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Moduli-induced axion problem Kazunori Nakayama (University of Tokyo) T.Higaki, KN, F.Takahashi, JHEP1307,005 (2013) [1304.7987] SUSY2013 @ ICTP, Trieste, Italy (2013/8/26)

What we have shown : Kahler moduli : T j = τ j + ia j moduli axion Moduli decays into very light axion : Too much axionic dark radiation τ j 2a j in light of PLANCK

Brief review of moduli problem

Moduli Problem [ Coughlan et al. (1983), Ellis et al. (1986), Banks et al. (1993), de Carlos et al. (1993) ] Moduli = Light scalar field in compactification of extra dimensions in String theory At H~m, moduli begins to oscillate around minimum with typical amplitude M P V (T ) M P T

Moduli Problem Moduli abundance ρ T s = 1 8 T R zi M P 2 10 5 GeV TR 10 6 GeV zi M P 2 Moduli lifetime T : reheat temperature R : moduli initial amplitude z i τ T m 3 T M 2 P 1 10 4 sec 1TeV m T 3 Big bang nucleosynthesis constraint ρ T s 10 14 GeV [ Kawasaki, Kohri, Moroi (2004) ]

Moduli Problem Moduli abundance ρ T s = 1 8 T R zi M P Moduli lifetime τ T m 3 T M 2 P 2 10 5 GeV 1 10 4 sec 1TeV Big bang nucleosynthesis constraint T : reheat temperature R : moduli initial amplitude z i m T 3 TR 10 6 GeV Moduli problem zi M P 2 ρ T s 10 14 GeV [ Kawasaki, Kohri, Moroi (2004) ]

Heavy moduli? Moduli decay before BBN (m T O(10) TeV) Heavy SUSY moduli (e.g., KKLT) m T m 3/2 Heavy non-susy moduli m T m 3/2

Heavy moduli? Moduli decay before BBN (m T O(10) TeV) Heavy SUSY moduli (e.g., KKLT) m T m 3/2 Moduli decay into gravitino Moduli-induced gravitino problem [Endo, Hamaguchi, Takahashi (2006), Nakamura,Yamaguchi (2006) ] Heavy non-susy moduli m T m 3/2 Moduli decay into its axionic partner Moduli-induced axion problem [ Cicoli, Conlon, Quevedo (2012), Higaki, Takahashi (2012), Higaki, KN, Takahashi (2013) ]

Moduli-induced axion problem T.Higaki, KN, F.Takahashi, 1304.7987

Moduli in typeiib string Kahler moduli : Shift symmetry : T T T + iα cf) 10d gauge symmetry C 4 C 4 + dλ Kahler potential : K = K(T + T ) T T τ + ia 2KTT axion Suppose that moduli stabilization does not give axion mass

General analysis on moduli decay T.Higaki, KN, F.Takahashi, 1304.7987 axion Γ(τ 2a) = 1 64π K 2 TTT K 3 TT m 3 τ τ gauge boson Γ(τ A µ A µ ) = N g 128π T f vis 2 (Ref vis ) 2 m 3 τ K TT f vis (T ) : gauge kinetic function Higgs boson Γ(τ HH) 1 8π g 2 T K TT Z u Z d m 3 τ K g(t + T )(H u H d +h.c.) Note : decay into their superpartners can also be sizable

General analysis on moduli decay T.Higaki, KN, F.Takahashi, 1304.7987 axion Γ(τ 2a) = 1 64π K 2 TTT K 3 TT m 3 τ τ Branching ratio into axion gauge boson (B a ) Higgs boson generally O(1) is Γ(τ A µ A µ ) = f vis (T ) Γ(τ HH) 1 8π N g 128π T f vis 2 (Ref vis ) 2 m 3 τ K TT : gauge kinetic function g 2 T K TT Z u Z d m 3 τ K g(t + T )(H u H d +h.c.) Note : decay into their superpartners can also be sizable

Planck constraint on Neff Radiation energy density ρ rad = 1+ 7 8 N eff 4/3 4 11 ρ γ CMB constraint: N eff =3.36 +0.68 0.64 @ 95%CL Planck+WMAP pol+ high l [Ade et al. 1303.5076] Axion dark radiation abundance: N eff = 43 7 1/3 10.75 g (T d ) B a 1 B a B a 0.2 Constraint on moduli stabilization model

Let us see some examples. 1. Large Volume Scenario 2. KKLT String axion model

Ex 1) Large Volume Scenario [ Balasubramanian et al. (2005), Conlon, Quevedo, Suruliz (2005) ] Swiss-Cheeze CY: V = V 0 V hole τ b The simplest : V 0 =(T b + T b )3/2 Kahler and Superpotential V hole =(T s + T s ) 3/2 D7 τ s K = 2 ln(v + ξ) W = W 0 + A s e 2πT s

