Dipole operator constraints on composite Higgs models

Transcription

1 Matthias König May 27th, 2014

2 Dipole operators: emerge from one-loop correction to fermion-photon coupling f i R f j L γ/g. Various observables are governed by dipole operatores such as electric dipole moments (EDMs), flavour- and CP-violating quark transitions well-measured observables provide important constraints on parameter space of NP models! [MK, M. Neubert, D. M. Straub (2014), ]

3 New physics effects of dipoles in CHM studied throughout literature [Agashe et al (2005), Phys.Rev. D , Agashe et al (2004), Phys.Rev.Lett , Gedalia et al (2009), Phys.Lett. B , Delaunay et al (2013), JHEP , N. Vignaroli (2012), Phys.Rev. D , Csaki et al (2011), Phys.Rev. D , Blanke et al (2012), JHEP , Beneke et al (2013), JHEP ,... ] We investigate impact of choice of flavour structure and heavy quark representations on the NP effects Minor mistakes found in literature (see paper for details)

4 Outline 1 Setup Two-site models with partial compositeness Fermion representations and custodial protections Flavour structure 2 Dipole operators in composite Higgs models Relevant phenomenology Results

5 Setup

6 Two-site models with partial compositeness [Contino et al (2006), hep-ph/ ] Lagrangian is split into three sectors: L CHM = L elementary + L composite + L mixing Simplified two-site model: SM-like elementary sector Composite sector with [SU(3) SU(2) L SU(2) R U(1) X ] symmetry Linear mass mixing between sectors realize partial compositeness

7 The doublet model Fermion representations as in MCHM4 [Agashe et al (2004), hep-ph/ ] Two doublets of heavy fermions: ( ) T Q = (2, 1) B 1/6 R = (U, D) (1, 2) 1/6 Quark mass Lagrangian: ( ) L m,quarks = Qm Q Q Rm Q R Y Q L HR R + Ỹ R L H Q R + h.c. L mix = λ L q L Q R + λ Ru Ū L t R + λ Rd D L b R Quark mass matrix: b R B R D R b L 0 λ L 0 B L 0 m Q Yv 2, m b = Yv λ L λ R D L λ Rd Ỹ v m Q m R 2 m R

8 The triplet model (TS10) Fermion representations as in MCHM10 Heavy fermions come in one bidoublet and two triplets: ( ) U 5 T T 5 ( ) 3 3 Q =, R = U, R B T = U 5 U D 2 3 2/3 3 2/3 D 2/3 Lagrangian: L m,quarks = Qm Q Q Rm R R R m R R [ Y Q L HR R + Y Q L HR R ] +Ỹ R L H Q R + Ỹ R L H Q R + h.c. L mix = λ L q L L R + λ Ru Ū L t R + λ Ru DL b R b L mixes with P L/R eigenstate B Z coupling is protected [Agashe et al (2006), Phys. Lett. B 641 p62]

9 The bidoublet model (TS5) Fermion representations as in MCHM5 Two bidoublets and two singlets: ( ) T T 5 Q u = 3, Q B T d = 2 3 2/3 ( B 1 3 B 4 3 T B ) 1/3, U, D Lagrangian: L m,quarks = Q U m Qu Q U Ūm R U [ ] Y Q U,L HU R + Ỹ Ū L H Q U,R + h.c. + (U D) L mix = λ Lu q L L U,R + λ Ru Ū L u R + (U D) B no P L/R eigenstate λ Ld! λ Lu m b m t naturally

10 Towards three generations Up till now, only considered only one generation of quarks. Find ways to generalize expressions to three generations. Every parameter is a matrix in flavour space, diagonalization no more feasible. Reconstruct expressions via mass insertion. e.g. y d λ Ld m 1 Q Ym 1 R λ Rd More or less exact depending on structure of matrices! We consider: flavour anarchy and U(N) symmetric models. [Barbieri et al (2012), ]

11 Flavour anarchic models Yukawa matrices are assumed to be structureless. Composite-elementary mixings λ are hierarchical: λ = diag (λ 1, λ 2, λ 3 ) Think of all Y as an average Yukawa coupling. Diagrammatic approach plagued by O(1) uncertainties. Constraints from tree level meson-antimeson mixing.

12 Flavour symmetric models Impose global symmetry on strong sector Consider the coice of U(3) 3 symmetry: Y ij = Y δ ij, m ij = mδ ij Mixings λ (either left-handed or right-handed) break the flavour symmetry. λ L break right-handed compositeness λ R break left-handed compositeness Breaking mixings need to reproduce the SM Yukawas. need different λ for up- and down-type quarks right-handed compositeness only possible in bidoublet model! [Cacciapaglia et al (2007), ] [M. Redi, A. Weiler (2014), v4]

13 Flavour symmetric models U(3) 3 flavour model successfully suppresses FCNC processes. But predicts large degrees of compositeness for (one chirality of) light quarks strongly constrained! Solution: only assume first two generations to transform under flavour symmetry U(2) 3. Larger parameter space: Y = diag(y, Y, Y 3 ), m Q = diag(m Q, m Q, m Q3 ) Allows for small degree of compositeness for the first two generations. [Barbieri et al (2012), ]

