A Minimal Composite Goldstone Higgs model

Transcription

1 A Minimal Composite Goldstone Higgs model Lattice for BSM Physics 2017, Boston University

2 Plan of the talk Introduction to composite Goldstone Higgs models Lattice results for the SU(2) Goldstone Higgs model

3 Higgs properties ATLAS and CMS Run 1 Total Stat. Syst. LHC Total Stat. Syst. ATLAS H γ γ ± 0.51 ( ± 0.43 ± 0.27) GeV v V m κ V 1 ATLAS and CMS LHC Run 1 W Z t CMS H γ γ ± 0.34 ( ± 0.31 ± 0.15) GeV or ATLAS H ZZ 4l ± 0.52 ( ± 0.52 ± 0.04) GeV CMS H ZZ 4l ± 0.45 ( ± 0.42 ± 0.17) GeV v F m κ F 1 10 ATLAS +CMS γ γ ± 0.29 ( ± 0.25 ± 0.14) GeV ATLAS +CMS 4l ± 0.40 ( ± 0.37 ± 0.15) GeV ATLAS +CMS γ γ +4l ± 0.24 ( ± 0.21 ± 0.11) GeV 2 10 τ b m H [GeV] Phys. Rev. Lett. 114, m H = ± 0.24 GeV ATLAS+CMS SM Higgs boson µ [M, ε] fit 68% CL 95% CL Particle mass [GeV] arxiv:

4 Higgs properties ATLAS and CMS LHC Run 1 Observed ±1σ Th. uncert. γ γ ZZ WW τ τ bb ggf VBF WH ZH σ tth B norm. to SM prediction

5 The SM Higgs? Spin 0? CP even? Coupling to other SM particles proportional to their mass? origin of mass ~ok Quantum effects consistent with SM Higgs / self couplings? It is Elementary or Composite? The properties of the Higgs provide strong constraints on Beyond SM physics

6 Anatomy of Composite Higgs L SM Higgs G SM = SU(3) SU(2) U(1) X

7 Anatomy of Composite Higgs L SM Higgs +L SD L SD = 1 4 F 2 µ + i /D Gauge group: G TC = SU(N), SP(N), SO(N),... Nf fermions Higgs Impostor : Scalar composite state W/Z mass generation new resonance spectrum (dark matter?)

8 Anatomy of Composite Higgs L SM Higgs +L SD +L int L int contains: (effective) interactions to generate SM fermion masses, 1 such as:, 2 UV qqo B 1 2 UV q qo F among SM fermions and operators O from SD other possible dim=6 or higher operators: (dangerous FCNC?) 1 2 UV qqqq

9 Anatomy of Composite Higgs UV L UV ~ TeV L SM Higgs +L SD +L int 5~10 TeV L g SM + new physics 1 TeV IR

10 Composite pngb Higgs Higgs is a (pseudo) Goldstone boson EW symmetry broken via radiative corrections Higgs is light Plus Higgs couplings Higgs mass Minus EW vacuum (mis)alignment Fermion masses

11 pngb Higgs Consider a SD with global symmetry breaking pattern G F! H F SU(2) L SU(2) R U(1) X which preserves custodial symmetry. To give the correct hypercharge to all SM fields we need a NGB with Higgs = (2,2) 0 2 G F /H F For EW breaking the minimal cosets are: 4 (, ) Complex SU(4) SU(4) 0 /SU(4) D 4 Pseudoreal SU(4)/Sp(4) 5 Real SU(5)/SO(5) SU(3) Nf=4 Fund Dirac SU(2) Nf=2 Fund Dirac SU(4) Nf=2.5 2-A Dirac

12 Vacuum (mis)alignment Loop corrections of EW gauge bosons will generate a potential for the Higgs but will not break EW symmetry (W/Z remain massless) top quark (and other SM fermions) corrections will offset the minimum and generically tend to align the vacuum in the EW symmetry breaking (TC) direction extra source of explicit breaking v F º = sinµ = sin hhi F º TC CH