Ex 1) Large Volume Scenario τs b 2 s A s 2 e 2b sτ s V = V Swiss-Cheeze CY: V = V 0 V hole V τ 3/2 e 2πτ s e 2πξ gs 1 b Minimization The simplest : V 0 =(T b + T b )3/2 Kahler and Superpotential b s A s W 0 τ s e b sτ s V 2 + ξ W 0 2 [ Balasubramanian et al. (2005), Conlon, Quevedo, Suruliz (2005) ] V hole =(T s + T s ) 3/2 gs 3/2 V 3 2/3 D7 τ b Large Volume Scenario (LVS) τ s K = 2 ln(v + ξ) W = W 0 + A s e 2πT s Stabilized a la KKLT m τs m as Stabilized by alpha correction. Im T b = a b Volume axion ( ) remains massless

Mass scales Gravitino mass m 3/2 e K/2 W 0 1 V for W 0 O(1) Moduli masses m τb 1 V 3/2 m ab =0 : Axion Soft mass (sequestered scenario) m soft 1 V 2 ( Moduli-matter coupling : m τs m as 1 V : Lightest modulus K MSSM = Φ i 2 +(zh u H d +h.c.) (T b + T b ) ) E.g., V 10 7 m 3/2 10 11 GeV m τb 10 7 GeV

Moduli decay rate [Cicoli, Conlon, Quevedo (2012), Higaki, Takahashi (2012) Angus, Conlon, Haisch, Powell (2013)] Two axion : τ b 2a Γ a = 1 48π m 3 τ b MP 2 Two Higgs : τ b 2H Γ H = z2 24π m 3 τ b MP 2 Branching ratio into axion: B a = 1 1+2z 2 Independent of moduli mass

Ex 2) QCD axion in KKLT String theoretic QCD axion model [ J.Conlon (2006), K.Choi, K.S.Jeong (2006) ] K = 2lnV [ K.Choi, K.S.Jeong (2006) ] V =(T 0 + T 0 )3/2 κ 1 (T 1 + T 1 )3/2 κ 2 (T 2 + T 2 )3/2 W = Ae αt 0 + Be β(t 1+nT 2 ) + W 0 D7 τ 0 τ 1 τ 2

SM brane wraps cycle T2 SM gauge kinetic function : L = A nt 1 T 2 s + ia f vis = T 2 4π d 2 θf vis W a W a +h.c. s τ 2 G a µνg µνa + a τ 2 G a µν G µνa SM D7 brane

SM brane wraps cycle T2 SM gauge kinetic function : L = A nt 1 T 2 s + ia f vis = T 2 4π d 2 θf vis W a W a +h.c. s τ 2 G a µνg µνa + a τ 2 G a µν G µνa QCD axion to solve strong CP problem SM D7 brane

SM brane wraps cycle T2 SM gauge kinetic function : L = A nt 1 T 2 s + ia f vis = T 2 4π d 2 θf vis W a W a +h.c. s τ 2 G a µνg µνa + a τ 2 G a µν G µνa Lightest moduli (saxion) QCD axion to solve strong CP problem SM D7 brane

Moduli (Saxion) decay rate Ms 3 1 n3 κ 2 1 + κ2 2 2 n 3 κ 2 1 V φ 3/2 m3 s Two axion : Γ a (n2 κ 2 1 κ 2 2) 2 768πκ 3 2 M 3 s M 2 P m s O(10 3 )TeV Gauge boson : Γ g κ 2 8π M 3 s M 2 P : Not loop suppressed Decay into gluon is sizable in contrast to (usual) saxion decay in SUSY axion model. [ T.Higaki, KN, F.Takahashi, 1304.7987 ]

Detecting/constraining axionic dark radiation The presence of axionic dark radiation seems to be ubiquitous in string theory N eff O(0.1) Can we probe it? Axion conversion into X-ray photon in galaxy cluster [ J.Conlon, M.C.D.Marsh, 1305.3603] Axion-photon conversion in the early Universe under primordial magnetic field Any other idea? [ T.Higaki, KN, F.Takahashi, 1306.6518]

B Detecting/constraining a axionic dark radiation γ The presence of axionic dark radiation seems L = a M F µν F µν to be ubiquitous in string theory N eff O(0.1) Can we probe it? Axion conversion into X-ray photon in galaxy cluster [ J.Conlon, M.C.D.Marsh, 1305.3603] Axion-photon conversion in the early Universe under primordial magnetic field Any other idea? [ T.Higaki, KN, F.Takahashi, 1306.6518]

Summary Light axions often appear after moduli stabilization Moduli branch into axion is generically O(1) Planck constraint : B a 0.2 The branch does not depend on moduli mass The problem exists even for heavy moduli Cosmological test of compactification Moduli-induced axion problem model (m T O(10) TeV)

Cosmological test of compactification model

Appendix

Possible Solutions to moduli problem 1. Thermal inflation for diluting moduli Dilution of baryon asymmetry Domain wall problem [ Lyth, Stewart (1996) ] 2. Adiabatic suppression mechanism [ A.Linde (1996) ] V c 2 H 2 T 2 + m 2 T (T T 0 ) 2 c 1 Suppression is not exponential but power in c High inflation scale & low reheat temp. is needed. [ KN, F.Takahashi, T.Yanagida (2011) ]