14 Dipole operators in composite Higgs models

15 Dipole operators Work in EFT approach, effective Hamiltonian: H eff = C qi q j V Q qi q j V + C q i q j V Q q i q j V i,j,q,v with q = u, d and V = γ, g Effective operators: Q qi q j γ = em q i 16π 2 ( q jσ µν P R q i ) F µν, Q q i q j γ = em q i 16π 2 ( q jσ µν P L q i ) F µν, Q qi q j g = g sm qi 16π 2 ( q jt a σ µν P R q i ) G aµν Q q i q j g = g sm qi 16π 2 ( q jt a σ µν P L q i ) G aµν

16 Phenomenology Observables involving dipole operators we considered: Observable Neutron EDM Effective operators involved Q qqγ, Q qqg B X s γ Q ( ) bsγ, Q( ) bsg B X d γ Q ( ) bdγ, Q( ) bdg ɛ /ɛ Q ( ) sdg A CP Q cug

17 Dipole operators in composite Higgs models Example: b sγ Standard model: W b s t t γ t b W W γ s Contributions from new physics: Heavy particles in the loop (composite fermions, composite gauge bosons) Contributions from O(v 2 ) corrections to gauge couplings Diagrams with Higgs (flavour violating Higgs couplings allowed!)

18 Dipole operators in composite Higgs models Calculation of NP effects: Matching of relevant diagrams to the operators obtain general formula for Wilson coefficients Mass-diagonalize Lagrangian Plug masses and couplings in mass-eigenbasis into Wilson coefficients Analytical expression for C qi q j V Perform RG running Derive bounds

19 Wilson coefficients: Leading contribution Leading correction: Y C qqv = a Ỹ qv m Q m R with a qv : numerical factor Generated by diagrams with a Higgs boson and a heavy fermion a W or Z boson and a heavy fermion in the loop. Three generations: C qqv = a qv q ij m qi q ij = v U Ld λ Lm 1 2 Q Ym 1 R Ỹ m 1 Q Ym 1 R λ RdU Rd

20 Wilson coefficients: Subleading corrections Especially interesting for models with Ỹ = 0, contributions arising from: Same diagrams as leading order: Y 2 m 2 h m 4 ψ (from expansion of loop function) Same diagrams as leading order: Y 2 λ 2 m 4 ψ (from expansion in λ/m ψ ) SM quarks and W or Z in the loop, O(v 2 ) correction to gauge coupling: Y 2 λ 2 m 4 ψ

21 Wilson coefficient: More subleading terms Barr-Zee type diagrams: g 2 16π 2 Y 2 m 2 ψ Heavy vector resonances and heavy fermions in loop: g 2 ρ M 2 ρ flavour-diagonal and real ignore Possible contributions from higher-dimensional operators not included in this simplified setup

22 Bounds on parameter space Bounds for the flavour anarchic case: d n B X s γ B X d γ ɛ /ɛ bound on: ( ( mq m ) R 1/2 Y Ỹ m 2 Q s 2 Rt Y 2 ) 1/2 ( mq m ) R 1/2 Y operator doublet triplet bidoublet (estimate) (estimate) Q ddv 3.6 TeV 5.1 TeV 4.1 TeV 0.8 TeV Q uuv 1.3 TeV 0.6 TeV 1.4 TeV 0.3 TeV Q ccg 1.1 TeV 1.7 TeV 1.5 TeV 0.5 TeV Q bbg 0.6 TeV 0.9 TeV 0.8 TeV 0.3 TeV Q ttg 0.3 TeV 0.4 TeV 0.4 TeV 0.2 TeV Q bsv 0.4 TeV 0.5 TeV 0.2 TeV 0.6 TeV 0.3 TeV Q bsv 0.7 TeV 1.0 TeV 0.4 TeV 1.1 TeV 0.3 TeV Q bdv 0.2 TeV 0.3 TeV 0.1 TeV 0.3 TeV 0.2 TeV Q bdv 0.6 TeV 0.8 TeV 0.3 TeV 0.9 TeV 0.3 TeV Q sdg 1.1 TeV 1.6 TeV 1.6 TeV 0.5 TeV Q sdg 1.1 TeV 1.6 TeV 1.6 TeV 0.5 TeV A CP Q cug 0.9 TeV 1.4 TeV 1.3 TeV 0.4 TeV Q cug 0.2 TeV 0.3 TeV 0.2 TeV 0.2 TeV

23 Bounds for flavour symmetric models Neutron electric dipole moment: Can show that only physical phase beside CKM reside in wrong-chirality Ỹ relevant bounds only for models with Ỹ 0! mψ Bound on: 2 (and mψ3 2 in U(2) 3 for third generation) Y Im Ỹ Y 3 Im Ỹ 3 operator doublet triplet bidoublet Q ddv 3.6 TeV 5.1 TeV 4.1 TeV Q uuv 1.3 TeV 0.6 TeV 1.4 TeV Q ccg 1.1 TeV 1.7 TeV 1.5 TeV Q bbg 0.6 TeV 0.8 TeV 0.8 TeV Q ttg 0.3 TeV 0.4 TeV 0.4 TeV

