Gravitational Waves from Hidden QCD Phase T ransition by Hiromitsu - PowerPoint PPT Presentation


 
 Gravitational Waves from 
 Hidden QCD Phase T ransition by Hiromitsu GOTO 
 Kanazawa University 
 in collaboration with 
 Mayumi AOKI, Jisuke KUBO 
 Based on Phys. Rev. D96 075045, (2017) arXiv:1709.07572 
 The 21st Regular Meeting of New Higgs Working Group Dec. 22, 2017


 EW Scale from 
 Classical Scale Invariance Breaking ✤ We focus on “Classical Scale Invariant Extension” 
 W.A. Bardeen, On naturalness in the standard model, FERMILAB-CONF-95-391 (1995) L SM | µ 2 → 0 λ HS ( S † S )( H † H ) + Scalar Portal Weakly : Colman-Weinberg Mechanism - Strongly : Dynamical Generation of Scale e.g. QCD 
 - Direct Transmission 
 J. Kubo, K. S. Lim, M. Lindner arXiv:1403.4262 S † S ∼ Λ 2 S † S H † H ⌦ ↵ ⌦ ↵ Scalar QCD λ HS H Indirect Transmission T. Hur, D-W. Jung, P. Ko and J-Y. Lee arXiv: 0709.1218, 1103.2571 ⌦ ¯ ⌦ ¯ λ HS h S i 2 H † H ∼ Λ 3 ↵ ↵ QCD yS ψψ ψψ H 2

✤ How can we test Indirect Transmutation? ⌦ ¯ ↵ Dynamical Origin : ψψ 6 = 0 Gauge Symmetry : G SM × SU( N c ) H T. Hur, D-W. Jung, P. Ko and J-Y. Lee arXiv: 0709.1218, 1103.2571 SM-singlet 
 N f L H H ⊃ − yS ¯ Explicit χ SB !! ψψ Vector-like Fermion Λ H h S i 6 = 0 h S SM-singlet Real Scalar V SM � � 1 L SM | µ 2 → 0 2 λ HS h S i 2 ( H † H ) EW D χ SB Dark Matter !! = Massive NG Bosons Hidden Baryon φ B × … U( N f ) L × U( N f ) R SU( N f ) V × U(1) V N 2 × f − 1 if y = 0 — we can obtain the symmetry by accident It may be good way to test it using DM as Hidden Hadron! 
 — BUT it becomes hopeless when couplings are too small… 3

✤ Our Target : Hidden Chiral Phase Transition 
 Explain not only Higgs but also Dark Matter Mass How deal with 
 QCD Phase Transition N f = 2+1 Pure SU(3) non-perturbative effect? ∞ Direct Calculation e.g. Lattice QCD cross over 3 = Effective Theory e.g. sigma model, 
 f N SM NJL model ,… m s What we have known so far In small y (Nc = Nf = 3) 
 1st-order PT realize First-order Chiral PT m u,d ∞ M. Holthausen, J. Kubo, K. S. Lim and M. Lindner, JHEP 1312 (2013) 076 
 Chiral limit 
 Y. Ametani, M. Aoki, HG, J. Kubo Phys Rev D 91(2015)115007 (Scale Invariance) How about GW from Hidden Chiral Phase Transition? 
 ⌦ ¯ — Chiral Condensation Not Higgs ↵ h h i 6 ψψ 4


 
 
 Nambu—Jona-Lasinio Model 
 for Low Energy Effective Theory ✤ NJL Model + U(1) A breaking term (KMT term) 
 ( N f = 3) L NJL = Tr ¯ ∂ − yS ) ψ + 2 G Tr Φ † Φ + G D (det Φ + h.c ) ψ ( i / 4-Fermi 6-Fermi cf. m c where ( Φ ) ij = ¯ ψ i (1 − γ 5 ) ψ j ✤ Same Global Symmetry as at Low Energy 
 L H U(3) L × U(3) R → SU(3) V × U(1) V U(1) A χ SB Pattern by KMT term 5

