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Composite Higgs Boson from Top Dynamics Composite Higgs boson from top dynamics Bogdan Dobrescu (Fermilab) Work with Hsin-Chia Cheng and Jiayin Gu (UC Davis): 1311.5928 Outline: Composite Higgs models • U(3) -symmetric Top-seesaw model • L Computation of the Higgs mass • Signatures of vectorlike quarks • University of California, Irvine – March 2015 ✬✬ ✩✩ ✬ ✤SM ✩ Spin-1 fields: Spin-1/2 fields: ✣ ✜ Gµ (8, 1, 0) qL (3, 2, +1/6) ✢ W µ (1, 3, 0) uR (3, 1, +2/3) Bµ (1, 1, 0) 3 dR (3, 1, 1/3) × − lL (1, 2, 1/2) Spin-0 field: H (1, 2, +1/2) − eR (1, 1, 1) − ✤★ ✫ SM ✪ ✧✣ ν G ✜✥ Spin-2 field: graviton with MPlanck-suppressed interactions ✢✦ (effective theory breaks down near 1016 TeV) ν masses require: c HHl l interactions, suppressed by M/c 1014 GeV M L L ≈ or additional spin-1/2 fields: 3 ν (1, 1,0) which together with × R the SM νL acquire Dirac masses. ✫✫ ✪✪ . ✬✬ ✩✩ ✬ ✤SM ✩ Spin-1 fields: Spin-1/2 fields: ✣ ✜ Gµ (8, 1, 0) qL (3, 2, +1/6) ✢ W µ (1, 3, 0) uR (3, 1, +2/3) Bµ (1, 1, 0) 3 dR (3, 1, 1/3) × − lL (1, 2, 1/2) Spin-0 field: H (1, 2, +1/2) − eR (1, 1, 1) − ✤★ ✫ SM ✪ ✧✣ ν G ✜✥ Spin-2 field: graviton with MPlanck-suppressed interactions ✢✦ (effective theory breaks down near 1016 TeV) ν masses require: c HHl l interactions, suppressed by M/c 1014 GeV M L L ≈ or additional spin-1/2 fields: 3 ν (1, 1,0) which together with × R the SM νL acquire Dirac masses. ✫✫ ✪✪ . ✬✬ ✩✩ ✬ ✤SM ✩ Spin-1 fields: Spin-1/2 fields: ✣ ✜ Gµ (8, 1, 0) qL (3, 2, +1/6) ✢ W µ (1, 3, 0) uR (3, 1, +2/3) Bµ (1, 1, 0) 3 dR (3, 1, 1/3) × − lL (1, 2, 1/2) Spin-0 field: H (1, 2, +1/2) − eR (1, 1, 1) − ✤★ ✫ SM ✪ ✧✣ ν G ✜✥ Spin-2 field: graviton with MPlanck-suppressed interactions ✢✦ (effective theory breaks down near 1016 TeV) ν masses require: c HHl l interactions, suppressed by M/c 1014 GeV M L L ≈ or additional spin-1/2 fields: 3 ν (1, 1,0) which together with × R the SM νL acquire Dirac masses. ✫✫ ✪✪ . Dark matter requires particle(s) beyond the SMν • G DM particle can be a fermion (Majorana or Dirac) or a boson (spin 0 or 1). DM particle may be part of a large hidden sector ... A 4th generation of chiral quarks and leptons is essentially • ruled out by the LHC searches for new quarks. Vectorlike quarks or leptons = fermions whose masses are gauge invariant; current limits on their masses around 700 GeV. Only spin-0 particle of the SMν : G Higgs boson discovered by the ATLAS and CMS collaborations mass near 125 GeV, SM-like couplings (so far). Is the Higgs doublet a composite field? If so, what are its constituents? What binds them inside the Higgs field? What are the experimental tests? Composite Higgs models - Nambu-Goldstone bosons 1984 - 1985: Kaplan, Georgi, Dugan, Banks, Dimopoulos, ... • QCD-like theories with Nambu-Goldstone bosons transforming as the SM Higgs doublet 2003 - ... : Agashe, Contino, Pomarol, Nomura, Redi, ... • Require vectorlike quarks Strongly coupled conformal Higgs sector 1999 - ... : Randall, Sundrum, Agashe, Delgado, May, ... • Warped extra dimension with bulk fields include vectorlike quarks. → Composite Higgs models - Top condensation 1989 - 1993: Nambu; Miransky, Tanabashi, Yamawaki; Mar- • ciano; Bardeen, Hill, Lindner; ... Strongly-coupled 4-fermion interactions Higgs doublet is a → bound state of t¯R and (t,b)L. 1997 - 1999: Hill, Dobrescu, Chivukula, Georgi, Tait, He, ... • Top-seesaw mechanism Higgs doublet is a bound state of a → vectorlike quark and (t,b)L. Top condensation g2 (t¯ ψ3 )(ψ¯3 t ) ψ3 = (t,b) Λ R L L R L L Similar to Nambu–Jona-Lasinio model 1961 g 1 t¯ ψ3 bound state ≫ → R L – same quantum numbers as the SM Higgs doublet! Fermion loop gives mass term in the potential 2 2 2 g Nc MH = Λ 1 − 8π2 ! Criticality condition: g>π 8/N bound state gets a VEV. c → p Second order phase transition: M 2 Λ is possible if g is tuned to be only slighly above g . H ≪ critical 4-fermion interaction is not confining. ¯ 3 If Higgs doublet is a tRψL bound state, then top Yukawa coupling is large m 600 GeV ... unless Λ M → t ≈ → Planck Top seesaw model Higgs boson is a bound state of top quark with a new quark χ. (BD, C. Hill, hep-ph/9712319, Chivukula et al, hep-ph/9809470) Binding may be due to some strongly-interacting heavy gauge bosons ✤✜χ ✤✜t ✣✢ ✣✢ Scale of Higgs compositeness may be as low as a few TeV. Minimal composite Higgs model (MCHM) with light scalars: B.D, hep-ph/9908391 Top seesaw: vectorlike quark χ, transforming as tR. 3 H is a χ¯RψL bound state. 