24 Bounds for flavour symmetric models Flavour violating observables: In U(3) 3 : Leading contribution Y Ỹ vanishes due to Y, Ỹ Id ) In U(2) 3 : Leading contribution is for left-handed compositeness! ( Y Ỹ m 2 ψ Y 3Ỹ3 m 2 ψ3 operator doublet triplet bidoublet Q bsv 0.37 TeV 0.52 TeV 0.22 TeV Y Next-to-leading correction: 2 s Rt mψ 2 s Lt Y ( ) TeV

25 Conclusions Leading contribution in models with Ỹ 0 comes from diagrams with a heavy fermion and a W, Z or Higgs Next-to-leading contributions suppressed by degree of compositeness important for 3rd generation quarks Anarchic models: Stringent bounds from neutron EDM (m ψ 4 TeV for Y Ỹ 1), even stronger for greater Y, Ỹ! Several bounds from flavour-violating observables in the 1-2 TeV range Flavour-symmetric models: Also strong bounds from neutron EDM, but on Y Im Ỹ instead of Y Ỹ can be avoided Bounds from flavour-violating observables are mild

26 Outlook Several experiments in construction to improve accuracy for neutron EDM stronger bound! [Hewett et al (2012), ] Flavour violating top-quark transitions t qγ, g not yet strongly constrained future LHC runs! Analysis to be done in more fundamental theory (pngh), leading order effects should be similar Lepton sector? (eg. µ eγ, d e,...) Full numerical analysis including all F = 1 and F = 2 processes and electroweak constraints... [Barbieri et al (2012), ]

27 Thank you for your attention!

28 Backup slides

29 Mass matrices TS4: M u ψ = t R T R U R t L 0 λ L 0 T L 0 m Q Yv 2 U L λ Ru Ỹ v 2 m R TS5: M u ψ = t R T R T R T 2/3R U R t L 0 λ Lu λ Ld 0 0 T L 0 m Qu 0 0 Yv 2 T L 0 0 m Qd 0 0 T 2/3L m Qu Yv 2 U L λ Ru Ỹ v 2 0 Ỹ v 2 m U

30 Mass matrices TS10: t R U R U R T R T 2/3R b R D R D R B R t L λ L 0 b L λ L U L λ M u Ru m R 0 Ỹ 2 v Ỹ v 2 D L ψ = U L 0 0 m R Ỹ 2 v Ỹ v M d λ Rd m R 0 Ỹ v 2 ψ = 2 D T L 0 Yv 2 Yv L 0 0 m R Ỹ v 2 m 2 Q 0 B T 2/3L 0 Yv Yv L 0 Yv Yv m m 2 2 Q Q T 5/3R U 5/3R U 5/3R T 5/3L m Q Yv Yv M 5/3 2 2 ψ = U 5/3L Ỹ v m 2 R 0 U 5/3L Ỹ v 0 m 2 R

31 Formulae 1 C qi q j γ,g = m ψ, X qi mx m qi mx 2 ( ) m qi ViψX L V jψx L + m q j ViψX R V jψx R FX 1 (Q ψ, Q X, x) ( m ψ V L iψx V R jψx ) F 2 X (Q ψ, Q X, x), C X Q ψ Q X C X Q ψ Q X C ddγ h, Z, ρ 0 1/3 0 C uuγ h, Z, ρ 0 2/3 0 W +, ρ + 4/3 1 W +, ρ + 1/3 1 W, ρ 2/3 1 W, ρ 5/3 1 G 4/9 0 G 8/9 0 C ddg h, W, ρ 1 0 C uug h, W, ρ 1 0 G 1/6 3/2 G 1/6 3/2

32 Loop functions ( 5x 4 FV 1 14x x 2 18x 2 log x 38x + 8 ) (Q ψ, Q V, x) = Q ψ 24(x 1) 4 ( 4x 4 49x x 3 log x + 78x 2 43x + 10 ) + Q V, 24(x 1) 4 ( x 3 FV 2 3x + 6x log x + 4 ) (Q ψ, Q V, x) = Q ψ 4(x 1) 3 ( x x 2 6x 2 log x 15x + 4 ) + Q V, 4(x 1) 3 ( x 3 FS 1 + 6x 2 3x 6x log x 2 ) (Q ψ, Q S, x) = Q ψ 24(x 1) 4 ( 2x 3 + 3x 2 6x 2 log x 6x + 1 ) + Q S, 24(x 1) 4 ( x 2 FS 2 + 4x 2 log x 3 ) ( x 2 2x log x 1 ) (Q ψ, Q S, x) = Q ψ + Q 4(x 1) 3 S. 4(x 1) 3