Moduli abundance V (T )=ch 2 T 2 + m 2 T (T z 0 ) 2 (c O(1)) [ For c 1, see KN, Takahashi, Yanagida, 1109.2073 ] H inf m T : T i z 0 ρ T s 1 8 T R z0 M P 2 H inf m T [ cf. Kallosh-Linde bound ] : T i H2 inf m 2 T z 0 ρ T s 1 8 T R z0 M P 2 Hinf m T 2 (m inf m T ) ρ T s 0 (m inf m T ) V (T ) T i z 0 T

General analysis on moduli decay T.Higaki, KN, F.Takahashi, 1304.7987 Moduli T K = K(T + T ) Canonically normalized moduli & axion T T τ + ia 2KTT Moduli decay into axion pair L = K TTT 2K 3/2 TT τ( a) 2 Γ(τ 2a) = 1 64π K 2 TTT K 3 TT m 3 τ Moduli decay into axino pair (if kinematically allowed) L = 1 2 K TTT K 3/2 TT τ iã σ µ µ ã + i( µ ã ) σ µ ã Γ(τ 2ã) = 1 8π K 2 TTT K 3 TT m 2 ãm τ

General analysis on moduli decay Coupling to MSSM sector T.Higaki, KN, F.Takahashi, 1304.7987 Gauge kinetic function f vis (T ) Moduli decay into gauge boson pair L = 1 4 2K TT (Ref vis ) Re( T f vis )τf a µνf µνa Im( T f vis )τf a µν F µνa Γ(τ A µ A µ ) = N g 128π T f vis 2 (Ref vis ) 2 m 3 τ K TT Moduli decay into gaugino pair 1 L = 4 2K TT (Ref vis ) ( T f vis )(FT T + F T T )+( T 2 f vis )F T τλ a λ a +h.c. Γ(τ λλ) N g 128π ( T f vis )(F T T + F T T ) 2 (Ref vis ) 2 m τ K TT Other terms are suppressed by gaugino mass

General analysis on moduli decay Coupling to MSSM sector T.Higaki, KN, F.Takahashi, 1304.7987 K Z u H u 2 + Z d H d 2 + g(t + T )(H u H d +h.c.) Moduli decay into Higgs boson pair L g T 2KTT Z u Z d ( 2 τ)(h u H d +h.c.) Γ(τ HH) 1 8π g 2 T K TT Z u Z d m 3 τ Other terms are suppressed by Higgs masses Moduli decay into higgsino pair L = 1 2KTT Z u Z d (2gT + gk T )m 3/2 + g T (F T T + F T T )+2g TTF T τ H u Hd +h.c Γ(τ H H) = 1 8π c τ h h 2 K TT Z u Z d m τ Other terms are suppressed by higgsino mass

Moduli-MSSM matter coupling SM on singularity Kahler potential : y phys = K MSSM = Φ i 2 +(zh u H d +h.c.) (T b + T b )a ek/2 y = τ 3/2 b Zi Z j Z k τ 3a/2 b Physical Yukawa should not depend on V [ Conlon, Cremades, Quevedo (2006) ] y a =1 No-scale form SM

Soft mass in the no-scale model K = 3ln G T G T =3 T + T 1 3 { Φ 2 + z(h u H d +h.c.)} 3 ln(t + T )+ Φ 2 + z(h u H d +h.c.) T + T T dominantly breaks SUSY m 2 φ = e G φ G k φg k R φ φt T G T G T + K φ φ = m 2 3/2 K φ φ 3K T T (K φ φt T K φ φk T φ φk T φ φ) φ G φ = φ G T =0 =0 mu-term in the no-scale model µ = e G/2 u G d = m 3/2 [g g T K T T K T ]=0 K g(t + T )(H u H d +h.c.) g = z T + T

SM D7 wrapping on 4-cycle T2 Kahler potential : K = (T 2 + T 2 )λ { Q i 2 + z(h u H d +h.c.)} V 2/3 y phys = ek/2 Zi Z j Z k y τ 3λ/2 2 y Yukawa dependence on T2 S DBI Σ 4d S 4d λγ i ( i + A i )λ =1 ψ 6 ψ 6 β for τ 2 βτ 2 y phys y phys β for τ 2 βτ 2 Σ ψ 6 ψ 6 d 4 x ψ 4 γ µ µ ψ 4 + Σ = τ 2 Σ ψ 6 φ 6ψ 6 d 4 xφ 4 ψ4 ψ 4 = y_phys SM D7 brane λ = 1 3 τ 2

Moduli-MSSM Gauge coupling DBI action S DBI = µ p p+1 d p+1 xe φ det (G + B 2πα F ) Dp brane worldvolume α (p 3)/2 4g s (2π) p 2 d p+1 x g tr F µν F µν gauge field on Dp brane Dp brane tension µ p = α (p+1)/2 (2π) p 4d gauge coupling : 1 g 2 YM = α(3 p)/2 g s (2π) p 2 V p 3 Kahler moduli Chern-Simons action S CS = µ p p+1 C q e 2πα F B 2 : Dp-brane R-R fields µ p C p+1 +2πα C p 1 trf +2π 2 α 2 p+1 p+1 p+1 axion C p 3 trf 2