Pacific 2019 @ Moorea 2019 Sep 3 (Aug 31- Sep 6) Hierarchy Problem: Implication to Cosmology (Supercooled universe) and Implication from Superstrings (Revolving D-branes) Satoshi Iso (KEK & Sokendai) 1 Hierarchy problem = Dynamics of EWSB and its Stability How EWSB occurs dynamically ? Who ordered the Higgs potential ? Why Higgs VEV <H> = 256 GeV , Higgs mass mH = 125 GeV ? Why are they stable against (possible) high energy scales? Cosmology early universe Particle physics DM, baryogenesis (LHC, ILC, …) Hierarchy TeV or beyond ? Problem Superstring unification Geometry of SM String threshold corrections 2 Today’s talk More about Hierarchy problem and classically conformal model [2] Implication to cosmology (the early universe) : Supercooled universe [3] Implication from superstrings : String threshold corrections 3 Rough picture of the Higgs potential: (at least) 3 important points Higgs potential 3 Energy scale 1 2 1 Higgs VEV v= 246 GeV à Particle physics (present universe) 2 UV scale e.g. MPlanck à Quantum Gravity, String 3 h=0 (origin) à Cosmology (early universe) All regions (1, 2, 3) are related by RG and theoretical biases. 4 2 important lessons from LHC (1) mass = 125 GeV "EW" physics may be directly related to PlancK scale physics without intermediate scales in between. (2) No deviations from SM / no TeV SUSY? New paradigm à classical conformality (CC) EWSB occurs, NOT by (classical) Higgs potential V(h) but by radiative corrections to it. Coleman-Weinberg mechanism 5 For the classical conformal idea to the hierarchy problem two conditions are necessary 1. No intermediate scales = EW directly connected to Planck. 2. String threshold corrections are controllable. (or Planck scale does not destabilize Higgs potential.) The first condition is suggested by Higgs mass 125 GeV. The second condition needs something more. I will show one example of non-SUSY vacua in superstring that satisfies the second condition. 6 An example of a bottom-up model of CC An additional sector to the SM is inevitably needed. Within SM, CW mechanism predicted Higgs mass lighter than 10 GeV. Okada, Orikasa, SI (09) A phenomenologically viable minimal extension will be also Lindner et.al. (10) (B-L)-extension of SM IR physics B-L sector @ TeV UV physics Standard U(1)B-L gauge Planck scale Model + SM singlet scalar V(h)=0 Right-handed ν No intermediate scales (1) B-L breaking by CW mechanism à triggers EWSB at 100 GeV Everything occurs radiatively. (2) Minimal extension of SM & Phenomenologically viable All new particles are predicted to be around EW - TeV 7 [1] Implication to Cosmology Thermal history of the universe Serpico, Shimada, SI (17) “Standard” Crossover Crossover T 100 GeV 100 MeV MeV ⇠ ⇠ ⇠ Inflation EW QCD phase transition phase transition BBN Reheating extremely supercooled (strong first order PT) χSB induces EWSB → cosmological consequences: GW, DM, PBH ... m2 =2λ h 2 m <m T T h ⟨ ⟩ φ h ≪ c q¯ q Λ SU(2) U(1) U(1) y h q¯ q (y Λ3 )h ⟨ i i⟩∼ QCD L × Y → i ⟨ i i⟩∼ i QCD (φ =0,h= vQCD) 1/3 yt tt¯ vQCD = ⟨ ⟩ ΛQCD !