∂ µ J L = µ µ � B µ ν � N f W Iµ ν + g ′ 2 B µ ν � µ ν � − g 2 W I = 32 π 2 • At quantum level, (B-L) is conserved but (B+L) is violated. E M sph e − S inst = e − 4 π Γ ∼ α � 10 − 165 � = . O B = b 0 − N f B = b 0 B = b 0 + N f [ A sph , ϕ sph ] [ A , ϕ ] L = l 0 − N f L = l 0 L = l 0 + N f Figure from hep-ph/0212305 (B+L) violating vacuum transition

B & L VIOLATION • At high temperature, (B+L) violating transition via thermal fluctuation E “sphaleron” M sph Γ B + L /V ∼ α 5 ln α − 1 T 4 . B = b 0 − N f B = b 0 B = b 0 + N f [ A sph , ϕ sph ] [ A , ϕ ] L = l 0 − N f L = l 0 L = l 0 + N f Figure from hep-ph/0212305 • (B+L) violating interaction is in thermal equilibrium for 100 GeV < T < T sph ∼ 10 12 GeV • L number can be transferred into B number and vice versa.

LEPTOGENESIS • Number for asymmetry ⎧ � ( β µ i ) 3 � n i − n i = gT 3 β µ i + O fermions , , ⎨ � ( β µ i ) 3 � 6 2 β µ i + O , bosons . ⎩ • chemical potentials in equilibrium (SM) (Yukawa) µ qi − µ H − µ dj = 0 , µ qi + µ H − µ uj = 0 , µ li − µ H − µ ej = 0 � � µ qi + 2 µ ui − µ di − µ li − µ ei + 2 ( ∑ Y=0) � = 0 µ H N f i (SU(2) inst.) � (3 µ qi + µ li ) = 0 i � (QCD inst.) (2 µ qi − µ ui − µ di ) = 0 i • equations can be expressed by 2 N f + 3 µ d = − 6 N f + 1 µ u = 2 N f − 1 µ e = 6 N f + 3 µ l , 6 N f + 3 µ l , 6 N f + 3 µ l , − 1 4 N f µ q = 3 µ l , µ H = 6 N f + 3 µ l .

LEPTOGENESIS • B & L relations � B = (2 µ qi + µ ui + µ di ) , B = c s ( B − L ); L = ( c s − 1)( B − L ) i � e c s = (8 N f + 4) / (22 N f + 13) L i = 2 µ li + µ ei , L = L i i • Non-zero B & L are generated if (B-L) ≠ 0 in equilibrium B modified Sakharov ’s B − L > 0 B − L = 0 condition B − L < 0 • B violation (ii) L • ( B-L) violation (i) B = C ( B − L ) (equilibrium) Figure from hep-ph/0212305

Q: How do we generate (B-L) ≠ 0 in the early universe?

THERMAL LEPTO. Fukugita, Yanagida; Luty; Campbell, Davidson, Olive; Buchmuller, Di Bari, Plumacher (02, 02) Decay of thermally produced RHN: If , N is abundantly produced. T > m N When (out-of-equilibrium decay), L CP T < m N W 3 1 it decays through neutrino coupling. 2 M i N i N i + h i α N i L α H u CPV in coupling produces asymmetry l H H H H ✏ 1 ⌘ Γ ( N 1 ! LH u ) � Γ ( N 1 ! ¯ L ¯ N H u ) N + + N 1 N 1 N 1 H Γ N 1 l l l l ✓ M 1 ◆ ⇣ m ν 3 ⌘ ✏ 1 ⇠ 2 ⇥ 10 − 10 � e ff . 10 6 GeV 0 . 05 eV washout factor N in equilibrium; n N /s ∼ 1 /g ∗ ∼ 1 / 200 n L = ✏ 1 n N m N 1 = s ' 0 . 3 ⇥ 10 − 10 ⇣ κ ⌘ ✓ ◆ ⇣ n B s ' 0 . 35 n L M 1 m ν 3 ⌘ δ e ff 10 9 GeV 0 . 1 0 . 05 eV Buchmuller, Di Bari, Plumacher (05) T R & 1 . 5 × 10 9 GeV requires (naively) for enough N production

GRAVITINO PROBLEM proportional to T R Gravitino problem: ⌘ 2 ✓ 1 GeV ◆ ✓ ◆ ⇣ m e T R G h 2 = 0 . 21 g gravitinos are thermally produced Ω TP 10 8 GeV e 1 TeV m 3 / 2 → Bolz, Brandenburg, Buchmüller; Strumia g a q i G g a G q i G G g c g c q j q j g a g b g c g a g b g c q j q j decays into LSP with long life-time; either producing too much DM or spoiling BBN ; upper bound for T R Kawasaki, Kohri, Moroi, Yotsuyanagi