✤ Self-Consistent Mean Field Approximation L NJL define “BCS” vacuum |”BCS” > = | σ , φ ( π ,K,…) > h Φ i = � 1 diag . ( σ , σ , σ ) + i ( λ a ) T φ a � � ( Φ ) ij = ¯ ψ i (1 − γ 5 ) ψ j 4 G CP 
 CP 
 ¯ φ ¯ ψγ 5 λψ ψψ σ Odd Even ¯ Interactions ψψ , σ , φ L MFA = Tr ¯ ∂ − M ) ψ + at most quadratic in fermions ψ ( i / Effective Potential with cutoff Λ H Internal fermion mass 8 G σ 2 − G D 3 16 G 3 σ 3 + V MFA = Through integrating out the internal fermion, 
 we can obtain non-zero < σ > (D χ SB) and 
 calculate the mass spectrum for hidden hadrons: M, m σ and m φ . 6

✤ Mass Spectrum and Dark Matter Annihilation 5000 M ( λ H , λ HS , λ S ) = (0 . 13 , 0 . 01 , 0 . 19) M mS mDM 4000 m φ < m S m φ > m S Mass [GeV] φ S φ SM 3000 φ φ SM S h S φ h This channel open φ h S 2000 m S 1000 m φ 0 0.001 0.01 0.1 1 y y -3 Need 2m φ = m S to obtain correct Ω DM y ≦ O(10 ) - -48 2 At most σ SI ~ 10 cm around m φ = 100 GeV - 1st-order PT 7

✤ Hidden Chiral Phase Transition V EFF ( S, σ , T ) = V h → 0 SM+ S ( S ) + V NJL ( S, σ ) + V CW ( S ) + V FT ( S, σ , T ) + V RING ( S, T ) where 2.5 λ H = λ S = 0.13 , λ HS = 0.02 M = σ + yS − G D 8 G 2 σ 2 2.0 y=0.005 y=0.007 y=0.006 1.5 L H ⊃ − yS ¯ < M >/ T ψψ 1.0 Not only σ but also S 
 get non-zero VEV 
 0.5 in generally y ≦ 0.006. 0.0 Y. Ametani, M. Aoki, HG and J. Kubo, 
 550 600 650 Phys. Rev. D 91 (2015) no.11, 115007 T [ GeV ] We assume 3D Euclidian Action for mean fields as " # ◆ 2 ◆ 2 Z − 1 σ ( S, σ , T ) + 1 Z ✓ d σ ✓ dS Z Z d 3 r S 3 ( T ) = + V EFF ( S, σ , T ) 2 2 dr dr Multi-Fields Tunneling 
 Compute at loop level overshot/undershot method does not work 8

✤ Bubble Nucleation from Hidden Chiral Tunneling Equations of Motion for Multi-Fields Tunneling " ◆ 2 # d 2 σ ∂ Z − 1 dr 2 + 2 ∂ V EFF ( S, σ , T ) + 1 σ ( S, σ , T ) d σ ✓ d σ dr = Z σ ( S, σ , T ) × 2 r ∂σ ∂σ dr ◆ 2 ϕ i ( ∞ ) = 0 d 2 S ∂ Z − 1 dr 2 + 2 dr = ∂ V EFF ( S, σ , T ) + 1 σ ( S, σ , T ) dS ✓ d σ with ϕ 0 2 i (0) = 0 r ∂ S ∂ S dr G 1 / 2 Λ = 1.82, (- G D ) 1 / 5 Λ = 2.29 In SCMF approximated NJL 
 σ disappear at symmetric phase 
 1.5 Z σ ( S / Λ = 0, σ / Λ ,T / Λ ) T/ Λ = 0 — Z σ ( σ ) → 0 as σ → 0 Λ 1 0 1.0 . 0 Λ = T/ Λ = 0.03 T/ Λ = 0.02 Λ / T Λ Compositeness condition 
 Λ 0.5 guarantee 
 the bounce solution! 0.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 σ / Λ 9

✤ How to Find Multi-Bounce Solution More generally C. L. Wainwright arXiv:1109.4189 Find initial position ( σ 0 , S 0 ) 
 0.08 doubly fine-tuned 0.06 d 2 σ d 2 S dr 2 + 2 dr 2 + 2 d σ dS dr = F σ ( σ , S ) dr = F S ( σ , S ) S / Λ H 0.04 r r 0.02 ϕ i ( ∞ ) = 0 ϕ 0 and i (0) = 0 with 0.00 — Change the Question ! — 0.00 0.05 0.10 0.15 σ / Λ H 0.10 Find tunneling path S( σ ) 
 0.15 σ (r) σ ( r )/ Λ H and S ( r )/ Λ H 0.10 satisfied N S [S( σ )] = 0 0.08 S( σ ) σ S(r) 0.05 0.00 0.06 ϕ 0 i (0) = 0 0 100 200 300 400 d 2 σ r Λ H dr 2 + 2 d σ with dr = F σ ( σ , S ( σ )) S / Λ H 0.04 ϕ i ( ∞ ) = 0 r 0.02 ◆ 2 N S ( S ( σ )) ≡ d 2 S ✓ d σ ✓ dS ◆ + F σ ( σ , S ( σ )) − F S ( σ , S ( σ )) d σ 2 dr d σ 0.00 0.00 0.05 0.10 0.15 10 σ / Λ H


