Higgs Vacuum Stability with Vector-like Fermions Shrihari - PowerPoint PPT Presentation

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Vacuum Stability with Vector-like Fermions Shrihari Gopalakrishna Institute of Mathematical Sciences (IMSc), Chennai IMHEP IOP Bhubaneswar Jan 20 19

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Talk Outline Vector-like Fermions (VLF) general aspects Vacuum decay basics Bounce configuration Higgs Vacuum Stability in the Standard Model with VLFs present nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability VLF basics BSM VLF Vector-like fermions have both L and R chiralities charged under a gauge-group. This allows a bare mass term. VLFs appear in many BSM extensions they are sometimes the lightest BSM states We study VLF effects on Higgs vacuum stability constraint on parameter space but any other new states will alter conclusions! nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability VLF basics Vector-like fermion (VLF) decoupling VLF has independent source of mass M (not given by m = λ v ) Can make M arbitrarily large Yukawa coupling can be small; so perturbative Nice decoupling behavior : S , T , U , h → γγ , gg → h , ... For instance h γγ , ggh couplings nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability VLF basics VLF signatures Observables Precision Electroweak Probes LHC signals Direct: b ′ → tW ,bZ; t ′ → bW , tZ , th ; χ → tW Indirect: Higgs coupling modifications FCNC probes Vacuum stability implications nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability LHC Search Limits Vector-like fermion ( t ′ , b ′ ) search [ATLAS: 1808.02343; PRL 2018] nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability EW Precision & Higgs coupling probes EWPrecision + Higgs Observables [S.Ellis, R.Godbole, SG, J.Wells; 1404.4398, JHEP 2014] Precision electroweak observables ( S , T , U ) Modifications to hgg , h γγ couplings: σ ( gg → h ) Γ( h → γγ ) Γ h → gg Γ h → γγ We compute ratios SM , using leading-order expressions SM QCD corrections to ratios small: [Furlan ’11] [Gori, Low ’13] µ ggh ≈ Γ γγ ZZ ≈ Γ gg γγ ≈ Γ gg Γ γγ ≈ Γ γγ γγ µ ggh µ VBF µ ggh ≈ µ VBF ; ; ; γγ γγ nulogo.png µ ggh Γ SM Γ SM Γ SM Γ SM Γ SM γγ gg gg γγ γγ ZZ

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability EW Precision & Higgs coupling probes 2¯ 2 + 1¯ 1 model Q + U model (ST Model like) : MVQD Model with Y χ = − 1 / 6 λ D = 1, M D = M Q , Y Q = (1 / 6 , − 1 / 6) (solid, dashed) nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability EW Precision & Higgs coupling probes Q + U model [Q+U model from MVQD model with Y χ = − 1 / 6] nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability EW Precision & Higgs coupling probes LHC constraints on Higgs couplings [ATLAS-CONF-2018-31] [CMS-HIG-17-031] nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential HIGGS EFFECTIVE POTENTIAL nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential RG-Improved Higgs Effective Potential Classical potential: V = m 2 2 h 2 + λ 4 h 4 h Quantum Effective Potential: V eff ( h ) = m 2 h 2 + λ eff ( h ) λ eff ( h ) h 4 h 4 h eff → 2 4 4 Set h ≡ µ ; λ eff ( h ) ≡ λ ( µ ) obeys an RGE like evolution: d λ ( µ ) d ln µ = β λ ( λ ( µ ) , y t ( µ ) , g 3 ( µ ) , g 2 ( µ ) , g 1 ( µ ) , ... ) nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential 1-loop SM RGE 24 λ 2 + 4 N c y 2 1 t λ − 2 N c y 4 t − 9 g 2 2 λ − 9 5 g 2 1 λ + 9 g 4 2 + 2 5 g 2 2 g 2 1 + 3 25 g 4 � � �� β λ = 16 π 2 8 1 � (3+2 N c ) � y t y 2 t − 8 g 2 3 − 9 4 g 2 2 − 17 20 g 2 β y t = 16 π 2 1 2 β g a = g 3 a b a 16 π 2 [We include some significant 2-loop β -functions (not shown)] nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential Effective VLF model and 1-loop RGE [SG, Arunprasath V: 1812.11303 [hep-ph]] An effective model with one SU(2) doublet χ and one SU(2) singlet ξ χχ − M ξ ¯ L ⊃ − M χ ¯ ξξ − (˜ y ¯ χ · H ∗ ξ + h . c . ) Their contributions to the RGE is: g 3 � � 3 2 β g 3 = 3 n 3 16 π 2 g 3 � � 2 2 3 N ′ β g 2 = c n 2 16 π 2 g 3 � � 2 n 2 Y 2 χ + n 1 Y 2 �� 1 4 5 N ′ β g 1 = 16 π 2 c ξ 2 nF � y 2 λ − 2 N ′ y 4 � 4 N ′ β λ = c ˜ c ˜ 16 π 2 nF � y 2 � 2 N ′ β yt = 16 π 2 y t c ˜ y 2+2 Nc y 2 y 2) � t +4 nF N ′ � (3˜ c ˜ y ˜ n VLQ g 2 3 − 9 4 g 2 2 − 17 20 g 2 β ˜ y = − 8ˆ 16 π 2 2 F 1 nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential 3 TeV VLQuark (VLQ) family ( χ + ξ ) M VLQ = 3 TeV M VLQ = 3 TeV 0.10 1.4 0.08 1.2 0.06 1.0 ( 1.0 ) y t ( μ ) ( 0.9 ) λ ( μ ) 0.04 0.8 ( 0.75 ) ( 0 ) 0.02 0.6 ( 0.3 ) ( 0.75 ) ( SM ) 0.00 0.4 ( 0.3 ) ( SM ) ( 1.0 ) ( 0.5 ) ( 0.4 ) - 0.02 0.2 5 10 15 5 10 15 log 10 μ ( GeV ) log 10 μ ( GeV ) nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential VLQ family ˜ ( M VL ) = 0.1 y ˜ ( M VL ) = 0.5 y 0.03 0.10 0.02 0.08 ( 1 E3 ) 0.06 0.01 λ ( μ ) ( 1 E4 ) λ ( μ ) 0.04 ( 1 E3 ) ( 1 E5 ) 0.00 ( 1 E5 ) ( 1 E7 ) 0.02 ( SM ) - 0.01 0.00 ( SM ) ( 1 E7 ) - 0.02 - 0.02 8 10 12 14 16 18 4 6 8 10 12 log 10 μ ( GeV ) log 10 μ ( GeV ) ˜ ( M VL ) = 0.5 ˜ ( M VL ) = 0.5 y y 0.6 1.1 1.0 ( 1 E3 ) 0.5 ( 1 E7 ) ( 1 E5 ) 0.4 0.9 g 3 ( μ ) ˜( μ ) ( 1 E3 ) y ( 1 E5 ) 0.8 0.3 0.7 ( 1 E7 ) 0.2 ( SM ) 0.6 0.1 3 4 5 6 7 8 9 10 5 10 15 log 10 μ ( GeV ) log 10 μ ( GeV ) nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability VACUUM STABILITY nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Vacuum Stability (Possible cases) The Higgs Electroweak (EW) Vacuum can be: Stable: EW vacuum is the global minium Metastable: EW vacuum is a false vacuum with τ decay > τ universe Unstable: EW vacuum is a false vacuum with τ decay < τ universe Singlet VLQ, Doublet VLQ or a VLQ family (with small ˜ y ) can render the Higgs EW vacuum stable for suitable parameters! y = 0 . 1, M VL � 10 5 GeV (example we considered earlier) Eg: With a VLQ family with ˜ the EW vacuum is absolutely stable. nulogo.png

Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Bounce configuration and Vacuum tunneling Computing vacuum decay probability [Coleman: Aspects of Symmetry] [M.Sher: Phys.Rep. 1989] If Higgs EW vacuum is not the true vacuum, vacuum tunneling can occur via a Bounce configuration To compute the tunneling probability, start with the Euclidean action: � 1 2 ( ∂ i h ) 2 + V eff ( h ) d 4 ρ � � S E [ h ] = Look for a stationary point of S E that is O (4) symmetric, � i.e. h ( ρ i ) = h B ( ρ ), where ρ = ρ i ρ i [Coleman, Glasser, Martin 1978] d 2 h d ρ 2 + 3 d ρ = ∂ V eff dh Equation of motion (EOM): ρ ∂ h B.C. ( dh / d ρ )( ρ =0) = 0 ; h ( ρ →∞ ) = v ; (starting value h 0 ) EOM is that of a classical particle in a potential − V eff with friction Solve this EOM to get h B ( ρ ) Probability that we would have tunneled into true vacuum in our Hubble volume: P tunl = ( h 0 / m t ) 4 e (404 − S B ) where S B ≡ S E [ h B ] If P tunl ∼ O (1), EW vacuum unstable and parameter disfavored! nulogo.png

ρ  Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Bounce configuration and Vacuum tunneling SM V eff , Bounce and P tunl 10 71 10 16 Veff ( μ ) ( GeV ) 4 10 13 10 46 h ( GeV ) 10 10 10 7 10 21 10 4 10 - 4 10 - 15 10 - 13 10 - 11 10 - 9 10 - 7 10 - 5 5 10 15 log 10 μ ( GeV ) P tunl ∼ 10 − 1013 For the SM: S B = 2866 = ⇒ SM EW vacuum is metastable , with τ decay ≫ τ universe [compare with Buttazzo et al, 2013] nulogo.png

 ρ Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Bounce configuration and Vacuum tunneling VLQ V eff , Bounce and P tunl [SG, Arunprasath V: 1812.11303 [hep-ph]] 10 48 10 8 Veff ( μ ) ( GeV ) 4 10 38 h ( GeV ) 10 6 10 28 10 18 10 4 10 8 10 - 2 100 10 - 7 10 - 6 10 - 5 10 - 4 2 4 6 8 10 12 0.001 0.010 0.100 log 10 μ ( GeV ) ⇒ P tunl ∼ 10 − 4 For VLQ family, M VL = 3 TeV, ˜ y = 0 . 57: S B = 469 = If ˜ y > 0 . 57, P tunl ∼ O (1), i.e. Higgs vacuum is unstable ; such values are disfavored nulogo.png