OUTLINE 1. Leptogenesis 2. AD mechanism along LHu direction 3. AD leptogenesis in DFSZ model with varying PQ scale 4. Summary

AFFLECK-DINE For a review, Dine, Kusenko (03) • Scalar field with B (or L) number, L = | ∂ µ φ | 2 − m 2 | φ | 2 j µ B = i ( φ ∗ ∂ µ φ − φ∂ µ φ ∗ ) • small quartic couplings L I = λ | φ | 4 + �φ 3 φ ∗ + δφ 4 + c.c. B CP ( for complex couplings ) • Eq. of motion y overdamp φ o φ = ( mt ) 3 / 4 sin( mt ) (radiation) t H � m , φ + ∂ V φ + 3 H ˙ ¨ ∂φ = 0 . φ o ( mt ) sin( mt ) (matter) If t φ = φ o is real. Im( ✏ + � ) � 3 o � i = a r m 2 ( mt ) 3 / 4 sin( mt + � r ) (radiation) φ i + 3 H ˙ ¨ φ i + m 2 φ i ≈ Im( � + δ ) φ 3 r . Im( ✏ + � ) � 3 o sin( mt + � m ) (matter) a m m 2 ( mt ) • Baryon number Im( ✏ + � ) � 4 o n B =2 a r sin( � r + ⇡ / 8) (radiation) m ( mt ) 3 / 2 Im( ✏ + � ) � 4 o 2 a m sin( � m ) (matter) m ( mt ) 2

POTENTIAL Complex quartic kicks scalar field to phase direction φ r φ i Q: How do we get large initial value?

SUSY BREAKING BY INFLATION Dine, Randall, Thomas (95, 96) • Large vacuum energy during inflation breaks SUSY - SUSY breaking potential arises and ~ H>>m V H ⊃ c H H 2 | φ | 2 negative c H is possible in non-minimal Kähler potential φ 4 - Together with or terms in F-term potential, φ 6 1 √ V = − H 2 | φ | 2 + M 2 | φ | 6 φ 0 ∼ HM

POTENTIAL When H>>m, scalar field stays at the potential minimum √ φ 0 ∼ HM φ r When H~m, scalar field starts oscillation φ i

AD LEPTOGENESIS Affleck, Dine; Dine, Randall, Thomas (95, 96) To realize AD mechanism, we need Murayama, Yanagida; Gherghetta, Kolda, Martin • light scalar (flat direction) carrying B or L number • small B (or L) and CP violating quartic potential In SUSY model, • LH u direction is flat (in SUSY limit) � � � � 0 v H u = L 1 = 0 v • quartic can be generated 1 + m SUSY ( a m φ 4 + h.c. ) L CP W 3 ( L i H u )( L i H u ) 2 M i 8 M linked to ( lightest ) neutrino mass m ν 1 ∼ v 2 M

AD LEPTOGENESIS Affleck, Dine; Dine, Randall, Thomas (95, 96) Murayama, Yanagida; Gherghetta, Kolda, Martin AD mechanism via LH u : 1 1 W 3 ( L i H u )( L i H u ) 8 M φ 4 W = 2 M i � | | 1 (F-term potential) 4 M 2 | φ | 6 . V F = φ | φ | 2 + m SUSY ( a m φ 4 + h.c. ) (soft SUSY breaking) V SB = m 2 8 M V H = − c H H 2 | φ | 2 + H 8 M ( a H φ 4 + h.c. ) (Hubble-induced SUSY breaking) 2 negative mass 2 � p Large VEV for H � m φ φ ' MH initial amplitude � i n L + 3 Hn L = m SUSY Eq. of motion: φ ∗ φ � φ ∗ ˙ 2 ( ˙ Im ( a m φ 4 ) + s: n L = i ˙ φ ) 2 M n L s = MT R ✓ m SUSY | a m | ◆ δ ph . where δ ph = sin(4 arg φ +arg a m ). p 12 M 2 H osc P

AD LEPTOGENESIS 1e+11 1e+10 1e+09 T R 1e+08 [GeV] 1e+07 1e+06 100000 10000 1e-12 1e-11 1e-10 1e-09 1e-08 1e-07 1e-06 Asaka, Fujii, Hamaguchi m ν 1 [eV] • Successful leptogenesis requires m ν 1 ∼ 10 − 9 eV ∼ × = 2 . 5 × 10 − 3 eV 2 = 7 . 4 × 10 − 5 eV 2 , | ∆ m 2 ∆ m 2 21 ∼ 31 | ∼ 2 ∼ − 3 2

OUTLINE 1. Leptogenesis 2. AD mechanism along LHu direction 3. AD leptogenesis in DFSZ model with varying PQ scale 4. Summary