 
 
 GW Signal from 
 Scale Invariant Hidden QCD PT ✤ HQCD Model Based on Classical Scale Invariance 
 Indirect Dimensional Transmission Fixed ⌦ ¯ ⌦ ¯ λ HS h S i 2 H † H ∼ Λ 3 ↵ ↵ ψψ yS ψψ H D χ SB as Origin 
 E χ SB: DM Mass & PT fixes HQCD Scale of EWPT & DM ✤ Strategy to Test HQCD with GW Spectrum 
 Model Parameter GW Parameter GW Spectrum NJL ( α , ˜ Ω GW ( f ) ( λ H , λ HS , λ S , y ) β ; T t ) V ( σ , S ) Test ( m DM , Λ H ) with LISA or DECIGO NJL 11

y ≧ 0.0001 
 by hand λ HS ≧ 0.0001 
 by hand λ HS ≦ 0.12 m h = 125 GeV, <h> = 246 GeV 
 m S = 2m DM ✤ Benchmark Points — A , B , C and D m c = y h S i cf. current mass Large Small E χ SB λ HS Small Large Model Parameter ( λ H , λ HS , λ S , y ) 12

✤ GW Spectrums for Benchmark Points using parameterization in C. Caprini et al. arXiv:1512.06239 “runaway” v w =1 GW signal from this model ( Λ H < 200 TeV) may appear in DECIGO. 13

Conclusion ✤ Scale Invariant QCD-like Hidden Sector ( Nc = Nf = 3 ) 
 We discussed indirect dimensional transmutation from 
 χ SB Pattern U(3) R × U(3) L → SU(3) V × U(1) V 
 In m DM < m S case 
 — Need Resonance Effect ( 2m DM = m S ) 
 — Poor testability in DM search because of small y 
 but chiral phase transition become first-order phase transition ✤ GW from Hidden QCD Phase Transitions 
 We predict the GW signal using SCMF approximated NJL analysis 
 They may appear O(0.01) ~ O(1) Hz region (DECIGO). 14

Conclusion ✤ Analysis of Multi-Fields Tunneling 
 More interesting if there exist two scale first-order PT 
 Method : Path Deformation ✤ Model including Strong Dynamics 
 Compatible with scale invariant extension and GW Prediction 
 — Effective model may be practical approach now… 
 — When DM is hidden Baryon, m DM ~ Λ H , 
 peak frequency of GW signal corresponds to DM mass directly 15

Backup Slides


 
 Beyond the Standard Model 
 from Higgs Mass term V SM = µ 2 ( H † H ) + λ H ( H † H ) 2 ＊ What is the origin of Higgs mass term? ＊ ONLY Higgs mass term breaks scale invariance ▸ RG Equation for the Higgs Mass 
 d ln µ = 3 m 2 dm 2 t − 3 g 2 − 3 g 2 ✓ ◆ h h 2 1 2 λ H + y 2 8 π 2 4 20 ▸ Fine-Tuning Problem h = (10 19 GeV) 2 − (10 19 GeV) 2 = (125 GeV) 2 m 2 17

“Fine-T uning Problem” 
 from Wilsonian RG Flow H. Aoki, S. Iso PhysRevD.86.013001 Who put Higgs near the critical line? ( λ 0 , m 0 ) @ Planck λ Symmetric 
 Broken 
 Phase Phase m 2 m 2 R > 0 R < 0 m 2 R ∼ O ( Λ 2 pl ) m 2 m 2 R = O ( Λ 2 R = 0 EW ) m 2 0 18

× Scale Invariant Extension W.A. Bardeen, FERMILAB-CONF-95-391 (1995) M pl Classical Scale Invariance V SM = µ 2 ( H † H ) + λ H ( H † H ) 2 No large intermediate scale below the Planck scale Low-energy is responsible 
 for the origin of low energy scales Hidden dynamics in TeV scale 
 explain Electroweak symmetry breaking EW — What is the dynamical origin of Higgs mass? QCD 19