13 Higgs couplings Couplings to the EW gauge bosons and SM fermions mimic those of the SM Higgs for small! g VVh = g SM VVh cosµ g VVhh = g SM VVhh cos2µ g h ff = g SM 1 + cµ 2 + h ff The S-parameter can be estimated via Weinberg sum rules: S / µ v m Ω 2 / sin 2 µ

14 Mass generation 1 2 UV qqo B 1 2 UV qo F E Technicolor way Partial Compositeness BSM UV L Int int [ [ BSM UV ]= t d 1 BSM UV q L O c St R +... L t L t d L 5/2 d L 5/2 UVBSM q q L F L L OF L + R t R t d R 5/2 d R 5/2 UV BSM t t R F R R OF R m L int Int [m ]= t[m ] m d 1 q L OSt c R +... L t L [m ] t [m ] q R t ] q L OF L + t [m R ] d L m d L 5/2 m d R 5/2 t R OF R +... MEW EW

15 Near Conformality / Walking α Running IR fixed point QCD-Like * IR conformal Λ TC Energy U Energy α Walking Deformed/ Near IR conformal Λ TC Λ ETC Energy

16 ETC TCquark Q L ψ R ψ R Q R ETC ETC Q L SM fermion ψ L Q R ψ L 1 2 UV qqo B m q ª v µ UV dim[ob ] 1

17 Partial Compositeness H m q / v L ( ) R ( ) q L q R Fermion masses are generated via linear couplings 1 2 UV qo F m q ª v µ UV 2(dim[OF ] 5/2) If dim[of] 2.5 then large SM fermion masses can be generated. E.g. if OF is a baryon, then we should have "B 2 (unitarity bound 3)

18 Partial Compositeness Models SU(3) with Nf>6 Fund Dirac fermions [Vecchi ] For SD models with only fermions and 2 representations [Ferretti ] G HC G/H SO(7, 9) 5 F 6 Spin SU(5) SO(7, 9) 5 Spin 6 F SO(5) Sp(4) 5 A 2 6 F SU(5) SO(5) SU(6) SO(6) U(1) SU(6) Sp(6) U(1) SU(4) 5 A 2 3 (F, F) SU(5) SO(10) 5 F 3 (Spin, Spin) SO(5) SU(3) SU(3) 0 SU(3) D U(1) Sp(4) 4 F 6 A 2 SU(4) SO(11) 4 Spin 6 F Sp(4) SO(10) 4 (Spin, Spin) 6 F SU(4) SU(4) 0 SU(4) 4 (F, F) 6 A 2 SU(5, 6) 4 (F, F) 3 (A 2, A 2 ) SU(4) D SU(6) SO(6) U(1) SU(6) SO(6) U(1) SU(4) SU(4) 0 SU(3) SU(3) 0 SU(4) D SU(3) D U(1)

19 Anomalous dimensions in PT Gauge theory based on gauge group G and nf fermions da d lnµ 2 = Ø(a) = Ø 0a 2 Ø 1 a 3 Ø 2 a 4 Ø 3 a 5 +O(a 6 ) d lnm d lnµ 2 = (a) 2 = 0a + 1 a a a 4 +O(a 5 ) B (a) = B 0 a + B 1 a2 + B 2 a3 +O(a 4 ) with a = Æ/4º = g 2 /16º 2

20 Anomalous dimensions in PT γ γ Ḇ proton γ + B γ m 4-loop γ m 3-loop n f see arxiv:

21 Anomalous dimensions: δ-expansion δ-expansion in Ryttov [ ] 1.0 γ Ḇ γ + B γ m γ n f see arxiv:

22 Fundamental Partial Compositeness See Sannino, Strumia, Tesi, Vigiani [ ] 1 2 UV qo F m q ª v µ UV 2(dim[OF ] 5/2) If the new strong sector feature elementary TColoured scalars then OF can be a composite S which have engineering dimension 5/2, so that no anomalous dimension is needed. Realistic models which can generate all SM masses have been built. F F F F F F F F

