Level Crossing between QCD Axion and ALP collaboration with Naoya Kitajima & Fuminobu Takahashi Ryuji Daido Tohoku Univ. 1505.07670 1510.06675 @TeVPa 2015 Kashiwa, Japan
Axions shift symmetry discrete shift symmetry Non-perturbative effect ・Axion Like Particles (e.g. String theory) 1/11 ・QCD axion (solves the strong CP) ✓ a a → a + C ◆� V ' Λ 4 1 � cos V = const F a a a θ 32 π 2 F ˜ F, | θ | . 10 − 10 L ⊃ a a H
Mixing 2/11 mixing temperature dependent T > 0 . 26 Λ QCD ✓ a ◆� ⌘ − 3 . 34 8 4 . 05 × 10 − 4 Λ 2 ⇣ V QCD = m a ( T ) 2 F 2 T 1 − cos QCD < Λ QCD F a m a ( T ) = a F a 3 . 82 × 10 − 2 Λ 2 QCD : F a T < 0 . 26 Λ QCD ✓ ◆� Λ 2 a H a V H = Λ 4 H n H + n a m H ≡ 1 − cos H F H /n H F H F a m a ( T = 0) m H m H < m a ( T = 0) m a ( T )
Level Crossing 3/11 Level crossing takes place! Hill, Ross, NPB 311, 253 (1988), Kitajima, Takahashi, 1411.2011 level crossing m 2 � � Mass m H m a ( T ) m 1 � � ✓ a ◆� V QCD = m a ( T ) 2 F 2 1 − cos a F a ✓ ◆� a H a V H = Λ 4 n H + n a 1 − cos H F H F a Time m H < m a ( T = 0)
High temperature Time evolution of the potential ALP Low temperature ALP global minima Crossing 4/11 Level heavy light θ ≡ a θ ≡ a F a F a n n o o i i x x a a D D C C Q Q θ H ≡ a H θ H ≡ a H F H F H ✓ a ◆� V QCD = m a ( T ) 2 F 2 1 − cos a F a ✓ ◆� a H a V H = Λ 4 n H + n a 1 − cos H F H F a
Timing of level crossing (ⅰ) (The axion starts to oscillate well before the level crossing.) The resonant transition occurs like the MSW effect. (ⅱ) The axion exhibits non-trivial behavior! 5/11 The potential changes adiabatically. The adiabaticity is broken. Kitajima, Takahashi, 1411.2011 RD, Kitajima, Takahashi, 1505.07670 RD, Kitajima, Takahashi, 1510.06675 H lc ⌧ H osc H lc ∼ H osc
6/11 RD, Kitajima, Takahashi, 1505.07670 Axion roulette 2.Initial energy is greater than the barrier. @ oscillation crest trough Two conditions satisfied, the axion passes through many crests and troughs of the potential. Axion roulette! ALP RD, Kitajima, Takahashi, 1510.06675 1.Kicked into different directions. π H lc 1 θ = O (0 . 1 − 1) H osc n 0.5 o i x n 2 a 2 /2 π f 2 a 0 � D C Q -0.5 ρ osc > Λ 4 − π -1 0 2 4 6 8 10 θ H 0 n 1 a 1 /2 π f 1
7/11 ALP (final value) Numerical Results QCD axion (initial value) The ALP takes different value even for . ( n H θ H ) f ( n H θ H ) f 1500 40 500 ( � H + 5 � ) f ( � H + 5 � ) f 20 0 0 - 500 - 20 - 1500 2.00000 2.00005 2.00010 0.5 1 1.5 2 2.5 3 θ i � i θ i � i θ i = a i F a The final value is highly sensitive to θ i δθ i ∼ 10 − 5 .
Numerical Results decay constant ALP mass 8/11 F H /n H [GeV] 10 12 ρ osc < Λ 4 ( n H θ H ) f Θ f 10 11 1000 100 H lc � & 1 10 H osc 0 H lc 10 10 . 0 . 1 10 - H osc 100 - 1000 - H lc 10 9 = O (0 . 1 − 1) 10 − 8 10 − 7 10 − 6 H osc ρ osc > Λ 4 m H [eV] F a = 10 12 GeV , θ i = 2 . 5 , n a = 5
If the axion roulette occurs, domain walls without cosmic strings are likely to be formed. It is cosmologically problematic. Solution 1 9/11 Domain wall problem Diluting the domain wall by inflation. It is unlikely that inflation continues until the QCD phase transition. ALP mass decay constant However, in our situation,..
Domain wall problem decay constant the spatial variation of . or ・Bias can be introduced if ・ determines identical minima. However, please note that.. Solution 2 10/11 ALP mass we cannot introduce bias. ・If the axion is trapped in identical minima, makes the domain wall unstable. Introduce a bias term and n H = 3 n H 0 2 π θ H n H � 1 ( θ H ) f < 2 π
・We studied level crossing between QCD axion and ALP. ・Stable domain wall is likely to be formed by the axion roulette. Summary ・We found that the axion roulette occurs if the timing of level crossing is close to that of oscillation. ・We determined the parameter region where the axion roulette takes place. or 11/11 the spatial variation of . for for 10 − 8 eV . m H . 5 × 10 − 7 eV , F H /n H . 10 11 GeV F a = 10 12 GeV 10 − 7 eV . m H . 5 × 10 − 6 eV , F H /n H . 10 9 GeV F a = 10 10 GeV ・Bias can be introduced if n H � 1 ( θ H ) f < 2 π
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