√2λh " ∼ g>0.2 g<0.2 After primordial inflation, hot universe starts at T>> TC . V (φ) (g2T 2 λ v2 /2)φ2 ∼ QCD − | mix| QCD Potential of the B-L scalar High- T β > 03m4 > 2Tr(m4 )+Dm4 D 41 m afewhundredGeV φ Z′ N h Z′ ∼ ∼ Ti mZ dλmix 1 mRHν,mφ mZ afewhundredGeV1M N =ln QCD ln QCD′ 2 2 ′ ⊙ T T = 6gB Lgmix + λmix( ) ≪ ∼ N ∼ N dt 16π2 − ··· T = T m ! " c Z′ 2 2 nd ∼ λmix gB Lgmix 2 inflation starts ∼− − V0 mZ′ ≃ φ valley 9 1 1 m2 =2λ h 2 m <m T T h ⟨ ⟩ φ h ≪ c q¯ q Λ SU(2) U(1) U(1) y h q¯ q (y Λ3 )h ⟨ i i⟩∼ QCD L × Y → i ⟨ i i⟩∼ i QCD (φ =0,h= vQCD) 1/3 yt tt¯ vQCD = ⟨ ⟩ ΛQCD !√2λh " ∼ g>0.2 g<0.2 V (φ) (g2T 2 λ v2 /2)φ2 Potential for B-L scalar field ∼ QCD − | mix| QCD High- T (h=0, φ=0) β > 03m4 > 2Tr(m4 )+Dm4 D 41 m afewhundredGeV φ Z′ N h Z′ ∼ ∼ T m Trapped in i Z′ dλmix 1 2 2 mRHν,mφ mZ′ afewhundredGeV1M N =ln QCD ln QCD ⊙ TN TN = 2symmetric6gB Lgmix + λmix( ) ≪ ∼ ∼ dt 16π − ··· T = T m ! " c Z′ phase for2 2 nd ∼ λmix gB Lgmix 2 inflation starts a ∼−long time− V0 mZ′ 2 2 ≃ m =2λ h mφ <mh T Tc Thermalh ⟨barrier⟩ ≪ φ never disappears (classical conformal) valley 10 1 1 1 m2 =2λ h 2 m <m T T h ⟨ ⟩ φ h ≪ c q¯ q Λ SU(2) U(1) U(1) y h q¯ q (y Λ3 )h ⟨ i i⟩∼ QCD L × Y → i ⟨ i i⟩∼ i QCD (φ =0,h= vQCD) 1/3 yt tt¯ vQCD = ⟨ ⟩ ΛQCD !√2λh " ∼ Supercooling of (B-L)+EW à PT much belowg>0.2 Tg<C 0.2 V (φ) (g2T 2 λ v2 /2)φ2 ∼ QCD − | mix| QCD High- T (h=0, φ=0) β > 03m4 > 2Tr(m4 )+Dm4 D 41 m afewhundredGeV φ Z′ N h Z′ ∼ ∼ T m Trapped in i Z′ dλmix 1 2 2 mRHν,mφ mZ′ afewhundredGeV1M N =ln QCD ln QCD ⊙ TN TN = 2symmetric6gB Lgmix +tunnelλmix( ) ≪ ∼ ∼ dt 16π − ··· T = T m ! " c Z′ phase for2 2 nd ∼ λmix gB Lgmix 2 inflation starts a ∼−long time− V0 mZ′ 2 2 ≃ m =2λ h mφ <mh T Tc Thermalh ⟨barrier⟩ ≪ φ never disappears (classical conformal) valley 11 1 1 1 Percolation of true vacuum Guth Weinberg (82) Bubbles of true vacuum are created by tunneling Tp : percolation temperature Universe is occupied with true vacuum bubbles 12 critical bubble action TP = percolation temperature S/T ~ 1/g3 can be calculated by tunneling rate. Serpico, Shimada, SI (17) B-L gauge coupling If g < 0.2, universe is never occupied with true vacuum until T decreases down to 100 MeV or much lower. Note that de Sitter fluctuation T = / 2 ⇡ is negligible at 100 MeV. ⇠ GH H 1/4 V m 13 0 ⇠ Z0 But when temperaturem2 =2decreasesλ h 2tom 100<m MeV atT (φ=0, h=0)T h ⟨ ⟩ φ h ≪ c q¯ q Λ3 SU(2) U(1) U(1) y h q¯ q (y Λ3 )h ⟨ i i⟩∼ QCD L × Y → i ⟨ i i⟩∼ i QCD (φ =0,h= vQCD) QGP, In the ordinary scenario, T Chirally Symmetric ¯ 1/3 χSB with Nf =(2+1) Crossover st y tt 1 - t is crossover ordervQCD = ⟨ ⟩ ΛQCD Hadron, !