0 ξ v t t , χ √2 R − L L χ mχt mχχ ! R ξ at scale Λ, upon integrating out H, matches the coefficient of the 4-fermion interactions: 8π2 ξ2 = Nc ln(Λ/mχ) Composite scalars are U(3)L triplets: 3 3 Ht ψ Hχ ψ Φt = t¯R L , Φχ = χ¯R L φ ∼ χ φχ ∼ χ t L L Two Higgs doublets and two singlets: 1 1 (ht + iAt) v + hχ + iAχ H = √2 , Hχ = √2 t H− Hχ− t 1 1 φt = (usγ + ϕt + iπt) , φχ = (ucγ + ϕχ + iπχ) √2 √2 Φ = Φt , Φχ The scalar field Φ is a 3 2 complex matrix × λ1 2 λ2 2 2 V = Tr (Φ†Φ) + Tr[Φ†Φ] + M Φ†Φ Φ 2 2 Φ h i Explicit U(2)R breaking effects which distinguish tR and χR: 2 2 2 δMtt Φt†Φt + δMχχ Φχ† Φχ + (MχtΦχ† Φt + H.c.) mass = µ χ¯ t µχχχ¯ χ + H.c. L − χt L R − L R Below Λ, these fermion masses map to tadpole terms for the SU(2)W -singlet scalars: V = (0, 0,C )Φ (0, 0,Cχχ)Φχ + H.c. tadpole − χt t − Matching at the scale Λ gives µχt 2 µχχ 2 Cχt Λ , Cχχ Λ . ≈ ξ ≈ ξ Effective potential below the compositeness scale: λ1 + λ2 2 2 2 V = (Φ†Φt) + (Φ† Φχ) + λ1 Φ†Φχ + λ2(Φ†Φt)(Φ† Φχ) scalar 2 t χ | t | t χ 2 2 2 +MttΦt†Φt + MχχΦχ† Φχ + (MχtΦχ† Φt + H.c.) (0, 0, 2C )Re Φ (0, 0, 2Cχχ)Re Φχ − χt t − In the large Nc limit, λ λ . 1 ≫ 2 Mass-squared matrix of the CP-even neutral scalars (ht, hχ, ϕt, ϕχ): 2 λ1 2 λ1 λ1 M ± + v 0 uvcγ uvsγ H 2 − 2 − 2 2 0 λ1v 0 λ1uvcγ λ1 2 λ1 2 2 λ1 2 uvcγ 0 M ± + 1+ s u u sγcγ − 2 H 2 γ 2 s2 λ1 λ1 2 γ 2 uvsγ λ1uvcγ u sγcγ λ1 1 u − 2 2 − 2 ! 2 2 Keeping the leading order in v /u and sγ: M 2 M 2 = λ v2s2 H± h 1 γ 2 2 2M + λ1u H± Higgs mass is suppressed by s , because in the limit of m 0 γ t → the U(3)L breaking tadpole terms vanish and the Hχ and πχ fields become Nambu-Goldstone bosons. ξ mt v sγ ≈ √2 yt ξ and sγ are related to the top Yukawa coupling sγ ≈ ξ ξ is expected to be between 3 and 4.5 s2 O(0.1). → γ ∼ 2 1 λ1 λ1m − M 2 1+ t′ y2 v2 h 2 2 2 t ≈ 2ξ ξ M ! H± In the fermion-loop approximation of NJL the ratio of couplings 2 λ1/(2ξ )=1. Scalar and gauge boson loops reduce this ratio: λ1 0.4 . 1 M < mt 2ξ2 ⇒ h Additional U(3) breaking effects from SU(2) U(1) interactions. L W × Y Higgs squared mass receives a correction: 2 Mρ ∆M 2 (0.08 v)2 h ≈ − f 2 Custodial symmetry is broken by the t χ mixing: − 3 v2ξ2 ξf T +4m2 ln 2m2 ≈ 2 2 t √ − t 16π αf " 2 2mt # T < 0.15 at 95% CL f > 3.5 TeV ⇒ Fine-tuning of order v2/f 2 ... Loopholes: higher-dimensional operators at the scale Λ may contribute to • the T parameter. If they are negative, the limit on f decreases. additional states at the TeV scale may cancel the contribution • of χ to the T parameter. Example: H.C. Cheng, J. Gu: 1406.6689 custodial symmetry is pre- served in the presence of a vectorlike quark transforming as (3,2,7/6) f & 1 TeV ⇒ Mass of the new quark: ξ mt f ′ ≈ √2 f > 3 TeV m > 8 TeV ⇒ t′ M > m We need a VLHC! H1 t′ W + t b g ¯ t′ b g h b g t¯′ W − ¯b ”Light” CP-odd scalar: MA > 1 TeV, gluon fusion through χ loop ... Story #2: Peculiar decays of vectorlike quarks All Standard Model fermions are chiral: their masses are not gauge invariant, and arise from the Higgs coupling. Vectorlike (i.e. non-chiral) fermions – a new form of matter. Masses allowed by SU(3) SU(2) U(1) gauge symmetry, c × W × Y naturally heavier than the t quark. ⇒ Usual LHC searches for vectorlike quarks rely on their decays into a SM quark and a W or Z or h0 boson. Depending on some parameters, the vectorlike quarks may predominantly decay into 3 SM quarks, or into one quark and two leptons, or into one quark plus a g or γ.
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