23 Minimal SU(2) pngb Higgs Lattice Results Based on [ ], [ ]

24 SU(2) Nf=2 fund Complete Lattice determination of spectrum including # and $ 4 lattice spacings (1 still ongoing) scale setting via w0 non-perturbative renormalization in RI-MOM scheme both chiral and continuum extrapolation SU(N) n f N

25 Simulation details Wilson fermions 4 volumes: 16, 24, 32, 48 ( infinite volume extrapolation) up to 9 different quark masses ( chiral extrapolation) 4 lattice spacings ( continuum extrapolation)

26 Scale Setting W (t) = t d dt [t 2 E(t)], W (w 2 0 ) 1 w 0 a cut LO cut NNLO β = 1.8 β = 2.0 β = 2.2 β = 2.3 χ w 0 w β = 1.8 β = 2.0 β = 2.2 β = y 2 = w (m) m PS y 2 = w (m) m PS w 0 (m 2 ps ) = w Ay 2 + By 4 log y 2

27 Goldstone bosons f PS = F " 1 a F x log m2 PS µ 2 + b F x + ± F a w 0 + F m 2 PS a w 0 # m 2 PS m f = 2B " 1 a M x log m2 ps µ 2 + b M x + ± M a w 0 + M m 2 ps a w 0 # χ w 0 FPS β = 1.8 β = 2.0 β = 2.2 β = 2.3 m f χ 2 w 0 mps β = 1.8 β = 2.0 β = 2.2 β = χ ( w mps ) χ ( w mps ) 2 w w 0 F = 0.078(4)(12) 0 B = 2.88(15)(17) ß 1/3 /F = 4.19(26)

28 Spin-1 Resonances w 0 m X = w 0 m X + A(w 0 m PS) 2 + B(w 0 m PS) 4 +C a w 0 χ w 0 mv β = 1.8 β = 2.0 β = 2.2 β = 2.3 χ w 0 ma β = 1.8 β = 2.0 β = 2.2 β = χ ( w 0 mps ) χ ( w 0 mps ) 2 m V /f PS = 13.1(2.2) m A /f PS = 14.5(3.6)

29 Spin-0 Resonances w 0 m X = w 0 m X + A(w 0 m PS) 2 + B(w 0 m PS) 4 +C a w 0 χ w 0 mσ β = 2.0 β = 2.2 χ w 0 ma β = 1.8 β = 2.0 β = 2.2 β = χ ( w 0 mps ) χ ( w 0 mps ) 2 m æ /f PS = 19.2(10.8) m a0 /f PS = 16.7(4.9)

30 Spin-0 Resonances w 0 m X = w 0 m X + A(w 0 m PS) 2 + B(w 0 m PS) 4 +C a w 0 β = 2.0 β = 2.2 χ w 0 mη ' χ ( w 0 mps ) 2 m 0/f PS = 12.8(4.7)

31 Spectrum - Summary m X F PS a 1 : 1(1 + ) a 0 : 1(0 + ) η 2 : 0(0 - ) ρ : 1(1 - ) σ : 0(0 + ) QCD N f = 2 0(0 + ) 1(0 + ) 1(1 + ) 1(1 - ) 0(0 - ) SU(2) N f = 2

32 Conclusions The SU(2) Nf=2 model provides an interesting and minimal strongly coupled template for composite Higgs models with SU(4)/Sp(4) symmetry The study of scalar sector is very challenging, but preliminary results are already available SU(2) model is a viable composite pngb Higgs model, with spin 1 and spin 0 resonances in the TeV region for sinµ ' 0.2 Outlook: better control of extrapolations reduce systematics for noisy channels Thank you! m X F PS a 1 : 1(1 + ) a 0 : 1(0 + ) η 2 : 0(0 - ) ρ : 1(1 - ) σ : 0(0 + ) QCD N f = 2 0(0 + ) 1(0 + ) 1(1 + ) 1(1 - ) 0(0 - ) SU(2) N f = 2