√2λh " ∼ Chirally BroKen µ g>0.2 g<0.2 In the present case, since h=0 2 2 2 2 V (φPisarsKi) WilczeK(g T(1983)QCD λmix vQCD/2)φ all Nf =6 quarks are massless ! ∼ − | | à 1st order phase transition for N 3 f ≥ β > 03m4 > 2Tr(m4 )+Dm4 D 41 m afewhundredGeV φ Z′ N h Z′ 14 ∼ ∼ T m m ,m m afewhundredGeV1M N =ln i ln Z′ RHν φ Z′ T QCD T QCD ≪ ∼ ⊙ N ∼ N T = T m c ∼ Z′ 1 m2 =2λ h 2 m <m T T h ⟨ ⟩ φ h ≪ c q¯ q Λ3 SU(2) U(1) U(1) y h q¯ q (y Λ3 )h ⟨ i i⟩∼ QCD SU(2)L ×L doubletY →with U(1)Y chargei ⟨ i i⟩∼ i QCD (φ =0,h= vQCD) Electroweakm2 =2λ h 2symmetrym <m isT brokenT (EWSB) Quigg Shrock (09) h ⟨ ⟩ φ h ≪ c 1/3 q¯iqi ΛQCD SU(2)L U(1)Y U(1)y tt¯ ⟨ ⟩∼ ×v =→ t⟨ ⟩ Λ 2 2 Higgs linear term is generatedQCD via Yukawa interaction QCD mh =2λ h mφ <mh T Tc !√2λh " ∼ ⟨ ⟩ ≪ 3 Witten (81) q¯iqi ΛQCD SU(2)L U(1)Y U(1) yih q¯iqi (yiΛQCD)h Buchmuller et al (90) ⟨ ⟩∼ × g>0.→2 g<0.2 ⟨ ⟩∼ Kuzmin et.al.(92) V (φ) (g2T 2 λ v2 /2)φ2 ∼ QCD − | mix| QCD β > 03QCDm4 χSB> 2Tr(triggersm4 )+ BDm-L and4 D EWSB41 m afewhundredGeV φ Z′ N h Z′ ∼ ∼ T m m ,m m afewhundredGeV1M N =ln i ln Z′ RHν φ Z′ T QCD T QCD ≪ ∼ ⊙ N ∼ N T = T m c ∼ Z′ 15 1 1 1 Cosmological consequences [ QCD + (B-L) + EW ] strong 1st order phase transition expected Bubble collsions à Sizable Stochastic Gravitational Waves from 1st order PT 2 h ⌦GW,0 100-10 C3 0.6 ⇣ 0.3 C2 11-11 ⇡ 10−10 ⇣ 0.3 β/ = 10 C1 ⇡ H eLISA sensitivities 0.15 from C.Caprini et al. (2016) 12 10−10-12 β/ = 100 H 13 10-13 ⇣ 0.3 10− ⇡ β/ = 1000 Serpico, Shimada, SI ('17) H -5 -4 Jinno, Takimoto ('17) 10 10 4 0.001 3 0.010 2 f0/Hz0.100 10− 10− 10− Hashino et.al. ('18) ...... Many other implications dilution factor 106 dilutes relics From high energy (high temperature) WIMP DM, baryon asymmetry à supercool DM Hambye Strumia Teresi(18) nd low reheat temperature after 2 mini-inFlation ( TR < 100 GeV) Baryon asymmetry at low T: e.g. Cold EWBG Konstandin, Servant (11) .... Enhanced scalar Fluctuations PBH by 1st order QCD PT or Ultra-compact mini halo Jedamzik (97), Ricotti et(09)16 m2 =2λ h 2 m <m T T h ⟨ ⟩ φ h ≪ c q¯ q Λ SU(2) U(1) U(1) y h q¯ q (y Λ3 )h ⟨ i i⟩∼ QCD L × Y → i ⟨ i i⟩∼ i QCD (φ =0,h= vQCD) 1/3 yt tt¯ vQCD = ⟨ ⟩ ΛQCD !√2λh " ∼ Summaryg>0.2 g< of0. 2 [1] Serpico, Shimada, SI (17) In classically conformal models motivated by naturalness, V (φ)=(g2T 2 λ v2 /2)φ2 the early universe is drasticallyQCD different− | mix | QCD extremeβ > 03 mSUPERCOOLING4 > 2Tr(m4 )+andDm the4 Dsecond41 inflationm afewhundredGeV with N~10 φ Z′ N h Z′ ∼ ∼ T m m ,m m afewhundredGeV1M N =ln i ln Z′ RHν φ Z′ T QCD T QCD ≪ ∼ ⊙ N ∼ N 100 MeV χSB (B-L)+EWSB Interesting cosmological conseQuences Stochastic GW, PBH, Cold EWBH, axion abundance , supercool DM Supercooling is also expected in other models, e.g.